Description
Real estate development inherits uncertainty & flexibility to a large degree. Traditional financial valuation techniques fail to account for this and thus we employ a real options model to study uncertainty & flexibility in real estate development.
Modelling Uncertainty & Flexibility in the Financial
Analysis of a Real Estate Development Project in
Switzerland
Master Thesis for the Degree of Master of Science
in Management, Technology and Economics (MTEC)
at the Swiss Federal Institute of Technology Zurich
by
Johannes Peter
BSc Civil Engineering ETH Zurich
Supervisor at ETH Zurich
Prof. Dr. Didier Sornette & Dr. Peter Cauwels (ETHZ, Chair of Entrepreneurial Risks)
Department of Management, Technology and Economics (MTEC)
Submitted to ETH Zurich
December 2012
Contact: [email protected]
Abstract i
Abstract
Real estate development inherits uncertainty & flexibility to a large degree. Traditional
financial valuation techniques fail to account for this and thus we employ a real options model
to study uncertainty & flexibility in real estate development.
Real option analysis has not found wide application in the real estate development practice yet
and we argue that this is due to a lack of pragmatism and comprehensibility of the com-
monly used models.
We therefore employ the so called “Engineering Approach” introduced by de Neufville and
Scholtes (2011) that is based on Monte-Carlo simulations to better analyse and communicate
uncertainty & flexibility in real estate development projects.
We develop a Monte-Carlo simulation model based on past data of identified risk drivers that
determine the value of a real estate development project. We employ copula and vector
autoregressive modelling techniques to account for interdependencies among these risk
drivers and apply the resulting simulation model to a large-scale development project in the
region of Zurich. Our analysis reveals the risk structure of this real estate development project
and shows how downside risk can be reduced by the use of flexibility.
Keywords: Real Options Analysis; Real Estate Development; Monte-Carlo Simulation;
Vector Autoregression; Copula ; Engineering Approach; Flexibility; Valuation
Acknowledgments ii
Acknowledgements
I would like to thank Dr. Peter Cauwels from the Chair of Entrepreneurial Risk at the ETH
Zurich, who kindly supported me in writing this thesis. By giving me advice and support
whenever I needed it, he helped me a great deal to make the work on this thesis a true
learning experience.
Also I would like to thank Othmar Ulrich and his team at Steiner AG, who provided me with
valuable insights into the real estate development practice and helped me to focus on the
practical part of this thesis. Werner Ramseyer from Sproll & Ramseyer AG provided me with
valuable insights into the Swiss valuation practice, Marc Petitjean from Helbling Beratung und
Bauplanung AG on the real estate development practice and Alain Chaney from IAZI AG on
the modelling of real estate data. I thank them for their kind support and their time. Stephan
Fahrländer from Fahrländer & Partner AG provided me with a rich data set on real estate
market data. Without his support I would not have been able to create the data based
financial model, we present here.
Furthermore I would like to thank Prof. Dr. David Geltner from the MIT, who generously
provided me with material on previous work done on the financial analysis of real estate
development projects. Finally I would like to thank Prof. Dr. Didier Sornette from the Chair
of Entrepreneurial Risk at the ETH Zurich who made the work on this truly exciting topic
possible.
Johannes Peter
Content iii
Content
Abstract ..................................................................................................................................... i
Acknowledgements .................................................................................................................. ii
Content ................................................................................................................................... iii
1 Introduction ....................................................................................................................... 1
2 Literature Review ............................................................................................................... 3
3 Real Estate Development Process ...................................................................................... 6
3.1 Insights from Professionals ....................................................................................................... 6
3.2 Definition .................................................................................................................................. 6
3.3 Steps in the Development Process ............................................................................................ 6
3.4 Risks in the Development Process ............................................................................................ 9
3.5 The Role of Flexibility & Uncertainty .................................................................................... 11
4 Valuation of Real Estate Development Projects .............................................................. 13
4.1 Common Practice ................................................................................................................... 13
4.1.1 Capitalised Earnings Method .......................................................................................... 13
4.1.2 Net Present Value Method .............................................................................................. 16
4.1.3 Shortcomings ................................................................................................................... 17
4.2 Real Option Analysis .............................................................................................................. 18
4.2.1 Binomial Approach ......................................................................................................... 19
4.2.2 Closed Form Solutions .................................................................................................... 20
4.2.3 Monte-Carlo Simulations ............................................................................................... 21
4.2.4 Critique and Choice of Method ...................................................................................... 21
5 Simulation Based Real Options Model ............................................................................ 24
5.1 Project Modelling Framework: The “Engineering Approach” ................................................ 24
5.1.1 Step 1: Create the Most Likely Initial Cash Flow Model ............................................... 25
5.1.2 Step 2: Incorporate Uncertainty into the Model ............................................................. 25
5.1.3 Step 3: Incorporate Flexibility into the Model ................................................................ 27
5.1.4 Step 4: Maximize Value by Applying Optimal Decision Rules ....................................... 27
5.2 Simulation Framework ............................................................................................................ 28
5.2.1 Overview ......................................................................................................................... 28
5.2.2 Risk Drivers ..................................................................................................................... 31
5.2.3 Data ................................................................................................................................. 33
5.2.4 Modelling ........................................................................................................................ 41
Content iv
5.2.5 Simulation of Future Scenarios ....................................................................................... 51
5.2.6 Simulation of Absolute Values ........................................................................................ 63
6 Application of the “Engineering Approach” to a Real Project - A Case Study in the
Canton of Zurich ............................................................................................................. 64
6.1 Case Background .................................................................................................................... 64
6.2 Step 1: Create the Most likely initial Cash Flow Model ......................................................... 67
6.3 Step 2: Incorporate Uncertainty into the Model ..................................................................... 70
6.4 Step 3: Incorporate Flexibility into the Model ........................................................................ 77
6.5 Step 4: Maximize Value by Applying Optimal Decision Rules .............................................. 80
7 Conclusion ....................................................................................................................... 82
8 References ........................................................................................................................ 84
Appendix ................................................................................................................................ 87
1 Introduction 1
1 Introduction
Real estate development is an important activity: It is the production factory of our cities that
transforms unproductive land to urban space for people to live, work and enjoy. It shapes the
character of the places we spend so much time in and if well done, can substantially improve
the quality of life. Real estate development is also an entrepreneurial activity: it involves the
decision to take the future of an area in one’s hands, to shape it to the needs of upcoming
generations and the aspiration to make it a truly successful product on the real estate market.
As such it is also a risky activity: Development binds large amounts of financial capital into a
fixed asset while it is not granted that the proceedings will be higher than the investment.
The financial success depends both on uncertain cost and uncertain revenues and in order to
be successful, one must assess these uncertainties to a high degree. Proper investment analysis
is crucial to deal with these uncertainties, to reduce and anticipate them whenever possible.
For more than ten years now real estate prices have been rising continuously and one might
be inclined to think that this trend will continue for another ten years. But among the many
things we can learn from history, one lesson is that the future is uncertain: just a few years ago
the global financial system was close to a meltdown and few would have predicted then the
strong growth in real estate prices that we observed in the past few years. Quo Vadis?
Real estate developers need to cope with uncertainty, think about it and find strategies to deal
with it. One way of doing so has always been flexibility. If demand for office space is low a
developer can wait and build when markets have recovered, or he can change the project to
another use. When looking into practice however, the employed financial analysis tools
neither properly account for flexibility, nor uncertainty when dealing with real estate
development projects.
One way of financial analysis that deals with flexibility & uncertainty is real options analysis.
This approach is closely linked to the valuation of financial options and is thus based on
assumptions that are not necessarily applicable in the world of real estate development.
Also we argue that due to a lack of accessibility and applicability, real options analysis has not
yet gained much attention in the Swiss real estate development practice. We thus introduce a
more intuitive, simulation based real options model grounded on the works of de Neufville,
Scholtes and Geltner. This so called “Engineering Approach” works with “classic” net present
value calculations and combines them with simulations of future market scenarios. Based on
these scenarios, decision rules are implemented and optimised to find the optimal behaviour
for the simulated future.
1 Introduction 2
Thereby we make flexibility & uncertainty more accessible in the analysis of real estate
development projects.
The thesis is structured in the following way: After a short review of the literature on real
options in Chapter 2, we give an overview of the real estate development process and the role
of risk, uncertainty & flexibility within this process in Chapter 3. In Chapter 4 we discuss the
current valuation practice in Switzerland and introduce real options analysis. In Chapter 5 we
present a simulation-based model and then show the applicability and the results of this
method on a case study in Chapter 6. Chapter 7 concludes this thesis and discusses possible
improvements of the model and directions for further research.
2 Literature Review 3
2 Literature Review
In this chapter we present the evolvement of real option theory applied to real estate development in
the recent past. This helps to understand the balancing act between academic theory and applicability
when working with real options in practice. Many terms that are mentioned in this chapter are dealt
with in more detail in subsequent chapters.
Real options are a popular topic in the recent literature: A search on the Web of Science
1
yields more than 100 publications related to real options every year over the last decade. The
origin of this popularity is closely linked to advances related to the pricing of financial
options. Black and Scholes (1973) opened up the field with their revolutionary equilibrium-
pricing model for financial options. Six years later Cox, Ross and Rubinstein (1979) already
mention the possibility to apply the approach on other problems than financial options in
their famous work on financial option pricing. In this article they introduce the binomial
approach that is still the basis for many real option valuations nowadays. Since then, real
options have been the subject of diverse studies and been applied to various fields of economic
research such as capital budgeting problems, valuations, micro-economic-decision-making
and more. Whenever dealing with uncertainty and/or flexibility thereby one is prone to come
over real options sooner or later. This has also led to some unintended fame of real options
when they were widely used as justification for the sky-high valuations of internet stocks
before the burst of the dotcom bubble in 2000 (Mauboussin 1999).
In the field of real estate research it took until 1985 for real options to find their applications.
Titman (1985) was the first to introduce a real option approach that is closely linked to the
binomial model of Cox, Ross and Rubinstein (1979) to value vacant land. With his model he
was able to explain the behaviour of many land owners who wait with construction in order to
profit from higher expected prices. He showed mathematically that higher uncertainty in the
future value of built property leads to a higher option value and thereby to a delay in the
exercise of the option. Eight years later Quigg (1993) gave evidence of these findings with the
first empirical study on the real option value of vacant land in Seattle. Her findings indicate
an average premium of 6% that is paid for the option to wait. Real options theory applied to
real estate and other fields of practice remained however a niche and only slowly gained more
attention with further publications. The theory was notably made more public by works of
Trigeorgis (1993) and later by Copeland (2001).
1
Web of Science is a large multi disciplinary knowledge database:http://isiknowledge.com/wos
2
Other developers in Switzerland such as Allreal, Mobimo and Priora have their own investment portfolio and develop mainly
2 Literature Review 4
Their work was thereby directed towards bridging the gap between academia and practice.
After publishing on the use of financial option models for the valuation of vacant land in
1989 (Geltner 1989), Geltner and Miller further introduced the Samuelson McKean Formula
as the “Black-Scholes formula of real estate” in their standard textbook on real estate finance
in 2001 (Geltner and Miller 2001).
Thereafter many publications were made on the topic of real options in real estate
development at the MIT Center for Real Estate under the supervision of Geltner: Among
them there is Hengels (2005) who introduced a model to evaluate large-scale real estate
development projects using binomial trees. The goal of his work was to make real options
theory using binomial trees accessible by practitioners. But one of the main drawbacks of this
approach became highly visible in his work: While the computational effort to analyse a
project becomes high very fast, the ability to conduct meaningful conclusions from the
analysis becomes more and more difficult. This is due to the fact that results are not easily
retraced in the model. We discuss this issue in Chapter 4.2 on the choice of our method.
Barman and Nash (2007) tried to overcome this shortcoming by using a combination of the
Samuelson McKean formula and Monte-Carlo simulations and Masunaga (2007) made a
comparative study of Monte-Carlo simulations and binomial trees to value real estate
development projects. As he concluded, there is a significant difference between the results
obtained by Monte-Carlo simulation and binomial tree evaluation. As Hodder, Mello et al.
(2001) pointed out before, this issue can be addressed by using risk adjusted discount rates
depending on the time to expiration of the option and the actual value of the underlying asset,
but the problem of accessibility would still not be addressed.
During that time de Neufville (2006) was working on real options using Monte-Carlo
simulations while focusing on the value of flexibility. This method was further developed into
the “Engineering Approach” and published in 2011 (de Neufville and Scholtes 2011). The
advantage of this approach is the specific development for practitioners and we thus make
extensive use of it within this study. Geltner and de Neufville (2012) further propose to use
both the “Engineering Approach” and the binomial real options model to make financial
analysis of real estate development projects. In this thesis we focus on the business
applicability of real options and the application of the “Engineering Approach” to a real
project in Switzerland, we therefore do not employ both methods.
Most of the proposed real option methods in the context of real estate development deal with
the “Anglo-Saxon” real estate development process (see e.g. Guthrie (2009)). However, there
is hardly anything on the Swiss real estate development practice (except for Maurer (2006)).
But why is this important? As we will see the Swiss real estate development practice is
2 Literature Review 5
different from the “Anglo-Saxon” way. This has an influence on the specification of the real
options model. A second reason is that real options analysis depends on the market where it is
applied. It is important to adapt the model to the specifics of this market especially when
dealing with Monte-Carlo simulations. Thirdly it is important to apply a theoretical approach
to real life situations, involve practitioners and analyse with them the benefits and merits of
the solutions “scientists” came up with. We handle these issues subsequently in the following
chapters.
3 Real Estate Development Process 6
3 Real Estate Development Process
This section gives a short overview of the typical processes involved in real estate development, while
highlighting some specialities of the Swiss developer environment. By understanding the process of
real estate development the reader should become aware of the importance of uncertainty & flexibility
within the field of real estate development. We first look at the steps that have to be taken for a
successful development and at the risks involved in this process. Finally we highlight the role of
flexibility & uncertainty in this context.
3.1 Insights from Professionals
In the course of this study various professionals in the field of real estate were met to discuss
the valuation of uncertainty & flexibility in the context of real estate development. We gained
insights into the professional real estate valuation domain thanks to Werner Ramseyer from
Sproll & Ramseyer AG. He explained to us in detail the current valuation practice for real
estate in Switzerland and kindly provided case studies. Marc Petitjean from Helbling Beratung
und Bauplanung AG gave us insights into the real estate development practice and Stephan
Fahrländer from Fahrländer & Partner AG provided us with a rich data set for the
development of the real estate market in Switzerland. Furthermore Alain Chaney from IAZI
AG gave very valuable input for modelling the real estate market. Finally Othmar Ulrich and
his team at Steiner AG were a very rich source of knowledge when discussing the applicability
of financial models, the valuation practice of real estate development projects and the
importance of uncertainty & flexibility in the real estate development process. Whenever
possible we try to incorporate insights from these professionals into this thesis.
3.2 Definition
Geltner and Miller (2007) define real estate development as the process where financial
capital becomes fixed as physical capital, or more broadly the process of transforming an idea
to reality. It includes all the steps from conceptualisation to realisation and sometimes sale of
a real estate project.
3.3 Steps in the Development Process
The steps to be taken in real estate development are similar internationally and among
projects. The specialities of the Swiss vs. the “Anglo-Saxon” development environment arise
from the different parties that are involved in these steps and thus the different risks that they
3 Real Estate Development Process 7
bear. We first go through the steps and then discuss the specialities of the Swiss development
environment.
1. Project Initiation
Schulte (2002) defines three initial states that lead to the initiation of a real estate
development project:
/ Site looking for use: When the piece of land to be developed is already given, it
is the task of the developer to come up with a project idea and a concept. The
developer defines a suitable use for the site that generates the highest possible
value. Value in this context does not mean economic value only, but also social
and ecological value. Only by taking all three aspects into account, developers
will generate sustainable solutions that guarantee long term success. For this he
needs to have a “feeling” for the real estate market and know what kind of uses
will be in demand at the given location not now but in the future. Therefore he
needs to be visionary and anticipate what works and what does not at a given
location.
/ Use looking for site: When the project idea is already given, the task is to find a
suitable location. The developer will need to have information sources that help
him find promising sites. A well-established network of people involved in the
land transaction market is crucial but also databases and newspapers are of use.
Since land acquisition cost is one of the main capital expenditures of a project
development, a detailed financial feasibility analysis of the identified selection is
of high importance. The phase is concluded with the successful purchase of a
plot or the obtainment of a right to build on it in the future.
/ Capital looking for site and use: The third initial state involves the processes of
finding a site and a use. The needed capabilities are largely the same as with the
two other initial states and not repeated here.
2. Project Conception
The second phase starts with an in-depth feasibility study regarding location, market,
usage, competition, risk and profitability. Based on these studies a detailed project
concept is prepared that serves as a basis for the communication with stakeholders.
Involved parties such as neighbours, politicians, investors and tenants are contacted and
the project is further specified in consideration of them. When the project is feasible and
well defined, architects and planners are hired for drawing designs of the future buildings
and planning the environment.
3 Real Estate Development Process 8
The final goal of this phase is the receipt of the building permit that authorises the start
of construction. Once construction has started, the project becomes very capital intense
and major changes of plans are very difficult and expensive to achieve. To reduce the risk
of vacancies it is therefore essential that future tenants are identified, involved and
committed to the project already before construction starts. Developers will thus look for
prospective tenants already during the project conception phase and not proceed until the
risk of vacancies is reduced substantially.
3. Project Realisation
A contractor, who manages the construction process and construction works, executes
construction until completion, often for a prearranged price. Thereby the contractor
takes over construction cost risk from the developer. The role of the developer in this
phase is that of controlling and managing the work executed by the contractor. Also he
will focus on finding additional tenants and buyers for the project.
4. Lease-Up & Tenant Finishes
During the lease-up period the project enters the market, additional tenants or buyers
commit themselves to the project and often a customized finish for the tenants is made.
Depending on how many tenants committed themselves to the project already in the
preceding phases, the risk of not leasing up the whole project can be substantial. Large
vacancies and or lower than expected rent contracts can have a severe impact on the
profitability of the project. Depending on the project and the market environment it can
take several months up to years until a project is fully leased out.
5. Stabilised Operation
Once the project is fully leased out, it enters the phase of stabilised operation where it
produces a hopefully stable and increasing cash flow for the lifetime of the object.
Subsequent investments for maintenance and sometimes redevelopments are necessary in
order to sustain the long term profitability of the object on the market.
Specialties of the Swiss Developer Environment
As pointed out before, specialities of the Swiss vs. the “Anglo-Saxon” real estate environment
arise not from the steps in the development but from the players that are involved in these
steps. Geltner et al. (2007), taking the viewpoint of the “Anglo-Saxon” development
environment, describe Step 1 and 2 of the project as the preliminary phase of a project. This
phase is often conducted by an “entrepreneurial” developer, who may or may not continue
with the project until completion. The construction and lease-up phase together represent the
“development” project where large amounts of capital are committed to the project.
3 Real Estate Development Process 9
In the “Anglo-Saxon” environment there are large developers, sometimes in the form of real
estate investment trusts, specialised only on this part of real estate development. Due to their
access to funding they can commit the large financial funds needed for construction and
either sell the project once it is stabilised, or keep it in their own portfolio. These developers
would however not invest in a project without a construction permit in place. The discussed
literature on real estate development focuses on Step 3 to Step 5 of the development, taking
the viewpoint of these developers.
In Switzerland however, the business environment is market by “entrepreneurial” developers,
such as Halter, Implenia, Steiner, Losinger and HRS
2
who pursue the project from Step 1 to
Step 4. For them the investment starts already before a construction permit is achieved often
with the purchase or optioning
3
of land. These developers will often sell the project to an
institutional investor with the receipt of the construction permit at the end of Step 2, the
“Project Conception” phase. Depending on the contract, the developer is responsible for
leasing up the project and delivering it for a specified price. After completion and the lease-up
period investors operating in Switzerland keep the project as a stabilised asset in their
portfolio. We therefore have institutional investors on the buy side that commit themselves
very early to the project and “entrepreneurial” developers that take the project through all
steps, but sell the project early on. Due to the sale of the project with the receipt of the
construction permit, the Swiss developer transfers some of the risk to the investor, which has
to be taken into account in the financial analysis of the project. Additionally developers in
Switzerland are often construction contractors, managing the construction work themselves,
thereby taking over construction cost risk. In this thesis we focus on the entrepreneurial
developer and investment analysis from his viewpoint.
3.4 Risks in the Development Process
Except for the case where the investor or final user is already committed to the project from
the beginning, real estate development is among the riskiest entrepreneurial activities (Schulte
2002). This comes from the fact that capital investments for product creation are high,
products are fixed to their location, served market segments are often small and demand is
highly uncertain. The correct assessment and management of risk is therefore indispensable
and belongs to the main capabilities of successful developers. Schulte (2002) defines the main
risks of real estate development as:
2
Other developers in Switzerland such as Allreal, Mobimo and Priora have their own investment portfolio and develop mainly
for themselves. While the model in this thesis can be applied to their investment perspective as well, we do not explicitly focus on
them.
3
Optioning in this context refers to the widespread practice of developers to pay a prearanged price for the land to the owner on
the condition that the construction permit is obtained.
3 Real Estate Development Process 10
/ Development Risk: The risk of not planning an adequate use for a specific location and
the risk of planning financially non-feasible projects
/ Time Risk: Due to the financial leverage of most projects time risk is among the most
important risk factors. Delays can harm the profit of developers substantially.
/ Approval Risk: All development projects need to be approved by the authorities.
Neighbours can raise objections that can result in financially harmful project changes.
/ Financing Risk: Development projects are financially daring undertakings that require
partners with corresponding financial power. Funding might not be achieved or might be
stopped due to delays or other problems resulting in the failure of a project and severe
financial consequences for the developer.
/ Building Ground Risk: The building ground bears high potential for additional cost and
delays. This is due to the fact that building grounds bear uncertainty regarding
supportable load and contamination that cannot be eliminated completely with
preliminary studies.
/ Cost Risk: Cost risks arise mainly from the long time horizon of development projects
and the uncertainty regarding the exact specification of the future product. Thus it is
often very difficult to predict exactly the production cost of a large-scale development
project and additional costs may arise from the other mentioned risk factors.
/ Market Risk: The final test of every project is when it comes to market. Are the
potential tenants willing to pay the calculated rents resp. is demand high enough to meet
the additional supply at the specified price? How much are investors willing to pay for
real estate assets? Real estate value is driven by the space market that couples demand
and supply for space and by capital markets (Geltner and Miller 2007). These two
markets are already difficult to assess in the present and their behaviour is much more
difficult to predict for multiple years ahead. Inevitably this leads to large uncertainty
when dealing with the market risk of real estate developments. Besides that real estate
markets behave in long lasting cycles that are characterised by periods of strong growth
in prices and high construction activity followed by phases of stagnation and price
decline (Dokko, Edelstein et al. 2001). Developers need to anticipate markets correctly
and make the right preparations and decisions based on their estimations.
In the context of market risk, a short excurse on the Swiss real estate crisis of the 1990s gives
us valuable insights into the harmful effects of such an event.
3 Real Estate Development Process 11
The Swiss Real Estate Crisis in the early 1990s
After the stock market crash in 1987, the Swiss National Bank (SNB) increased liquidity and
decreased interest rates to counter negative effects of the crash and prevent a slackening
economy. The economy however recovered faster than expected and the increased supply of
liquidity together with an overheating economy lead to inflation rates of 5% by the end of
1989 (Jetzer 2007). At the same time investors shifted their interest due to the uncertainty in
stock markets from stocks towards real estate that was assumed to be a more reliable and save
asset class. This lead to a further increase in prices for real estate that were already at a high
level in the mid 1980s. Due to the high inflation rates by the end of the 1989 the SNB
increased short term interest rates drastically from 3.8% in July 1988 up to 9.5% in January
1990 (Jetzer 2007). Additionally the Swiss government passed a bill in October 1989 on land
laws that hindered the speculative trade of land and increased capital requirements to
purchase land (Meier 2009). The strong increase in interest rate brought the strong growth in
real estate prices to an end, which was followed by a decrease in prices of 20% (Jetzer 2007).
Especially regional banks that were highly active in the real estate mortgage market incurred
large losses on their assets. In October 1991 the “Spar- und Leihkasse Thun” had to close
down due to high write offs on mortgage loans, leading to the first bank run in Switzerland
since the 1930s (Holderegger 2006). Between 1991 and 1996 more than half of the original
180 regional banks disappeared (Jetzer 2007). As Meier (2009) points out, among the causes
for the real estate crisis were low interest rates, high liquidity in the finance system and also a
lax mortgage granting policy of many banks during that time. This is an interesting aspect in
the light of the current market environment were interest rates are lower than in the late
1980s (currently 1.5% for a 5 year fixed mortgage) and banks recently pledged to increase
their lending standards based on self regulation (Chapman 2012). We see the effects of the
early 1990s crisis on the real estate market in the data later on.
3.5 The Role of Flexibility & Uncertainty
As we have seen there are multiple risks/uncertainties involved in real estate development.
The developer has several tools to deal with this and among the most important are the right
analysis and the corresponding action towards these risks. A developer can e.g. decrease the
approval risk by integrating authorities early on and he can reduce building ground risk
through detailed analysis by specialists.
Another tool in dealing with risks is the use of flexibility: A developer can e.g. adapt the
project to a changing market environment, postpone development until markets are more
favourable, split the project up in multiple subprojects and realise them in succession, etc.
3 Real Estate Development Process 12
It is this skilful management of flexibility that often makes the difference between successful
development and financial failure. But flexibility & uncertainty do not remain constant over
the duration of a project.
Figure 1: Flexibility, Uncertainty and Cumulative Investment in the Development Process
Source: Own illustration based on Geltner et al (2007) and Schulte (2002)
As illustrated in Figure 1 flexibility & uncertainty decrease during the life time of a project.
Uncertainty can thereby be reduced by analysis and commitments of prospective
buyers/tenants, while flexibility decreases when decisions are made. At the same time more
and more capital is bound to the project as illustrated by the red line in Figure 1. Only when
uncertainty is reduced by a fair degree, one is willing to commit large amounts of capital.
At the beginning of the development, there is almost complete freedom on what to build or
where to invest but then the project becomes more and more specified and things are not
changed that easily anymore. It is thus of utmost importance to make the right adjustments to
a project while flexibility is still high and possibly preserve certain flexibility that could be of
value later on. In order to make best use of flexibility, a developer has to know where it is,
how important/valuable it is, which one to preserve and when best to exercise it. It lies in the
competence of the successful developer to know this due to his experience and intuition.
While probably most developers would agree that they have a lot of experience and intuition,
the question if there are not any quantifiable tools to deal with uncertainty & flexibility arises.
This leads us to our next chapter about the valuation practice of development projects.
2. Project
Conception
1. Project
Initiation
3. Project
Construction
4. Lease-up &
Tenant Finishes
5. Stabilised
Operation
! Cumulative Investment
! Uncertainty
! Flexibility
C
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Land Purchase /
Land Optioning
Construction Permit
Start Construction
Construction
Completion
Development
Completion
F
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&
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4 Valuation of Real Estate Development Projects 13
4 Valuation of Real Estate Development Projects
In the fist part of this chapter we describe the capitalised earnings method and the net present value
method, which constitute the prevailing methods in valuation practice of real estate development in
Switzerland. In addition, we highlight both their strengths and weaknesses and stress the need for
better tools to deal with uncertainty & flexibility. In the second part of this chapter, we introduce real
options analysis as a method that effectively deals with uncertainty & flexibility in the context of
valuation. We discuss the reasons why the approach has not found wide application in the real estate
development practice yet and stress the need for a more applicable and intuitive model. This leads us
to a simulation based model that we introduce in detail in Chapter 5.
4.1 Common Practice
As shown by Müller (2007) in his study on the valuation practices in Switzerland, the
capitalised earnings and the net present value method (NPV) prevail in the appraisal of real
estate development projects. We thus introduce these two methods in this chapter and use
them later on in our model. When discussing the valuation of real estate development projects
it is important to differentiate between the valuation of existing, built real estate that already
entered the phase of stabilised operation, and the valuation of a project that is in one of the
preceding phases of the development process introduced in Chapter 3. This comes from the
fact that the two cases inherit different risk structures: in the case of a development project,
the future value of the asset can only be estimated and incurs a large degree of uncertainty.
Additionally the process of obtaining the asset involves binding large amounts of financial
capital that does not generate positive cash flow until tenants move in or the project is sold.
Now how should we estimate the value of the development project? As we will see, the
process is first to know what the asset would be worth if it existed today (value of the built,
stabilised asset), and then to account for the risk of obtaining that asset. So we need to have
the concept of valuing built assets and development projects in mind when discussing the
valuation of real estate development projects.
4.1.1 Capitalised Earnings Method
The capitalised earnings method is foremost a method to value stabilised real estate assets.
The developer can however use it to estimate the value of a real estate development project.
This is done by estimating the value of the project if it would exist today (value of the built
project), using the capitalised earnings method, and then deducting all costs until completion
of the project. The resulting value is the profit of the developer, hence this method is also
4 Valuation of Real Estate Development Projects 14
known as the developer calculation. It is also used when the value of land has to be estimated:
The developer then estimates the value of the built project and deducts costs for construction,
financing and development. The difference between value and cost is the maximum value of
land. The developer will however not want to pay this maximum value for the land, since then
he has no profit. The value of a built project can be approximated by:
1. Calculating the annual Gross Operating Income (GOI) of the project by
multiplying the leasable square meters with the expected average rent per square
meter per year. Vacancies are deducted from the GOI. The result is the expected
yearly cash flow from our building:
!"# ! !
!
! !"#$!"%"#&"' ! ! ! !"#"$#% "#$%&
2. Calculating the value of the project by dividing the GOI by the cap rate:
!"#$% !
!"#
!"#$"%&
"#$'&
Equation (4.2) is equivalent to the dividend discount model introduced by Gordon (1962)
developed to value an asset based on an infinite series of dividend payments D growing at rate
g with constant cost of capital r :
!"#$% ! !
!
!
!!!
!
!!!
!
!
!!!
"#$(&
Equation (4.3) is a converging geometric series with the partial sum:
!"#$% ! !
!
!
!!!
!!!
"#$#&
When we set growth to zero, (4.4) becomes to:
!"#$% !
!
!
!
"#$)&
(4.5) is the value of a constant dividend payment discounted at rate r into perpetuity. The
growth rate g has a strong influence on the value and setting it to zero might seem misleading
on first sight. This is however how the capitalised earnings equation is set up in the
professional real estate valuation domain according to Canonica (2009) and Fierz (2005), two
of the standard books on valuation in Switzerland. Doing otherwise would imply an
estimation on rental growth from the valuation professional, which is not applicable since it is
basically a speculation about the future. As pointed out by W. Ramseyer, the real estate
valuation expert is foremost concerned with the value of an object at the present moment of
time and neither in the future nor in the past. Seen from this view point a zero growth rate g
as in equation (4.5) becomes justified. There are however other valuation standards, where a
4 Valuation of Real Estate Development Projects 15
growth rate g is employed as described in Geltner et al. (2007). Other authors such as Hoesli,
Jani et al. (2005) employ a model with growth rate to describe real estate values. We will
however, stick to the concept of (4.5), since it captures the main drivers of real estate value
and is easier to model since we do not have to make a rather difficult estimate on growth.
Furthermore it is often employed in practice.
In (4.5) we calculate the value with net dividend income D0. GOI in (4.2) however does not
directly correspond to net dividend income since cost for operation and maintenance of the
property are not accounted for yet. Therefore the cap rate in (4.2) consists of the cost of
capital r plus an addition that accounts for operation and maintenance of the property. These
additions are according to Fierz (2005) between 1.0 to 1.5% for new properties.
The cost of capital r consists of the weighted average cost of capital (WACC) of the investor.
According to practitioners the WACC in real estate often consists of 60% to 70% of debt
capital and 30% to 40% equity capital. The cost of debt capital is thereby determined by
interest rates while the cost of equity capital is determined by the required return of the
investor.
Especially in the current market environment with very low interest rates, we can observe the
high influence of decreasing cap rates due to a reduced WACC on the value of real estate
assets. Since cost of capital is decreasing, cap rates are decreasing as well and the value of real
estate increases from a valuation standpoint. It can be seen how (4.2) brings together the two
drivers of real estate value if we interpret the GOI as the result of the space market and the
cap rate as the result of the capital market.
Now that the developer estimated the expected value of the project he estimates the projected
cost of the project consisting of:
/ Land acquisition costs
/ Planning & development cost s
/ Construction costs
/ Financing costs
The projected profit is calculated by subtracting the costs from the prospective value of the
project. If this profit is high enough to compensate the developer for the subjective risks, the
developer will proceed with further analysis of the project. Often the feasibility analysis is
used to determine if the acquisition costs of the project (in most cases the land cost) are at an
acceptable level or if not stated, how much the developer is able to pay while still having an
acceptable profit.
4 Valuation of Real Estate Development Projects 16
While the feasibility analysis can be done rather easily and without looking too much into
details, it is important to understand that it is only useful as a first step in the financial
analysis and that further analysis is needed to optimally assess the investment opportunity
(Gelter et al. 2007) . This is due to the fact that the capitalised earnings method does not
appropriately take into account opportunity cost of capital, the time it takes to achieve profits
and the risk involved. One consequence of this is that it becomes very difficult to decide
between mutually exclusive projects when only applying the capitalised earnings method.
Müller (2007) points out however that many real estate professionals in Switzerland use the
capitalised earnings method as their main method to assess a development project, which
emphasises the importance of providing more sophisticated models for investment decisions
in real estate development. This leads us to the next method: The net present value method.
4.1.2 Net Present Value Method
The basic idea behind the net present value method is to not only look at the absolute profit
but also at the time it takes to acquire that profit, the risk involved and the opportunity cost of
capital. Cash flows that lie in the future are discounted to the present using an appropriate
discount rate. The discount rate accounts not only for the time value of money (e.g. the risk
free rate) but also for the riskiness of the future cash flow by applying an appropriate risk
adjusted discount rate. Thereby future cash flows are “valued” in the present, can be compared
with each other and the overall project can be assessed. When we discount the net cash flow
of each period of a project to the present we obtain the net present value (NPV). The NPV
method is also used in the context of valuing stabilised real estate assets, where it is basically a
more diligent estimation than with the capitalised earnings method underpinned by the same
principles. In the context of real estate development the application is however different. In
this study we take the viewpoint of the developer, who sells the project to an investor during
or after the development process. Here the sales volume and the costs of the project are
discounted to the present using an appropriate discount rate. The sales volume thereby is
estimated using the capitalised earnings method. The NPV makes a statement about which
project to choose among mutually exclusive projects. The decision rule thereby is:
/ Maximize the NPV across all mutually exclusive alternatives
/ Never choose an alternative that has: NPV < 0
4 Valuation of Real Estate Development Projects 17
With the equation:
!"# !
!"
!
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!
!
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"#$*&
with
CFt : cash flow at time t
r : risk adjusted discount rate
The NPV valuation is the standard tool used in real estate development and other fields to
value investment projects. The method is easy to use and intuitively comprehensible which is
probably why it enjoys such large popularity. There are however some shortcomings that we
need to discuss.
4.1.3 Shortcomings
Disadvantages of the capitalised earnings method are that it does not account properly for the
risk and the opportunity cost of capital. The NPV method effectively deals with these by
using a risk adjusted discount rate and the timing of cash flows, suffers however from other
problems in correctly assessing the value of a development project. Especially in terms of
flexibility & uncertainty the usual way of applying the NPV fails to account important
aspects. As we know from the overview of the real estate development process done in
Chapter 3, these are two very important factors and thus we discuss their role in the NPV
method here.
Flexibility
One of the main problems in applying the “classic” NPV method is the inability to account
for flexibility in the assessment of a project. NPV analysis assumes that all cash flows will
occur according to the calculation, which neglects the fact that managers actually manage
their projects and make adjustments when things do not go as planned or new opportunities
arise. As we discussed earlier, the exercise and planning for flexibility is one of the major tools
a developer has to manage risks in the development process.
When we only employ the classic NPV method we fail to account for the value of flexibility
and possibly understate the value of a project or even worse, fail to recognise, plan and exploit
flexibility in the development process.
Uncertainty
A second problem of the NPV method is firstly the consideration of uncertainty over the
choice of an appropriate discount rate and secondly the consideration of uncertainty over the
estimated cash flows. Let us first discuss the discount rate: The discount rate accounts for the
4 Valuation of Real Estate Development Projects 18
time value of money and also for the riskiness of the cash flows. While the time value of
money can be approximated by the risk free rate, how does one know which discount rate to
choose for the risk involved? In Switzerland discount rates for real estate development range
between 8 to 14% according to practitioners. In order to calculate conservative developers are
inclined to use a higher discount rate, the larger the uncertainty in a project is, but larger
uncertainty means higher upward and downward potential. The use of a higher discount rate
then penalises foremost the larger downward potential, making them unattractive from an
investment point of view. However this penalising might be unjustified, since there is also a
higher upward potential in such a project, that one could make use of, while not having to
face the downward outcome by e.g. using flexibility. The question to choose an appropriate
discount rate then becomes difficult. The second problem with the NPV method is the
assumption of deterministic fixed cash flows in the calculation. How does one know which
values to choose if there is large uncertainty in these cash flows? One way to deal with this is
scenario analysis where multiple possible cash flows are considered.
We discussed the currently used valuation methods and the problems arising from applying
them. Since real estate development involves uncertainty & flexibility, we need better tools for
the financial analysis and decision-making process of projects. We thus introduce real option
analysis as a method that effectively deals with this issue in the next part of this chapter.
4.2 Real Option Analysis
Real option analysis (ROA) is an elegant way of handling flexibility & uncertainty in
investment projects. Similar to financial options, Copeland (2001) defines a real option as
“the right, but not the obligation, to take an action (e.g., deferring, expanding, contracting, or
abandoning) at a predetermined cost called the exercise price, for a predetermined period of
time – the life of the option.”
The idea behind it is, that we have uncertainty in the outcome of projects and flexibility that
allows us to take actions accordingly. For example when markets have a downturn during the
lifetime of the project (uncertainty), we do not have to face the full downside, but can e.g.
abandon the project (flexibility) thereby cutting our losses.
This is very similar to financial options traded on financial markets: By obtaining a financial
call option, we get the right but not the obligation to buy a certain stock for a certain price in
the future. If at maturity, the stock price is higher than the exercise price of the option, we
win. If at maturity, the stock price is lower than the exercise price however, our option
becomes worthless. The parallels of financial options and real world projects led to the
4 Valuation of Real Estate Development Projects 19
application of the financial option theory to real world projects. This is an important causality
to bear in mind when applying real option frameworks since this origin of the approach from
financial options has some benefits but also some drawbacks.
A very elegant feature of real options as a valuation tool is that it can be used directly as an
extension of the conventional NPV method. Mun (2002) proposed the concept of the
expanded NPV as a combination of the option value and the conventional NPV method:
!"# ! !" !"#"$%&' + !" !"#$#
!"#$%&' !"#$% ! !"#"$%&' !" !"#$%&' + !"#$ !" !"#$%&%'( !"#$%&'
!"#$%&!& !"# ! !"# ! !"#$%&' !"#$%
This formulation of a real option lets us define the value of the option in a straightforward
way as the difference in value between a project with and without the option. When a project
has no flexibility, the value of the option is simply zero. Also when a project is without
uncertainty our option is worthless, since there is no flexibility we could employ. Only when
there is both uncertainty and flexibility there is option value and the higher the uncertainty,
the higher this option value becomes. This stands in contrast to the standard financial theory
that tells us that uncertainty is something that decreases value. Uncertainty means up and
downward potential however and with options we can make use out of this, hence real
options like uncertainty (Geltner and de Neufville 2012).
The way to do real option analysis is to recognise uncertainty, think about flexibility and
compare the case with flexibility against the one without. If this results in a positive number,
we have found an option of value. Mun (2006) thereby derives the value of ROA from 50%
thinking about it, 25% of number crunching and another 25% of interpretation of results. The
thinking about flexibility & uncertainty, model and value it, and then designing the project
accordingly is really the essence of the approach.
There are three main approaches to apply real option analysis:
/ Binomial Approach
/ Closed Form Solutions
/ Monte-Carlo Simulation
4.2.1 Binomial Approach
The binomial approach introduced by Cox, Ross and Rubinstein (1979) is a widely used
method to value financial and real options.
The binomial approach is based on the assumption of:
4 Valuation of Real Estate Development Projects 20
/ Perfect markets: Full information is available, therefore there are no arbitrage
opportunities, there is no sure gain of money.
/ Complete markets: Any risk can be replicated without transaction cost.
/ Rational behaviour: Market participants act rationally and therefore exercise
options in an optimal way.
/ Geometric Brownian Motion: In most models the underlying asset follows a
geometric brownian motion, also known as a random walk.
Under these assumptions investors will be indifferent in holding the actual option or of
owning a replicated portfolio consisting of bonds and equity that results in the same payoff
structure. We can then value this replicated portfolio using the risk free rate and risk free
probabilities that account for the risky payoff structure.
The lifetime of an option is split up in multiple time steps, resulting in multiple up-or-down
movements of the underlying asset, thereby creating a tree of possible states of the underlying
asset. The value of the option is then calculated by working the tree backwards from the end
to the beginning. At each node the value of the option is calculated taking into account the
state of the underlying asset and possible states one step ahead. The advantage of this method
compared to classic NPV valuation is that we do not account for the riskiness of the pay-out
structure over the discount rate but with probabilities, thereby separating risk and the time
value of money.
4.2.2 Closed Form Solutions
There are several closed-form solutions such as the Black-Scholes (Black et al. 1973) or the
Samuelson McKean formula (Geltner et al. 2007) and many more abbreviations for specific
options. These closed form solutions can often be interpreted as binomial models with
infinitesimally small time steps, which was already showed for the Black-Scholes formula by
Cox, Ross and Rubinstein (1979). The closed form solutions have the advantage that they are
easy to implement and give a result very quickly once the parameters are estimated. However
they are usually made only for valuing a very specific kind of option (e.g. American or
European option) thus they do not allow for complex pay out structures. As with the binomial
models they only allow for one kind of option within a project and do not account for
interchanges of multiple options. However, as we know from real estate development, there
are several options available to us, which makes the approach applicable only for certain cases
(e.g. the value of vacant land). The underlying process of these solutions is in most cases a
geometric Brownian motion that is based on the lognormal distribution with constant
variance !. While this might be somewhat close to what we observe in stock markets it is
4 Valuation of Real Estate Development Projects 21
highly questionable that the value of development projects behave this way. After all there are
multiple factors influencing the value. Furthermore it can be difficult to estimate or
communicate the significance of the results, since these models give out one specific number
that needs to be interpreted with great care. Also the models make it extremely important to
understand the underlying processes and assumptions exactly since without it one is prone to
using the wrong model and/or drawing the wrong conclusions.
4.2.3 Monte-Carlo Simulations
Other widely used methods for valuing real options are based on Monte-Carlo simulations.
This approach uses thousands of randomly generated scenarios of possible future market
outcomes and calculates the value of the project under these scenarios. As with the other real
option frameworks, the value of the option is the difference between the project with and
without the option but here we do not necessarily base the model on the idealised
assumptions of financial option models (de Neufville and Scholtes 2011). As we will see this
so called “Engineering Approach” gives us great flexibility in dealing with real options. One
of the difficulties with this approach however is that we have to implement flexibility into the
model manually so that it behaves under the market scenarios as we specify it. This can be
seen as a disadvantage against the other two approaches that exercise options always in an
optimal way. Another difficulty lies in the modelling of the underlying asset value. In contrast
to the other models, we are free to choose how the value of our project is determined and we
do not rely on the geometric Brownian motion. Depending on the required sophistication of
the model, one will need to apply advanced statistical tools that are to be handled with great
care, in order to get meaningful results. However, once the model is implemented it offers
great possibilities for adaptation and analysis, which makes it a good tool for analysis.
4.2.4 Critique and Choice of Method
Although real option theory enjoys large popularity in academia and other industries, it is
rarely used in the Swiss real estate practice (see (Müller 2007)).
Why is that so? One of the reasons comes from the theory itself: The valuation of an asset
using a replicating portfolio and the non-arbitrage argument may be a very elegant way in
theory, but in reality, although real estate is a traded asset, it is impossible to find a replicating
portfolio with the same risk exposure as that of a development project. Also it is clear, that
since the real estate market is rather intransparent and transactions are infrequent, it is far
from the no arbitrage assumption. So when we work with these assumptions we have to be
very careful with interpretation. De Neufville et al. (2011) put it as: “We need to resist the
temptation to apply the techniques of financial options blindly to such projects [technical projects].
4 Valuation of Real Estate Development Projects 22
We need to handle such applications with great care. This is because the context of technological
projects differs significantly from that of financial transactions. The assumptions underlying the
theory of financial options are not generally valid for projects, and that theory is thus of limited value
for the design and implementation of technological systems.”
Other authors such as Copeland (2001) argue that the assumptions underlying financial
options are no real problem since they are already implied in the risk-adjusted-discount-rate
of the NPV. Also we have to acknowledge that of course all models are simplifications of the
real world and assumptions help us to get closer to the truth in order to make meaningful
decisions. Conversations with industry professionals however suggested other reasons more
linked to the business world that real options have not made the leap into the Swiss real estate
development practice yet:
1. Development projects in Switzerland often start with the securing of land. At that stage
often no concrete building project exists, usage is only feebly defined and the threat of
the public voting against a large construction project is always there. The risks involved
in this first stage of the project are often of equal or higher importance than that of the
market risk. The decision maker has to take care of all involved risks and cannot rely too
much on the numerical result that comes out of a real option valuation.
2. Real options analysis values a project higher than with normal NPV analysis. This is
inherent in the system, since the option adds value to the NPV. Decision makers
however want to calculate conservatively, since they still want to have margin when
things turn out differently than expected. So why should one bother to make the analysis
only to get a small additional value, when he already knows that he has some security
margin?
3. Decision makers take over large responsibility towards their superiors or shareholders.
None of them wants to argue over the applicability of a replicating portfolio as the reason
for an investment decision. Things need to be easily understood, defendable and
communicated in order to have impact. This is not necessarily the case with real options
so far.
This makes clear that we need to use an applicable approach that clearly shows the value of
the analysis in order to have impact with real option analysis. In our view the mentioned
“Engineering Approach” using Monte-Carlo simulations is the method of choice for such a
goal.
We will go into the specifics of the model that we use into the subsequent sections. However,
the main reasons for this choice are the following:
4 Valuation of Real Estate Development Projects 23
Add-on Character
As will be shown in the successive chapters, the approach can be implemented rather easily to
the existing framework of a developer. Developers make their investment calculations mostly
with Excel, therefore they are familiar with the basic functions of the program and are able to
modify calculations according to their needs. The model we apply is basically an enhancement
of the widely used spreadsheet calculations in Excel by overlapping the existing calculations
with simulations of the future real estate market and implementing flexibility.
Comprehensibility
Users can follow the process from changes in the real estate market to changes in the value of
the project and since they are familiar with the NPV method, they understand the valuations
and their implications. Numbers can be tracked and manipulated giving confidence in the
results and avoiding the black-box phenomenon. In contrast to the binomial approach we do
not employ the assumptions of financial options theory but work with normal NPV. This is
not perfect either of course but is easier to comprehend since practitioners are used to work
with it.
Customisation
Customisation is easily possible by changing input parameters such as rent levels, vacancies
and capitalisation rates. The framework can be adapted to the specific project or the
simulations can be added to an existing NPV valuation framework. It is also possible (and
strongly advised) to perform extensive sensitivity analysis on the specific project that helps to
further understand and optimize market risk exposure of the project.
We discussed the current valuation practice of real estate development projects and advocated
the need for incorporating uncertainty & flexibility into the valuation for a more profound
analysis and decision-making process. We then introduced real option analysis as a promising
way to effectively deal with uncertainty & flexibility and discussed reasons why the method
has not yet found wide application in the real estate development practice. We came to the
conclusion that we need a more applicable and intuitive approach to have impact in practice.
This let us favour the “Engineering Approach” as an analysis framework for real estate
development projects. In the next chapter we look at this framework in detail and show how
we can apply and configure it for the Swiss real estate market.
5 Simulation Based Real Options Model 24
5 Simulation Based Real Options Model
In the following chapter we first explain the “Engineering Approach” introduced by de Neufville and
Scholtes (2011). This framework helps us to assess flexibility & uncertainty in a real estate
development context and we use it extensively in our case study in Chapter 6. In the second part of
this chapter we first look at the development of prices, vacancies and cap rates in the region of Zurich
Unterland and then introduce two models for simulation based on this data. This simulation
framework generates possible future scenarios of the real estate market, which allows analysing real
estate development project under these scenarios.
5.1 Project Modelling Framework: The “Engineering Approach”
The “Engineering Approach” is designed to help practitioners design better systems by
analysing flexibility & uncertainty. In order to be applicable, the approach is based on
pragmatic and simplifying assumptions that differ from the binomial and the closed form real
options models.
Instead of working with a replicating portfolio and risk neutral probabilities as used in the
binomial and the closed form real options model, the “Engineering Approach” works with net
present values with constant discount rates as we know them. We therefore do not value cash
flows, based on the theoretical sound framework introduced in Chapter 4.2.1.
But should we not build up on this theoretical framework and present answers that are as
correct as possible, that “get things right” as exactly as possible? De Neufville et al. (2011)
describe this aspect of their approach as: “…we believe that our modest aspiration to “get it
better” is more likely to improve practice. Indeed the concept of “getting it right” is difficult to defend
once we accept that modelling the performance of socio-technological systems is as much an art as
science.”
We argue for an applicable approach in Chapter 4.2.4 and hypothesise that ROA with
binomial trees or closed form solutions have not been widely adopted in practice because they
lack the pragmatism that is needed “to get things better” instead of “getting things right”.
They are too closely linked to the “correct” valuation of financial options that they lack the
flexibility to be easily adapted to real projects. We believe that by applying the “Engineering
Approach” we are better able to catch the essence of real options analysis, which is to think
about flexibility & uncertainty, model and value it, and then to make better project analysis
and decision-making.
5 Simulation Based Real Options Model 25
The “Engineering Approach” is divided into four steps:
/ Creating the most likely initial cash flow model
/ Incorporate uncertainty into the model
/ Incorporate flexibility into the model and
/ Maximize value by applying an optimal decision rule
We introduce the four steps in detail here and apply them to our case study later on.
5.1.1 Step 1: Create the Most Likely Initial Cash Flow Model
The first step is to create a pro forma cash flow model incorporating development and
construction cost, project scale, schedule and the estimated sales volume. The sales volume,
the estimated value of the finished project on the market, is calculated using the capitalised
earnings method. The cash flows are discounted to present values, using an appropriate
discount rate, which results in the NPV of the project. As we know from Chapter 4.1.3
“Shortcomings”, the resulting NPV neither incorporates uncertainty in cash flows nor
flexibility yet, but since it is the standard valuation tool it serves as a good benchmark against
which we can compare our further calculations. We will therefore call the result of this
calculation the “base case”.
5.1.2 Step 2: Incorporate Uncertainty into the Model
We enhance our initial cash flow pro forma by recognising uncertainty. We do this by
identifying the risk drivers that determine our future cash flows and then try to model them.
For our case we assume that the future cash flows only depend on the real estate market and
therefore make a model of this real estate market. We will then use this model to simulate
subsequent scenarios of this market. By doing so we can generate thousands of possible future
scenarios and their corresponding cash flows. As shown in Figure 2, this results in a
distribution of possible outcomes rather than one estimated value as we obtained it from the
“base case”. Since we do not yet incorporate flexibility, we will call this the “static case”. We
analyse the “static” case using histograms and cumulative probability curves of the resulting
NPV distribution, as shown in Figure 2 and 3.
5 Simulation Based Real Options Model 26
Figure 2: Example of a NPV Distribution
Source: Own illustration
Figure 3: Example of a Cumulative Probabilities Curve and Expected NPV
Source: Own illustration
With the help of these graphs we get a feeling for the range of possible outcomes and can
better understand the risk structure of the project. The cumulative probabilities curve can also
be described as the value at risk and gain (VARG) curve. It states the probability of an
outcome below or above a certain NPV. A flat VARG curves thereby indicates a wide range
of possible outcomes whereas a steep curve indicates a low range.
The vertical line depicts the mean or expected value of the distribution. We will call this the
expected net present value (ENPV). The shape of these graphs depends on the simulation
model that we use and the cash flow structure of the project. In order to draw right
conclusions, it is crucial to use an appropriate simulation model. We will therefore give a
detailed analysis on different approaches and how it can be done in Chapter 5.2 on the
simulation framework.
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5 Simulation Based Real Options Model 27
5.1.3 Step 3: Incorporate Flexibility into the Model
Now that we have combined our project with a wide range of possible market scenarios, we
can think of actions to take when certain scenarios occur. These will be our options, since we
can always choose whether or not to exercise them. Our available options highly depend on
the specific project and in real estate these often include:
/ Option to delay (e.g. wait with construction until market recovers from a downturn)
/ Option to switch (e.g. switch from an office to a housing use)
/ Option to abandon (e.g. sell the property for salvage value)
/ Option to phase (e.g. build only part of the project and the rest later)
/ Option to expand (e.g. build an extension of the project)
We can model these options by including decision rules into our spreadsheet model. For
decision rules to work we need first a trigger value that triggers a certain action, and secondly
an execution variable that leads to the actual change in the model.
A decision rule then has the form of: “if variable A (the trigger value, e.g. value of apartments)
falls bellow a certain threshold, then variable B (the execution variable e.g. variable for delay
of construction for one year) will be one and thus lead to a delay in the successive cash flow of
one year .”
When we let the simulation of scenarios run, actions will be taken depending on the specific
scenario and therefore a scenario sensitive distribution of NPV outcomes is obtained. When
analysing the resulting distribution curves it is our goal to decrease the amount of negative
outcomes and to increase the amount of positive ones. This corresponds to a shift of the
VARG curve to the right. We will call this calculation model the “flexible case”.
This third step forces us to think about our available options and what to do in advance
before things turn out to be different than in the base case scenario. It is this thinking about
options and how to preserve and use them that gives additional value due to flexibility. Figure
1: Flexibility, Uncertainty and Cumulative Investment in the Development Process on page
12 shows how flexibility decreases during the development process. Thanks to simulations we
are now able to identify and quantify the most valuable options from the beginning, keep
them alive during the development and exercise them if needed. This is one of the main
advantages of this methodology.
5.1.4 Step 4: Maximize Value by Applying Optimal Decision Rules
The fourth step deals with finding the right set of decision rules that optimises the overall
outcome. Additional sensitivity analysis is performed on the model. Which value to optimise,
depends largely on the decision maker. In our study we focus on the NPV, but a decision
5 Simulation Based Real Options Model 28
maker might be interested in other profitability metrics such as the internal rate of return or
the absolute return. This can be implemented as well. The optimal combination is found by
experimenting with different combination of decision rules and project parameters.
5.2 Simulation Framework
After introducing the “Engineering Approach” we now look in detail at our data and how to
model it. First we give an overview of what, why and how we are going to model the risk
drivers of a real estate development project. Then we look at our data, the development of the
observations depicted in the data in the past years and on correlations among the data. In the
third part of this chapter we introduce two ways to model this data with the goal of obtaining
a model for simulation.
5.2.1 Overview
Goal
We want to obtain a model for the simulation of risk drivers for real estate development
projects. We need this model to analyse possible future values of a real estate development
projects from the viewpoint of a developer.
What to Model
The first question to answer towards this goal is that of what we actually need to model. We
are interested in the value of real estate assets in the future, since this is one of the main
success drivers of a real estate development project. In Chapter 4 we discuss that the gross
operating income and the capitalisation rate approximates the value of a finished real estate
project. These two variables determine to a large degree how much an investor is willing to
pay for a real estate asset to a developer or, if the asset remains in a portfolio, what the book
value of the asset is. It is thus apparent that we need to model these two variables. Another
important part of a real estate development project are condominiums. These are directly sold
to private persons already before, during and after the construction phase. Depending on the
project, they also have a large influence on the bottom line of the developer and thus we are
interested in modelling them as well. Further, construction cost is an important aspect of a
development project that inhibits uncertainty, so this is something we will want to model as
well. We go into more detail on what we need to model in Chapter 5.2.2 on the risk drivers
of the model and continue here with the overview of the model.
5 Simulation Based Real Options Model 29
Time Horizon
Since real estate development takes time, we are interested in a rather long time horizon into
the future. Development projects take from initiation to stabilised operation at least 4 to 5
years. Since we are interested in flexibility and therefore also consider the delay of
construction we take into account a simulation horizon of 10 years.
How to Model
The second question we need to answer is that of how to model these variables. The method
we use is to look at past data for the variables of interest, so called time series, and fit a model
to this data. This model is then used for the simulation of future variables. A simple model is
that of a trend plus noise model. The model takes the form of:
!
!
! ! ! ! ! ! ! !
!
")$%&
with
yt : data point at time t (e.g. GOI)
t : time
a,b: constant parameters to be estimated
"t: randomly distributed error terms
The term a!t + b is the model trend line and "t the noise around the trend. We can estimate
the model using ordinary least squares (OLS) method on the past data, thereby minimizing
the sum of squared vertical distances between the data and the predicted model, in this case
the trend line. By extrapolating the trend into the future and generating new noise around the
trend, using random draws from e.g. a normal distribution, we generate simulations of the
model into the future. This is illustrated in Figure 4 :
Figure 4 : Simulation with a Trend + Noise Model
Source: Own illustration
!
#!
$!!
$#!
%!!
%#!
! # $! $# %! %# &! &# '! '# #!
!
"
#
$
%
'
(
$
)
*
+
,
-
+
+
($)*.
()*+ ,+-)+.
(-+/0
,)*12345/
5 Simulation Based Real Options Model 30
This rather simple approach neglects however that the time series of interest do not
necessarily follow a constant trend and also that there might be dependence with other
variables that need to be considered. Also we see already in Figure 4 that the generated
simulation does not inherit the same characteristics as the past time series it is based on: The
simulated line jumps above and below the trend line in shorter time intervals than in the past.
We will thus have to employ more complex modelling techniques.
Stationarity
Additionally in order to use a model for simulations, we have to use the concept of
stationarity. A stationary time series has the property that the probabilistic character of the
series does not change over time, so that any section of the time series is “typical” for every
other section with the same length (Dettling 2012). If any section of the time series is typical
for every other section and if we can assume that this property holds also in the future, then
we can use this time series also for forecasts of future time series. A stationary time series has
constant expectation E[Xt], constant variance Var(Xt) and the covariance between the
observations Cov(Xt1,Xt2), i.e. the dependency structure, depends only on the lag between the
observations. Now most time series are not stationary. Every time series with e.g. a trend or a
deterministic seasonal pattern violates the concept of stationarity. By transforming and
decomposing the data, we can however often find a stationary process. Actually the
introduced trend + noise model (5.1) is already such a decomposition. The goal of such a
decomposition is to find one that yields a stationary noise process "t. As we stated already we
often cannot assume a trend that remains constant over time as in the trend + noise model.
One way of dealing with this is to work with logarithmic returns rather than the raw time
series. Thereby we detrend and normalise the data and hopefully obtain a stationary noise
process.
Working with Logarithmic Returns
A common practice when modelling time series and analysing dependence among them is to
work with logarithmic returns (log returns). By using log returns we focus on the relative
change of the time series, which is directly comparable to the relative change in other time
series. Additionally we remove piecewise a linear trend if there existed one. Throughout this
chapter we thus work with logarithmic returns rather than discrete returns. Log returns have
the convenient property that they are additive and easily obtained from time series by taking
the natural logarithm of the series and differentiating by one time step:
5 Simulation Based Real Options Model 31
!
!!!
! !"
!
!!!
!
!
! !" !
!!!
! !" !!
!
! " )$' &
with
rt+1 : logarithmic return between time t and t+1
yt,yt+1: data point at time t
Independent on which model we use for simulation, we first transform the data to
logarithmic returns, fit a model to it, and use this model for the simulation of a future horizon
of 10 years. We thus generate future logarithmic returns that we can apply to the value we
observe at present and thereby obtain our desired prediction of future time series:
!
!!!
! !
!
! !
!
!!!
")$(&
with
t : time of last observed data point
rt+1: predicted return for one time step ahead
yt+1: one time step ahead prediction of data point
Indices & Absolute Values
As we are going to see, most of the data used in this study is based on indices rather than
absolute values. For our calculations on real estate development projects we need absolute
values however. We address this by first estimating the model on the indexed data as
described above and then using an absolute value currently observed in the market as the start
value of our simulation. We thus assume that the absolute value will behave the same as the
index it is based on. This is not necessarily true if we choose values that do not correspond to
the index, so we should use only start values that actually correspond to the used index.
After this overview on what and how we are going to model, we now look into the details of
the model.
5.2.2 Risk Drivers
The question is what exactly do we need to model to simulate the value of a real estate
development project. As we discussed in Chapter 4 on the valuation practice, a real estate
asset from the investment perspective is determined by the GOI and the capitalisation rate.
Additionally, we often have a part of the development project consisting of condominiums
that are directly sold to private owners.
5 Simulation Based Real Options Model 32
Investment Asset
Let us first look at the part of the project that enters the market as a real estate investment
asset (no condominiums) and estimate the value it would have today. In real estate
development a project often consists of multiple uses such as housing, office and commercial.
For simplicity we work with per m
2
values:
!"#$%
!""#$
!
!"#
!"!#$
!"#$"%&
")$#&
!"#
!"!#$
! !"#
!"#$%&'
! !"#
!""#$%
! !"#
!"##$%&'()
")$)&
!"#
!"#$%&'
! !"#$
!"#$!"#
! !! ! !"#"$#%
!"#$%&'
! ")$*&
!"#
!""#$%
! !"#$
!""#$%
! !! ! !"#"$#%
!""#$%
! ")$,&
!"#
!"##$%&'()
! !"#$
!"##$%&'()
! !! ! !"#"$#%
!"##$%&'()
! ")$-&
For estimating the value of a real estate asset, we thus have to model rents, vacancies and cap
rates for all uses.
Condominiums
Let us shortly discuss the condominiums that are also often a part of the development project.
Buyers of condominiums do not take the investor perspective of calculating rents and cap
rates, but base their decision to buy a condominium on their budget and preference. Since in
Switzerland most condominiums are partly financed with mortgage loans, mortgage rates play
an important role on their affordability. Condominium prices are measured on a per m
2
basis
for specific regions in Switzerland which makes it possible to use the corresponding indices
directly for modelling.
Deal Noise & Vacancy
When an developer sells a project to an investor, there is always a certain amount of
uncertainty around the valuation price, depending on the bargaining power of the two parties
negotiating (Geltner and Miller 2007). We will address this by introducing an independent
variable “deal noise” to account for this. Additionally developers in Switzerland sell a project
often before the receipt of the building permit with a certain amount of space already
preleased to prospective tenants. There remains however often some vacancy risk that the
investor will want to have compensated. We take this into account by applying twice the
vacancy rate observed on the market on our sales price to the investor.
5 Simulation Based Real Options Model 33
Also when selling condominiums, the price might differ from the current market price due to
the location, marketing success and specifics of the project. We will thus use deal noise on
condominiums as well.
Construction Cost
On the cost side we have the construction cost as our only risk driver. We are hereby looking
at the market risk of construction cost, assuming that the developer estimated the cost of his
project accurately and that the cost risk is therefore only driven by the uncertainty of variable
prices for the same services and goods.
Table 1 gives a summary on the discussed risk drivers that we need to model:
Table 1: Risk Drivers
Earnings Side Cost Side
Rents (Housing, Office, Commercial) Construction Cost
Vacancies (Housing, Office, Commercial)
Cap Rates
Transaction Prices Condominiums
Deal Noise
The total sales price of a project to investors and private buyers can then be stated as:
!"#$%
!"!#$
! !
!""#$
! !"#$%
!""#$
! !
!""#$
! !
!"#$"
! !
!"!"#
! !
!"#$"
")$.&
with
#Asset, #Condo : deal noise asset and condominiums
$Asset, ACondo : saleable space in m
2
PCondo : price condominiums per m
2
ValueAsset : value of the asset according to (5.4)
And the cost including construction cost risk as:
!"#$
!"!#$
! !"#$
!"#$
!!"#$
!"#"$%&'"()
!!"#$
!"#$#%"#&
!! ! !"#$
!"#$%&'(%)"#
")$%/&
with
! : construction cost uncertainty
5.2.3 Data
The independent real estate and urban development consulting company Fahrländer &
Partner Raumentwicklung AG (FPRE) provided us with data specific for the region where our
case study is located. The data is extracted from the Real Estate Scenario Cockpit (Fahrländer
2012) of FPRE and covers the time span from 1985 to 2011 in yearly time steps. The RESC
is constructed with data from multiple rent indices, data from the Federal Statistics Office,
5 Simulation Based Real Options Model 34
the cantons and other sources. For replication of our results one is advised to use the freely
available data for rents provided by the Swiss National Bank
4
. We used this data source also
for the data on construction cost and gross domestic product.
Whenever analysing real estate data, it is important to clearly understand its nature. In our
data set we look at the evolution of rents, vacancies and cap rates from 1985 to 2011. During
that time the products on the space market have changed substantially: while a new apartment
in 1985 with an automatic dishwasher was in an upper price range, it is standard equipment
in new apartments nowadays. Similar examples can be made for windows, heating, elevator,
etc. Changes in quality also occurred in terms of location: with the increased supply of
mobility, locations further away from cities have become more attractive. This is especially the
case with suburban areas, that became much more attractive due to increased mobility
services. Furthermore the real estate market is very heterogeneous: objects differ from each
other substantially in terms of size, location, age, etc. We therefore do not deal with a
commodity like gold that does not change over the years and is the same wherever it is
bought. We can account for this by using hedonic pricing models that take into account
quality properties of the objects. The method used on our data set is described for rents by
Wüst&Partner (2000) and for condominium transaction prices by Fahrländer (2012).
Table 2 gives an overview of the used data:
Table 2: Data Used in this Study
Data Category Time Resolution Region Source
Rents, Vacancies Housing, Office,
Commercial
1985 - 2011 Yearly Zurich Unterland FPRE
Transaction Prices Condominiums 1985 – 2011 Yearly Zurich Unterland FPRE
Cap Rates Housing, Office,
Commercial
1985 – 2012 Yearly Zurich Unterland FPRE
Construction Cost
Index
Cost Index all
Constructions
1998 – 2011 Yearly Canton of Zurich SNB
Gross Domestic
Product
Economy 1990 - 2011 Yearly Switzerland SNB
We now describe the obtained data and highlight specifics of their behaviour in the past.
Rent Revenues
We use indices for the rent revenues of the different usages (housing, office and commercial).
The indices correspond to rents observed in the MS (mobilité spaciale) region Zurich
Unterland and do not include vacancies yet. For further information on the locality of this
region one is advised to look at Schuler (2005). An important notion is that the rent indices
4
www.snb.ch
5 Simulation Based Real Options Model 35
are based on asking prices for rents and not on average revenues observed in actual properties.
Due to restrictions and long-term contracts it is difficult for owners of real estate to
immediately adjust rents to current asking prices and thus their revenues will tend to be lower
on average. For real estate development however, the use of asking prices comes in handy,
since development projects come new to market and we can assume that they will generate
revenues close to current asking prices. For housing the used index corresponds to middle
class multi-family dwellings, for office and commercial, it is the average asking price observed
in the specified region.
Figure 5 shows the development of rent revenues during the observed time period. We see a
sharp increase in rents from 1985 to 1990 with a peak in 1991, a sharp decline thereafter and
since 1998/1999 a steady growth. The sharp decline in rents is associated with the real estate
crisis in the early nineties we discussed in Chapter 3.4. From the figure we can already see
that the three indices behave somewhat correlated. The indices of office and commercial
space are identical until 1996 and behave strongly correlated thereafter. The equality of the
two indices in the beginning of the series comes from the index construction that itself is
based on multiple rent indices. Apparently rents for commercial and office use are based on
the same data source during the beginning of the data. This will have further implications for
our model later on.
Figure 5: Rent Revenue Index Zurich Unterland
(Source: RESC Fahrländer & Partner)
Vacancies
For vacancies we have the same usages and data source as for rent revenues. These are the
vacancies that we observe on the overall market. Here we see exactly identical values for office
and commercial uses, which is why there are only two lines visible in Figure 6 instead of
5 Simulation Based Real Options Model 36
three. Values vary from 2% up to almost 18% in the middle of the 1990s for office &
commercial uses while they stay between small 0.5 and 2% for housing use. Again we see the
effect of the burst of the real estate bubble in the early 1990s that resulted in large vacancy
rates for office & commercial uses. Interestingly it did not affect vacancies in the housing
market very much. We can therefore legitimately assume that office and commercial uses had
more risk of vacancies and therefore loss of earnings in the past than housing.
Figure 6: Vacancies Zurich Unterland
Source: RESC Fahrländer & Partner)
Transaction Prices Condominiums
We use the transaction price index of middle class condominiums for our analysis.
Condominiums enjoy large popularity especially in recent years, which can be seen in the
large price increase of almost 50% from 2000 to 2011. We can also observe that
condominium prices have a very similar price development as that of housing rents.
Figure 7: Transaction Price Index Condominiums Zurich Unterland
Source: RESC Fahrländer & Partner
5 Simulation Based Real Options Model 37
CapRates
From the RESC we obtained value indices for housing, office and commercial uses. These
value indices were constructed by using the equation:
!"#$% ! !"#$ ! !! ! !"#"$#%!!!"#$"%& ")$%%&
The cap rate thereby consists of an empirically measured premium plus a WACC consisting
of 60% leverage, based on mortgage rates and 40% equity capital, based on bond rates and on
an additional premium for real estate. This approach corresponds to the calculation of cap
rates in Chapter 4. To obtain cap rates from the value indices, we solve equation (5.11) for
cap rates using the already described rent and vacancy data and levelled them on 5% for the
year 2011. We thereby obtain three time series of cap rates pictured in Figure 8:
Figure 8 : Cap Rates Zurich Unterland
Source: Own calculation based on RESC Fahrländer & Partner
The levelling on 5% is a rather a simplified approach to estimate cap rates but since we are
more interested in the relative change and the correlation with rents and vacancies, the
absolute value should not matter too much. As seen in Figure 8, all three cap rate time series
behave highly correlated and because we do not want to unnecessarily complicate our model,
we aggregated cap rates into one single time series by taking the average of the previous three
cap rates. For our model we are going to use this aggregated time series as our input. The
result is illustrated in Figure 9.
An important thing to note with cap rates in a historic context is that they are currently at a
very low level due to the interest rate policy of the SNB. As soon as interest rates start to rise
again, this will have an influence on cap rates, which will result in decreasing real estate value
if rent revenues do not rise simultaneously.
5 Simulation Based Real Options Model 38
Figure 9: Average Cap Rates Zurich Unterland
Source: RESC Fahrländer & Partner
Construction Cost Index
We use the construction cost index from the SNB for the region of Zurich. The index is
quarterly available since 1998. From 1998 to 2011 construction cost have been rising on
average by 1.6% per year.
Figure 10 : Construction Cost Index
Source: SNB
Real Gross Domestic Product
We use the real gross domestic product (GDP) as our exogenous variable for the VAR-model
we introduce later on. We work with the real GDP because we expect the economic activity
to have an influence on expenditure on rents and condominiums, and also on vacancy rates
especially in the office and commercial market. Unfortunately we have data only for the time
5 Simulation Based Real Options Model 39
period from 1990 until 2011 and not for the whole time period of the other data sets starting
in 1985. The yearly percentage change is the growth in GDP and depicted in Figure 11.
Since we look at the changes per year we lose one data point for 1990. We see a negative
growth in GDP from 1991 to 1993. This corresponds to the time of the real estate crisis, so
while growth was close to zero we had also decreasing prices. The second time when GDP
growth was very low is 2002 and 2003. When we look at were GDP growth was close to zero
and zero growth in 2002 and 2003 and again negative growth in 2009.
Figure 11 : Growth in Real GDP 1991 - 2011
Source: SNB
Interpretation of Data in the Light of Forecasting
Our data for office & commercial uses are almost identical and we use a very simplified
method to calculate our cap rates. Furthermore we have only yearly data points and not the
full time span for all data sets. To assume that we can conduct an exact forecast out of this
data would not be very credible. But then again we have millions of data sets about financial
markets and even with this huge data history it is apparently not possible to develop accurate
forecasts. After all, the saying goes that forecasting using past data is like driving a car
looking through the rear window. Something that might go fairly well when we already know
the road ahead but gets extremely difficult when we face the unexpected (Dettling 2012).
This is of course also true for the real estate market, especially when looking at the burst of
the recent real estate bubble in the US.
We presume however, that by capturing important properties and relations of data in the past
we can get a model that yields credible paths of the future. This does not presume that we
know what is going to happen, which is impossible, but gives us a sense of what is possible.
5 Simulation Based Real Options Model 40
We now look at relations that we observe in our data set and implications of this for our
modelling framework.
Correlation & Trends
We see already by eye that rents and prices over all uses rise and fall in positive correlation
during the observation period. We also observe that there seems to be a trend in the evolution
of rents and condominium prices. While the office and commercial market had a very sharp
correction in the early nineties, the decline in housing rents was much lower. We will
therefore expect more volatility in the rents for office and commercial space than for housing
space.
To study the dependence among variables we calculate the linear correlation between the log
returns of the data. Correlation coefficients range between -1 and 1. A value close to 1 or -1
thereby indicates strong positive or negative correlation, while a coefficient close to 0 indicates
no linear correlation. Looking at the correlation coefficients of the data in Table 3, we observe
indeed a positive correlation of around 0.5 between housing, office, commercial rents and
condominium prices. Further we see that the office and commercial rents are indeed very
similar due to their high correlation coefficient of 0.9 and the similar correlation coefficients
also with other time series. While there is small negative correlation of -0.2 between housing
rents and housing vacancies we do not see this for office/commercial rents and
office/commercial vacancies. We further observe negative correlation of -0.5 between housing
rents and cap rates indicating that when cap rates go up, housing rents go down. This
correlation is however less profound for office rents (-0.24) and commercial rents (-0.17).
Table 3 : Correlation Matrix Data Zurich Unterland
Housing
Rents
Office
Rents
Comm.
Rents
Housing
Vacanc.
Office
Vacanc.
Comm.
Vacanc.
Condo.
Prices
Cap
Rates
Housing
Rents
1.00
Office
Rents
0.54 1.00
Comm.
Rents
0.56 0.90 1.00
Housing
Vacanc.
-0.21 -0.64 -0.64 1.00
Office
Vacanc.
0.33 -0.06 -0.08 0.28 1.00
Comm.
Vacanc.
0.33 -0.06 -0.08 0.28 1.00 1.00
Condo.
Prices
0.50 0.43 0.43 -0.26 0.28 0.28 1.00
Cap
Rates
-0.52 -0.24 -0.17 -0.12 -0.10 -0.10 -0.04 1.00
5 Simulation Based Real Options Model 41
Rents & Vacancy
One would expect that when vacancies in a region go up, that rents will start to fall. This is a
question of balancing out supply and demand in the space market where vacancies indicate a
high level of supply that is not absorbed by the market. In order to match supply and demand
we would thus expect a decrease in prices. When looking at Figure 5 and Figure 6, we see by
eye that while office & commercial vacancies went up during the nineties, prices decrease
substantially. Looking at correlation coefficients however, we see only a small negative
correlation between housing rents and housing vacancies and no correlation between office
and commercial rents and office and commercial vacancies. It is however important to note
here that we are currently looking at correlation among log returns at the same time t.
However, there might be a lagged dependence between e.g. office rents and office vacancies
so that rising vacancies have an effect on rents one or two years later. We discuss this further
when modelling our data later on.
Cap Rates
Cap rates went down substantially before the early nineties crisis while rents were rising,
resulting in very high values for real estate. Since 1999 cap rates are falling, which is reflected
in the higher valuation of real estate all over Switzerland.
After discussing the data, let us shortly recapitulate what we did so far and what the next
steps are towards reaching the goal of modelling the risk drivers for the financial analysis of a
real estate development project: In Chapter 5.2.2 on the risk drives, we discussed what we
have to model. We then looked at past data that describes the behaviour of these variables in
Chapter 5.2.3. The next step is to find an appropriate model that we can fit to this data. After
fitting a model to the data, we can then use it to generate simulation of future variables. This
is a necessity to incorporate uncertainty into the “Engineering Approach”.
5.2.4 Modelling
We first introduce a Copula and then a Vector Autoregressive (VAR) model that we fit to the
data. These two models have the property that they take into account interdependence among
the multiple time series, which is something we want to consider when using the model for
simulation later on.
5 Simulation Based Real Options Model 42
We use the following techniques for modelling our risk drivers:
Table 4: Techniques used for Modelling
Risk Driver Method
Rents VAR- & Copula Model
Transaction Prices Condominiums VAR- & Copula Model
Vacancies VAR- & Copula Model
Cap Rate VAR- & Copula Model
Construction Cost Copula Model
Copula Model
In the overview in Chapter 5.2.1 we discuss that by taking log returns we wish to obtain a
stationary process that we can model. Let us assume that this is true and the obtained log
returns are stationary. We then have nine time series of stationary processes that we can fit a
model to. Let us further assume that all these time series follow a normal Gaussian
distribution each with constant mean and variance. We could then estimate mean and
variance based on our data and use random draws from the calibrated Gaussian distributions
to generate simulated returns. These we could use for the simulation of future outcomes.
Now there is a major flaw if we make simulation like this: we neglect an important property
of our data, which is their dependence on each other. We already discussed that for example
housing rents and condominium prices are correlated and thus it would makes sense to take
this into account in our model. Otherwise the simulated time series would behave completely
independent from each other, which will certainly not be very feasible in our case. Copulas are
a way to account for correlation among multiple time series and thus we employ them here.
Definition
Copulas are mathematical tools that are useful for the simulation of linearly correlated data.
They gained large attention and distribution in investment banks and insurance companies
before the latest financial crisis. It was assumed to be possible to price the rather complex
financial derivative class of collateralised debt obligations (CDOs) that were at the core of the
late crisis, with the help of Gaussian copulas (Salmon 2009). In the context of blindly trusting
in financial models, they therefore have some similarity to the Black-Scholes model that is
blamed for the stock market crash in 1987. The reason for their large distribution however is
that they have some very useful properties that we can make use of:
Copulas are joint distribution functions that link a multidimensional distribution to its one
dimensional marginals. These marginals can be made standard uniform, which makes them
5 Simulation Based Real Options Model 43
ideal for further transformation and simulation. Embrechts (2009) explains the basics of
copulas as:
In the one dimensional case we have a random variable X with a continuous cumulative
distribution function F. We have U = F(X) with U as a standard uniform distributed variable
[0,1]. We can also transform this back by applying the inverse cumulative distribution
function: X = F
-1
(U). When we have the multivariate case we can write the joint cumulative
distribution function F( x1 , x2 ) as:
! !
!
! !
!
! !!!
!
!
!
! !
!
!
!
! ")$%'&
With C as our copula: A multivariate distribution function with standard uniform marginals
(U1, U2). Formula (5.11) couples the marginals F1(x1), F2(x2) to the joint cumulative
distribution function F(x1,x2) via the copula. Sklar (1959) showed that there exists a unique
copula for n-dimensional multivariate distribution functions if the marginals are continuous.
Let us now look on the joint realisations as obtained from the two dimensional Gaussian and
t-copula with standard normal marginals as depicted in Figure 12 and Figure 13.
Figure 12: Gaussian Copula with Correlation of 0.7
Source: (Neslehova 2006)
We see that the Gaussian copula indeed produces linearly correlated marginals since
realisations are clustered around a linear slope and not randomly distributed, as seen in the
scatterplot in Figure 12. Now there are also different copulas than the Gaussian that yield
different dependency structures. One of these is for example the t-copula as depicted in
Figure 13:
5 Simulation Based Real Options Model 44
Figure 13: t-Copula with Correlation of 0.7 and 4 df
Source: (Neslehova 2006)
While both copulas have the same correlation coefficient of 0.7, the t-copula yields more
clustering of realisations among the tails compared to the Gaussian copula. We see this, when
we compare e.g. the lower left corner of Figure 13 with the lower left corner of Figure 12.
The t-copula is thus better suited to model dependence among extreme events than the
Gaussian copula. There are however other copulas that take into account the asymmetry in
correlation meaning that while there might be correlation among the right tail of the
distribution, there is little or none on the left tail or vice versa. Modellers have a wide variety
of choices available to choose among copulas and to find one that “best” suits their data. As
Embrechts (2009) points out in this context, there is no obvious answer in the question on
which copula to use. It really depends on the data and the dependence structure one wishes to
model especially in the light of changing circumstances. While one might find a copula (or
more generally a model) that fits the observed dependence perfectly, it remains questionable if
the relations modelled will also hold in the future. If the market circumstances change, as in
the case with the pricing of CDOs using Gaussian copulas, then previous valid models often
become obsolete. This is something we have to be aware of when modelling dependencies.
Application
We use the above result to create joint distribution functions with the dependencies we
specify. The first step is to choose a copula that suits the correlation structure of the data. If
correlations among the tails are observed (tail dependence), then e.g. a t-copula might be
applicable.
In our case we have a data set consisting of 27 data points for every time series. This is not a
large data set for analysing the dependence structure of the data and we have to choose a
5 Simulation Based Real Options Model 45
copula that fits all dependencies. We thus make an estimate on what the dependence
structure could possibly look like. Since we do not have sufficient data to study and model tail
dependence of the variables, we choose the Gaussian copula to describe the dependence
structure of our data.
Once we decide on a copula, we feed it with the dependence structure we found in our data.
This is described by the linear correlation matrix depicted in Table 3. The copula then gives
us the standard uniform marginals with the dependence structure still in place. We can use
these marginals together with a distribution function that fits our data. This is the second
convenient property of the copula: we can choose a distribution function that fits our data and
this for every single time series. Let us look on the descriptive statistics of our data:
Table 5: Descriptive Statistics Log-Returns Data
Housing
Rents
Office
Rents
Comm.
Rents
Housing
Vacanc.
Office
Vacanc.
Comm.
Vacanc.
Cond.
Price
Cap Rates
Mean 0.02 0.02 0.01 0.02 0.04 0.04 0.02 0.00
Std. Dev. 0.04 0.08 0.09 0.38 0.30 0.30 0.04 0.07
Skewness 0.86 0.55 0.50 0.47 -0.29 -0.29 0.09 0.92
Kurtosis 0.66 -0.01 -0.33 -0.62 0.33 0.33 0.51 2.65
In Table 5 we depict the four moments of the risk drivers that describe their distribution. We
see a positive mean for all risk drivers except for cap rates which is zero, meaning that the
average log return of the risk drivers was positive in the past. Further we note that the
vacancies have a high standard deviation of 0.3 indicating that log returns show a wide
distribution of possible outcomes. Further we see skewness in the data. Skewness describes
the asymmetry of the distribution. Thereby a negative value indicates a long left tail of the
probability distribution while a positive value indicates a long right tail of the distribution.
For rents we see positive skewness indicating that rents have a long right tail, while vacancies
have a longer left tail. The kurtosis we see in the last line is shown here as excess kurtosis in
comparison to the standard normal distribution. A positive value depicts higher kurtosis than
the standard normal and a negative depicts lower kurtosis. Kurtosis can be interpreted as the
peakedness of the distribution, meaning the width of the peak. Peakedness comes together
with fat tails, meaning that the tails of the distribution still have a relatively high probability
of occurrence. A high kurtosis indicates a narrow peak with fat tails, while a low kurtosis
indicates a wide peak with thin tails in comparison to the standard normal distribution. Cap
rates have a high kurtosis indicating that the distribution has a narrow peak and fat tails. Now
since we observe skewness and kurtosis in our data it would be elegant to choose a
distribution that can account for this. The normal Gaussian distribution that we use for the
example in the beginning of this section does not serve us well in this case, since it is defined
5 Simulation Based Real Options Model 46
only by mean and variance. Luckily there are many other distributions in the toolbox of a
financial modeller and a commonly used one that accounts for skewness and kurtosis is the
Normal Inverse Gaussian (NIG) distribution. We thus use this distribution, calibrate it over
the mean, variance, skewness and kurtosis from our data depicted in Table 5 and apply it to
the standard uniform marginals obtained from the copula. We thereby create a joint
multivariate distribution with the marginals following the NIG and a dependence structure
still in place as we specified it. We can then use this distribution for simulations just as in the
example in the beginning of this section but this time considering correlation and, due to the
NIG, even skewness and kurtosis of the data.
While this process might seem rather tedious to do, it can be easily implemented in
MATLAB together with the NIG-package by Werner (2006).
Results
We use the described method to simulate 10’000 correlated log returns and obtain the
following descriptive statistics:
Table 6: Simulated vs. Original Data Copula Model
Housing
Rents
Office
Rents
Comm.
Rents
Housing
Vacanc.
Office
Vacanc.
Comm.
Vacanc.
Condo.
Prices
Cap
Rates
Mean
Simulation
0.02 0.02 0.01 0.02 0.04 0.04 0.02 0.00
Mean
Data
0.02 0.02 0.01 0.02 0.04 0.04 0.02 0.00
Std .Dev.
Simulation
0.04 0.08 0.09 0.38 0.30 0.30 0.04 0.07
Std. Dev.
Data
0.04 0.08 0.09 0.38 0.30 0.30 0.04 0.07
Skewness
Simulation
0.80 0.48 0.45 0.43 -0.24 -0.24 0.08 0.87
Skewness
Data
0.86 0.55 0.50 0.47 -0.29 -0.29 0.09 0.92
Kurtosis
Simulation
1.13 0.28 0.32 0.28 0.22 0.22 0.59 2.17
Kurtosis
Data
0.66 -0.01 -0.33 -0.62 0.33 0.33 0.51 2.65
We can already see by eye that mean and standard deviation of the simulated variables are
very much the same for the simulated variables and the original data. For skewness there are
deviation in the region of 0.05 from the original data, which is not very much. Kurtosis on the
other hand seems to be not captured that well by the NIG distribution. There are deviations
from the original data ranging from 0.08 up to 0.9. Apparently the NIG distribution thus did
not work so with the kurtosis of the distribution. Looking at the correlation matrix we see the
following results:
5 Simulation Based Real Options Model 47
Table 7: Correlation Matrix Simulated Log-Returns
Housing
Rents
Office
Rents
Comm.
Rents
Housing
Vacanc.
Office
Vacanc.
Comm.
Vacanc.
Condo.
Prices
Cap
Rates
Housing
Rents
1.00
Office
Rents
0.53 1.00
Comm.
Rents
0.56 0.90 1.00
Housing
Vacancies
-0.21 -0.62 -0.62 1.00
Office
Vacancies
0.33 -0.06 -0.08 0.27 1.00
Comm.
Vacancies
0.33 -0.06 -0.08 0.27 1.00 1.00
Condo.
Prices
0.50 0.43 0.43 -0.26 0.28 0.28 1.00
Cap
Rates
-0.51 -0.23 -0.17 -0.12 -0.10 -0.10 -0.03 1.00
If we compare this correlation matrix to the one in Table 3 on page 40, we see by eye that
they are very similar. Differences range in the region of 0.00 to 0.03, which is very little.
Thus we can assume that our copula model really captures important relations among the
time series and is able to simulate new variables that inherit these dependencies. From the
descriptive statistics we can further assume that except for the tails these simulated variables
also follow a similar distribution as our original data. This is an excellent result so let us use
this model for the simulation of future outcomes of our risk drivers, right?
Not so fast. So far we have only looked at dependence between the different time series at the
same time t, but what about dependence of observations within one time series itself? What
happens if observation rt+1 is dependent on rt? The introduced copula model is only valid if the
observations are independent from each other across time, if there is no dependence between
rt and rt+h for all lags h. We then say that there is no serial correlation and that the
observations within the time series are independent. We check for this by looking at the
autocorrelation and the partial autocorrelation
5
by calculating the correlation coefficient across
time with specific lags. The autocorrelation result for the log returns of housing rents is
depicted in Figure 14:
5
Partial autocorrelation measures remaining dependency after autocorrelation has been accounted for.
5 Simulation Based Real Options Model 48
Figure 14: Autocorrelation Log-Returns Housing Rents
Source: Own illustration
We see significant autocorrelation of 0.8 for a lag of 1 year and of 0.4 for a lag of two years in
the housing rent data. We also have significant autocorrelation for the log returns of the other
time series as depicted in Figure 43 in Appendix I. This speaks against our copula model
because there, we do not take autocorrelation into account. Luckily there is another tool
available that considers autocorrelation and dependence among time series. This is the class of
vector autoregressive models that we introduce next.
Vector Autoregressive Model (VAR)
Definition
Like the copula, a VAR model is a mathematical tool to capture linear interdependencies
among multiple time series. A VAR model explains its evolution based on its own lags and
the lags of the other variables in the model. This makes it a powerful and flexible tool for
modelling multiple time series since the evolution of one time series is also dependent on the
other ones. We further have the advantage to make the model dependent on exogenous
variables. We can then use this exogenous variable in our forecast, adding a deterministic part
to the model. This is of interest to make the model more stable and to analyse different
scenarios. A VAR models takes the form of:
!
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! !
!
!
!!!
! ! ! !
!
!
!!!
! !
!
! ! ! !! !!! !!! ! ")$%(&
where yt = (y1t,….,yKt)’ is a ( K × 1 ) random vector, Ai is fixed ( K × K ) coefficient matrix, cEx
= (c1 ,…, ck)’ is a ( K × 1 ) fixed vector of coefficents allowing for the possibility of a
exogenous term with observations yEx,t. et = (e1t, …, eKt)’ is a ( K × 1 ) vector containing error
5 Simulation Based Real Options Model 49
terms with zero mean E(01) = 0, covariance matrix E(21 213) = 42 and no serial correlation E(et
e’t-k) = 0. p is the lag order of the model.
Written in matrix notation a VAR with lag p = 1, VAR(1), and two variables takes the form
of:
!
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Application
When applying this model to our data then e.g. the condominium log return for a VAR(1) is
determined by:
")$%)&
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! !
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! !
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with:
H_R : Housing Rents
rCondo,t: log return condominium at time t
aCondo,Condo,t-1 , aCondo,H_R, t-1 : lag coefficients for lag t-1
rCondo,t-1 , rH_R,t-1 : previous log returns at time t-1
aCondo,GDP : coefficient for GDP at time t
rGDP,t : log return GDP at time t
eCondo,t : correlated error term for condominiums at time t
We estimate the coefficients of the model by using ordinary least square method on our data
set of past time series. We chose a lag-2 model over a lag-1 model based on Akaike’s
Information Criterion (AIC), which is a standard tool in statistics for the selection of models.
Further we use real GDP as an exogenous variable for our model. We do this with the
intention of “gluing” the model to a deterministic variable once we use it for forecasting.
Depending on the stability of the model, estimated variables otherwise go quickly out of
bounds of what one would expect to be reasonable. We use the GDP as an exogenous
variable, since it is an indication of the economic activity and we expect this to have an
influence on our risk drivers. The drawback of using the GDP as exogenous variable is that
we have only data from 1990 until 2011. This means that we must use this time span for the
other variables as well. We thus loose 5 years of data in our already small data set, resulting in
21 observations of log returns. Further we cannot use the VAR model for simulations when
two endogenous variables are very similar. The covariance matrix of the error terms then
becomes singular, which is a property that makes it unsuitable for Cholesky decomposition.
Cholesky decomposition is however something we need for simulation. As we discussed
5 Simulation Based Real Options Model 50
earlier, office and commercial rents are very similar or identical in the data set and thus we
have to work with either the time series for office or the one for commercial use. We choose
the time series for office rents and vacancies and will thus assume that commercial rents and
vacancy behave the same as their office use counterparts. Considering that the correlation
coefficient is 0.9 between office and commercial rents and that vacancies are identical in the
data set, we can assume that this simplification does not alter results too much.
Once we have estimated the model, we test the significance of the estimated coefficients by
looking at their p-values. We test the null hypothesis that coefficients are zero using t-
statistics and consider coefficients with a p-value above 0.1 to be non significant. The statistic
programming environment of R together with the “VARS” package by (Pfaff 2008) is used to
estimate the model.
Results
The estimated coefficient matrix is shown below in Table 8. Further results on the estimation
of coefficients are found in Appendix II:
Table 8: Lag Coefficient Matrix A
Condo.
Price
(Condo)
Housing
Rents
(H_R)
Office/Com.
Rents
(O_R)
Housing
Vacancy
(H_V)
Office/Com.
Vacancy
(O_V)
Cap Rate
(CAP)
Condo.l1 - - - - - -
Condo.l2 0.41 - - -5.07 - 0.43
H_R.l1 1.47 0.92 - 13.75 - -1.83
H_R.l2 -0.50 -0.26 - - 3.80 1.52
O_R.l1 - - -0.44 - - -
O_R.l2 0.49 - - - 5.80 -
H_V.l1 - -0.03 -0.09 - 0.36 -
H_V.l2 - - -0.08 0.36 - -
O_V.l1 - - - 0.56 - -0.04
O_V.l2 - - - 0.70 - -0.06
CAP.l1 0.74 - -0.72 - 5.45 0.50
CAP.l2 - - 0.58 5.01 - -
GDP 0.74 0.35 0.95 - - -0.38
The columns depict the estimated coefficients for one risk driver. So we see that e.g. housing
rents depend on the lagged log returns of themselves (H_R.l1 and H_R.l2) on lagged housing
vacancy (H_V.l1) and on GDP. GDP has a significant positive influence on rents and
condominium prices and a negative influence on cap rates. That means that when the GDP
log return is positive, this has a positive influence on rent log returns and a negative one on
cap rates. We do however not see an influence of current GDP on vacancy. We did however
not test for the influence of lagged GDP on current vacancy, since we could not implement
5 Simulation Based Real Options Model 51
this into the model with the used statistical package. However, this surely would be an
interesting aspect to look at in further research.
By looking at Table 8 we also see some lagged variables that have an extremely large influence
on current returns. This is foremost the case for the estimation of vacancies e.g. for lag 1
housing rent (H_R.l1) on housing vacancy (H_V) the estimated coefficient is 13.8. Such
large variables do not speak for the adequacy of the model to use it for forecasting since
already small errors in the estimation of e.g. housing rents have a very strong influence on
housing vacancy one time step ahead. Also we have some dependencies we would not expect
to be so strong such as the negative influence of lag 2 condominium returns (Condo.l2)
(aH_V,Condo.l2=-5.07) on current housing vacancies. One can hardly think of a rational
explanation of why the return in condominium prices should influence housing vacancies that
much two years later. We could correct for this by setting the corresponding coefficient to
zero but then again this might not be adequate, since statistically there is an influence. Also
setting a significant coefficient to zero leads to a chain reaction in the whole model since it is
set up in way that everything is interdependent. As we will see when applying the model for
forecasting, it is one thing to estimate a model that fits the data well and quite something else
to create a model that is “realistic” in the sense of generating credible results.
We illustrate this in the next section, where we use the estimated model for the simulation of
future scenarios.
5.2.5 Simulation of Future Scenarios
After fitting a model to our data we now use it for the simulation of scenarios. We can easily
generate thousands of scenarios and analyse how the real estate development project performs
under these. Assuming that the estimated dependency structure depicted in the model holds
also in the future, we should be able to generate credible results. However, this assumption
might not hold, since dependence among variables does not necessarily remain constant.
Future events might alter the dependency among the variables, leaving our model invalid.
This leads to the fact that our simulations will always include quite some inaccuracy and be a
good deal away from accurate forecasts or even predictions. It is our intention, however, to
estimate the range of possible outcomes and then to identify and quantify valuable options
under these outcomes. It is thus not necessary to have a perfect, crystal ball like model for
forecasting, which is impossible anyway. The model should help to be prepared for the
uncertainty lying ahead and make the flexibility we have in dealing with it more tangible.
Simulations with a VAR Model in Excel
5 Simulation Based Real Options Model 52
We use Excel to generate simulations of scenarios and to analyse them. This is convenient for
the practitioner, since he can thus implement the simulation mechanism directly as an add-on
to existing project calculations. The first step however, is to do simulations of the risk drivers
and analyse, if these results are credible and thus, if they should be used in conjunction with
the development project calculations.
The input of the VAR model is according to (5.13) a vector of correlated error terms. In our
case we have six error terms at time t, one for every variable: et = (et,Condo, et,H_R,..., et,CAP). For
simulations we assume these error terms to follow a normal distribution with zero mean,
variance and correlation among these error terms being the same as the error terms from the
estimated model. We call this a noise process and generate it in Excel using the implemented
NORMSINV() and RAND() function. The NORMSINV() is the inverse of the standard
normal Gaussian cumulative distribution function where we can add variance later on. We
generate new independent error terms following a standard normal distribution by using X =
F
-1
(U), with F
-1
() as the inverse cumulative distribution function and U[0,1] generated by
RAND(). We generate multiple error terms by using “Data Tables” in Excel that allow for
the storage of simulation results. Correlation among the error terms and variance is taken into
account by using the Cholesky decomposition on the covariance matrix of error terms from
the model estimation and multiplying the decomposed lower triangular matrix with the
uncorrelated error terms. As the copula, this is a method to account for correlation among
multiple time series. The result is the desired vector of correlated error terms, in our case et =
(et,Condo, et,H_R,..., et,CAP), that is used together with the lag coefficient matrix A in Table 8 and
the last two log returns of the data set (rt-1, rt-2) to generate simulations. For every time step
ahead we get a set of randomly generated log returns following the properties of our model.
Now to see the evolution of the future scenarios, we apply the simulated log returns to the last
observations of our data set using (5.3): !
!
! !
!!!
! !
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, for t = 1, 2, … n with n as the desired
simulation horizon.
We simulate 2000 times a simulation horizon of 10 years, assuming a deterministic constant
growth in GDP of 2%. Simulations yielded the following results:
5 Simulation Based Real Options Model 53
Figure 15: Simulation of Condominiums with a VAR(2) Model
Source: Own illustration
We see a strong upward slope in condominium prices estimated by the model with an average
price 45% higher after five years and almost doubled after ten years. The 90% confidence
interval depicted by the 95
th
percentile (upper red curve) and 5
th
percentile (lower red curve)
indicate a high upward potential while the possibility to fall below the start price is very low.
Figure 16: Simulation of Housing Rents with a VAR(2) Model
Source: Own illustration
Housing rents remain in a smaller confidence interval than the condominium prices and
increase on average 14% compared to the start value. The 90% confidence interval has an
upper bound of +36% and a lower bound of -7% after 10 years.
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Real estate development inherits uncertainty & flexibility to a large degree. Traditional financial valuation techniques fail to account for this and thus we employ a real options model to study uncertainty & flexibility in real estate development.
Modelling Uncertainty & Flexibility in the Financial
Analysis of a Real Estate Development Project in
Switzerland
Master Thesis for the Degree of Master of Science
in Management, Technology and Economics (MTEC)
at the Swiss Federal Institute of Technology Zurich
by
Johannes Peter
BSc Civil Engineering ETH Zurich
Supervisor at ETH Zurich
Prof. Dr. Didier Sornette & Dr. Peter Cauwels (ETHZ, Chair of Entrepreneurial Risks)
Department of Management, Technology and Economics (MTEC)
Submitted to ETH Zurich
December 2012
Contact: [email protected]
Abstract i
Abstract
Real estate development inherits uncertainty & flexibility to a large degree. Traditional
financial valuation techniques fail to account for this and thus we employ a real options model
to study uncertainty & flexibility in real estate development.
Real option analysis has not found wide application in the real estate development practice yet
and we argue that this is due to a lack of pragmatism and comprehensibility of the com-
monly used models.
We therefore employ the so called “Engineering Approach” introduced by de Neufville and
Scholtes (2011) that is based on Monte-Carlo simulations to better analyse and communicate
uncertainty & flexibility in real estate development projects.
We develop a Monte-Carlo simulation model based on past data of identified risk drivers that
determine the value of a real estate development project. We employ copula and vector
autoregressive modelling techniques to account for interdependencies among these risk
drivers and apply the resulting simulation model to a large-scale development project in the
region of Zurich. Our analysis reveals the risk structure of this real estate development project
and shows how downside risk can be reduced by the use of flexibility.
Keywords: Real Options Analysis; Real Estate Development; Monte-Carlo Simulation;
Vector Autoregression; Copula ; Engineering Approach; Flexibility; Valuation
Acknowledgments ii
Acknowledgements
I would like to thank Dr. Peter Cauwels from the Chair of Entrepreneurial Risk at the ETH
Zurich, who kindly supported me in writing this thesis. By giving me advice and support
whenever I needed it, he helped me a great deal to make the work on this thesis a true
learning experience.
Also I would like to thank Othmar Ulrich and his team at Steiner AG, who provided me with
valuable insights into the real estate development practice and helped me to focus on the
practical part of this thesis. Werner Ramseyer from Sproll & Ramseyer AG provided me with
valuable insights into the Swiss valuation practice, Marc Petitjean from Helbling Beratung und
Bauplanung AG on the real estate development practice and Alain Chaney from IAZI AG on
the modelling of real estate data. I thank them for their kind support and their time. Stephan
Fahrländer from Fahrländer & Partner AG provided me with a rich data set on real estate
market data. Without his support I would not have been able to create the data based
financial model, we present here.
Furthermore I would like to thank Prof. Dr. David Geltner from the MIT, who generously
provided me with material on previous work done on the financial analysis of real estate
development projects. Finally I would like to thank Prof. Dr. Didier Sornette from the Chair
of Entrepreneurial Risk at the ETH Zurich who made the work on this truly exciting topic
possible.
Johannes Peter
Content iii
Content
Abstract ..................................................................................................................................... i
Acknowledgements .................................................................................................................. ii
Content ................................................................................................................................... iii
1 Introduction ....................................................................................................................... 1
2 Literature Review ............................................................................................................... 3
3 Real Estate Development Process ...................................................................................... 6
3.1 Insights from Professionals ....................................................................................................... 6
3.2 Definition .................................................................................................................................. 6
3.3 Steps in the Development Process ............................................................................................ 6
3.4 Risks in the Development Process ............................................................................................ 9
3.5 The Role of Flexibility & Uncertainty .................................................................................... 11
4 Valuation of Real Estate Development Projects .............................................................. 13
4.1 Common Practice ................................................................................................................... 13
4.1.1 Capitalised Earnings Method .......................................................................................... 13
4.1.2 Net Present Value Method .............................................................................................. 16
4.1.3 Shortcomings ................................................................................................................... 17
4.2 Real Option Analysis .............................................................................................................. 18
4.2.1 Binomial Approach ......................................................................................................... 19
4.2.2 Closed Form Solutions .................................................................................................... 20
4.2.3 Monte-Carlo Simulations ............................................................................................... 21
4.2.4 Critique and Choice of Method ...................................................................................... 21
5 Simulation Based Real Options Model ............................................................................ 24
5.1 Project Modelling Framework: The “Engineering Approach” ................................................ 24
5.1.1 Step 1: Create the Most Likely Initial Cash Flow Model ............................................... 25
5.1.2 Step 2: Incorporate Uncertainty into the Model ............................................................. 25
5.1.3 Step 3: Incorporate Flexibility into the Model ................................................................ 27
5.1.4 Step 4: Maximize Value by Applying Optimal Decision Rules ....................................... 27
5.2 Simulation Framework ............................................................................................................ 28
5.2.1 Overview ......................................................................................................................... 28
5.2.2 Risk Drivers ..................................................................................................................... 31
5.2.3 Data ................................................................................................................................. 33
5.2.4 Modelling ........................................................................................................................ 41
Content iv
5.2.5 Simulation of Future Scenarios ....................................................................................... 51
5.2.6 Simulation of Absolute Values ........................................................................................ 63
6 Application of the “Engineering Approach” to a Real Project - A Case Study in the
Canton of Zurich ............................................................................................................. 64
6.1 Case Background .................................................................................................................... 64
6.2 Step 1: Create the Most likely initial Cash Flow Model ......................................................... 67
6.3 Step 2: Incorporate Uncertainty into the Model ..................................................................... 70
6.4 Step 3: Incorporate Flexibility into the Model ........................................................................ 77
6.5 Step 4: Maximize Value by Applying Optimal Decision Rules .............................................. 80
7 Conclusion ....................................................................................................................... 82
8 References ........................................................................................................................ 84
Appendix ................................................................................................................................ 87
1 Introduction 1
1 Introduction
Real estate development is an important activity: It is the production factory of our cities that
transforms unproductive land to urban space for people to live, work and enjoy. It shapes the
character of the places we spend so much time in and if well done, can substantially improve
the quality of life. Real estate development is also an entrepreneurial activity: it involves the
decision to take the future of an area in one’s hands, to shape it to the needs of upcoming
generations and the aspiration to make it a truly successful product on the real estate market.
As such it is also a risky activity: Development binds large amounts of financial capital into a
fixed asset while it is not granted that the proceedings will be higher than the investment.
The financial success depends both on uncertain cost and uncertain revenues and in order to
be successful, one must assess these uncertainties to a high degree. Proper investment analysis
is crucial to deal with these uncertainties, to reduce and anticipate them whenever possible.
For more than ten years now real estate prices have been rising continuously and one might
be inclined to think that this trend will continue for another ten years. But among the many
things we can learn from history, one lesson is that the future is uncertain: just a few years ago
the global financial system was close to a meltdown and few would have predicted then the
strong growth in real estate prices that we observed in the past few years. Quo Vadis?
Real estate developers need to cope with uncertainty, think about it and find strategies to deal
with it. One way of doing so has always been flexibility. If demand for office space is low a
developer can wait and build when markets have recovered, or he can change the project to
another use. When looking into practice however, the employed financial analysis tools
neither properly account for flexibility, nor uncertainty when dealing with real estate
development projects.
One way of financial analysis that deals with flexibility & uncertainty is real options analysis.
This approach is closely linked to the valuation of financial options and is thus based on
assumptions that are not necessarily applicable in the world of real estate development.
Also we argue that due to a lack of accessibility and applicability, real options analysis has not
yet gained much attention in the Swiss real estate development practice. We thus introduce a
more intuitive, simulation based real options model grounded on the works of de Neufville,
Scholtes and Geltner. This so called “Engineering Approach” works with “classic” net present
value calculations and combines them with simulations of future market scenarios. Based on
these scenarios, decision rules are implemented and optimised to find the optimal behaviour
for the simulated future.
1 Introduction 2
Thereby we make flexibility & uncertainty more accessible in the analysis of real estate
development projects.
The thesis is structured in the following way: After a short review of the literature on real
options in Chapter 2, we give an overview of the real estate development process and the role
of risk, uncertainty & flexibility within this process in Chapter 3. In Chapter 4 we discuss the
current valuation practice in Switzerland and introduce real options analysis. In Chapter 5 we
present a simulation-based model and then show the applicability and the results of this
method on a case study in Chapter 6. Chapter 7 concludes this thesis and discusses possible
improvements of the model and directions for further research.
2 Literature Review 3
2 Literature Review
In this chapter we present the evolvement of real option theory applied to real estate development in
the recent past. This helps to understand the balancing act between academic theory and applicability
when working with real options in practice. Many terms that are mentioned in this chapter are dealt
with in more detail in subsequent chapters.
Real options are a popular topic in the recent literature: A search on the Web of Science
1
yields more than 100 publications related to real options every year over the last decade. The
origin of this popularity is closely linked to advances related to the pricing of financial
options. Black and Scholes (1973) opened up the field with their revolutionary equilibrium-
pricing model for financial options. Six years later Cox, Ross and Rubinstein (1979) already
mention the possibility to apply the approach on other problems than financial options in
their famous work on financial option pricing. In this article they introduce the binomial
approach that is still the basis for many real option valuations nowadays. Since then, real
options have been the subject of diverse studies and been applied to various fields of economic
research such as capital budgeting problems, valuations, micro-economic-decision-making
and more. Whenever dealing with uncertainty and/or flexibility thereby one is prone to come
over real options sooner or later. This has also led to some unintended fame of real options
when they were widely used as justification for the sky-high valuations of internet stocks
before the burst of the dotcom bubble in 2000 (Mauboussin 1999).
In the field of real estate research it took until 1985 for real options to find their applications.
Titman (1985) was the first to introduce a real option approach that is closely linked to the
binomial model of Cox, Ross and Rubinstein (1979) to value vacant land. With his model he
was able to explain the behaviour of many land owners who wait with construction in order to
profit from higher expected prices. He showed mathematically that higher uncertainty in the
future value of built property leads to a higher option value and thereby to a delay in the
exercise of the option. Eight years later Quigg (1993) gave evidence of these findings with the
first empirical study on the real option value of vacant land in Seattle. Her findings indicate
an average premium of 6% that is paid for the option to wait. Real options theory applied to
real estate and other fields of practice remained however a niche and only slowly gained more
attention with further publications. The theory was notably made more public by works of
Trigeorgis (1993) and later by Copeland (2001).
1
Web of Science is a large multi disciplinary knowledge database:http://isiknowledge.com/wos
2
Other developers in Switzerland such as Allreal, Mobimo and Priora have their own investment portfolio and develop mainly
2 Literature Review 4
Their work was thereby directed towards bridging the gap between academia and practice.
After publishing on the use of financial option models for the valuation of vacant land in
1989 (Geltner 1989), Geltner and Miller further introduced the Samuelson McKean Formula
as the “Black-Scholes formula of real estate” in their standard textbook on real estate finance
in 2001 (Geltner and Miller 2001).
Thereafter many publications were made on the topic of real options in real estate
development at the MIT Center for Real Estate under the supervision of Geltner: Among
them there is Hengels (2005) who introduced a model to evaluate large-scale real estate
development projects using binomial trees. The goal of his work was to make real options
theory using binomial trees accessible by practitioners. But one of the main drawbacks of this
approach became highly visible in his work: While the computational effort to analyse a
project becomes high very fast, the ability to conduct meaningful conclusions from the
analysis becomes more and more difficult. This is due to the fact that results are not easily
retraced in the model. We discuss this issue in Chapter 4.2 on the choice of our method.
Barman and Nash (2007) tried to overcome this shortcoming by using a combination of the
Samuelson McKean formula and Monte-Carlo simulations and Masunaga (2007) made a
comparative study of Monte-Carlo simulations and binomial trees to value real estate
development projects. As he concluded, there is a significant difference between the results
obtained by Monte-Carlo simulation and binomial tree evaluation. As Hodder, Mello et al.
(2001) pointed out before, this issue can be addressed by using risk adjusted discount rates
depending on the time to expiration of the option and the actual value of the underlying asset,
but the problem of accessibility would still not be addressed.
During that time de Neufville (2006) was working on real options using Monte-Carlo
simulations while focusing on the value of flexibility. This method was further developed into
the “Engineering Approach” and published in 2011 (de Neufville and Scholtes 2011). The
advantage of this approach is the specific development for practitioners and we thus make
extensive use of it within this study. Geltner and de Neufville (2012) further propose to use
both the “Engineering Approach” and the binomial real options model to make financial
analysis of real estate development projects. In this thesis we focus on the business
applicability of real options and the application of the “Engineering Approach” to a real
project in Switzerland, we therefore do not employ both methods.
Most of the proposed real option methods in the context of real estate development deal with
the “Anglo-Saxon” real estate development process (see e.g. Guthrie (2009)). However, there
is hardly anything on the Swiss real estate development practice (except for Maurer (2006)).
But why is this important? As we will see the Swiss real estate development practice is
2 Literature Review 5
different from the “Anglo-Saxon” way. This has an influence on the specification of the real
options model. A second reason is that real options analysis depends on the market where it is
applied. It is important to adapt the model to the specifics of this market especially when
dealing with Monte-Carlo simulations. Thirdly it is important to apply a theoretical approach
to real life situations, involve practitioners and analyse with them the benefits and merits of
the solutions “scientists” came up with. We handle these issues subsequently in the following
chapters.
3 Real Estate Development Process 6
3 Real Estate Development Process
This section gives a short overview of the typical processes involved in real estate development, while
highlighting some specialities of the Swiss developer environment. By understanding the process of
real estate development the reader should become aware of the importance of uncertainty & flexibility
within the field of real estate development. We first look at the steps that have to be taken for a
successful development and at the risks involved in this process. Finally we highlight the role of
flexibility & uncertainty in this context.
3.1 Insights from Professionals
In the course of this study various professionals in the field of real estate were met to discuss
the valuation of uncertainty & flexibility in the context of real estate development. We gained
insights into the professional real estate valuation domain thanks to Werner Ramseyer from
Sproll & Ramseyer AG. He explained to us in detail the current valuation practice for real
estate in Switzerland and kindly provided case studies. Marc Petitjean from Helbling Beratung
und Bauplanung AG gave us insights into the real estate development practice and Stephan
Fahrländer from Fahrländer & Partner AG provided us with a rich data set for the
development of the real estate market in Switzerland. Furthermore Alain Chaney from IAZI
AG gave very valuable input for modelling the real estate market. Finally Othmar Ulrich and
his team at Steiner AG were a very rich source of knowledge when discussing the applicability
of financial models, the valuation practice of real estate development projects and the
importance of uncertainty & flexibility in the real estate development process. Whenever
possible we try to incorporate insights from these professionals into this thesis.
3.2 Definition
Geltner and Miller (2007) define real estate development as the process where financial
capital becomes fixed as physical capital, or more broadly the process of transforming an idea
to reality. It includes all the steps from conceptualisation to realisation and sometimes sale of
a real estate project.
3.3 Steps in the Development Process
The steps to be taken in real estate development are similar internationally and among
projects. The specialities of the Swiss vs. the “Anglo-Saxon” development environment arise
from the different parties that are involved in these steps and thus the different risks that they
3 Real Estate Development Process 7
bear. We first go through the steps and then discuss the specialities of the Swiss development
environment.
1. Project Initiation
Schulte (2002) defines three initial states that lead to the initiation of a real estate
development project:
/ Site looking for use: When the piece of land to be developed is already given, it
is the task of the developer to come up with a project idea and a concept. The
developer defines a suitable use for the site that generates the highest possible
value. Value in this context does not mean economic value only, but also social
and ecological value. Only by taking all three aspects into account, developers
will generate sustainable solutions that guarantee long term success. For this he
needs to have a “feeling” for the real estate market and know what kind of uses
will be in demand at the given location not now but in the future. Therefore he
needs to be visionary and anticipate what works and what does not at a given
location.
/ Use looking for site: When the project idea is already given, the task is to find a
suitable location. The developer will need to have information sources that help
him find promising sites. A well-established network of people involved in the
land transaction market is crucial but also databases and newspapers are of use.
Since land acquisition cost is one of the main capital expenditures of a project
development, a detailed financial feasibility analysis of the identified selection is
of high importance. The phase is concluded with the successful purchase of a
plot or the obtainment of a right to build on it in the future.
/ Capital looking for site and use: The third initial state involves the processes of
finding a site and a use. The needed capabilities are largely the same as with the
two other initial states and not repeated here.
2. Project Conception
The second phase starts with an in-depth feasibility study regarding location, market,
usage, competition, risk and profitability. Based on these studies a detailed project
concept is prepared that serves as a basis for the communication with stakeholders.
Involved parties such as neighbours, politicians, investors and tenants are contacted and
the project is further specified in consideration of them. When the project is feasible and
well defined, architects and planners are hired for drawing designs of the future buildings
and planning the environment.
3 Real Estate Development Process 8
The final goal of this phase is the receipt of the building permit that authorises the start
of construction. Once construction has started, the project becomes very capital intense
and major changes of plans are very difficult and expensive to achieve. To reduce the risk
of vacancies it is therefore essential that future tenants are identified, involved and
committed to the project already before construction starts. Developers will thus look for
prospective tenants already during the project conception phase and not proceed until the
risk of vacancies is reduced substantially.
3. Project Realisation
A contractor, who manages the construction process and construction works, executes
construction until completion, often for a prearranged price. Thereby the contractor
takes over construction cost risk from the developer. The role of the developer in this
phase is that of controlling and managing the work executed by the contractor. Also he
will focus on finding additional tenants and buyers for the project.
4. Lease-Up & Tenant Finishes
During the lease-up period the project enters the market, additional tenants or buyers
commit themselves to the project and often a customized finish for the tenants is made.
Depending on how many tenants committed themselves to the project already in the
preceding phases, the risk of not leasing up the whole project can be substantial. Large
vacancies and or lower than expected rent contracts can have a severe impact on the
profitability of the project. Depending on the project and the market environment it can
take several months up to years until a project is fully leased out.
5. Stabilised Operation
Once the project is fully leased out, it enters the phase of stabilised operation where it
produces a hopefully stable and increasing cash flow for the lifetime of the object.
Subsequent investments for maintenance and sometimes redevelopments are necessary in
order to sustain the long term profitability of the object on the market.
Specialties of the Swiss Developer Environment
As pointed out before, specialities of the Swiss vs. the “Anglo-Saxon” real estate environment
arise not from the steps in the development but from the players that are involved in these
steps. Geltner et al. (2007), taking the viewpoint of the “Anglo-Saxon” development
environment, describe Step 1 and 2 of the project as the preliminary phase of a project. This
phase is often conducted by an “entrepreneurial” developer, who may or may not continue
with the project until completion. The construction and lease-up phase together represent the
“development” project where large amounts of capital are committed to the project.
3 Real Estate Development Process 9
In the “Anglo-Saxon” environment there are large developers, sometimes in the form of real
estate investment trusts, specialised only on this part of real estate development. Due to their
access to funding they can commit the large financial funds needed for construction and
either sell the project once it is stabilised, or keep it in their own portfolio. These developers
would however not invest in a project without a construction permit in place. The discussed
literature on real estate development focuses on Step 3 to Step 5 of the development, taking
the viewpoint of these developers.
In Switzerland however, the business environment is market by “entrepreneurial” developers,
such as Halter, Implenia, Steiner, Losinger and HRS
2
who pursue the project from Step 1 to
Step 4. For them the investment starts already before a construction permit is achieved often
with the purchase or optioning
3
of land. These developers will often sell the project to an
institutional investor with the receipt of the construction permit at the end of Step 2, the
“Project Conception” phase. Depending on the contract, the developer is responsible for
leasing up the project and delivering it for a specified price. After completion and the lease-up
period investors operating in Switzerland keep the project as a stabilised asset in their
portfolio. We therefore have institutional investors on the buy side that commit themselves
very early to the project and “entrepreneurial” developers that take the project through all
steps, but sell the project early on. Due to the sale of the project with the receipt of the
construction permit, the Swiss developer transfers some of the risk to the investor, which has
to be taken into account in the financial analysis of the project. Additionally developers in
Switzerland are often construction contractors, managing the construction work themselves,
thereby taking over construction cost risk. In this thesis we focus on the entrepreneurial
developer and investment analysis from his viewpoint.
3.4 Risks in the Development Process
Except for the case where the investor or final user is already committed to the project from
the beginning, real estate development is among the riskiest entrepreneurial activities (Schulte
2002). This comes from the fact that capital investments for product creation are high,
products are fixed to their location, served market segments are often small and demand is
highly uncertain. The correct assessment and management of risk is therefore indispensable
and belongs to the main capabilities of successful developers. Schulte (2002) defines the main
risks of real estate development as:
2
Other developers in Switzerland such as Allreal, Mobimo and Priora have their own investment portfolio and develop mainly
for themselves. While the model in this thesis can be applied to their investment perspective as well, we do not explicitly focus on
them.
3
Optioning in this context refers to the widespread practice of developers to pay a prearanged price for the land to the owner on
the condition that the construction permit is obtained.
3 Real Estate Development Process 10
/ Development Risk: The risk of not planning an adequate use for a specific location and
the risk of planning financially non-feasible projects
/ Time Risk: Due to the financial leverage of most projects time risk is among the most
important risk factors. Delays can harm the profit of developers substantially.
/ Approval Risk: All development projects need to be approved by the authorities.
Neighbours can raise objections that can result in financially harmful project changes.
/ Financing Risk: Development projects are financially daring undertakings that require
partners with corresponding financial power. Funding might not be achieved or might be
stopped due to delays or other problems resulting in the failure of a project and severe
financial consequences for the developer.
/ Building Ground Risk: The building ground bears high potential for additional cost and
delays. This is due to the fact that building grounds bear uncertainty regarding
supportable load and contamination that cannot be eliminated completely with
preliminary studies.
/ Cost Risk: Cost risks arise mainly from the long time horizon of development projects
and the uncertainty regarding the exact specification of the future product. Thus it is
often very difficult to predict exactly the production cost of a large-scale development
project and additional costs may arise from the other mentioned risk factors.
/ Market Risk: The final test of every project is when it comes to market. Are the
potential tenants willing to pay the calculated rents resp. is demand high enough to meet
the additional supply at the specified price? How much are investors willing to pay for
real estate assets? Real estate value is driven by the space market that couples demand
and supply for space and by capital markets (Geltner and Miller 2007). These two
markets are already difficult to assess in the present and their behaviour is much more
difficult to predict for multiple years ahead. Inevitably this leads to large uncertainty
when dealing with the market risk of real estate developments. Besides that real estate
markets behave in long lasting cycles that are characterised by periods of strong growth
in prices and high construction activity followed by phases of stagnation and price
decline (Dokko, Edelstein et al. 2001). Developers need to anticipate markets correctly
and make the right preparations and decisions based on their estimations.
In the context of market risk, a short excurse on the Swiss real estate crisis of the 1990s gives
us valuable insights into the harmful effects of such an event.
3 Real Estate Development Process 11
The Swiss Real Estate Crisis in the early 1990s
After the stock market crash in 1987, the Swiss National Bank (SNB) increased liquidity and
decreased interest rates to counter negative effects of the crash and prevent a slackening
economy. The economy however recovered faster than expected and the increased supply of
liquidity together with an overheating economy lead to inflation rates of 5% by the end of
1989 (Jetzer 2007). At the same time investors shifted their interest due to the uncertainty in
stock markets from stocks towards real estate that was assumed to be a more reliable and save
asset class. This lead to a further increase in prices for real estate that were already at a high
level in the mid 1980s. Due to the high inflation rates by the end of the 1989 the SNB
increased short term interest rates drastically from 3.8% in July 1988 up to 9.5% in January
1990 (Jetzer 2007). Additionally the Swiss government passed a bill in October 1989 on land
laws that hindered the speculative trade of land and increased capital requirements to
purchase land (Meier 2009). The strong increase in interest rate brought the strong growth in
real estate prices to an end, which was followed by a decrease in prices of 20% (Jetzer 2007).
Especially regional banks that were highly active in the real estate mortgage market incurred
large losses on their assets. In October 1991 the “Spar- und Leihkasse Thun” had to close
down due to high write offs on mortgage loans, leading to the first bank run in Switzerland
since the 1930s (Holderegger 2006). Between 1991 and 1996 more than half of the original
180 regional banks disappeared (Jetzer 2007). As Meier (2009) points out, among the causes
for the real estate crisis were low interest rates, high liquidity in the finance system and also a
lax mortgage granting policy of many banks during that time. This is an interesting aspect in
the light of the current market environment were interest rates are lower than in the late
1980s (currently 1.5% for a 5 year fixed mortgage) and banks recently pledged to increase
their lending standards based on self regulation (Chapman 2012). We see the effects of the
early 1990s crisis on the real estate market in the data later on.
3.5 The Role of Flexibility & Uncertainty
As we have seen there are multiple risks/uncertainties involved in real estate development.
The developer has several tools to deal with this and among the most important are the right
analysis and the corresponding action towards these risks. A developer can e.g. decrease the
approval risk by integrating authorities early on and he can reduce building ground risk
through detailed analysis by specialists.
Another tool in dealing with risks is the use of flexibility: A developer can e.g. adapt the
project to a changing market environment, postpone development until markets are more
favourable, split the project up in multiple subprojects and realise them in succession, etc.
3 Real Estate Development Process 12
It is this skilful management of flexibility that often makes the difference between successful
development and financial failure. But flexibility & uncertainty do not remain constant over
the duration of a project.
Figure 1: Flexibility, Uncertainty and Cumulative Investment in the Development Process
Source: Own illustration based on Geltner et al (2007) and Schulte (2002)
As illustrated in Figure 1 flexibility & uncertainty decrease during the life time of a project.
Uncertainty can thereby be reduced by analysis and commitments of prospective
buyers/tenants, while flexibility decreases when decisions are made. At the same time more
and more capital is bound to the project as illustrated by the red line in Figure 1. Only when
uncertainty is reduced by a fair degree, one is willing to commit large amounts of capital.
At the beginning of the development, there is almost complete freedom on what to build or
where to invest but then the project becomes more and more specified and things are not
changed that easily anymore. It is thus of utmost importance to make the right adjustments to
a project while flexibility is still high and possibly preserve certain flexibility that could be of
value later on. In order to make best use of flexibility, a developer has to know where it is,
how important/valuable it is, which one to preserve and when best to exercise it. It lies in the
competence of the successful developer to know this due to his experience and intuition.
While probably most developers would agree that they have a lot of experience and intuition,
the question if there are not any quantifiable tools to deal with uncertainty & flexibility arises.
This leads us to our next chapter about the valuation practice of development projects.
2. Project
Conception
1. Project
Initiation
3. Project
Construction
4. Lease-up &
Tenant Finishes
5. Stabilised
Operation
! Cumulative Investment
! Uncertainty
! Flexibility
C
u
m
u
l
a
t
i
v
e
I
n
v
e
s
t
m
e
n
t
Land Purchase /
Land Optioning
Construction Permit
Start Construction
Construction
Completion
Development
Completion
F
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i
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i
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&
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4 Valuation of Real Estate Development Projects 13
4 Valuation of Real Estate Development Projects
In the fist part of this chapter we describe the capitalised earnings method and the net present value
method, which constitute the prevailing methods in valuation practice of real estate development in
Switzerland. In addition, we highlight both their strengths and weaknesses and stress the need for
better tools to deal with uncertainty & flexibility. In the second part of this chapter, we introduce real
options analysis as a method that effectively deals with uncertainty & flexibility in the context of
valuation. We discuss the reasons why the approach has not found wide application in the real estate
development practice yet and stress the need for a more applicable and intuitive model. This leads us
to a simulation based model that we introduce in detail in Chapter 5.
4.1 Common Practice
As shown by Müller (2007) in his study on the valuation practices in Switzerland, the
capitalised earnings and the net present value method (NPV) prevail in the appraisal of real
estate development projects. We thus introduce these two methods in this chapter and use
them later on in our model. When discussing the valuation of real estate development projects
it is important to differentiate between the valuation of existing, built real estate that already
entered the phase of stabilised operation, and the valuation of a project that is in one of the
preceding phases of the development process introduced in Chapter 3. This comes from the
fact that the two cases inherit different risk structures: in the case of a development project,
the future value of the asset can only be estimated and incurs a large degree of uncertainty.
Additionally the process of obtaining the asset involves binding large amounts of financial
capital that does not generate positive cash flow until tenants move in or the project is sold.
Now how should we estimate the value of the development project? As we will see, the
process is first to know what the asset would be worth if it existed today (value of the built,
stabilised asset), and then to account for the risk of obtaining that asset. So we need to have
the concept of valuing built assets and development projects in mind when discussing the
valuation of real estate development projects.
4.1.1 Capitalised Earnings Method
The capitalised earnings method is foremost a method to value stabilised real estate assets.
The developer can however use it to estimate the value of a real estate development project.
This is done by estimating the value of the project if it would exist today (value of the built
project), using the capitalised earnings method, and then deducting all costs until completion
of the project. The resulting value is the profit of the developer, hence this method is also
4 Valuation of Real Estate Development Projects 14
known as the developer calculation. It is also used when the value of land has to be estimated:
The developer then estimates the value of the built project and deducts costs for construction,
financing and development. The difference between value and cost is the maximum value of
land. The developer will however not want to pay this maximum value for the land, since then
he has no profit. The value of a built project can be approximated by:
1. Calculating the annual Gross Operating Income (GOI) of the project by
multiplying the leasable square meters with the expected average rent per square
meter per year. Vacancies are deducted from the GOI. The result is the expected
yearly cash flow from our building:
!"# ! !
!
! !"#$!"%"#&"' ! ! ! !"#"$#% "#$%&
2. Calculating the value of the project by dividing the GOI by the cap rate:
!"#$% !
!"#
!"#$"%&
"#$'&
Equation (4.2) is equivalent to the dividend discount model introduced by Gordon (1962)
developed to value an asset based on an infinite series of dividend payments D growing at rate
g with constant cost of capital r :
!"#$% ! !
!
!
!!!
!
!!!
!
!
!!!
"#$(&
Equation (4.3) is a converging geometric series with the partial sum:
!"#$% ! !
!
!
!!!
!!!
"#$#&
When we set growth to zero, (4.4) becomes to:
!"#$% !
!
!
!
"#$)&
(4.5) is the value of a constant dividend payment discounted at rate r into perpetuity. The
growth rate g has a strong influence on the value and setting it to zero might seem misleading
on first sight. This is however how the capitalised earnings equation is set up in the
professional real estate valuation domain according to Canonica (2009) and Fierz (2005), two
of the standard books on valuation in Switzerland. Doing otherwise would imply an
estimation on rental growth from the valuation professional, which is not applicable since it is
basically a speculation about the future. As pointed out by W. Ramseyer, the real estate
valuation expert is foremost concerned with the value of an object at the present moment of
time and neither in the future nor in the past. Seen from this view point a zero growth rate g
as in equation (4.5) becomes justified. There are however other valuation standards, where a
4 Valuation of Real Estate Development Projects 15
growth rate g is employed as described in Geltner et al. (2007). Other authors such as Hoesli,
Jani et al. (2005) employ a model with growth rate to describe real estate values. We will
however, stick to the concept of (4.5), since it captures the main drivers of real estate value
and is easier to model since we do not have to make a rather difficult estimate on growth.
Furthermore it is often employed in practice.
In (4.5) we calculate the value with net dividend income D0. GOI in (4.2) however does not
directly correspond to net dividend income since cost for operation and maintenance of the
property are not accounted for yet. Therefore the cap rate in (4.2) consists of the cost of
capital r plus an addition that accounts for operation and maintenance of the property. These
additions are according to Fierz (2005) between 1.0 to 1.5% for new properties.
The cost of capital r consists of the weighted average cost of capital (WACC) of the investor.
According to practitioners the WACC in real estate often consists of 60% to 70% of debt
capital and 30% to 40% equity capital. The cost of debt capital is thereby determined by
interest rates while the cost of equity capital is determined by the required return of the
investor.
Especially in the current market environment with very low interest rates, we can observe the
high influence of decreasing cap rates due to a reduced WACC on the value of real estate
assets. Since cost of capital is decreasing, cap rates are decreasing as well and the value of real
estate increases from a valuation standpoint. It can be seen how (4.2) brings together the two
drivers of real estate value if we interpret the GOI as the result of the space market and the
cap rate as the result of the capital market.
Now that the developer estimated the expected value of the project he estimates the projected
cost of the project consisting of:
/ Land acquisition costs
/ Planning & development cost s
/ Construction costs
/ Financing costs
The projected profit is calculated by subtracting the costs from the prospective value of the
project. If this profit is high enough to compensate the developer for the subjective risks, the
developer will proceed with further analysis of the project. Often the feasibility analysis is
used to determine if the acquisition costs of the project (in most cases the land cost) are at an
acceptable level or if not stated, how much the developer is able to pay while still having an
acceptable profit.
4 Valuation of Real Estate Development Projects 16
While the feasibility analysis can be done rather easily and without looking too much into
details, it is important to understand that it is only useful as a first step in the financial
analysis and that further analysis is needed to optimally assess the investment opportunity
(Gelter et al. 2007) . This is due to the fact that the capitalised earnings method does not
appropriately take into account opportunity cost of capital, the time it takes to achieve profits
and the risk involved. One consequence of this is that it becomes very difficult to decide
between mutually exclusive projects when only applying the capitalised earnings method.
Müller (2007) points out however that many real estate professionals in Switzerland use the
capitalised earnings method as their main method to assess a development project, which
emphasises the importance of providing more sophisticated models for investment decisions
in real estate development. This leads us to the next method: The net present value method.
4.1.2 Net Present Value Method
The basic idea behind the net present value method is to not only look at the absolute profit
but also at the time it takes to acquire that profit, the risk involved and the opportunity cost of
capital. Cash flows that lie in the future are discounted to the present using an appropriate
discount rate. The discount rate accounts not only for the time value of money (e.g. the risk
free rate) but also for the riskiness of the future cash flow by applying an appropriate risk
adjusted discount rate. Thereby future cash flows are “valued” in the present, can be compared
with each other and the overall project can be assessed. When we discount the net cash flow
of each period of a project to the present we obtain the net present value (NPV). The NPV
method is also used in the context of valuing stabilised real estate assets, where it is basically a
more diligent estimation than with the capitalised earnings method underpinned by the same
principles. In the context of real estate development the application is however different. In
this study we take the viewpoint of the developer, who sells the project to an investor during
or after the development process. Here the sales volume and the costs of the project are
discounted to the present using an appropriate discount rate. The sales volume thereby is
estimated using the capitalised earnings method. The NPV makes a statement about which
project to choose among mutually exclusive projects. The decision rule thereby is:
/ Maximize the NPV across all mutually exclusive alternatives
/ Never choose an alternative that has: NPV < 0
4 Valuation of Real Estate Development Projects 17
With the equation:
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CFt : cash flow at time t
r : risk adjusted discount rate
The NPV valuation is the standard tool used in real estate development and other fields to
value investment projects. The method is easy to use and intuitively comprehensible which is
probably why it enjoys such large popularity. There are however some shortcomings that we
need to discuss.
4.1.3 Shortcomings
Disadvantages of the capitalised earnings method are that it does not account properly for the
risk and the opportunity cost of capital. The NPV method effectively deals with these by
using a risk adjusted discount rate and the timing of cash flows, suffers however from other
problems in correctly assessing the value of a development project. Especially in terms of
flexibility & uncertainty the usual way of applying the NPV fails to account important
aspects. As we know from the overview of the real estate development process done in
Chapter 3, these are two very important factors and thus we discuss their role in the NPV
method here.
Flexibility
One of the main problems in applying the “classic” NPV method is the inability to account
for flexibility in the assessment of a project. NPV analysis assumes that all cash flows will
occur according to the calculation, which neglects the fact that managers actually manage
their projects and make adjustments when things do not go as planned or new opportunities
arise. As we discussed earlier, the exercise and planning for flexibility is one of the major tools
a developer has to manage risks in the development process.
When we only employ the classic NPV method we fail to account for the value of flexibility
and possibly understate the value of a project or even worse, fail to recognise, plan and exploit
flexibility in the development process.
Uncertainty
A second problem of the NPV method is firstly the consideration of uncertainty over the
choice of an appropriate discount rate and secondly the consideration of uncertainty over the
estimated cash flows. Let us first discuss the discount rate: The discount rate accounts for the
4 Valuation of Real Estate Development Projects 18
time value of money and also for the riskiness of the cash flows. While the time value of
money can be approximated by the risk free rate, how does one know which discount rate to
choose for the risk involved? In Switzerland discount rates for real estate development range
between 8 to 14% according to practitioners. In order to calculate conservative developers are
inclined to use a higher discount rate, the larger the uncertainty in a project is, but larger
uncertainty means higher upward and downward potential. The use of a higher discount rate
then penalises foremost the larger downward potential, making them unattractive from an
investment point of view. However this penalising might be unjustified, since there is also a
higher upward potential in such a project, that one could make use of, while not having to
face the downward outcome by e.g. using flexibility. The question to choose an appropriate
discount rate then becomes difficult. The second problem with the NPV method is the
assumption of deterministic fixed cash flows in the calculation. How does one know which
values to choose if there is large uncertainty in these cash flows? One way to deal with this is
scenario analysis where multiple possible cash flows are considered.
We discussed the currently used valuation methods and the problems arising from applying
them. Since real estate development involves uncertainty & flexibility, we need better tools for
the financial analysis and decision-making process of projects. We thus introduce real option
analysis as a method that effectively deals with this issue in the next part of this chapter.
4.2 Real Option Analysis
Real option analysis (ROA) is an elegant way of handling flexibility & uncertainty in
investment projects. Similar to financial options, Copeland (2001) defines a real option as
“the right, but not the obligation, to take an action (e.g., deferring, expanding, contracting, or
abandoning) at a predetermined cost called the exercise price, for a predetermined period of
time – the life of the option.”
The idea behind it is, that we have uncertainty in the outcome of projects and flexibility that
allows us to take actions accordingly. For example when markets have a downturn during the
lifetime of the project (uncertainty), we do not have to face the full downside, but can e.g.
abandon the project (flexibility) thereby cutting our losses.
This is very similar to financial options traded on financial markets: By obtaining a financial
call option, we get the right but not the obligation to buy a certain stock for a certain price in
the future. If at maturity, the stock price is higher than the exercise price of the option, we
win. If at maturity, the stock price is lower than the exercise price however, our option
becomes worthless. The parallels of financial options and real world projects led to the
4 Valuation of Real Estate Development Projects 19
application of the financial option theory to real world projects. This is an important causality
to bear in mind when applying real option frameworks since this origin of the approach from
financial options has some benefits but also some drawbacks.
A very elegant feature of real options as a valuation tool is that it can be used directly as an
extension of the conventional NPV method. Mun (2002) proposed the concept of the
expanded NPV as a combination of the option value and the conventional NPV method:
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This formulation of a real option lets us define the value of the option in a straightforward
way as the difference in value between a project with and without the option. When a project
has no flexibility, the value of the option is simply zero. Also when a project is without
uncertainty our option is worthless, since there is no flexibility we could employ. Only when
there is both uncertainty and flexibility there is option value and the higher the uncertainty,
the higher this option value becomes. This stands in contrast to the standard financial theory
that tells us that uncertainty is something that decreases value. Uncertainty means up and
downward potential however and with options we can make use out of this, hence real
options like uncertainty (Geltner and de Neufville 2012).
The way to do real option analysis is to recognise uncertainty, think about flexibility and
compare the case with flexibility against the one without. If this results in a positive number,
we have found an option of value. Mun (2006) thereby derives the value of ROA from 50%
thinking about it, 25% of number crunching and another 25% of interpretation of results. The
thinking about flexibility & uncertainty, model and value it, and then designing the project
accordingly is really the essence of the approach.
There are three main approaches to apply real option analysis:
/ Binomial Approach
/ Closed Form Solutions
/ Monte-Carlo Simulation
4.2.1 Binomial Approach
The binomial approach introduced by Cox, Ross and Rubinstein (1979) is a widely used
method to value financial and real options.
The binomial approach is based on the assumption of:
4 Valuation of Real Estate Development Projects 20
/ Perfect markets: Full information is available, therefore there are no arbitrage
opportunities, there is no sure gain of money.
/ Complete markets: Any risk can be replicated without transaction cost.
/ Rational behaviour: Market participants act rationally and therefore exercise
options in an optimal way.
/ Geometric Brownian Motion: In most models the underlying asset follows a
geometric brownian motion, also known as a random walk.
Under these assumptions investors will be indifferent in holding the actual option or of
owning a replicated portfolio consisting of bonds and equity that results in the same payoff
structure. We can then value this replicated portfolio using the risk free rate and risk free
probabilities that account for the risky payoff structure.
The lifetime of an option is split up in multiple time steps, resulting in multiple up-or-down
movements of the underlying asset, thereby creating a tree of possible states of the underlying
asset. The value of the option is then calculated by working the tree backwards from the end
to the beginning. At each node the value of the option is calculated taking into account the
state of the underlying asset and possible states one step ahead. The advantage of this method
compared to classic NPV valuation is that we do not account for the riskiness of the pay-out
structure over the discount rate but with probabilities, thereby separating risk and the time
value of money.
4.2.2 Closed Form Solutions
There are several closed-form solutions such as the Black-Scholes (Black et al. 1973) or the
Samuelson McKean formula (Geltner et al. 2007) and many more abbreviations for specific
options. These closed form solutions can often be interpreted as binomial models with
infinitesimally small time steps, which was already showed for the Black-Scholes formula by
Cox, Ross and Rubinstein (1979). The closed form solutions have the advantage that they are
easy to implement and give a result very quickly once the parameters are estimated. However
they are usually made only for valuing a very specific kind of option (e.g. American or
European option) thus they do not allow for complex pay out structures. As with the binomial
models they only allow for one kind of option within a project and do not account for
interchanges of multiple options. However, as we know from real estate development, there
are several options available to us, which makes the approach applicable only for certain cases
(e.g. the value of vacant land). The underlying process of these solutions is in most cases a
geometric Brownian motion that is based on the lognormal distribution with constant
variance !. While this might be somewhat close to what we observe in stock markets it is
4 Valuation of Real Estate Development Projects 21
highly questionable that the value of development projects behave this way. After all there are
multiple factors influencing the value. Furthermore it can be difficult to estimate or
communicate the significance of the results, since these models give out one specific number
that needs to be interpreted with great care. Also the models make it extremely important to
understand the underlying processes and assumptions exactly since without it one is prone to
using the wrong model and/or drawing the wrong conclusions.
4.2.3 Monte-Carlo Simulations
Other widely used methods for valuing real options are based on Monte-Carlo simulations.
This approach uses thousands of randomly generated scenarios of possible future market
outcomes and calculates the value of the project under these scenarios. As with the other real
option frameworks, the value of the option is the difference between the project with and
without the option but here we do not necessarily base the model on the idealised
assumptions of financial option models (de Neufville and Scholtes 2011). As we will see this
so called “Engineering Approach” gives us great flexibility in dealing with real options. One
of the difficulties with this approach however is that we have to implement flexibility into the
model manually so that it behaves under the market scenarios as we specify it. This can be
seen as a disadvantage against the other two approaches that exercise options always in an
optimal way. Another difficulty lies in the modelling of the underlying asset value. In contrast
to the other models, we are free to choose how the value of our project is determined and we
do not rely on the geometric Brownian motion. Depending on the required sophistication of
the model, one will need to apply advanced statistical tools that are to be handled with great
care, in order to get meaningful results. However, once the model is implemented it offers
great possibilities for adaptation and analysis, which makes it a good tool for analysis.
4.2.4 Critique and Choice of Method
Although real option theory enjoys large popularity in academia and other industries, it is
rarely used in the Swiss real estate practice (see (Müller 2007)).
Why is that so? One of the reasons comes from the theory itself: The valuation of an asset
using a replicating portfolio and the non-arbitrage argument may be a very elegant way in
theory, but in reality, although real estate is a traded asset, it is impossible to find a replicating
portfolio with the same risk exposure as that of a development project. Also it is clear, that
since the real estate market is rather intransparent and transactions are infrequent, it is far
from the no arbitrage assumption. So when we work with these assumptions we have to be
very careful with interpretation. De Neufville et al. (2011) put it as: “We need to resist the
temptation to apply the techniques of financial options blindly to such projects [technical projects].
4 Valuation of Real Estate Development Projects 22
We need to handle such applications with great care. This is because the context of technological
projects differs significantly from that of financial transactions. The assumptions underlying the
theory of financial options are not generally valid for projects, and that theory is thus of limited value
for the design and implementation of technological systems.”
Other authors such as Copeland (2001) argue that the assumptions underlying financial
options are no real problem since they are already implied in the risk-adjusted-discount-rate
of the NPV. Also we have to acknowledge that of course all models are simplifications of the
real world and assumptions help us to get closer to the truth in order to make meaningful
decisions. Conversations with industry professionals however suggested other reasons more
linked to the business world that real options have not made the leap into the Swiss real estate
development practice yet:
1. Development projects in Switzerland often start with the securing of land. At that stage
often no concrete building project exists, usage is only feebly defined and the threat of
the public voting against a large construction project is always there. The risks involved
in this first stage of the project are often of equal or higher importance than that of the
market risk. The decision maker has to take care of all involved risks and cannot rely too
much on the numerical result that comes out of a real option valuation.
2. Real options analysis values a project higher than with normal NPV analysis. This is
inherent in the system, since the option adds value to the NPV. Decision makers
however want to calculate conservatively, since they still want to have margin when
things turn out differently than expected. So why should one bother to make the analysis
only to get a small additional value, when he already knows that he has some security
margin?
3. Decision makers take over large responsibility towards their superiors or shareholders.
None of them wants to argue over the applicability of a replicating portfolio as the reason
for an investment decision. Things need to be easily understood, defendable and
communicated in order to have impact. This is not necessarily the case with real options
so far.
This makes clear that we need to use an applicable approach that clearly shows the value of
the analysis in order to have impact with real option analysis. In our view the mentioned
“Engineering Approach” using Monte-Carlo simulations is the method of choice for such a
goal.
We will go into the specifics of the model that we use into the subsequent sections. However,
the main reasons for this choice are the following:
4 Valuation of Real Estate Development Projects 23
Add-on Character
As will be shown in the successive chapters, the approach can be implemented rather easily to
the existing framework of a developer. Developers make their investment calculations mostly
with Excel, therefore they are familiar with the basic functions of the program and are able to
modify calculations according to their needs. The model we apply is basically an enhancement
of the widely used spreadsheet calculations in Excel by overlapping the existing calculations
with simulations of the future real estate market and implementing flexibility.
Comprehensibility
Users can follow the process from changes in the real estate market to changes in the value of
the project and since they are familiar with the NPV method, they understand the valuations
and their implications. Numbers can be tracked and manipulated giving confidence in the
results and avoiding the black-box phenomenon. In contrast to the binomial approach we do
not employ the assumptions of financial options theory but work with normal NPV. This is
not perfect either of course but is easier to comprehend since practitioners are used to work
with it.
Customisation
Customisation is easily possible by changing input parameters such as rent levels, vacancies
and capitalisation rates. The framework can be adapted to the specific project or the
simulations can be added to an existing NPV valuation framework. It is also possible (and
strongly advised) to perform extensive sensitivity analysis on the specific project that helps to
further understand and optimize market risk exposure of the project.
We discussed the current valuation practice of real estate development projects and advocated
the need for incorporating uncertainty & flexibility into the valuation for a more profound
analysis and decision-making process. We then introduced real option analysis as a promising
way to effectively deal with uncertainty & flexibility and discussed reasons why the method
has not yet found wide application in the real estate development practice. We came to the
conclusion that we need a more applicable and intuitive approach to have impact in practice.
This let us favour the “Engineering Approach” as an analysis framework for real estate
development projects. In the next chapter we look at this framework in detail and show how
we can apply and configure it for the Swiss real estate market.
5 Simulation Based Real Options Model 24
5 Simulation Based Real Options Model
In the following chapter we first explain the “Engineering Approach” introduced by de Neufville and
Scholtes (2011). This framework helps us to assess flexibility & uncertainty in a real estate
development context and we use it extensively in our case study in Chapter 6. In the second part of
this chapter we first look at the development of prices, vacancies and cap rates in the region of Zurich
Unterland and then introduce two models for simulation based on this data. This simulation
framework generates possible future scenarios of the real estate market, which allows analysing real
estate development project under these scenarios.
5.1 Project Modelling Framework: The “Engineering Approach”
The “Engineering Approach” is designed to help practitioners design better systems by
analysing flexibility & uncertainty. In order to be applicable, the approach is based on
pragmatic and simplifying assumptions that differ from the binomial and the closed form real
options models.
Instead of working with a replicating portfolio and risk neutral probabilities as used in the
binomial and the closed form real options model, the “Engineering Approach” works with net
present values with constant discount rates as we know them. We therefore do not value cash
flows, based on the theoretical sound framework introduced in Chapter 4.2.1.
But should we not build up on this theoretical framework and present answers that are as
correct as possible, that “get things right” as exactly as possible? De Neufville et al. (2011)
describe this aspect of their approach as: “…we believe that our modest aspiration to “get it
better” is more likely to improve practice. Indeed the concept of “getting it right” is difficult to defend
once we accept that modelling the performance of socio-technological systems is as much an art as
science.”
We argue for an applicable approach in Chapter 4.2.4 and hypothesise that ROA with
binomial trees or closed form solutions have not been widely adopted in practice because they
lack the pragmatism that is needed “to get things better” instead of “getting things right”.
They are too closely linked to the “correct” valuation of financial options that they lack the
flexibility to be easily adapted to real projects. We believe that by applying the “Engineering
Approach” we are better able to catch the essence of real options analysis, which is to think
about flexibility & uncertainty, model and value it, and then to make better project analysis
and decision-making.
5 Simulation Based Real Options Model 25
The “Engineering Approach” is divided into four steps:
/ Creating the most likely initial cash flow model
/ Incorporate uncertainty into the model
/ Incorporate flexibility into the model and
/ Maximize value by applying an optimal decision rule
We introduce the four steps in detail here and apply them to our case study later on.
5.1.1 Step 1: Create the Most Likely Initial Cash Flow Model
The first step is to create a pro forma cash flow model incorporating development and
construction cost, project scale, schedule and the estimated sales volume. The sales volume,
the estimated value of the finished project on the market, is calculated using the capitalised
earnings method. The cash flows are discounted to present values, using an appropriate
discount rate, which results in the NPV of the project. As we know from Chapter 4.1.3
“Shortcomings”, the resulting NPV neither incorporates uncertainty in cash flows nor
flexibility yet, but since it is the standard valuation tool it serves as a good benchmark against
which we can compare our further calculations. We will therefore call the result of this
calculation the “base case”.
5.1.2 Step 2: Incorporate Uncertainty into the Model
We enhance our initial cash flow pro forma by recognising uncertainty. We do this by
identifying the risk drivers that determine our future cash flows and then try to model them.
For our case we assume that the future cash flows only depend on the real estate market and
therefore make a model of this real estate market. We will then use this model to simulate
subsequent scenarios of this market. By doing so we can generate thousands of possible future
scenarios and their corresponding cash flows. As shown in Figure 2, this results in a
distribution of possible outcomes rather than one estimated value as we obtained it from the
“base case”. Since we do not yet incorporate flexibility, we will call this the “static case”. We
analyse the “static” case using histograms and cumulative probability curves of the resulting
NPV distribution, as shown in Figure 2 and 3.
5 Simulation Based Real Options Model 26
Figure 2: Example of a NPV Distribution
Source: Own illustration
Figure 3: Example of a Cumulative Probabilities Curve and Expected NPV
Source: Own illustration
With the help of these graphs we get a feeling for the range of possible outcomes and can
better understand the risk structure of the project. The cumulative probabilities curve can also
be described as the value at risk and gain (VARG) curve. It states the probability of an
outcome below or above a certain NPV. A flat VARG curves thereby indicates a wide range
of possible outcomes whereas a steep curve indicates a low range.
The vertical line depicts the mean or expected value of the distribution. We will call this the
expected net present value (ENPV). The shape of these graphs depends on the simulation
model that we use and the cash flow structure of the project. In order to draw right
conclusions, it is crucial to use an appropriate simulation model. We will therefore give a
detailed analysis on different approaches and how it can be done in Chapter 5.2 on the
simulation framework.
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5.1.3 Step 3: Incorporate Flexibility into the Model
Now that we have combined our project with a wide range of possible market scenarios, we
can think of actions to take when certain scenarios occur. These will be our options, since we
can always choose whether or not to exercise them. Our available options highly depend on
the specific project and in real estate these often include:
/ Option to delay (e.g. wait with construction until market recovers from a downturn)
/ Option to switch (e.g. switch from an office to a housing use)
/ Option to abandon (e.g. sell the property for salvage value)
/ Option to phase (e.g. build only part of the project and the rest later)
/ Option to expand (e.g. build an extension of the project)
We can model these options by including decision rules into our spreadsheet model. For
decision rules to work we need first a trigger value that triggers a certain action, and secondly
an execution variable that leads to the actual change in the model.
A decision rule then has the form of: “if variable A (the trigger value, e.g. value of apartments)
falls bellow a certain threshold, then variable B (the execution variable e.g. variable for delay
of construction for one year) will be one and thus lead to a delay in the successive cash flow of
one year .”
When we let the simulation of scenarios run, actions will be taken depending on the specific
scenario and therefore a scenario sensitive distribution of NPV outcomes is obtained. When
analysing the resulting distribution curves it is our goal to decrease the amount of negative
outcomes and to increase the amount of positive ones. This corresponds to a shift of the
VARG curve to the right. We will call this calculation model the “flexible case”.
This third step forces us to think about our available options and what to do in advance
before things turn out to be different than in the base case scenario. It is this thinking about
options and how to preserve and use them that gives additional value due to flexibility. Figure
1: Flexibility, Uncertainty and Cumulative Investment in the Development Process on page
12 shows how flexibility decreases during the development process. Thanks to simulations we
are now able to identify and quantify the most valuable options from the beginning, keep
them alive during the development and exercise them if needed. This is one of the main
advantages of this methodology.
5.1.4 Step 4: Maximize Value by Applying Optimal Decision Rules
The fourth step deals with finding the right set of decision rules that optimises the overall
outcome. Additional sensitivity analysis is performed on the model. Which value to optimise,
depends largely on the decision maker. In our study we focus on the NPV, but a decision
5 Simulation Based Real Options Model 28
maker might be interested in other profitability metrics such as the internal rate of return or
the absolute return. This can be implemented as well. The optimal combination is found by
experimenting with different combination of decision rules and project parameters.
5.2 Simulation Framework
After introducing the “Engineering Approach” we now look in detail at our data and how to
model it. First we give an overview of what, why and how we are going to model the risk
drivers of a real estate development project. Then we look at our data, the development of the
observations depicted in the data in the past years and on correlations among the data. In the
third part of this chapter we introduce two ways to model this data with the goal of obtaining
a model for simulation.
5.2.1 Overview
Goal
We want to obtain a model for the simulation of risk drivers for real estate development
projects. We need this model to analyse possible future values of a real estate development
projects from the viewpoint of a developer.
What to Model
The first question to answer towards this goal is that of what we actually need to model. We
are interested in the value of real estate assets in the future, since this is one of the main
success drivers of a real estate development project. In Chapter 4 we discuss that the gross
operating income and the capitalisation rate approximates the value of a finished real estate
project. These two variables determine to a large degree how much an investor is willing to
pay for a real estate asset to a developer or, if the asset remains in a portfolio, what the book
value of the asset is. It is thus apparent that we need to model these two variables. Another
important part of a real estate development project are condominiums. These are directly sold
to private persons already before, during and after the construction phase. Depending on the
project, they also have a large influence on the bottom line of the developer and thus we are
interested in modelling them as well. Further, construction cost is an important aspect of a
development project that inhibits uncertainty, so this is something we will want to model as
well. We go into more detail on what we need to model in Chapter 5.2.2 on the risk drivers
of the model and continue here with the overview of the model.
5 Simulation Based Real Options Model 29
Time Horizon
Since real estate development takes time, we are interested in a rather long time horizon into
the future. Development projects take from initiation to stabilised operation at least 4 to 5
years. Since we are interested in flexibility and therefore also consider the delay of
construction we take into account a simulation horizon of 10 years.
How to Model
The second question we need to answer is that of how to model these variables. The method
we use is to look at past data for the variables of interest, so called time series, and fit a model
to this data. This model is then used for the simulation of future variables. A simple model is
that of a trend plus noise model. The model takes the form of:
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the model using ordinary least squares (OLS) method on the past data, thereby minimizing
the sum of squared vertical distances between the data and the predicted model, in this case
the trend line. By extrapolating the trend into the future and generating new noise around the
trend, using random draws from e.g. a normal distribution, we generate simulations of the
model into the future. This is illustrated in Figure 4 :
Figure 4 : Simulation with a Trend + Noise Model
Source: Own illustration
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5 Simulation Based Real Options Model 30
This rather simple approach neglects however that the time series of interest do not
necessarily follow a constant trend and also that there might be dependence with other
variables that need to be considered. Also we see already in Figure 4 that the generated
simulation does not inherit the same characteristics as the past time series it is based on: The
simulated line jumps above and below the trend line in shorter time intervals than in the past.
We will thus have to employ more complex modelling techniques.
Stationarity
Additionally in order to use a model for simulations, we have to use the concept of
stationarity. A stationary time series has the property that the probabilistic character of the
series does not change over time, so that any section of the time series is “typical” for every
other section with the same length (Dettling 2012). If any section of the time series is typical
for every other section and if we can assume that this property holds also in the future, then
we can use this time series also for forecasts of future time series. A stationary time series has
constant expectation E[Xt], constant variance Var(Xt) and the covariance between the
observations Cov(Xt1,Xt2), i.e. the dependency structure, depends only on the lag between the
observations. Now most time series are not stationary. Every time series with e.g. a trend or a
deterministic seasonal pattern violates the concept of stationarity. By transforming and
decomposing the data, we can however often find a stationary process. Actually the
introduced trend + noise model (5.1) is already such a decomposition. The goal of such a
decomposition is to find one that yields a stationary noise process "t. As we stated already we
often cannot assume a trend that remains constant over time as in the trend + noise model.
One way of dealing with this is to work with logarithmic returns rather than the raw time
series. Thereby we detrend and normalise the data and hopefully obtain a stationary noise
process.
Working with Logarithmic Returns
A common practice when modelling time series and analysing dependence among them is to
work with logarithmic returns (log returns). By using log returns we focus on the relative
change of the time series, which is directly comparable to the relative change in other time
series. Additionally we remove piecewise a linear trend if there existed one. Throughout this
chapter we thus work with logarithmic returns rather than discrete returns. Log returns have
the convenient property that they are additive and easily obtained from time series by taking
the natural logarithm of the series and differentiating by one time step:
5 Simulation Based Real Options Model 31
!
!!!
! !"
!
!!!
!
!
! !" !
!!!
! !" !!
!
! " )$' &
with
rt+1 : logarithmic return between time t and t+1
yt,yt+1: data point at time t
Independent on which model we use for simulation, we first transform the data to
logarithmic returns, fit a model to it, and use this model for the simulation of a future horizon
of 10 years. We thus generate future logarithmic returns that we can apply to the value we
observe at present and thereby obtain our desired prediction of future time series:
!
!!!
! !
!
! !
!
!!!
")$(&
with
t : time of last observed data point
rt+1: predicted return for one time step ahead
yt+1: one time step ahead prediction of data point
Indices & Absolute Values
As we are going to see, most of the data used in this study is based on indices rather than
absolute values. For our calculations on real estate development projects we need absolute
values however. We address this by first estimating the model on the indexed data as
described above and then using an absolute value currently observed in the market as the start
value of our simulation. We thus assume that the absolute value will behave the same as the
index it is based on. This is not necessarily true if we choose values that do not correspond to
the index, so we should use only start values that actually correspond to the used index.
After this overview on what and how we are going to model, we now look into the details of
the model.
5.2.2 Risk Drivers
The question is what exactly do we need to model to simulate the value of a real estate
development project. As we discussed in Chapter 4 on the valuation practice, a real estate
asset from the investment perspective is determined by the GOI and the capitalisation rate.
Additionally, we often have a part of the development project consisting of condominiums
that are directly sold to private owners.
5 Simulation Based Real Options Model 32
Investment Asset
Let us first look at the part of the project that enters the market as a real estate investment
asset (no condominiums) and estimate the value it would have today. In real estate
development a project often consists of multiple uses such as housing, office and commercial.
For simplicity we work with per m
2
values:
!"#$%
!""#$
!
!"#
!"!#$
!"#$"%&
")$#&
!"#
!"!#$
! !"#
!"#$%&'
! !"#
!""#$%
! !"#
!"##$%&'()
")$)&
!"#
!"#$%&'
! !"#$
!"#$!"#
! !! ! !"#"$#%
!"#$%&'
! ")$*&
!"#
!""#$%
! !"#$
!""#$%
! !! ! !"#"$#%
!""#$%
! ")$,&
!"#
!"##$%&'()
! !"#$
!"##$%&'()
! !! ! !"#"$#%
!"##$%&'()
! ")$-&
For estimating the value of a real estate asset, we thus have to model rents, vacancies and cap
rates for all uses.
Condominiums
Let us shortly discuss the condominiums that are also often a part of the development project.
Buyers of condominiums do not take the investor perspective of calculating rents and cap
rates, but base their decision to buy a condominium on their budget and preference. Since in
Switzerland most condominiums are partly financed with mortgage loans, mortgage rates play
an important role on their affordability. Condominium prices are measured on a per m
2
basis
for specific regions in Switzerland which makes it possible to use the corresponding indices
directly for modelling.
Deal Noise & Vacancy
When an developer sells a project to an investor, there is always a certain amount of
uncertainty around the valuation price, depending on the bargaining power of the two parties
negotiating (Geltner and Miller 2007). We will address this by introducing an independent
variable “deal noise” to account for this. Additionally developers in Switzerland sell a project
often before the receipt of the building permit with a certain amount of space already
preleased to prospective tenants. There remains however often some vacancy risk that the
investor will want to have compensated. We take this into account by applying twice the
vacancy rate observed on the market on our sales price to the investor.
5 Simulation Based Real Options Model 33
Also when selling condominiums, the price might differ from the current market price due to
the location, marketing success and specifics of the project. We will thus use deal noise on
condominiums as well.
Construction Cost
On the cost side we have the construction cost as our only risk driver. We are hereby looking
at the market risk of construction cost, assuming that the developer estimated the cost of his
project accurately and that the cost risk is therefore only driven by the uncertainty of variable
prices for the same services and goods.
Table 1 gives a summary on the discussed risk drivers that we need to model:
Table 1: Risk Drivers
Earnings Side Cost Side
Rents (Housing, Office, Commercial) Construction Cost
Vacancies (Housing, Office, Commercial)
Cap Rates
Transaction Prices Condominiums
Deal Noise
The total sales price of a project to investors and private buyers can then be stated as:
!"#$%
!"!#$
! !
!""#$
! !"#$%
!""#$
! !
!""#$
! !
!"#$"
! !
!"!"#
! !
!"#$"
")$.&
with
#Asset, #Condo : deal noise asset and condominiums
$Asset, ACondo : saleable space in m
2
PCondo : price condominiums per m
2
ValueAsset : value of the asset according to (5.4)
And the cost including construction cost risk as:
!"#$
!"!#$
! !"#$
!"#$
!!"#$
!"#"$%&'"()
!!"#$
!"#$#%"#&
!! ! !"#$
!"#$%&'(%)"#
")$%/&
with
! : construction cost uncertainty
5.2.3 Data
The independent real estate and urban development consulting company Fahrländer &
Partner Raumentwicklung AG (FPRE) provided us with data specific for the region where our
case study is located. The data is extracted from the Real Estate Scenario Cockpit (Fahrländer
2012) of FPRE and covers the time span from 1985 to 2011 in yearly time steps. The RESC
is constructed with data from multiple rent indices, data from the Federal Statistics Office,
5 Simulation Based Real Options Model 34
the cantons and other sources. For replication of our results one is advised to use the freely
available data for rents provided by the Swiss National Bank
4
. We used this data source also
for the data on construction cost and gross domestic product.
Whenever analysing real estate data, it is important to clearly understand its nature. In our
data set we look at the evolution of rents, vacancies and cap rates from 1985 to 2011. During
that time the products on the space market have changed substantially: while a new apartment
in 1985 with an automatic dishwasher was in an upper price range, it is standard equipment
in new apartments nowadays. Similar examples can be made for windows, heating, elevator,
etc. Changes in quality also occurred in terms of location: with the increased supply of
mobility, locations further away from cities have become more attractive. This is especially the
case with suburban areas, that became much more attractive due to increased mobility
services. Furthermore the real estate market is very heterogeneous: objects differ from each
other substantially in terms of size, location, age, etc. We therefore do not deal with a
commodity like gold that does not change over the years and is the same wherever it is
bought. We can account for this by using hedonic pricing models that take into account
quality properties of the objects. The method used on our data set is described for rents by
Wüst&Partner (2000) and for condominium transaction prices by Fahrländer (2012).
Table 2 gives an overview of the used data:
Table 2: Data Used in this Study
Data Category Time Resolution Region Source
Rents, Vacancies Housing, Office,
Commercial
1985 - 2011 Yearly Zurich Unterland FPRE
Transaction Prices Condominiums 1985 – 2011 Yearly Zurich Unterland FPRE
Cap Rates Housing, Office,
Commercial
1985 – 2012 Yearly Zurich Unterland FPRE
Construction Cost
Index
Cost Index all
Constructions
1998 – 2011 Yearly Canton of Zurich SNB
Gross Domestic
Product
Economy 1990 - 2011 Yearly Switzerland SNB
We now describe the obtained data and highlight specifics of their behaviour in the past.
Rent Revenues
We use indices for the rent revenues of the different usages (housing, office and commercial).
The indices correspond to rents observed in the MS (mobilité spaciale) region Zurich
Unterland and do not include vacancies yet. For further information on the locality of this
region one is advised to look at Schuler (2005). An important notion is that the rent indices
4
www.snb.ch
5 Simulation Based Real Options Model 35
are based on asking prices for rents and not on average revenues observed in actual properties.
Due to restrictions and long-term contracts it is difficult for owners of real estate to
immediately adjust rents to current asking prices and thus their revenues will tend to be lower
on average. For real estate development however, the use of asking prices comes in handy,
since development projects come new to market and we can assume that they will generate
revenues close to current asking prices. For housing the used index corresponds to middle
class multi-family dwellings, for office and commercial, it is the average asking price observed
in the specified region.
Figure 5 shows the development of rent revenues during the observed time period. We see a
sharp increase in rents from 1985 to 1990 with a peak in 1991, a sharp decline thereafter and
since 1998/1999 a steady growth. The sharp decline in rents is associated with the real estate
crisis in the early nineties we discussed in Chapter 3.4. From the figure we can already see
that the three indices behave somewhat correlated. The indices of office and commercial
space are identical until 1996 and behave strongly correlated thereafter. The equality of the
two indices in the beginning of the series comes from the index construction that itself is
based on multiple rent indices. Apparently rents for commercial and office use are based on
the same data source during the beginning of the data. This will have further implications for
our model later on.
Figure 5: Rent Revenue Index Zurich Unterland
(Source: RESC Fahrländer & Partner)
Vacancies
For vacancies we have the same usages and data source as for rent revenues. These are the
vacancies that we observe on the overall market. Here we see exactly identical values for office
and commercial uses, which is why there are only two lines visible in Figure 6 instead of
5 Simulation Based Real Options Model 36
three. Values vary from 2% up to almost 18% in the middle of the 1990s for office &
commercial uses while they stay between small 0.5 and 2% for housing use. Again we see the
effect of the burst of the real estate bubble in the early 1990s that resulted in large vacancy
rates for office & commercial uses. Interestingly it did not affect vacancies in the housing
market very much. We can therefore legitimately assume that office and commercial uses had
more risk of vacancies and therefore loss of earnings in the past than housing.
Figure 6: Vacancies Zurich Unterland
Source: RESC Fahrländer & Partner)
Transaction Prices Condominiums
We use the transaction price index of middle class condominiums for our analysis.
Condominiums enjoy large popularity especially in recent years, which can be seen in the
large price increase of almost 50% from 2000 to 2011. We can also observe that
condominium prices have a very similar price development as that of housing rents.
Figure 7: Transaction Price Index Condominiums Zurich Unterland
Source: RESC Fahrländer & Partner
5 Simulation Based Real Options Model 37
CapRates
From the RESC we obtained value indices for housing, office and commercial uses. These
value indices were constructed by using the equation:
!"#$% ! !"#$ ! !! ! !"#"$#%!!!"#$"%& ")$%%&
The cap rate thereby consists of an empirically measured premium plus a WACC consisting
of 60% leverage, based on mortgage rates and 40% equity capital, based on bond rates and on
an additional premium for real estate. This approach corresponds to the calculation of cap
rates in Chapter 4. To obtain cap rates from the value indices, we solve equation (5.11) for
cap rates using the already described rent and vacancy data and levelled them on 5% for the
year 2011. We thereby obtain three time series of cap rates pictured in Figure 8:
Figure 8 : Cap Rates Zurich Unterland
Source: Own calculation based on RESC Fahrländer & Partner
The levelling on 5% is a rather a simplified approach to estimate cap rates but since we are
more interested in the relative change and the correlation with rents and vacancies, the
absolute value should not matter too much. As seen in Figure 8, all three cap rate time series
behave highly correlated and because we do not want to unnecessarily complicate our model,
we aggregated cap rates into one single time series by taking the average of the previous three
cap rates. For our model we are going to use this aggregated time series as our input. The
result is illustrated in Figure 9.
An important thing to note with cap rates in a historic context is that they are currently at a
very low level due to the interest rate policy of the SNB. As soon as interest rates start to rise
again, this will have an influence on cap rates, which will result in decreasing real estate value
if rent revenues do not rise simultaneously.
5 Simulation Based Real Options Model 38
Figure 9: Average Cap Rates Zurich Unterland
Source: RESC Fahrländer & Partner
Construction Cost Index
We use the construction cost index from the SNB for the region of Zurich. The index is
quarterly available since 1998. From 1998 to 2011 construction cost have been rising on
average by 1.6% per year.
Figure 10 : Construction Cost Index
Source: SNB
Real Gross Domestic Product
We use the real gross domestic product (GDP) as our exogenous variable for the VAR-model
we introduce later on. We work with the real GDP because we expect the economic activity
to have an influence on expenditure on rents and condominiums, and also on vacancy rates
especially in the office and commercial market. Unfortunately we have data only for the time
5 Simulation Based Real Options Model 39
period from 1990 until 2011 and not for the whole time period of the other data sets starting
in 1985. The yearly percentage change is the growth in GDP and depicted in Figure 11.
Since we look at the changes per year we lose one data point for 1990. We see a negative
growth in GDP from 1991 to 1993. This corresponds to the time of the real estate crisis, so
while growth was close to zero we had also decreasing prices. The second time when GDP
growth was very low is 2002 and 2003. When we look at were GDP growth was close to zero
and zero growth in 2002 and 2003 and again negative growth in 2009.
Figure 11 : Growth in Real GDP 1991 - 2011
Source: SNB
Interpretation of Data in the Light of Forecasting
Our data for office & commercial uses are almost identical and we use a very simplified
method to calculate our cap rates. Furthermore we have only yearly data points and not the
full time span for all data sets. To assume that we can conduct an exact forecast out of this
data would not be very credible. But then again we have millions of data sets about financial
markets and even with this huge data history it is apparently not possible to develop accurate
forecasts. After all, the saying goes that forecasting using past data is like driving a car
looking through the rear window. Something that might go fairly well when we already know
the road ahead but gets extremely difficult when we face the unexpected (Dettling 2012).
This is of course also true for the real estate market, especially when looking at the burst of
the recent real estate bubble in the US.
We presume however, that by capturing important properties and relations of data in the past
we can get a model that yields credible paths of the future. This does not presume that we
know what is going to happen, which is impossible, but gives us a sense of what is possible.
5 Simulation Based Real Options Model 40
We now look at relations that we observe in our data set and implications of this for our
modelling framework.
Correlation & Trends
We see already by eye that rents and prices over all uses rise and fall in positive correlation
during the observation period. We also observe that there seems to be a trend in the evolution
of rents and condominium prices. While the office and commercial market had a very sharp
correction in the early nineties, the decline in housing rents was much lower. We will
therefore expect more volatility in the rents for office and commercial space than for housing
space.
To study the dependence among variables we calculate the linear correlation between the log
returns of the data. Correlation coefficients range between -1 and 1. A value close to 1 or -1
thereby indicates strong positive or negative correlation, while a coefficient close to 0 indicates
no linear correlation. Looking at the correlation coefficients of the data in Table 3, we observe
indeed a positive correlation of around 0.5 between housing, office, commercial rents and
condominium prices. Further we see that the office and commercial rents are indeed very
similar due to their high correlation coefficient of 0.9 and the similar correlation coefficients
also with other time series. While there is small negative correlation of -0.2 between housing
rents and housing vacancies we do not see this for office/commercial rents and
office/commercial vacancies. We further observe negative correlation of -0.5 between housing
rents and cap rates indicating that when cap rates go up, housing rents go down. This
correlation is however less profound for office rents (-0.24) and commercial rents (-0.17).
Table 3 : Correlation Matrix Data Zurich Unterland
Housing
Rents
Office
Rents
Comm.
Rents
Housing
Vacanc.
Office
Vacanc.
Comm.
Vacanc.
Condo.
Prices
Cap
Rates
Housing
Rents
1.00
Office
Rents
0.54 1.00
Comm.
Rents
0.56 0.90 1.00
Housing
Vacanc.
-0.21 -0.64 -0.64 1.00
Office
Vacanc.
0.33 -0.06 -0.08 0.28 1.00
Comm.
Vacanc.
0.33 -0.06 -0.08 0.28 1.00 1.00
Condo.
Prices
0.50 0.43 0.43 -0.26 0.28 0.28 1.00
Cap
Rates
-0.52 -0.24 -0.17 -0.12 -0.10 -0.10 -0.04 1.00
5 Simulation Based Real Options Model 41
Rents & Vacancy
One would expect that when vacancies in a region go up, that rents will start to fall. This is a
question of balancing out supply and demand in the space market where vacancies indicate a
high level of supply that is not absorbed by the market. In order to match supply and demand
we would thus expect a decrease in prices. When looking at Figure 5 and Figure 6, we see by
eye that while office & commercial vacancies went up during the nineties, prices decrease
substantially. Looking at correlation coefficients however, we see only a small negative
correlation between housing rents and housing vacancies and no correlation between office
and commercial rents and office and commercial vacancies. It is however important to note
here that we are currently looking at correlation among log returns at the same time t.
However, there might be a lagged dependence between e.g. office rents and office vacancies
so that rising vacancies have an effect on rents one or two years later. We discuss this further
when modelling our data later on.
Cap Rates
Cap rates went down substantially before the early nineties crisis while rents were rising,
resulting in very high values for real estate. Since 1999 cap rates are falling, which is reflected
in the higher valuation of real estate all over Switzerland.
After discussing the data, let us shortly recapitulate what we did so far and what the next
steps are towards reaching the goal of modelling the risk drivers for the financial analysis of a
real estate development project: In Chapter 5.2.2 on the risk drives, we discussed what we
have to model. We then looked at past data that describes the behaviour of these variables in
Chapter 5.2.3. The next step is to find an appropriate model that we can fit to this data. After
fitting a model to the data, we can then use it to generate simulation of future variables. This
is a necessity to incorporate uncertainty into the “Engineering Approach”.
5.2.4 Modelling
We first introduce a Copula and then a Vector Autoregressive (VAR) model that we fit to the
data. These two models have the property that they take into account interdependence among
the multiple time series, which is something we want to consider when using the model for
simulation later on.
5 Simulation Based Real Options Model 42
We use the following techniques for modelling our risk drivers:
Table 4: Techniques used for Modelling
Risk Driver Method
Rents VAR- & Copula Model
Transaction Prices Condominiums VAR- & Copula Model
Vacancies VAR- & Copula Model
Cap Rate VAR- & Copula Model
Construction Cost Copula Model
Copula Model
In the overview in Chapter 5.2.1 we discuss that by taking log returns we wish to obtain a
stationary process that we can model. Let us assume that this is true and the obtained log
returns are stationary. We then have nine time series of stationary processes that we can fit a
model to. Let us further assume that all these time series follow a normal Gaussian
distribution each with constant mean and variance. We could then estimate mean and
variance based on our data and use random draws from the calibrated Gaussian distributions
to generate simulated returns. These we could use for the simulation of future outcomes.
Now there is a major flaw if we make simulation like this: we neglect an important property
of our data, which is their dependence on each other. We already discussed that for example
housing rents and condominium prices are correlated and thus it would makes sense to take
this into account in our model. Otherwise the simulated time series would behave completely
independent from each other, which will certainly not be very feasible in our case. Copulas are
a way to account for correlation among multiple time series and thus we employ them here.
Definition
Copulas are mathematical tools that are useful for the simulation of linearly correlated data.
They gained large attention and distribution in investment banks and insurance companies
before the latest financial crisis. It was assumed to be possible to price the rather complex
financial derivative class of collateralised debt obligations (CDOs) that were at the core of the
late crisis, with the help of Gaussian copulas (Salmon 2009). In the context of blindly trusting
in financial models, they therefore have some similarity to the Black-Scholes model that is
blamed for the stock market crash in 1987. The reason for their large distribution however is
that they have some very useful properties that we can make use of:
Copulas are joint distribution functions that link a multidimensional distribution to its one
dimensional marginals. These marginals can be made standard uniform, which makes them
5 Simulation Based Real Options Model 43
ideal for further transformation and simulation. Embrechts (2009) explains the basics of
copulas as:
In the one dimensional case we have a random variable X with a continuous cumulative
distribution function F. We have U = F(X) with U as a standard uniform distributed variable
[0,1]. We can also transform this back by applying the inverse cumulative distribution
function: X = F
-1
(U). When we have the multivariate case we can write the joint cumulative
distribution function F( x1 , x2 ) as:
! !
!
! !
!
! !!!
!
!
!
! !
!
!
!
! ")$%'&
With C as our copula: A multivariate distribution function with standard uniform marginals
(U1, U2). Formula (5.11) couples the marginals F1(x1), F2(x2) to the joint cumulative
distribution function F(x1,x2) via the copula. Sklar (1959) showed that there exists a unique
copula for n-dimensional multivariate distribution functions if the marginals are continuous.
Let us now look on the joint realisations as obtained from the two dimensional Gaussian and
t-copula with standard normal marginals as depicted in Figure 12 and Figure 13.
Figure 12: Gaussian Copula with Correlation of 0.7
Source: (Neslehova 2006)
We see that the Gaussian copula indeed produces linearly correlated marginals since
realisations are clustered around a linear slope and not randomly distributed, as seen in the
scatterplot in Figure 12. Now there are also different copulas than the Gaussian that yield
different dependency structures. One of these is for example the t-copula as depicted in
Figure 13:
5 Simulation Based Real Options Model 44
Figure 13: t-Copula with Correlation of 0.7 and 4 df
Source: (Neslehova 2006)
While both copulas have the same correlation coefficient of 0.7, the t-copula yields more
clustering of realisations among the tails compared to the Gaussian copula. We see this, when
we compare e.g. the lower left corner of Figure 13 with the lower left corner of Figure 12.
The t-copula is thus better suited to model dependence among extreme events than the
Gaussian copula. There are however other copulas that take into account the asymmetry in
correlation meaning that while there might be correlation among the right tail of the
distribution, there is little or none on the left tail or vice versa. Modellers have a wide variety
of choices available to choose among copulas and to find one that “best” suits their data. As
Embrechts (2009) points out in this context, there is no obvious answer in the question on
which copula to use. It really depends on the data and the dependence structure one wishes to
model especially in the light of changing circumstances. While one might find a copula (or
more generally a model) that fits the observed dependence perfectly, it remains questionable if
the relations modelled will also hold in the future. If the market circumstances change, as in
the case with the pricing of CDOs using Gaussian copulas, then previous valid models often
become obsolete. This is something we have to be aware of when modelling dependencies.
Application
We use the above result to create joint distribution functions with the dependencies we
specify. The first step is to choose a copula that suits the correlation structure of the data. If
correlations among the tails are observed (tail dependence), then e.g. a t-copula might be
applicable.
In our case we have a data set consisting of 27 data points for every time series. This is not a
large data set for analysing the dependence structure of the data and we have to choose a
5 Simulation Based Real Options Model 45
copula that fits all dependencies. We thus make an estimate on what the dependence
structure could possibly look like. Since we do not have sufficient data to study and model tail
dependence of the variables, we choose the Gaussian copula to describe the dependence
structure of our data.
Once we decide on a copula, we feed it with the dependence structure we found in our data.
This is described by the linear correlation matrix depicted in Table 3. The copula then gives
us the standard uniform marginals with the dependence structure still in place. We can use
these marginals together with a distribution function that fits our data. This is the second
convenient property of the copula: we can choose a distribution function that fits our data and
this for every single time series. Let us look on the descriptive statistics of our data:
Table 5: Descriptive Statistics Log-Returns Data
Housing
Rents
Office
Rents
Comm.
Rents
Housing
Vacanc.
Office
Vacanc.
Comm.
Vacanc.
Cond.
Price
Cap Rates
Mean 0.02 0.02 0.01 0.02 0.04 0.04 0.02 0.00
Std. Dev. 0.04 0.08 0.09 0.38 0.30 0.30 0.04 0.07
Skewness 0.86 0.55 0.50 0.47 -0.29 -0.29 0.09 0.92
Kurtosis 0.66 -0.01 -0.33 -0.62 0.33 0.33 0.51 2.65
In Table 5 we depict the four moments of the risk drivers that describe their distribution. We
see a positive mean for all risk drivers except for cap rates which is zero, meaning that the
average log return of the risk drivers was positive in the past. Further we note that the
vacancies have a high standard deviation of 0.3 indicating that log returns show a wide
distribution of possible outcomes. Further we see skewness in the data. Skewness describes
the asymmetry of the distribution. Thereby a negative value indicates a long left tail of the
probability distribution while a positive value indicates a long right tail of the distribution.
For rents we see positive skewness indicating that rents have a long right tail, while vacancies
have a longer left tail. The kurtosis we see in the last line is shown here as excess kurtosis in
comparison to the standard normal distribution. A positive value depicts higher kurtosis than
the standard normal and a negative depicts lower kurtosis. Kurtosis can be interpreted as the
peakedness of the distribution, meaning the width of the peak. Peakedness comes together
with fat tails, meaning that the tails of the distribution still have a relatively high probability
of occurrence. A high kurtosis indicates a narrow peak with fat tails, while a low kurtosis
indicates a wide peak with thin tails in comparison to the standard normal distribution. Cap
rates have a high kurtosis indicating that the distribution has a narrow peak and fat tails. Now
since we observe skewness and kurtosis in our data it would be elegant to choose a
distribution that can account for this. The normal Gaussian distribution that we use for the
example in the beginning of this section does not serve us well in this case, since it is defined
5 Simulation Based Real Options Model 46
only by mean and variance. Luckily there are many other distributions in the toolbox of a
financial modeller and a commonly used one that accounts for skewness and kurtosis is the
Normal Inverse Gaussian (NIG) distribution. We thus use this distribution, calibrate it over
the mean, variance, skewness and kurtosis from our data depicted in Table 5 and apply it to
the standard uniform marginals obtained from the copula. We thereby create a joint
multivariate distribution with the marginals following the NIG and a dependence structure
still in place as we specified it. We can then use this distribution for simulations just as in the
example in the beginning of this section but this time considering correlation and, due to the
NIG, even skewness and kurtosis of the data.
While this process might seem rather tedious to do, it can be easily implemented in
MATLAB together with the NIG-package by Werner (2006).
Results
We use the described method to simulate 10’000 correlated log returns and obtain the
following descriptive statistics:
Table 6: Simulated vs. Original Data Copula Model
Housing
Rents
Office
Rents
Comm.
Rents
Housing
Vacanc.
Office
Vacanc.
Comm.
Vacanc.
Condo.
Prices
Cap
Rates
Mean
Simulation
0.02 0.02 0.01 0.02 0.04 0.04 0.02 0.00
Mean
Data
0.02 0.02 0.01 0.02 0.04 0.04 0.02 0.00
Std .Dev.
Simulation
0.04 0.08 0.09 0.38 0.30 0.30 0.04 0.07
Std. Dev.
Data
0.04 0.08 0.09 0.38 0.30 0.30 0.04 0.07
Skewness
Simulation
0.80 0.48 0.45 0.43 -0.24 -0.24 0.08 0.87
Skewness
Data
0.86 0.55 0.50 0.47 -0.29 -0.29 0.09 0.92
Kurtosis
Simulation
1.13 0.28 0.32 0.28 0.22 0.22 0.59 2.17
Kurtosis
Data
0.66 -0.01 -0.33 -0.62 0.33 0.33 0.51 2.65
We can already see by eye that mean and standard deviation of the simulated variables are
very much the same for the simulated variables and the original data. For skewness there are
deviation in the region of 0.05 from the original data, which is not very much. Kurtosis on the
other hand seems to be not captured that well by the NIG distribution. There are deviations
from the original data ranging from 0.08 up to 0.9. Apparently the NIG distribution thus did
not work so with the kurtosis of the distribution. Looking at the correlation matrix we see the
following results:
5 Simulation Based Real Options Model 47
Table 7: Correlation Matrix Simulated Log-Returns
Housing
Rents
Office
Rents
Comm.
Rents
Housing
Vacanc.
Office
Vacanc.
Comm.
Vacanc.
Condo.
Prices
Cap
Rates
Housing
Rents
1.00
Office
Rents
0.53 1.00
Comm.
Rents
0.56 0.90 1.00
Housing
Vacancies
-0.21 -0.62 -0.62 1.00
Office
Vacancies
0.33 -0.06 -0.08 0.27 1.00
Comm.
Vacancies
0.33 -0.06 -0.08 0.27 1.00 1.00
Condo.
Prices
0.50 0.43 0.43 -0.26 0.28 0.28 1.00
Cap
Rates
-0.51 -0.23 -0.17 -0.12 -0.10 -0.10 -0.03 1.00
If we compare this correlation matrix to the one in Table 3 on page 40, we see by eye that
they are very similar. Differences range in the region of 0.00 to 0.03, which is very little.
Thus we can assume that our copula model really captures important relations among the
time series and is able to simulate new variables that inherit these dependencies. From the
descriptive statistics we can further assume that except for the tails these simulated variables
also follow a similar distribution as our original data. This is an excellent result so let us use
this model for the simulation of future outcomes of our risk drivers, right?
Not so fast. So far we have only looked at dependence between the different time series at the
same time t, but what about dependence of observations within one time series itself? What
happens if observation rt+1 is dependent on rt? The introduced copula model is only valid if the
observations are independent from each other across time, if there is no dependence between
rt and rt+h for all lags h. We then say that there is no serial correlation and that the
observations within the time series are independent. We check for this by looking at the
autocorrelation and the partial autocorrelation
5
by calculating the correlation coefficient across
time with specific lags. The autocorrelation result for the log returns of housing rents is
depicted in Figure 14:
5
Partial autocorrelation measures remaining dependency after autocorrelation has been accounted for.
5 Simulation Based Real Options Model 48
Figure 14: Autocorrelation Log-Returns Housing Rents
Source: Own illustration
We see significant autocorrelation of 0.8 for a lag of 1 year and of 0.4 for a lag of two years in
the housing rent data. We also have significant autocorrelation for the log returns of the other
time series as depicted in Figure 43 in Appendix I. This speaks against our copula model
because there, we do not take autocorrelation into account. Luckily there is another tool
available that considers autocorrelation and dependence among time series. This is the class of
vector autoregressive models that we introduce next.
Vector Autoregressive Model (VAR)
Definition
Like the copula, a VAR model is a mathematical tool to capture linear interdependencies
among multiple time series. A VAR model explains its evolution based on its own lags and
the lags of the other variables in the model. This makes it a powerful and flexible tool for
modelling multiple time series since the evolution of one time series is also dependent on the
other ones. We further have the advantage to make the model dependent on exogenous
variables. We can then use this exogenous variable in our forecast, adding a deterministic part
to the model. This is of interest to make the model more stable and to analyse different
scenarios. A VAR models takes the form of:
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where yt = (y1t,….,yKt)’ is a ( K × 1 ) random vector, Ai is fixed ( K × K ) coefficient matrix, cEx
= (c1 ,…, ck)’ is a ( K × 1 ) fixed vector of coefficents allowing for the possibility of a
exogenous term with observations yEx,t. et = (e1t, …, eKt)’ is a ( K × 1 ) vector containing error
5 Simulation Based Real Options Model 49
terms with zero mean E(01) = 0, covariance matrix E(21 213) = 42 and no serial correlation E(et
e’t-k) = 0. p is the lag order of the model.
Written in matrix notation a VAR with lag p = 1, VAR(1), and two variables takes the form
of:
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Application
When applying this model to our data then e.g. the condominium log return for a VAR(1) is
determined by:
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with:
H_R : Housing Rents
rCondo,t: log return condominium at time t
aCondo,Condo,t-1 , aCondo,H_R, t-1 : lag coefficients for lag t-1
rCondo,t-1 , rH_R,t-1 : previous log returns at time t-1
aCondo,GDP : coefficient for GDP at time t
rGDP,t : log return GDP at time t
eCondo,t : correlated error term for condominiums at time t
We estimate the coefficients of the model by using ordinary least square method on our data
set of past time series. We chose a lag-2 model over a lag-1 model based on Akaike’s
Information Criterion (AIC), which is a standard tool in statistics for the selection of models.
Further we use real GDP as an exogenous variable for our model. We do this with the
intention of “gluing” the model to a deterministic variable once we use it for forecasting.
Depending on the stability of the model, estimated variables otherwise go quickly out of
bounds of what one would expect to be reasonable. We use the GDP as an exogenous
variable, since it is an indication of the economic activity and we expect this to have an
influence on our risk drivers. The drawback of using the GDP as exogenous variable is that
we have only data from 1990 until 2011. This means that we must use this time span for the
other variables as well. We thus loose 5 years of data in our already small data set, resulting in
21 observations of log returns. Further we cannot use the VAR model for simulations when
two endogenous variables are very similar. The covariance matrix of the error terms then
becomes singular, which is a property that makes it unsuitable for Cholesky decomposition.
Cholesky decomposition is however something we need for simulation. As we discussed
5 Simulation Based Real Options Model 50
earlier, office and commercial rents are very similar or identical in the data set and thus we
have to work with either the time series for office or the one for commercial use. We choose
the time series for office rents and vacancies and will thus assume that commercial rents and
vacancy behave the same as their office use counterparts. Considering that the correlation
coefficient is 0.9 between office and commercial rents and that vacancies are identical in the
data set, we can assume that this simplification does not alter results too much.
Once we have estimated the model, we test the significance of the estimated coefficients by
looking at their p-values. We test the null hypothesis that coefficients are zero using t-
statistics and consider coefficients with a p-value above 0.1 to be non significant. The statistic
programming environment of R together with the “VARS” package by (Pfaff 2008) is used to
estimate the model.
Results
The estimated coefficient matrix is shown below in Table 8. Further results on the estimation
of coefficients are found in Appendix II:
Table 8: Lag Coefficient Matrix A
Condo.
Price
(Condo)
Housing
Rents
(H_R)
Office/Com.
Rents
(O_R)
Housing
Vacancy
(H_V)
Office/Com.
Vacancy
(O_V)
Cap Rate
(CAP)
Condo.l1 - - - - - -
Condo.l2 0.41 - - -5.07 - 0.43
H_R.l1 1.47 0.92 - 13.75 - -1.83
H_R.l2 -0.50 -0.26 - - 3.80 1.52
O_R.l1 - - -0.44 - - -
O_R.l2 0.49 - - - 5.80 -
H_V.l1 - -0.03 -0.09 - 0.36 -
H_V.l2 - - -0.08 0.36 - -
O_V.l1 - - - 0.56 - -0.04
O_V.l2 - - - 0.70 - -0.06
CAP.l1 0.74 - -0.72 - 5.45 0.50
CAP.l2 - - 0.58 5.01 - -
GDP 0.74 0.35 0.95 - - -0.38
The columns depict the estimated coefficients for one risk driver. So we see that e.g. housing
rents depend on the lagged log returns of themselves (H_R.l1 and H_R.l2) on lagged housing
vacancy (H_V.l1) and on GDP. GDP has a significant positive influence on rents and
condominium prices and a negative influence on cap rates. That means that when the GDP
log return is positive, this has a positive influence on rent log returns and a negative one on
cap rates. We do however not see an influence of current GDP on vacancy. We did however
not test for the influence of lagged GDP on current vacancy, since we could not implement
5 Simulation Based Real Options Model 51
this into the model with the used statistical package. However, this surely would be an
interesting aspect to look at in further research.
By looking at Table 8 we also see some lagged variables that have an extremely large influence
on current returns. This is foremost the case for the estimation of vacancies e.g. for lag 1
housing rent (H_R.l1) on housing vacancy (H_V) the estimated coefficient is 13.8. Such
large variables do not speak for the adequacy of the model to use it for forecasting since
already small errors in the estimation of e.g. housing rents have a very strong influence on
housing vacancy one time step ahead. Also we have some dependencies we would not expect
to be so strong such as the negative influence of lag 2 condominium returns (Condo.l2)
(aH_V,Condo.l2=-5.07) on current housing vacancies. One can hardly think of a rational
explanation of why the return in condominium prices should influence housing vacancies that
much two years later. We could correct for this by setting the corresponding coefficient to
zero but then again this might not be adequate, since statistically there is an influence. Also
setting a significant coefficient to zero leads to a chain reaction in the whole model since it is
set up in way that everything is interdependent. As we will see when applying the model for
forecasting, it is one thing to estimate a model that fits the data well and quite something else
to create a model that is “realistic” in the sense of generating credible results.
We illustrate this in the next section, where we use the estimated model for the simulation of
future scenarios.
5.2.5 Simulation of Future Scenarios
After fitting a model to our data we now use it for the simulation of scenarios. We can easily
generate thousands of scenarios and analyse how the real estate development project performs
under these. Assuming that the estimated dependency structure depicted in the model holds
also in the future, we should be able to generate credible results. However, this assumption
might not hold, since dependence among variables does not necessarily remain constant.
Future events might alter the dependency among the variables, leaving our model invalid.
This leads to the fact that our simulations will always include quite some inaccuracy and be a
good deal away from accurate forecasts or even predictions. It is our intention, however, to
estimate the range of possible outcomes and then to identify and quantify valuable options
under these outcomes. It is thus not necessary to have a perfect, crystal ball like model for
forecasting, which is impossible anyway. The model should help to be prepared for the
uncertainty lying ahead and make the flexibility we have in dealing with it more tangible.
Simulations with a VAR Model in Excel
5 Simulation Based Real Options Model 52
We use Excel to generate simulations of scenarios and to analyse them. This is convenient for
the practitioner, since he can thus implement the simulation mechanism directly as an add-on
to existing project calculations. The first step however, is to do simulations of the risk drivers
and analyse, if these results are credible and thus, if they should be used in conjunction with
the development project calculations.
The input of the VAR model is according to (5.13) a vector of correlated error terms. In our
case we have six error terms at time t, one for every variable: et = (et,Condo, et,H_R,..., et,CAP). For
simulations we assume these error terms to follow a normal distribution with zero mean,
variance and correlation among these error terms being the same as the error terms from the
estimated model. We call this a noise process and generate it in Excel using the implemented
NORMSINV() and RAND() function. The NORMSINV() is the inverse of the standard
normal Gaussian cumulative distribution function where we can add variance later on. We
generate new independent error terms following a standard normal distribution by using X =
F
-1
(U), with F
-1
() as the inverse cumulative distribution function and U[0,1] generated by
RAND(). We generate multiple error terms by using “Data Tables” in Excel that allow for
the storage of simulation results. Correlation among the error terms and variance is taken into
account by using the Cholesky decomposition on the covariance matrix of error terms from
the model estimation and multiplying the decomposed lower triangular matrix with the
uncorrelated error terms. As the copula, this is a method to account for correlation among
multiple time series. The result is the desired vector of correlated error terms, in our case et =
(et,Condo, et,H_R,..., et,CAP), that is used together with the lag coefficient matrix A in Table 8 and
the last two log returns of the data set (rt-1, rt-2) to generate simulations. For every time step
ahead we get a set of randomly generated log returns following the properties of our model.
Now to see the evolution of the future scenarios, we apply the simulated log returns to the last
observations of our data set using (5.3): !
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, for t = 1, 2, … n with n as the desired
simulation horizon.
We simulate 2000 times a simulation horizon of 10 years, assuming a deterministic constant
growth in GDP of 2%. Simulations yielded the following results:
5 Simulation Based Real Options Model 53
Figure 15: Simulation of Condominiums with a VAR(2) Model
Source: Own illustration
We see a strong upward slope in condominium prices estimated by the model with an average
price 45% higher after five years and almost doubled after ten years. The 90% confidence
interval depicted by the 95
th
percentile (upper red curve) and 5
th
percentile (lower red curve)
indicate a high upward potential while the possibility to fall below the start price is very low.
Figure 16: Simulation of Housing Rents with a VAR(2) Model
Source: Own illustration
Housing rents remain in a smaller confidence interval than the condominium prices and
increase on average 14% compared to the start value. The 90% confidence interval has an
upper bound of +36% and a lower bound of -7% after 10 years.
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