Case Study on Tenge Oil Tango

Description
An oil is any neutral, nonpolar chemical substance, that is a viscous liquid at ambient temperatures, and is immiscible with water but soluble in alcohols or ethers. Oils have a high carbon and hydrogen content and are usually flammable and slippery. Oils may be animal, vegetable, or petrochemical in origin, and may be volatile or non-volatile.

Case Study on Tenge Oil Tango

CONTENTS



1 introduction

2 history and context

3 literature review

4 data sources and properties

5 structural and empirical models

6 results and conclusions

references

appendix



TABLES and FIGURES





1


4


8


18


23


34


42


44


figure 3.1
figure 3.2
figure 3.3
table 4.1
table 4.2
table 4.3
figure 4.1
table 5.1
table 5.2
table 6.1
table 6.2
table 6.3
figure 6.1
table 6.4
table A


portfolio composition as rational consumer choice part 1
portfolio composition as rational consumer choice part 2
spot to futures price convergence
unit root tests with trend and intercept
unit root tests with intercept only
second unit root tests with trend and intercept
price series over the sample period
cointegration tests
specification and residuals tests
static hedge ratio estimates and performance
rolling estimation performance
static hedge ratio estimates and performance post break
time structure of conditional correlation
GARCH estimates and hedging performance
rolling hedge ratio estimates


9
10
12
19
20
21
22
29
33
34
35
35
37
38
44
1 INTRODUCTION


Since its independence signalled the final dissolution of the Soviet Union in
December 1991, the Republic of Kazakhstan has made a cossack pursuit of economic
liberalisation, with a succession of quick, but well advised, shifts towards its now
notably market based economy
1
. Not least amongst these were the managed
2
float of
the Kazakhstani tenge ( ? ) on 5
th
April 1999, the simultaneous relaxation of trade
barriers, and the vast pensions overhaul detailed in chapter two. Another motivator to
the float, besides the demands on currency reserves of a fixed regime, was the
looming contagion of the Russian financial crisis, which Kazakhstan had successfully
fended off since the previous August but which had all but eliminated demand for the
country's metals - their second great export sector after oil, itself suffering from low
world prices. But, as a major food and goods exporter to its smaller Central Asian
neighbours and to many eastern bloc countries, this freeing of the central bank's hand
brought with it the typical side effect of exposing Kazakhstani international trade and
investment to currency risks. Beyond these risks' effect on Central Asian poverty, an
International Monetary Fund (Palmer, 2004) report on the state of cumulative fund
pension schemes in Kazakhstan made clear that institutional investors, starved of
domestic equity opportunities and heavily invested abroad, were woefully un-
insulated against exchange rate shifts. Despite the existence of a domestic dollar
futures market on the Kazakhstan Stock Exchange
3
, the report
4
labels this far too thin
to allow for effective hedging of the some 45% of institutional investors' assets
denominated in (or linked to) dollars. Kazakhstani institutional investors are therefore
in dire need of alternative instruments with which to cross hedge tenge exchange risks
and this paper sets out to assess the potential for such a hedge based on more heavily
traded futures.


By definition cross hedges are based on assets different to the cash position they are
applied to, but some relationship must exist so that swings in the value of the spot can
be offset by associated swings in the hedging instrument's value. Indeed, without
theoretical justification for such a relationship, past successes of a hedging instrument
cannot be assumed to carry on into the future. Thus, following their preliminary
investigation into commodity/currency cross hedging - one of the earliest conducted -
Eaker and Grant (1987) highlight that "there is a need to identify those economic
factors which make a particular commodity a likely candidate to match a particular

1

2

IMF Country Report No. 04/337 and details in chapter 2
Formal inflation targeting is not in place, but government intervention until October 2007 has been
described by all sources as minimal
3
Sadly price series for these futures are not available, making consideration of their potential hedging
performance impossible.
4
IMF Country Report No. 04/337


1
HEDGING TENGE with OIL FUTURES


currency". As if in answer, Chen and Rogoff (2002) propose that, particularly for
developing countries, the major determinant of exchange rate fluctuations -
specifically those volatile but persistent shocks that seemingly contradict Purchasing
Power Parity and other traditional monetary models - might be price changes for a
primary export commodity
5
, or several such, on a country's terms of trade. It is in light of
these observations and the predominance of oil (70%) among Kazakhstan's exports that
it seems justified to examine commodity based cross hedging for the Tenge.


Benet (1990) finds evidence that a fairly random selection of commodity futures
match a basket of currency futures as a hedge of exchange rate risk. International
Financial Series data shows that Kazakhstan's foreign trade is well spread between
European countries, for which liquid futures markets exist, and FSU/Middle eastern
states, for which they do not, presenting an obstacle against using a currency to
currency cross hedge, which further promotes a commodity to currency hedge.


The work of Johnson (1960) suggests that hedgers will choose a proportion of hedged
to unhedged assets within their position, so as to reduce uncertainty on the return it
will yield - by a proportion consistent with their risk to return preferences. In a cross
hedge there is no reason to believe that changes in the value of a unit of the spot asset
should coincide with equal changes to a single futures contract's price, and so the
number of contracts needed for each cash asset to provide a desirable return is by no
means clear. In the literature (eg Stein, 1961) this proportion is embodied in the hedge
ratio. The arsenal of methods for determining such hedge ratios is extensive, with
each derived from the optimisation of one specific objective function (Lien and Tse,
2002; Chen, Lee and Shrestha, 2002). The most popular is inarguably the Ederington
Minimum Variance hedge ratio, deployed among many others by Benet (1990) and
Kroner and Sultan (1993) - on whose work I shall base a large part of my study. As
the name would suggest the MV hedge ratio produces a portfolio with minimal
volatility, and it is estimated most simply by choosing the ratio that minimises the
variance for an observed sample of cash and futures prices. Both the MV and its
analogue for commoving processes - sometimes called the Error Correction Model
Ratio - suffer from the criticism that their focus on volatility neglects to consider the
actual returns expected on a portfolio - as Johnson (1960) and the mean-variance
framework would demand. An answer to this criticism are the optimum mean-
variance and Sharpe ratios, the former of which allows for an (admittedly subjective)
risk aversion parameter to tailor the balance of variance reduction and speculative
return, and the latter maximising expected return relative to risk (Chen, Lee and
Shrestha, 2002). Nevertheless, I employ the MV/ECM ratio as a general test of risk



5



To borrow a term from Benet's (1990) informal attempt at a link






2
HEDGING TENGE with OIL FUTURES


reduction capacity, and find no reason to investigate further with more realistic hedge
ratios - to give a hint of my results.


The estimation method just described for the MV ratio quite obviously assumes that
the hedging period shares the same variance minimising futures position as the
estimation sample. To escape this assumption, at the penalty of statistical complexity
here and transaction costs in practice, I also explore dynamic estimations of the
minimum variance hedge ratio that allow the futures position to change over time with
the relationship linking cash and futures prices. The first of these is little more than a
continually updating extension of the static method (Sercu and Wu, 1999), but I follow
this with a more sophisticated GARCH procedure, advocated by Kroner and Sultan
(1993) and Chakraborty and Barkoulas (1999), which reflects widely held beliefs on
the nature of exchange rate and oil futures price behaviour.


In contrast to much of the early literature on cross hedging, but in line with Benet
(1990), the more subjective ex ante, or out of sample, assessment of each ratio's
performance is used alongside the objective ex post, or in sample appraisal. While the
latter is a fair indication of the "relatedness" of cash and futures assets and the futures'
potential to achieve a specific objective function, it is meaningless to actual hedgers,
who will select instruments based on their expected performance against future rate
shifts. The former measure imitates the real world dilemma for a hedger: predicting
the best position to take for the future, based only on currently available information.


This paper is divided into six chapters: The next provides some background
information on Kazakhstan, its currency, and oil, while expanding on the justification
for exchange rate hedging in institutional investors' dollar exposure. Chapter three is a
literature review. Chapters four and five detail the data used and the models tested
respectively. Chapter six presents the results of the investigation and draws
conclusions.



















3
2 HISTORY and CONTEXT


The reader could be forgiven for being unfamiliar with the recent - or otherwise -
history of Kazakhstan, and for bearing some scepticism on its worthiness as a topic of
study. Indeed, the world's ninth largest country spent most of the last fifty years
hidden between curtain and veil. However, with the recent economic changes coming
over Russia and China, and the political re-alignment of Afghanistan and Pakistan, the
substantial proven oil and gas reserves at Tengiz - along with a potentially massive
reserve under the northern Caspian - have brought the country back to the Western
conscious. In fact Kazakhstan is expected to become one of the word's top 10 oil
producers over the next two decades - though its long term proven reserves mean this
position will not be sustained indefinitely (Najman, Pomfret, Raballand and Sourdin,
2006). From a global perspective, Kazakhstan is also critical to regional welfare as a
dominant goods and food supplier to the neighbouring fledgling republics of
Kyrgyzstan, Tajikistan, Turkmenistan, and Uzbekistan.


Having been a Russian possession since the time of the great game, Kazakhstan had
built up, particularly during the soviet era, a sizable ethnic Russian population.
Following the declaration of independence in December 1991, repatriation of these
ethnic Russians led to a fall in the population from around 17 million to roughly 15
million
6
, leaving the Russian and Kazakh populations better balanced, but the demand
collapsed (along with that from Russia) and the economy initially contracted (Lloyd et
al, 1994). The dominance of primary commodities now among its exports might give
the illusion that the country's economy had regressed to being extraction based, but
this is not the case: The general population has always been well educated - though
the advent of Kazakhstani students in western universities is only a recent trend,
thanks to recent legislation making study abroad a viable option - and a healthy
services sector makes up some 50%
7
of economic activity. Thanks to soaring oil and
metals prices, the recession of the 90s gave way to growth of around 10% per year so
far this decade.



PENSIONS in KAZAKHSTAN

During all this turmoil and leading into the economic boom, the floating of the Tenge
was by no means the only of Kazakhstan's major shifts away from a centrally planned
economy: The government made it clear that they would pursue a capitalist growth
model, and exemplifying this transition were the 1998 reforms of national pension

6
7

CIA World Factbook: 15,340,533 (July 2008 est.)
CIA World Factbook: 49.8% (2005)





4
HEDGING TENGE with OIL FUTURES


provisions. Public expectations of financial support in old age, a legacy of the soviet
era
8
, made an effective pensions system an essential development to satisfy demand
while relieving the massive strain on current resources. The scheme inherited from the
Former Soviet Union, which prevailed until 1997, awarded a standard fixed
component supplemented by a variable element based on "years of service" - and the
nature of that service - and clearly did not comply with the country's sworn new
capitalist principals. Moreover, the pre-1998 system was plagued by inefficiency in
collection with planned inter-raion
9
payments often neglected by the local collection
administrations, motivated only to collect enough for their local liabilities. When this
pay-as-you-go system was finally itself retired in 1998 a new Defined Financial
Contribution scheme was implemented, combined with a transition version of the pay-
as-you-go for existing claimants. Both new systems sought to address the issue of "fair"
distribution of pension funds, by making payments according to wage, and hence
contribution
10
as in the DFC system this is a fixed 10% of an individual's salary.
Workers under the DFC scheme can choose between a default state administered
fund, and fifteen private accumulation pension funds, but the (declining) majority still
choose the former.


Despite the startling efficiency with which the new pensions system was brought into
operation, with overhauled collection and distribution via banks (unheard of in other
former soviet states), the institutional investors of Kazakhstan were still limited by
one important factor, namely the lack of domestic opportunities for the investment of
their funds - a sad state of affairs when Levine and Zervos (1996) suggest a major
contribution by financial markets' development to growth. Kazakhstan's stock market
KASE has existed (under various names) since 1993 in but according to the IMF
(Palmer, 2004):


"Despite its name, the Kazakhstan Stock Exchange (KASE) remains primarily an
organized place for trade in government securities..."

Whereas individuals may tie their accumulated capital into small scale private
investment projects, this is not an option for a large scale institution, and so the
pension funds - state and private - have been forced to invest abroad in order to
achieve their target 5% real returns
11
. Indeed, in 2004 some 40% of the funds' assets
were denominated in dollars, while 85% of tenge denominated corporate bonds were

8
For workers in dangerous or otherwise undesirable working conditions, retirement was sometimes
possible as young as 40. While in 1996 over 32 percent of old age pensioners were younger than 60.
(Palmer, 2004)
9
A Raion is the local administrative unit of the republic of Kazakhstan, with Oblasts the regional
division.
10
Though the special privilege of early retirement remains available to workers in hazardous
enbironments.
11
IMF Country Report No. 04/337 (2004)


5
HEDGING TENGE with OIL FUTURES


dollar linked; which should hopefully be evidence enough of Kazakhstani pension
holder's commitment to foreign assets.


Both the Capital Asset and Arbitrage Pricing Models suggest that there should be no
incentive to risk elimination through hedging, either because diversifiable risk should
be eliminated by holding a suitably mixed portfolio, or because non-diversifiable risk
should award a premium on expected returns (Eaker and Grant, 1987). However,
amendments to this theory, based around variable cash flows' effects on agents'
decisions through the threat of financial distress, can be used to justify hedging
behaviour in developed economies - indeed one of the earliest models of hedging, that
of Telser (1955), was geared around financial distress. For pension funds in general,
financial distress occurs when the portfolio of assets falls into deficit relative to the
fund's liabilities to those drawing their pensions. With so many of their assets
denominated in dollars (and liabilities denominated in tenge) the volatility of
exchange rates clearly represents a major threat of deficit to Kazakhstani pension
funds, and so it is of great interest to find a cost effective method of currency risk
reduction.


Despite this incentive, the lack of domestic investment opportunities in Kazakhstan is
sadly mirrored by a lack of risk management professionals. In the entire country there
are only fifty chartered actuaries (compare this to the 15700 charted in the UK), to
perform all those risk management functions required by the sixteen funds, as well as
government and corporate entities. Under this evidence, and the IMF's emphasis of
need for better risk management, it seems fair to consider risk management in general
underdeveloped in Kazakhstan, and any research likely to improve the situation well
justified.


In so far as the liabilities faced by the pension funds are concerned; enough arable
land lies within Kazakhstan's borders, and enough soviet industry was based there
(and retained by the republic), for it to remain relatively self sufficient. Nevertheless,
the some 50% of Kazakhstani GNI spent on imports is dominated by Russia (40% of
imports), and more recently China (10%) (IMF IFS). Whether these figures translate
into making hedges of the ruble- and yuan- dollar exchange rates more pressing
concerns for consumers is a matter for further investigation, but when the tenge has
been pegged it has been to the dollar which would suggest that goods prices are not
dictated by Russia and China - hence a hedge of the dollar rate to either currency
would not suffice to cover liabilities.



OIL in KAZAKHSTAN



6
HEDGING TENGE with OIL FUTURES



Oil production in Kazakhstan dates back to the first half of the twentieth century but
even though these stocks were increasingly tapped during the 1970s and 1980s
agricultural produce remained the country's principal export throughout the soviet era
(Pomfret, 1995). With the 1990s and independence came the interest of the global oil
market, such as Chevron's buying into the project soon to be known as
TengizChevroil . However, the 90s oil boom that could have been was delayed a
decade by the inevitable maritime border disagreements that followed the break up of
the USSR, and bureaucratic mechanisms hung over from that former era. It was
therefore hand in hand with the economic reforms alluded to above that Kazakhstan's oil
industry took off, with the period of greatest growth (around 14% p.a.) starting in
1999 (Najman, Pomfret, Raballand, Sourdin, 2005).


Because of its landlocked nature, the principal obstacle to the Kazakhstani oil industry
has always be transportation. Until the inauguration of the Caspian Pipeline
Consortium's line in Autumn 2001, pipes out of Kazakhstan were monopolised by
Russia and exporters had at times been confronted with highly constraining practices
by the transport giant Transneft. Recently competition between the (still part Russian)
CPC and the western developed Baku-Tbilisi-Ceyhan has further alleviated
monopolistic activities for the Caspian shore fields. Such practices do still continue to
limit the expansion of central Kazakhstani fields, but competition is likely to improve
further over the coming decade with recent Chinese ownership of fields heralding
projects to pipe oil east through Xinjiang (Najman, Pomfret, Raballand, Sourdin,
2005).


The largest and best known of the country's oil fields is Tengiz on the north eastern
shores of the Caspian sea, but since its discovery in 1979 other major sites have been
found further inland at Kumkol and Uzen. The greatest future prospect though, and
the source of aforementioned border disputes, is the Kashagan field found under the
northern Caspian in 2000, holding an estimated 45 billion barrels of oil (Najman,
Pomfret, Raballand, Sourdin, 2005).


With no immediate limits on Kazakhstan's oil production, or any sign that world oil
prices will collapse it seems likely that the country will continue to reap massive
energy revenues, and until better financial infrastructure is in place this will mean
increasing foreign investment and increasing exposure to currency risks.









7
3 LITERATURE REVIEW

In talking of Kazakhstani institutional investors seeking to eliminate currency risk, I
may have suggested a very narrow view of hedging. In fact, where the IMF's reports
have highlighted currency risks, the call is for better risk management - taking a
position which better represents the risk to return preference of pension holders - not
necessarily risk elimination. The traditional view of hedging
12
was indeed of a world
with distinct hedgers and speculators; unsophisticated hedgers hoping to pass off the
entire risk of a position they were forced to hold, and sophisticated speculators willing
to take on that risk in exchange for an expected profit
13
. This position of the theorists
was challenged in the 1950s by Holbrook Working (1953, 1962), who was then the
Stanford Professor of Prices and Statistics but was familiar with actual market
practices from his role as associate director of the Food Research Institute. Working's
great offensive came in a 1953 article in the American Economic Review: Through
interviews with members of the grain industry, he revealed that many of those with
positions in both the spot and futures markets, who would usually have been called
hedgers, were altering their spot positions, according to their expectations for
upcoming relative price changes, to earn returns and thereby taking speculative risks.
He continued to term these market participants hedgers, and called for an expansion
of the theory to allow for other behaviours, besides risk elimination, which he
considered dominant among actual hedgers. Intuition should have been enough to
justify taking Working seriously, as large specialised goods procurers could hardly be
expected to be wholly ignorant of their market's behaviours, or willing to take a
backseat while pure speculators reaped higher expected returns.


Johnson (1960) took up the challenge but, after his own surveys of New York Coffee
hedgers, sought to moderate Working's position to one where risk reduction remained
the primary, but not sole, motivation for taking positions in both markets - and where
actual, rather than only relative, expected price changes are the driver for speculation.
His insight was that the hedger and speculator of traditional theory were in fact polar
extremes on a scale of market participants, all placing different values on relative
certainty, and therefore choosing a different combination of expected return and
uncertainty through different portfolios of hedged and unhedged cash positions.
Through a model based around individuals' risk-return utility functions, he laid the
foundations for the modern portfolio theory treatment of hedging: Hedge ratios - the



12
13



See for instance Hawtrey 1940 (Johnson, 1960)
Certainly, if a higher expected return for speculators was not originally part of the conceived
structure, then it was introduced with Tobin's Theory of liquidity preference and Keynes' Treatise on
money. That said, Working's description of markets viewed as speculators' playgrounds only would
suggest risk loving as the conceived drive for speculation.


8
HEDGING TENGE with OIL FUTURES


value of the hedging instrument adopted as a proportion of the cash position -
minimising risk for a given expected return.


Despite his merging of hedging and speculation, Johnson's model provides an
analytical solution - through a derivation similar to that coming below - for a pure
hedger only. The underlying consumer choice style model does, however, extend to
speculation when the expected return for either the spot or the futures is non-zero. In
that model the hedging decision revolves around two optimisation problems,
illustrated by the diagrams below;



Futures /$ E(R) = r
E(R) = 2r
E(R) = 3r


Cash /$




Var(R) = o
2
Min [ Var(R)/E(R) ]


Var(R) = 4o
2


Var(R) = 9o
2

Fig. 3.1


This first diagram (fig.3.1) shows the plane of combinations between the spot
(assumed to always be long, as per older hedging theory) and a single hedging
instrument (long or short). Here the points of tangency between elliptic iso-variance
sets and linear iso-expected return sets represent the locus of combinations between
cash and futures that minimise risk for a given expected return.


















9
HEDGING TENGE with OIL FUTURES



o(R) /$


Min [ Var(R)/E(R) ]



Utility = u


Utility = 2u







E(R) /$








Fig. 3.2








This second diagram (fig. 3.2) shows the plane of all possible combinations between
expected return and variance. Mapped onto this we have indifference curves dictated
by our agent's risk-return utility function, along with the set of pairs derived in the
first diagram. Now the point of tangency between indifference curve and minimum
variance set gives the agent's optimal choice of expected return and variance,
translating back to their optimal portfolio of cash and futures in the former diagram.


There is one quite obvious flaw to Johnson's treatment, in that he takes the variance of
return as proxy for all the risk a portfolio represents to its holder. Telser (1955)
concurrently - albeit independently of Working's challenge - developed a
portfoliobased theory of hedging, but based his framework around the avoidance of
a "disaster" return threshold - more realistically mirroring the financial distress
justifications of hedging. Through the Tchebycheff inequality he shows variance
minimisation to be sufficient for the avoidance of such a threshold and this broadens
work based on Johnson to cover a more general market participant
14
. Nonetheless,
minimising variance relative to expected returns, or simply minimising variance for a
pure hedge, assumes that the risk-return utility function of the agent in question is
quadratic - that their perception of risk is limited to the second moment of the
portfolio return's distribution only - or that portfolio returns have a symmetric

14

Though the inequality means there might be a portfolio with higher expected return which also
avoids disaster


10
HEDGING TENGE with OIL FUTURES


distribution (with Gaussian tails). This flaw was in fact not addressed until relatively
recently, with the advent of more sophisticated objective functions, like the maximum
utility and minimum semi-variance conditions (Chen, Lee and Shrestha, 2002).


Returning briefly to Working's (1953) work, there are two other points of note:
Despite their long history, Working describes some confusion prior to the 1950s as to
the primary function of futures markets. Prior to statistical treatment, it seems that
they were viewed largely as vehicles for speculation, with hedging a minor ancillary
role
15
. However, Working presents (somewhat speculative) evidence suggesting that
the activity of futures markets is driven by those with a position in the underlying
cash market. Speculation's role is deemed less significant for volume but of course
very necessary for the existence of hedging, which the author gives as one reason for
the existence of a few broad markets restricted to a single grade for most commodities -
rather than many thin markets tailored to specific grades of produce. The second
point, and another reason for the broad few, comes from the author's direct
investigation of whether hedging Pacific North Western wheat with Chicago futures
held any advantage over futures on the thinner Seattle Market. The results indicated
that hedging for risk reduction with more liquid but less correlated futures was
".comparable with insurance that covers losses above some stated minimum", which
would be more desirable to those with concave risk aversion. If true, this point could
prove reassuring for my own study as it suggests that near-perfect parallel movement
of spot and futures prices is not necessary to ensure a desirable hedge.


Though it was Johnson who provided an analytic solution to a "risk" minimising
balance of futures to cash, and also an in sample measure of hedging effectiveness,
Ederington (1979) is often credited with the so called Minimum Variance hedge ratio -
or even the Ederington Minimum Variance ratio, as it is sometimes called.
Ederington's great contribution is in fact in his application of that ratio and measure to
time series data for several simple hedges, where futures exist for the specific cash
position and are used as the hedging instrument. It is quite intuitive that as a futures
contract nears its expiration date, and comes closer to being a contract for immediate
delivery, its value should grow to be equal to that of a spot position, while similarly
fluctuations in its value should grow to match the spot's volatility. This intuition
(illustrated in fig.3 below) has the obvious result for hedging that futures with more
immediate delivery dates should serve as better hedges, and this is confirmed by
Ederington's results, which show improved (in sample) risk elimination for "nearby
contracts" over "distant contracts" with longer times to expiry. The implication for my
study is that the obvious choices of hedging instrument, particularly when the


15


This would indeed be consistent with the "casino hypothesis" described by Fry (1988, p23) as
prevalent for much of the early 20
th
century


11
HEDGING TENGE with OIL FUTURES


termination date of the hedge is uncertain, are those futures which are closest to
expiry - often called "the nearby".



Price /$



Futures price





Spot price




Expiry


Time /days Fig. 3.3


Not until Anderson's and Danthine's (1981) work is an analytic solution derived for a
hedge ratio which considers expected returns, as the portfolio based theory
acknowledged by Johnson and Ederington would demand. Naturally an optimum
hedge ratio must be the result of an optimisation problem, and so the authors' critical
step is to introduce an objective function incorporating returns. However, here there
necessarily enters some subjectivity into the problem, as the portfolio theory of
hedging suggests agents adopt positions in both markets according to their individual
risk-return preferences. The hedger's preference is introduced by Anderson and
Danthine through a coefficient of risk aversion, _, in the objective function below:


E(t
~
) ÷
1
_ var(t
~
)
2
t~ = ~
1
y ÷ p
0
y ÷ ( ~1
f
÷ p
0
f
) f
p p

where y is the number of units of the cash asset held, f the corresponding (vector of)
number(s) of futures contracts, p
t
is the price of once unit of the spot at time t, p
t
f
is
the (vector of) futures price(s) at the same instant, and
~
denotes a random variable
16
.


Maximisation of this objective function yields the following optimal futures position
17



16



Those parenthetical arguments reflect the situation of a composite hedge, allowed for by Anderson
and Danthine in their model.
17
In the case of hedging with a single instrument.


12
HEDGING TENGE with OIL FUTURES


p pp
f=
1 p
0f
÷ E( ~1
f
) + y cov(~1
f
, ~
1
)
_ var( p ~1
f
) var( ~1
f
) p

This expression can be broken down, with the second term representing the variance
minimising position, identical to those derived by Johnson (1960) and Ederington
(1979), and the first representing the adjustment to this position necessary to provide
the preferred expected return. The astute observer might recognise the coefficient of y
in the second term as the expression for a linear estimator according to least squares
regression, and indeed one of the reasons that the speculative term is often ignored in
empirical studies is that the risk minimising term can be easily computed and its
effectiveness measured according to the vast and well recognised OLS framework.


The earliest review of the effectiveness of hedging exchange rate risk with commodity
futures comes in Eaker and Grant's (1987) "Cross hedging foreign currency risk".
Though commodity cross hedging is admittedly an afterthought, the emphasis of their
work being on using other currencies' futures for the hedge, the mechanics of cross
hedging with any futures are largely the same - indeed they are almost identical to
hedging with the spot asset's own futures - and their methodology is therefore of great
interest to my study. Moreover, cross hedging with other currencies' futures could be
seen as the principal alternative to commodity-currency cross hedging and its relative
performance will have no small bearing on the interpretation of my results.


The authors choose to look only at the pure hedging potential of the commodity
futures and consider only the variance minimising part of Anderson and Danthine's
decomposition, which is to say that they employ the minimum variance hedge ratio.
Of course by effectively choosing an objective function which ignores expected
portfolio return, the authors leave their results inconsistent with the portfolio theory of
hedging, and incomplete as a measure of practical hedging potential. An innovation
on previous work, however, is Eaker's and Grant's testing of hedging effectiveness ex ante,
or out of sample, by applying the hedge ratio computed for the first half of the sample
to the remaining period.


The first US dollar exchange rates to be considered are those for sterling, the
Canadian dollar, and the yen. As currencies with futures markets, the authors are able
to compare the risk reduction between periods achieved through simple and cross
hedges. They find that, both ex post and ex ante, simple
18
hedges provide excellent
risk reduction for all three currencies - as one would expect from theory - while
currency-currency cross hedges perform at best moderately, and at worst
detrimentally. The results for composite hedges suggest that, with futures available in

18
The risk reduction is not perfect because the maturity of the instruments does not match that of the
cash positions, making for basis risk


13
HEDGING TENGE with OIL FUTURES


the spot currency, cross hedging with other currencies' futures can only worsen out of
sample risk reduction. Meanwhile, the opposite is implied when the spot's own
futures are not used, with multiple cross hedging instruments generally outperforming
one alone.


The authors acknowledge that testing cross hedging where a simple hedge is available is
artificial and go on to test the effectiveness of the same futures, plus those for the
Deutschemark, as hedging instruments for the Italian lira, Spanish peseta, Greek
drachma, and the South African rand. This is more relevant to my own study than the
first (control) group, as Tenge futures are not available in the volumes needed for a
simple hedge. Consistently for the three European spots it is seen that the best hedges
consist of (ideally multiple) European futures, and that useful risk reduction is
achieved. The rand denominated cash position, however, benefits from nothing but a
sterling-yen composite cross hedge. The authors describe these findings as consistent
with the intuition that the economic significance of the hedging instrument's economy to
the spot's economy is the crucial factor in the effectiveness of a currency-currency cross
hedge.


Finally, and most relevant to this paper, the authors follow a similar procedure testing
the risk reduction for cash positions in every currency using gold futures. The authors
cite gold's role as a "currency substitute", and its intuitive importance to the rand, as
justifications for its use, but the results are far more conclusive than these arguments.
Gold is overwhelmingly rejected as a hedging instrument; increasing the risk for cash
positions in seven of the nine currencies examined, and showing uselessly slim risk
reduction for even the rand. This would indeed be discouraging for hopes of a
commodity hedge of the tenge, were it not for work such as that of Cashin, Cespedes,
and Sahay (2000) which suggests that the South African real exchange rate is in fact
tied to other commodities, and that gold is generally uncorrelated with its producer's
currencies. Meanwhile, it should be considered that the most heavily traded currency
futures cannot be expected to share the same relationship to the tenge as European
currencies do to one another, making a currency-currency cross hedge a less viable
option in my case.


Another limitation to their research, acknowledged by Eaker and Grant, is that they
make little attempt at formal theoretical justification for the relative quality of
different hedges. For currency-currency hedges, more recent work may use no-
arbitrage conditions to justify a link, while for commodity currency hedges this detail
is improved upon to a degree by Benet (1990) and can be fleshed out further for LDC
economies, as Bowman (forthcoming) does, with Chen's and Rogoff's (2002)
extension of the Balassa-Samuelson model.



14
HEDGING TENGE with OIL FUTURES



Where for Eaker and Grant commodity-currency cross hedging was a curiosity, for
Bruce A Benet (1990) it is in itself the focus of his study, and where the former
authors tested for the trivial case of developed economies, Benet investigates those
minor currencies where a commodity futures based hedge might fill the breach of no
currency futures. As mentioned, he also attempts to provide theoretical justification
for a link between "primary export commodity" prices and the exchange rate:


Traditional flow theories of exchange rate determination argue that
exchange rates reflect underlying supply and demand characteristics for
currencies. Changes in exchange rates should be generated by changes in
the demand (supply) for goods and services exported (imported). Demand
changes are influenced by export price changes. So a positive correlation
should exist between exchange rate movements and export commodity (and
commodity futures) price changes.

The author sets out two strengths of verification for his model: He deems that the
model would be weakly confirmed should hedging a currency with its primary export
commodities' futures - those commodities representing a disproportionately large share
of the nation's exports - successfully reduce the exchange rate risk of holding that
currency. The support for the model could be termed strong, he argues, were there
indication that hedging performance was positively related to both the share of exports
represented by the commodity and the market share in a commodity held by the
country. In the case of Kazakhstan, the first of these conditions for strong support
might be seen when hedging with oil futures - being easily the dominant export.


Benet sets about testing his model with a set of thirteen countries - all without
currency futures - and sixteen primary export commodities. Of these countries
Norway is the only economy bearing much resemblance to that of Kazakhstan, with oil
and metals representing similar proportions of exports - but both most likely priced
exogenously - and a recently floated currency.


The testing methodology is generally similar to that employed by Eaker and Grant,
with tests of the hedging effectiveness of each primary export commodity for each
country, in sample - to verify the model - and then out of sample - to measure the
practicality of hedging. One differentiating feature of Benet's investigation is the use of
a currency futures basket as a benchmark for hedging effectiveness.


The effectiveness of hedges is highly variable, with some even increasing portfolio
risk. For Norway ex post hedging performance is encouragingly strong, but ex ante
effectiveness is alternately good and terrible between periods, suggesting hedge ratio
variability that might make the practice unrealistic. This hedge ratio variability is a



15
HEDGING TENGE with OIL FUTURES


problem the author notes (without reference) as being prevalent among less developed
countries. If such qualities are observed in static hedges of the tenge, then it will be
even more critical to test dynamic strategies, as frequently re-calculating the hedge
ratio over the life of the hedge might make such strategies practical even if the static
hedge were useless.


Overall, the author finds support for the weak form of his theory with hedges generally
reducing risk. Indeed, composite hedging with commodities is found to be as effective
on average as hedging with a basket of other currencies' futures. The stronger form of
his hypothesis, however, is not supported, with no indication that export share for
commodities or market share for countries has any influence on the effectiveness of
the corresponding commodity's hedge of the respective currency. This is not
necessarily damning, as the model I will propose suggests no role for market share in
dictating a commodity's suitability.

An element notable for its absence from the aforementioned commodity-currency
cross hedging studies was a firm theoretical link between exchange rate and the
commodity prices. Bowman (2005) breaches this gap by referring to a current strand
of the macroeconomic literature investigating the role of real price shocks as the
principal driver of real exchange rate fluctuations - see for instance Chen and Rogoff
(2003) or Cashin, Cespedes and Sahay (2004). The author first takes the time to test
cointegration of her target countries' real effective exchange rates and the real price of
their principal exports, and then proceeds to test various variance minimising hedges.


The paper's treatment of hedging lends more critical support for commodity currency
cross hedging to Benet's results. Despite her approach being based around
Ederington's Minimum Variance ratio (and a naïve one-to-one hedge) only, which of
course neglect expected returns, Bowman uses Sharpe ratios to assess the performance
of the hedge ex ante, oddly setting her objective function at odds with her measure of
hedging success. This is redeemed by a very worthwhile innovation on Benet, in that
the hedges tested are not all in a single commodity's futures, but rather are composite
hedges composed of those commodities used to produce the real price index in the first
half of the paper. These composite hedges are seen to easily outperform the simple
hedges, with the maximum of four hedging instruments providing the best
performance for both countries. Among the single commodity hedges implemented,
some were seen to outperform the unhedged spot and some were even seen to
outperform the risk free rate, but surprisingly it was not necessarily those futures with
the strongest correlation to the nominal exchange rate - as measured by R
2
- that
proved the best hedging instruments - as measured by out of sample risk reduction.





16
HEDGING TENGE with OIL FUTURES


A concern that might validly be raised is that the author chooses to use the minimum
variance ratio over the error correction model ratio, on the strength of a finding in her
previous paper, without having tested for non-stationarity in the nominal exchange rate
series. A unit root in the nominal series, as might be portended by the unit root in the
real, should properly be dealt with by use of an error correction framework to estimate
the hedge ratio, in order to allow for reversion behaviour to the assets prices' long
term equilibrium relationship
19
.


The extant body of literature on commodity-currency cross hedging is overtly lacking
in more technical treatments of the ratio estimation problem. I therefore look to the
parallel library on currency-currency cross hedging for improved estimators, where a
good source is Kroner and Sultan (1993). Their paper contrasts the performance the
OLS estimator for the minimum variance hedge ratio, used in all the papers touched
upon above, with the Error Correction augmented OLS estimator, which was so
readily dismissed by Bowman, and a dynamic hedging strategy - which I will borrow
for my own study. This dynamic estimator revolves around the assumption of
conditionally heteroskedastic errors in the relationship between cash and futures -
whereby the volatility of both assets' returns is a function of the immediately observed
past volatility. The authors note a significant improvement in performance under the
assumption of a GARCH structure, with some 4.5% additional variance elimination
out of sample.


Another vein of estimation procedures, outside the scope of this paper, are explored by
Sercu and Wu (1999), who, noting the large errors inherent in regression based
estimation, choose to use simple predictors based only on the most recently observed
price for each asset. They test both random walk and "unbiased expectations"
behaviours for the prices, and find no small success in doing so. These price based
estimators considerably out perform regression derived estimates but are not easily
translated from currency-currency into commodity-currency hedging, due to the
greater complexity of models linking exchange rate to currency prices - through
Covered Interest Parity and a "triangular no-arbitrage" condition price rules can be
derived relating one commodity with just the instrument's futures and the interest rate
differential.










19










As per Chen Lee and Shrestha (2002)













17
4 DATA SOURCES and PROPERTIES


The aim of this study is to identify a liquidly traded futures contract to serve in place
of the sparsely traded tenge futures. Naturally though, no specific futures exist for
Kazakhstan's own oils and I must therefore substitute alternative crude oil futures.
Among the current internationally traded blends, that can be assumed liquid enough,
Urals would seem the most obvious choice of substitute as Kazakhstani oil was
transmitted by Russian pipes until the CPC pipeline was inaugurated and geographic
proximity should imply similar transport costs since. However, futures prices for Ural
oil are only available from 2006. My second choice then is Brent oil futures; Brent
serves as the benchmark for most oil moving west and also, as a light borderline-
sweet blend, most closely resembles the makeup of CPC (CPC Blend Assay and
Composition, Chevron).


Although I will assume basis risk is negligible next to inter-asset price risk, the
selection of contract maturities available for futures contracts represent s a
complication in that it makes for multiple futures prices at any one time. It is
reasonable to assume that it is the nearby contract that will be the most heavily traded
at any one time (except perhaps for the last few weeks before delivery (Kroner and
Sultan, 1993)) while also closest to the underlying asset's price behaviour, due to the
convergence effect described in the previous chapter. It is for these reasons that I
choose Datastream's ICE continuous futures price series for Brent crude, which
always takes the price of the nearby contract and thereby replicates the behaviour of a
hedger who always updates to the closest contract to maturity immediately before his
current contract expires ("Datastream Data - the facts", Thompson Financial, 2003).
ICE Brent futures are contracts for a single barrel (bbl) and expire 16 to 20 days
before the beginning of the delivery month. Contracts for the next seventy two
consecutive months are always available, so the nearest contract will always have no
more than a month to expiry.


The exchange rate series chosen is the WM standardised Reuters daily mean spot rate,
also from Datastream. The period of the study is dictated by the period over which the
Tenge has been free-floating
20
, and I therefore initially consider this series from 4
th
April 1999. The financial crisis of last autumn, called a foreign speculative attack by
Kazakhstani authorities, forced a temporary pegging of the tenge, which the
government insists will come to an end in the first quarter of 2009, and makes
October 2007 the end of my study period. Given the government's commitment to

20


Though this in fact coincides with the ascendancy of oil among the country's exports (Najman,
Pomfret, Sourdin, Raballand, 2006)


18
HEDGING TENGE with OIL FUTURES


market economics thus far, and their trouble with a fixed exchange rate in 1998, there
is every reason to believe the re-float will happen when stated.

The model I shall present in the next section proposes a linear relationship between
the logs of the exchange rate and oil price, rather than the prices themselves. The
series I actually work with for the remainder of this paper are therefore the logs of the
ICE continuous and WMR datasets.


As I am looking to control for errors in variables problems, caused by bid ask noise
among other things, I narrow the two daily series to produce weekly (every fourth
observation) and monthly (every twentieth observation) series.


Though the daily data series is extensive and regression on many sub-samples should
be effective, when the data is reduced to weekly and monthly frequencies one has to
be careful, in conducting out of sample testing, to ensure that the division of the time
series is into sub samples that will give optimal performance for both the ratio
estimation procedure and the effectiveness testing. As I later find cause to also
estimate using data starting 1 Jan 2003, and must be able to fairly compare
performance, I choose an estimation period for ex ante tests which provides a
sufficient margin after this date for OLS to be effective - while leaving enough of the
sample for effectiveness measures to be effective.







01/06/199
9
-
28/09/200
7

01/01/200
3
-
28/09/200
7








$/?


$ / bbl


$/?


$ / bbl





Lags


1


0


1


0



Daily
ADF


-2.26


-2.73


-2.03


-2.67





KPS
S

1.20*


0.90*


0.39*


0.63*





Lags


0


0


0


0



Weekly
ADF


-2.41


-2.63


-2.03


-2.72





KPS
S

0.54*


0.41*


0.20*


0.32*





Lag
s

0


0


0


0



Monthly
ADF


-2.40


-2.17


-2.38


-3.11





KPS
S

0.29*


0.27*


0.10*


0.13*

Table 4.1 shows the results of unit root tests, with a deterministic trend and intercept, for all the log-series
that I will eventually work with. * denotes rejection at the 5% significance level. Lags for the ADF tests
were selected automatically according to the Akeike criterion. Bandwidths for the KPSS tests, which were
configured with the Bartlett kernel, were selected according to the Newey West criterion.







19
HEDGING TENGE with OIL FUTURES









01/06/199
9
-
28/09/200
7

01/01/200
3
-
28/09/200
7









$/?


$ / bbl


$/?


$ / bbl






Lags


1


0


1


0





Daily
ADF


0.30


-1.40


-1.64


-0.93






KPS
S

3.64*


5.28*


4.00*


4.30*






Lags


0


0


0


0





Weekly
ADF


0.18


-1.30


-1.65


-0.82






KPS
S

1.59*


2.32*


1.75*


1.85*






Lag
s

0


0


0


0





Monthly
ADF


-0.23


-1.44


0.49


-1.09






KPS
S

0.71*


1.06*


0.90*


0.92*

Table 4.2 shows the results of unit root tests, with intercept only, for all the log-series that I will eventually
work with. * denotes rejection at the 5% significance level. Lags for the ADF tests were selected
automatically according to the Akeike criterion. Bandwidths for the KPSS tests, which were configured
with the Bartlett kernel, were selected according to the Newey West criterion.

For nominal price and exchange rate data, I found the daily series running from the
beginning of April 1999 to be ambiguously non-stationary, with Augmented Dickey
Fuller tests suggesting no-unit root and Kwiatkowsky Phillip Schmidt Shin tests
reporting the opposite. This could arguably be due to an adjustment period
surrounding the float causing the exchange rate to follow an exceptional process;
indeed the exchange rate's movement is visibly different for the April and May of that
year - visible in figure 4.1. I therefore omit the first two months of the tenge's
floating behaviour from the study, and start instead from 1 June 1999. Unit root tests
detailed in table 4.1, followed by those detailed in table 4.2, show the existence of a
unit root now robust to all standard tests
21
. I choose to use both ADF and KPSS as
these two established unit root tests have opposite null hypotheses, and serve as good
complements to one another (Habib and Kalmova, 2007).


Though my hedge ratio estimation procedures will be based on the first differences of
these series, and might therefore be safe from spurious regressions even in the case of
first order integration, knowing whether the prices are I(1) is important in that it leads
into the question of cointegration, which I shall explore in the next chapter. What is
important, if I am to avoid spurious results, is that the series are not of higher
integrating order than I(1), as this would imply that the differenced series were not
I(0). Table 4.3 shows unit root test, with deterministic trends and intercepts, and
confirms that the log-series are indeed I(1).


21


As the series are logs, they cannot take negative values, and the case of a random walk with no
intercept needn't be explored (as this is equivalent to supposing a random walk around zero).


20
HEDGING TENGE with OIL FUTURES










01/06/1999
-
28/09/2007



01/01/2003
-
28/09/2007









$/?


$/ bbl


$/?


$/ bbl






Lag
s

0


0


0


0





Daily
ADF


-38.1*


-48.6


-28.0*


-37.5*






KPS
S

0.11


0.06


0.06


0.04






Lag
s

0


0


0


0





Weekly
ADF


-18.6*


-21.3*


-14.9*


-16.0*






KPS
S

0.08


0.06


0.04


0.05






Lag
s

0


0


0


0





Monthly
ADF


-8.38*


-12.1*


-6.48*


-9.79*






KPSS


0.08


0.09


0.04


0.10


Table 4.3 shows the results of unit root tests, with intercept and deterministic trend, for the first differences
of all the log-series that I will eventually work with. * denotes rejection at the 5% significance level. Lags
for the ADF tests were selected automatically according to the Akeike criterion. Bandwidths for the KPSS
tests, which were configured with the Bartlett kernel, were selected according to the Newey West criterion.



Weak as graphical inference is, returning to figure 4.1 one can see some encouraging
coincidences of each series' peaks with the other's troughs, over the long run at least.
However, the six month intervals on the time axes allow one to observe that the finer
movement, week-to-week or month-to-month (the timescale I will be hedging), may
just as possibly be disparate.



























21





1
7
0




1
6
0




1
5
0




1
4
0




1
3
0




1
2
0




1
1
0




1
0
0




9
0





80
K Z T
/
U S D


U S D
/
B B L


H
E
D
G
I
N
G

T
E
N
G
E

w
i
t
h

O
I
L

F
U
T
U
R
E
S





90




80




70




60




50




40




30




20




10




0
01/04/99 01/10/99 01/04/00 01/10/00 01/04/01 01/10/01 01/04/02 01/10/02 01/04/03 01/10/03 01/04/04 01/10/04 01/04/05 01/10/05
01/04/06 01/10/06 01/04/07
01/04/99
01/10/99 01/04/00 01/10/00 01/04/01 01/10/01 01/04/02 01/10/02 01/04/03 01/10/03 01/04/04 01/10/04
01/04/05 01/10/05 01/04/06 01/10/06 01/04/07


Figure 4.1 Left is shown the movement of the tenge dollar exchange rate over the free floating period.
On the right is the dollar price of a barrel of oil over that same period.









22
5 STRUCTURAL and EMPIRICAL MODELS

Thus far I have neglected to justify a link between the tenge-dollar exchange rate and
the futures price of oil with anything more than allusions to the predominance of oil
among Kazakhstan's exports; I shall now do so. The terms of trade - and by induction
export prices - have long been postulated as an important determinant of exchange
rates, but since Meese's and Rogoff's (1983) paper, showing that no model of the time
forecast exchange rates any more effectively than a random walk, such real shocks
have taken a leading role in many models. Among the most popular of these are a
variant of Dornbusch's expectations overshooting model, and an extension of the Balassa-
Samuelson model (Rogoff, 1996; Chen and Rogoff, 2002; Cashin, Cespedes and
Sahay, 2003; Habib and Kalmova, 2007). On the precedent of Bowman (2005) I
choose the latter model, though somewhat akin to Dornbusch I will assume that
financial market participants' expectations will bring the effects of fundamentals'
changes to bear instantaneously in the presence of sticky prices or wages.


The original Balassa-Samuelson model links per capita income to a country's relative
price level, but in the modified form I shall adopt from Cashin, Cespedes and Sahay
(2003) it describes a process akin to "the dutch disease", whereby an export price
boom causes the real value of a currency to appreciate (Frankel, 2005). The model
considers the interaction of two differentiated countries, within a continuum of other
economies of both types: The first is an exporter of a single primary commodity with
no power over its prices - not unreasonable assumptions for Kazakhstan given oil's
70% share of its exports and its position down the table of oil producers. The second
country imports the former's primary commodity and combines it with its
domestically produced intermediate good to produce a tradable good, which is
consumed in all countries along with a locally produced and priced non-tradable good
- again this framework describes Kazakhstan's oil industry well, as almost no
processing or refinement of crude is carried out domestically. Critically the law of one
price is assumed to hold between the economies for the tradable good, while within
each country labour is the only factor of production and is fully mobile between
sectors. These latter two assumptions make the domestic economy's production
functions Y
N
= a
N
L
N
and Y
X
= a
X
L
X
, where Y is production, a is technology/fixed
capital, and L is labour, and allow me through profit maximisation to show that:

P
N
= a
X
P
X

a
N

Where P
N
denotes the domestic price of the non-traded good, and P
X
the world price
for the country's export.





23
HEDGING TENGE with OIL FUTURES


For the demand side of the economy I assume that households have a (homogeneous
degree zero) Cobb-Douglas type utility function based on their consumption of the
tradable and non-tradable goods. It can be shown that a unit of consumption then costs
the domestic price level P;
P = P
N
¸
P
T
1÷ ¸


In the same manner as for the developing country's production, wages equate between
the non-traded (N) and intermediate (I) goods sectors of the foreign (*) economy,
giving:

P *
N
= a *
I
P *
I

a *
N

Both countries then contribute symmetrically to the production of the tradable good
(T) through a Cobb-Douglas production function, which can then be manipulated to
give the foreign unit price of the tradable good:
P *
T
= P *
|
X P *
1
I÷ |
With the assumption that foreign consumers share the utility function of domestic
consumers - a more realistic assumption for an FSU country redefining its economy
than for developing economies with more subsistence cultures, such as many of those
considered by Cashin et al (2003). Hence:
P* = P *
¸
N P *
1
T÷ ¸
The law of one price for both the tradable good and export commodity, combined
with some simple algebra then yield a relationship between the real exchange rate and
world export price:

EP =
P*

a
X
a *
N
P
*
X

a *
I
a
N
P
*
I

¸




Taking the natural logarithm of both sides of this equation leaves a straightforward
linear relationship between the log of the exchange rate, E, and the log of the primary
export's price (along with productivity and price differentials that I shall assume are
relatively static over the eight year test period).


Of course futures are not oil itself but contracts written upon it, contracts which are
rarely completed at that. Nevertheless, even the possibility of delivery means that
arbitrage should force the prices of future and underlying to converge on nearing the
expiry date, as discussed in Chapter 3. Until full convergence, the difference between
the price specified by a futures contract and its underlying asset is known as the basis.
My choice of futures price series assumes that the hedger always holds a contract with
at most one month until expiry, and as my assessment of out of sample hedging
performance is for one month exposures the futures price will be close to convergence


24
HEDGING TENGE with OIL FUTURES


for a significant part of that exposure. I therefore treat basis risk as inconsequential
beside asset price separation risk, and follow Kroner and Sultan (1993) in making no
allowances for it in my study.


I am theorising then that oil futures should co-move with the tenge exchange rate, and
that a position in one opposite to that in the other should serve to fix the value of a
combined portfolio. That is; a hedge between the two should be possible.


As the body of work described in chapter 3 would demand, I set aside the idea of this
being a "naïve" one-to-one hedge as inconsistent with both portfolio theory and
imperfect parallel price movement. Instead I adopt the utility maximisation
framework developed by Johnson (1960) - and detailed in that chapter - coupled with
the analysis of Anderson and Danthine (1981) suggesting that a mean-variance
optimising portfolio can be decomposed into a pure hedging position and a
speculative position. This result of Anderson's and Danthine's would suggest that,
providing enough variance can be eliminated by a variance minimising hedge, a
position can then be tailored to any agent's degree of risk aversion. As I can't know the
relative risk-return valuation of the foreign securities purchased by the Kazakhstani
accumulation pension funds, any speculation on those funds' risk aversion's
implications for currency risk would be rendered pointless
22
. One of my measures of
the usefulness of commodity futures in hedging the dollar-tenge exchange rate will
therefore simply be their ability to remove risk, as indicated by the effectiveness of a
minimum variance hedge
23
. Support for the minimum variance hedge as a general
indicator of performance for the accumulated pension funds' needs comes in Telser's
(1955) 'disastrous return' model, which could be considered to mirror pension funds'
avoidance of a critical deficit (beyond a safety margin), and which simplifies to a
variance minimisation problem. For the sake of parsimony, I will begin my
investigation with the most easily implemented, and therefore cheapest, hedging model.
I will then progress to more sophisticated models in order to gauge their relative
improvement at risk elimination.


As it is pension funds that interest me, the periods over which I must assess risk
reduction will vary from months, for the closest liabilities, to several years, for
productive investments of new pension payers' contributions. However, assuming that
liabilities will be paid on some multiple of a monthly basis, optimal risk reduction for
the pension funds needs can be shown through optimal monthly reduction. One might

22

Even with a realistic coefficient of risk aversion for the pension funds, the market valuation of risk
might differ between the currency and securities markets, making the net risk return position
impossible to judge from the currency position alone.
23
This would in fact be the optimal hedge were both the spot and futures series martingales. The risk
aversion of hedgers and its consequent risk premiums makes it highly unlikely that this assumption
would hold for futures at least.


25
HEDGING TENGE with OIL FUTURES


suppose that the best hedge ratio estimate for that monthly hedge would come from
monthly data. However, previous work (Sercu and Wu, 2003; among others) has
shown that more frequent data can out-perform less frequent regardless of the hedging
period, which is consistent with my model of a single relationship between exchange
rate and oil price across all timescales. The one potential pitfall of using denser
estimation data is that any day-to-day noise (errors-in-variables such as the bouncing
of transaction prices between the different the bid and ask sides of the market) over
the basic signal becomes more prominent (Sercu and Wu, 2003). Alongside my
investigation of the general cross-hedging potential of oil futures, I therefore also look
to compare, for every estimator, the performance of the different frequencies of data
mentioned in the previous chapter.


To derive a minimum variance hedge ratio for a single period, we loosely follow
Johnson (1960) in considering a portfolio consisting of one unit (Tenge) of the cash
position, with log-dollar value S, andì units of a single type and maturity of futures,
with log-dollar value F. The variance of the return for this portfolio is then given by


var(X

t
÷ X



t÷ 1


) = var(S
t
÷ S
t
÷
1
) + ì
2
var(F
t
÷ F
t
÷
1
) + 2ì cov(S
t
÷ S
t
÷
1
, F
t
÷ F
t
÷
1
),
X
t
= S
t
+ ì ? F
t


While the expected return is given by


E (X

t
÷ X



t÷ 1


) = E(S
t
÷ S
t
÷
1
) + ì E(F
t
÷ F
t
÷
1
)


As the former expression is a variance, hence everywhere positive and infinite as
ì ÷ · , optimisation by setting its first derivative equal to zero will yield a global
minimum. The value ofì at this minimum will then be


ì MV = cov(S
t
÷ S
t
÷
1
, F
t
÷ F
t
÷
1
)
var(F
t
÷ F
t
÷
1
)

Which is clearly the same pure hedge component seen in Anderson's and Danthine's
analysis. This of course means that under the correct assumptions our best estimate of
the minimum variance hedge ratio,ì
MV
, is the same as the Ordinary Least Squares
estimator for a futures price regressor and spot price regressand:


? S
t
= o + ì MV ? F
t
+ c
t
(5.1)
Where ? is the difference operator.



26
HEDGING TENGE with OIL FUTURES



Naturally, as my model has pushed me to work in log-series, the above does not
produce an optimal number of futures contracts to hold relative to cash, as might be
expected of a literal hedge ratio, but rather a ratio of changes in log-price. Fortunately
(for values close to zero) differences in logs are equivalent to percentage returns on
the value of each unit of the asset held - makingì
MV
the exchange rate's elasticity with
respect to oil futures' price - an alternative to dollar returns often chosen by hedging
theorists . This therefore makesì
MV
the ratio of the value of futures held to the value of cash
held. A repercussion of this observation often swept over by authors that work in
differenced log-prices or percentage returns (for instance Chen, Lee and Shrestha,
2002) is that this meansì
MV
is not truly a "static" hedge ratio, because the proportion of futures
contracts to cash held must be continually updated as their prices change. To see this,
note that there is no initial outlay in taking up a futures contract, but that marking to
market
24
guarantees that futures price changes are felt by the
hedger, so that the (time t+1) return on a portfolio, R
x
, obeys:

(c s
? X = R
x
=
s t+ 1
÷ c
f
f
t
+
1
) ÷ ( c
s
s
t
÷ c
f
f
t
)
c
s
s
t
c
s
( s
t
+
1
÷ s
t
) ÷ c
f
( f
t
+
1
÷ f
t
)
=
c
s
s
t

c
s
s
t
R
s
÷ c
f
f
t
R
f

=
c
s
s
t

c
f
f
t
= R
s
÷ R
f

c
s
s
t
= ? S
t
+
1
÷ ì ? F
t
+ 1



The above also serves to simplify my statistical treatment of the hedge's effects, as it
allows me to find the return of the portfolio through the linear combination of the
individual assets' returns, as I might with simple dollar returns.


The only remaining aspect of the above treatment which might seem questionable in
practice is that I have assumedì can take any valuable, when of course only integer
numbers of contracts can be taken on. However, dealing with a single tenge liability is
of course an idealisation and, when scaled up to the millions that the pension funds
hold in assets, infinite divisibility of the futures contracts simply scales up to
reflecting the divisibility of a near infinite number of contracts.

Though both the nominal exchange rate and oil futures log-series were identified as
I(1) in the previous chapter, this estimation procedure is performed on the first

24

I shall ignore the time value effects related to instantaneously realised changes in portfolio value




27
HEDGING TENGE with OIL FUTURES


differences of these series, eliminating any danger of spurious regression under OLS.
However, for both the daily and weekly series, Bresuch-Godfrey tests suggest serial
correlation of the residuals and Breusch-Pagan-Godfrey (maximum likelihood) tests
show signs of heteroskedasticity - seen in table 5.2 at the end of this chapter. I
therefore employ Newey-West standard errors to ensure any inference is based on
consistent statistics.


Within the "static" hedging framework I initially use for the minimum variance ratio, the
standard measure of two securities' relevance to one another is in sample (or ex post)
assessment via the goodness of fit of the regression (Johnson, 1960). The goodness
of fit is of course of little relevance to a practicing hedger looking to eliminate
perceived future risk using current information. I therefore also make use of an out of
sample (or ex ante) analogue. This consists of calculating the MV ratio for some sub
series, evaluating the variance of the cash position combined with the implied
proportion of futures for another distinct sub series, and then taking the ratio of
variance removed to unhedged variance for the latter (Eaker and Grant, 1987).
Algebraically this is simply


e = 1 ÷ var(? S
t
÷ ì (u )? F
t
: t e O
A
)
var(? S
t
: t e O
A
)
Where;
u = {? S
s
, ? F
s
: s e O
B
}
O

A
·
O

B
=0


In this study the ex ante measure will only ever be applied to consecutive sub series,
so that O = {a, a + 1,...a + b} and O = {a + b, a + b + 1,...a + b + c) . B A


In contrast to my chosen approach, Bowman (2004) uses Sharpe's (1994) ratio over
the hedged period as a measure of hedging effectiveness. I feel that such a measure,
which weighs variance reduction against expected abnormal return, is a contradictory
choice of metric when the ratio has been derived from a variance only objective
function
25
.


The results based on OLS are not encouraging, but this could be explained by a
number of factors, as suggested by Kroner and Sultan (1993). The first possibility is
that the two I(1) series are in fact cointegrated, that is, though they do not each have
fixed equilibrium levels to which they return, the apparent random walk of one might

25

Were it not for the poor pure hedging performance observed in the next chapter, it would be prudent
to follow minimum variance testing with an examination of the ability of Sharpe optimising hedge
ratios with the Sharpe metric to achieve the 5% objective return sought by Kazakhstani pension funds


28
HEDGING TENGE with OIL FUTURES


be mirrored in the other due to some long run dependency. Though one might still
expect a relationship between the price changes seen in both, a regression based only
on the inflations would be neglecting any tendency to return to this long run
equilibrium relationship (as opposed to value). The resultant bias (towards zero) in the
hedge ratio would be corrected by the introduction of an Error Correction Term for
the long run relationship into the regression equation
26
(Kroner and Sultan, 1993),
however there is some debate as to the significance of this effect for overall hedging
performance (Sercu and Wu, 1999).


To assess whether cointegration could indeed be affecting my various hedges'
performance - though it seems unlikely it could erode an otherwise effective hedge to
the degree seen in the next chapter - I conduct a standard Johansen style cointegration
test. This test is asymptotic so the size of the daily dataset should ensure a robust
result, though it does have its detractors and we cannot be sure of its accuracy for the
weekly or monthly series (Hubricht, Lutkepohl, Saikonnen, 2001).


Daily Weekly Monthly



Trace test
P(N=0|u)
Trace test
P(Ns1|u)
Rank test
P(N=0|u)
Rank test
P(Ns1|u)


Long run F/S
Jun 99 -
Sep 07

0.004


0.576


0.026


0.576


-0.2052
Jan 03 -
Sep 07

0.268


0.176


0.345


0.176


-
Jun 99 -
Sep 07

0.021


0.967


0.012


0.967


-0.1913
Jan 03 -
Sep 07

0.204


0.293


0.211


0.293


-
Jun 99 -
Sep 07

0.318


0.720


0.253


0.720


-
Jan 03 -
Sep 07

0.577


0.323


0.610


0.323


-

Table 5.1 shows the p-values of Johansen cointegration tests, with u the set of observations for the frequency
and timeframe described in the column head, and N the number of cointegrating relationships hypothesised
to be in the system. P values are as per MacKinnon-Haug-Michelis (1999). Bottom row shows futures
coefficient of normalised cointegrating vector.

It can be seen from Table 5.1 that Johansen tests clearly support the cointegration of
both the daily and weekly time series, over the whole sample, with both trace and
eigenvalue tests rejecting the null of no cointegrating relationships while neither can
reject the null of up to one cointegrating relationship. Also reported in the table is the
cointegrating vector, relating the two series in equilibrium, which I will soon use
according to Kroner's and Sultan's (1993) model.


26


The method is often known as Dynamic Ordinary Least Squares





29
HEDGING TENGE with OIL FUTURES



Their treatment is identical to the approach already detailed for the minimum variance
hedge ratio up until the point of conducting a regression: Rather than regressing the
return of the exchange rate against (a constant and) the futures' return alone, the
current deviation from the long term relationship - called the Error Correction Term
- is included as a second regressor, making the regression equation


? S
t
= · + ì
MV
? F
t
+ ¸ (S
t
÷ bF
t
) + c
t
(5.2)


Where ? is the difference operator, c
t
is a normally distributed independent error
term, and b is a coefficient producing an I(0) combination of S and F
27
.


As with regression 5.1 I will test the effectiveness of the Error Correction modified
hedge ratio estimators with both ex post and ex ante measures. Technically for the ex
ante assessment the cointegrating vector should be re-estimated for the smaller data
set, but for the sake of simplicity I will assume that the difference will be negligible - a
failure of the model will continue to have the same implications under this
assumption.



DYNAMIC ESTIMATORS

Having seen that the introduction of an error correction term does little to improve the
minimum variance hedge's performance, I abandon any hopes that the oil-tenge
relationship is uniform over time along with the simplicity of "static" hedge ratios,
and instead assume that pension funds' utility function(s) are time separable. Among the
alternative, dynamic, hedging strategies the most easily implemented is the rolling
hedge, whereby the minimum variance ratio is re-estimated for every increment of the
hedging period, taking into account more data on the returns' distribution as the
information set grows.


Perhaps the best way to present an analysis is through Lien's and Tse's (2002)
framework, as the change from the previous regression is quite straightforward, being
no more than a simple generalisation of our previous model to incorporate the
conditionality of the variances to the information set u t (basically the set of all
observations from time 0 to time t-1) - this treatment can also be viewed as an
expansion on the ex ante measure I described above.


27


I assume that this b will be effectively the same for this linear causal model as the non-causal vector
derived coefficient in table 5.1


30
HEDGING TENGE with OIL FUTURES


var(? X
t
| u
t
) = var(? S
t
| u
t
) + ì
2
var(? F
t
| u
t
) + 2ì cov(? S
t
, ? F
t
| u
t
)
t e |0,T | c Z


Leading to the new conditional minimum variance hedge ratio


ì MV = cov(S
t
÷ S
t
÷
1
, F
t
÷ F
t
÷
1
| u
t
)
t
var(F
t
÷ F
t
÷
1
| u
t
)
(5.3)


The futures position taken at time t is then based on this ratio rather than that used at
time t-1. This means the method produces an out of sample estimate for the hedge
ratio


The advantage of this standard rolling hedge model is that if the structural relationship
between exchange rate and oil price alters during the sample period, then this change
does not interfere with the estimation of the earlier relationship. However, the obvious
flaw in that logic is that if data from the earlier relationship is still being used then it
will interfere with OLS regression's estimation of a new relationship's parameters. One
remedy might be a rolling window of a fixed length, progressively ignoring early data
as it incorporates newer observations, but any theoretical justification for a specific
window length would probably be justification for a more detailed break point model.
Instead I make a (still speculative but more justifiable) assumption about the possible
nature of the relationship, by assuming conditional heteroskedasticity for both series.


A lagrange multiplier test for the absence of conditional heteroskedasticity in the
residuals of regression 5.1 strongly rejects the null (table 5.2), for daily data at least,
and instead favours the presence of some form of AutoRegressive Conditional
Heteroskedasticity. Moreover, there is a growing body of evidence to justify such an
assumption for both exchange rates and oil prices. Particularly popular is my
proposed structure of conditional heteroskedasticity following an ARMA(1,1) process -
making it a GARCH(1,1) model as per Kroner and Sultan (1993) - which is typified by
persistent periods of high volatility interspersed with similar periods of low volatility,
a pattern often observed in price data. I choose this over other conditionally
heteroskedastic models, based on GARCH's superior performance in the exchange
rate study of McCurdy and Morgan (1988) and the oil futures study of Adrangi,
Chatrath, Dhanda and Raffiee (2001).


The GARCH consistent error correction treatment I employ is based on that of Kroner
and Sultan (1993), being a bivariate error correction model with structure:



31
HEDGING TENGE with OIL FUTURES



? S
t
= o
s
+ |
s
(S
t
÷
1
÷ o F
t
÷
1
) + c




st
?
F
t
= o

f

+ |
f
(S
t
÷
1
÷ o F
t
÷
1
) + c

f

t


c
st



h c

u
t
~ N (0, H
t
)
ft


0
1






(5.4)
H
t
=
s0 t


h
f

t

µ
µ
h
s
t
1
0


h
f

t



h
2
t = a
s
+
b
s
c s


2
s t÷ 1


+ c
s
h
2
s



t÷1

h
2
f

t

= a
f
+ b
f
c

2
f t÷ 1

+ c
f

h
2
f

t÷ 1


This Constant Conditional Correlation model
28
is so called becauseµ is assumed
constant over the sample period, with less than unit absolute value, and represents the
correlation between the cash and futures assets' deviations from their equilibrium
values. The long run relationship between cash and futures prices is now captured by
the ratioo, as derived from the Johansen cointegration
29
while the|s represent the system's speed
of return to equilibrium after shocks. Table 5.1 shows that error correction is not
relevant behaviour for some of the series, in which cases both|s will be set to zero. This
will not be detrimental to the estimation procedure, as the basic vector equation will
still remove any intercept present in the differenced series, leaving error terms which
the GARCH system then seeks to explain by comparison with one another.


By the same optimisation procedure as before, this leads to a time-varying hedge ratio
based on the conditional second moments of the returns:
µ h
s
t
h
f
t
ì
MV = t

h
2
f t


Though ARMA style forecasting of the above ratio would be relatively
straightforward, I restrict my study to the in sample effectiveness of such a hedge, and
make comparisons with the variance elimination achieved in sample by the OLS
derived minimum variance ratio.



28
29



With unrestricted intercepts
As this cointegrating vector was derived through a vector model, it will be consistent with both cash
and futures being treated as endogenous


32
HEDGING TENGE with OIL FUTURES


J-B BG BPG Chow ARCH(1)


01/06/1999 - 9541 106.1 27.69 32.5 316.7
28/09/2007 (0.00) (0.00) (0.00) (0.00) (0.00)
01/01/2003 - 1278 63.91 5.457 - 99.34
28/09/2007 (0.00) (0.00) (0.02) (0.00)

01/06/1999 - 2416 16.02 10.58 17.7 2.664
28/09/2007 (0.00) (0.00) (0.00) (0.00) (0.10)
01/01/2003 - 618 3.328 2.481 - 0.779
28/09/2007 (0.00) (0.19) (0.12) (0.38)

01/06/1999 - 102 4.608 0.908 11.7 1.038
28/09/2007 (0.00) (0.10) (0.34) (0.00) (0.31)
01/01/2003 - 41 1.418 0.523 - 0.048
28/09/2007 (0.00) (0.49) (0.47) (0.83)

Table 5.2 shows the statistics (and probabilities) for various specification and residuals tests. J-B is the
Jarque-Berra, which in all cases is insignificant, supporting the assumption of normal residuals for OLS
inference. Skew is the skewness (third moments) of the residual series, which might support a different
ARCH specification were the J-B statistics significant. BG is the chi-square distributed Breusch -Godfrey
statistic, for a test with two lags. BPG is the chi-square distributed Breusch-Pagan-Godfrey statistic. Chow is
the likelihood ratio test statistic for the null breakpoint hypothesis that there is no structural break at
01/01/2003. ARCH(1) is a LaGrange Multiplier test statistic for the null of no conditional
heteroskedasticity in the residuals.

































33
D
a
i
l
y


W
e
e
k
l
y


M
o
n
t
h
l
y


6 RESULTS and CONCLUSIONS

Table 6.1 shows the results of my initial estimation of the Minimum Variance hedge
ratio, for both the entire sample period (as a test of ex post effectiveness) and the first
half of the period (as a test of ex ante effectiveness on the second half). These results,
for the most simplistic of the hedging models I test, are decidedly negative; with the
minimum variance position in the futures contracts eliminating arbitrarily small
amounts of risk in the ex post case, and potentially increasing portfolio variance when
applied out of sample - when contrasted with Benet's (1990) average ex post
performance of R
2
=0.89 and best ex ante hedge at e=0.66. That the hedge ratio is so
small in some instances should not, however, be mistaken for further evidence against
the hedge's importance; it is simply an artefact of the cash position being in a single
tenge, with relatively little value next to the barrel of oil delivered on the futures
contract. Nevertheless, in no case is the hedge ratio significantly non-zero which casts
serious doubt on any consistent relationship between cash and futures price changes.
Relative hedging effectiveness between the data sets is harder to judge, with no clear
pattern of improvement or deterioration in hedging performance with observation
frequency. The daily estimates seem to perform more consistently, in and out of
sample, which might alleviate concerns about errors-in-variables. Meanwhile the
monthly series seems to provide a considerably better fit than its opponents in sample.
That said, over a smaller sample we might expect a greater impact from coincidental
co-movement, making arbitrary risk change more substantial. In truth the
effectiveness is so consistently poor between data frequencies, I am unable to make
any inference on the relative benefits of the different balances of sample size and
errors-in-variables. It is therefore necessary that I continue to test all three frequencies
when I later progress to dynamic models.


Data Ex post Ex ante
Frequency
OLS f
MV
P(f
MV
=0|u) R
2
f
mv
P(f
mv
=0|u) e
Daily 0.0027 0.12 0.001 0.0025 0.14 0.004
Weekly 0.0034 0.55 0.000 0.0029 0.59 0.005
Monthly 0.0081 0.48 0.004 -0.0013 0.88 -0.002
ECM
Daily 0.0034 0.05 0.011 0.0032 0.04 0.006
Weekly 0.0064 0.26 0.030 0.0059 0.24 0.010
Table 6.1 for regression 5.1 and 5.2.Where f
MV
is the minimum variance hedge ratio based on data between
01/06/1999 and 28/09/2007*, while f
mv
is the minimum variance hedge ratio based on the sub-sample ending
30/12/2004. R
2
is the (adjusted) goodness of fit for f
MV
, while e is the proportion of the unhedged position's



34
HEDGING TENGE with OIL FUTURES


monthly variance removed, out of sample, by taking a relative position of f
mv
futures over the period
16/10/2003 to 13/09/2007. *Or its weekly/four-weekly sub-sample for the corresponding regressions.

Assuming that there is some underlying link between the two variables - unlikely as
this may seem given the significance and fit of table 6.1's hedge ratios - the failure of
OLS to identify this relationship must be attributed to the violation of one of its
underlying assumptions. As discussed in the previous chapter, one feature of the
relationship neglected by the previous treatment, but shown to be relevant for daily
and weekly frequencies by the Johansen tests detailed in table 5.1, is the cointegration
of those series. In the hope of retaining the simplicity of OLS based estimation for
hedges based at least on high frequency data, I introduce an error correction term into
the regression. The results in the lower section of table 6.1 are for this Error
Correction modified regression. For weekly data a consistent relationship between
exchange rate and oil price remains as questionable as before, as the ratios remain
decidedly insignificant, but daily elasticity estimates, particularly over the first half of
the sample, are much more convincing. For both series there is enough improvement
in ex post risk reduction, over the regression that ignored the long run equilibrating
behaviour of the series, to be comparable with the weakest of Benet's (1990) hedges.
Meanwhile, out of sample the previously observed consistency of the daily estimate's
performance is reinforced, while there is a marked improvement in the predictive
power of OLS on the weekly series. Nevertheless, it should be stressed that with such
insignificant weekly estimates, with and without the error correction term, no reliable
inference on relative performance can be made, and this result serves only as a remote
hope that some further modification of my method will yield more practical results.


Given the sound theoretical basis for interaction between prices and exchange rates
discussed in previous chapters, it seems likely that the failures of static hedges are
because other factors determining that interaction have varied too significantly across
the sample period, making the assumption of a constant beta invalid. My first attempt
to mitigate this problem takes the form of a rolling window hedge, whereby the
coefficient relating oil price to exchange rate is continually re-estimated throughout
the hedging period. In practice this would lead to greater transaction costs, but given
the poor performance of the static hedge, these costs would have to be bourn to gain
anything from cross hedging with oil futures. The left hand side of table 6.2 shows the
results of rolling window dynamic monthly hedges, estimated from daily, weekly, and
monthly (four weekly) data series. It is apparent from the low e values, for daily and
weekly frequencies, that the dynamic hedge at best only matches the static procedure
for risk elimination. Indeed, for all series the tightly banded variances hint that there
might be no relationship at all between exchange rate and oil futures price; perhaps
merely the results of insignificant and unsubstantiated hedge ratios, like those of the




35
HEDGING TENGE with OIL FUTURES


static hedge, generating random gains and losses in variance which cancel out over the
seventy six rolling regressions.


























































36
HEDGING TENGE with OIL FUTURES



Data
Frequenc 01/06/1999 - 28/09/2007 01/01/2003 - 28/09/2007
y
Var(Au) Var(AS) e Var(Au) Var(AS) e
Daily 3.236x10 -4 3.248x10
-4
0.004 3.214x10 -4 3.248x10 -4 0.010
Weekly 3.251x10
-4
3.248x10
-4
-0.001 3.230x10
-4
3.248x10
-4
0.006
Monthly 3.242x10
-4
3.248x10
-4
0.002 3.207x10
-4
3.248x10
-4
0.013

Table 6.2 shows the dynamic performance for hedge ratios derived progressively from equation 5.3 over the
periods at the column heads. Hereu is the log of the month t value of the portfolio (1, f
t
M1
V
) over the sub ÷
period starting 06/01/2005. S is the unhedged spot position over the same period. A is the monthly
difference operator.


Examination of the conditional correlation series produced in estimating the rolling
hedge, as shown in figure 6.1, suggests a significant change in the structure of the
cross hedging relationship at the start of 2003. This shift in the structural relationship
cannot be easily reconciled with any political or industrial change, as we would not
expect any marginal (further) relaxation of government controls to have so radical an
effect and the greatest industrial change in the period (the opening of the Caspian
Pipeline Consortium pipeline) should have taken effect in 2001/02. Nevertheless,
Chow Breakpoint tests strongly reject the null of no such change at every frequency
(see table 5.2), and as it would invalidate both the static and rolling estimates based on
all prior information, I repeat the above estimations for the sub period starting 1
January 2003. The static results are presented in table 6.3 and the dynamic in the right
hand portion of table 6.2.



Data Ex post Ex ante
Frequency
OLS f
MV
P(f
MV
=0|u) R
2
f
mv
P(f
mv
=0|u) e
Daily 0.0085 0.00 0.005 0.0125 0.00 -0.003
Weekly 0.0128 0.18 0.008 0.0208 0.017 0.031
Monthly 0.0260 0.26 0.024 0.0088 0.62 0.015


Table 6.3 for regression 5.1 and 5.2.Where f
MV
is the minimum variance hedge ratio based on data between
01/01/2003 and 28/09/2007*, while f
mv
is the minimum variance hedge ratio based on the sub-sample ending
30/12/2004. R
2
is the goodness of fit for f
MV
, while e is the proportion of the unhedged position's variance
removed out of sample, by taking a relative position of f
mv
futures over the period 01/01/2005 to
28/09/2007*. *Or its weekly/four-weekly sub-sample for the corresponding regressions.







37
HEDGING TENGE with OIL FUTURES



0.1



0.05



0
2 000 Ja n 2 00 1 Ja n 20 02 Ja n 2 003 Ja n 2 00 4 Ja n 20 05 Ja n 2 00 6 Ja n 2 00 7 Ja n


-0.05



-0.1



-0.15
Monthly
Weekly
Daily
-0.2

Figure 6.1 (above) shows the conditional correlations for the various data frequencies starting from January
2000 - and hence ignoring initial estimates' instability, caused by small generating samples. After highly
volatile movement until January 2001, which might simply be caused by estimation error, there is a clear
two years of very stable correlation between the series. This then collapses into something resembling a
random walk or highly correlated autoregressive process. Below is shown the effect of this correlation
structure on the hedge ratio estimated.

0.015


0.01


0.005


0
2000 Jan 2001 Jan 2002 Jan 2003 Jan 2004 Jan 2005 Jan 2006 Jan 2007 Jan

-0.005


-0.01


-0.015


-0.02

Monthly
-0.025 Weekly
Daily

-0.03





38
r
h
o


K

Z

T

/

B

B
L


HEDGING TENGE with OIL FUTURES


Table 6.3 shows improvements in the fit and significance of the hedge ratios relative to
their counterparts in table 6.1, but the performance of the hedges in terms of risk
reduction is still uselessly low. Out of sample, the static hedges continue to show
potential for a detrimental effect on returns, but this fact, combined with low p-values
and the 1-6% ex post R
2
s for these ratios (not shown), once again suggests that there
may be a shift in the underlying nature of the exchange rate-oil relationship between the
estimation and hedging periods - if any such relationship actually exists. With so rich a
daily data series I could continue to isolate structural changes without (further) risking
the integrity of OLS estimation, but with no clear economic justifications for the
changes, this would be of no help to an actual hedger. The results on the right hand side
of table 6.2 on the other hand show improved ex ante performance for all frequencies.
However, that both the weekly and monthly hedges are outperformed by their static
rivals, again forces me to question the stability of the relationship across this sample.


Daily Weekly Monthly
01/06/99- 01/01/03- 01/06/99- 01/01/03- 01/06/99- 01/01/03-
o
s

P
z
(o
s
=0)

o
f



|
s



|
f



a
s
8.53x10
-3

(0.00)
0.1574
(0.00)
-0.0012
(0.00)
0.0276
(0.00)
1.66x10
-8

(0.00)
19.5x10
-3

(0.00)
0.0011
(0.03)

-


-

3.25x10
-8

(0.00)
-4.23x10
-3

(0.00)
0.0146
(0.14)
-6.90x10
-5

(0.00)
1.56x10
-4

(0.28)
25.4x10
-8

(0.00)
1.33x10
-3

(0.00)
0.0041
(0.18)

-


-

232x10
-8

(0.03)
-2.43x10
-3

(0.00)
0.0152
(0.18)

-


-

208x10
-8

(0.08)
4.98x10
-3

(0.00)
0.0188
(0.07)

-


-

-330x10
-8

(0.56)

a
f
8.23x10 -6
(0.00)
15.5x10
(0.03)

-6
153x10
(0.18)

-6
1023x10
(0.92)

-6
4066x10
(0.92)

-6
91.6x10
-6

(0.75)

b
s



b
f



c
s



c
f



µ
log(L)
"R
2
"
0.1916
(0.00)
0.0435
(0.00)
0.8320
(0.00)
0.9386
(0.00)
0.0402
(0.06)
16698
-0.001
0.1300
(0.00)
0.0429
(0.00)
0.8802
(0.00)
0.9147
(0.00)
0.0916
(0.00)
9195
0.003
0.3277
(0.00)
0.495
(0.10)
0.7585
(0.00)
0.8806
(0.00)
-0.0280
(0.55)
2497
-0.007
0.3035
(0.00)
-0.0096
(0.88)
0.7192
(0.00)
0.3459
(0.96)
0.0801
(0.25)
1355
0.013
0.4104
(0.00)
-0.0114
(0.91)
0.6854
(0.00)
0.5604
(0.90)
-0.0096
(0.94)
429
-0.004
-0.0783
(0.02)
-0.1137
(0.16)
1.1412
(0.00)
1.1012
(0.00)
0.1206
(0.34)
251
0.034
Table 6.4 shows the results of regression 5.4 with L the likelihood, and R
2
the in sample effectiveness of
the implied dynamic hedge ratio - comparable with ex post performance in the static hedge.




39
HEDGING TENGE with OIL FUTURES


The last method tested is by far the most complex, as it makes use of a dynamic model
for the conditional covariances underlying the tenge-oil relationship, and would
represent considerable transaction costs if actually implemented - particularly if
revised daily. However, if any technique is to capture a fine structure missed by the
previous models, in the available data, then it would certainly have to incorporate this
level of complexity. Moreover, the use of an ARCH/GARCH model is strongly
supported, at least for daily data, by the statistics in table 5.2. Table 6.4 gives details
of the GARCH regressions' results for both the whole period, and for 2003 onwards,
along with their performance in terms of portfolio variance reduction.


Table 6.4 tells a now familiar story, with (in sample
30
) hedges detrimental over the
whole sample and hedging performance little better than under static estimates for the
later sample, which in turn suggests uselessly poor out of sample performance.
Moreover, µ, the critical link between the short run behaviour of the two variables, is
insignificantly non-zero for all weekly and monthly data. This once again strikes a
blow to my belief that there should be a link between oil's price and the tenge's value
relative to the dollar. My choice of a GARCH structure for the exchange rate returnsat
least seem reasonably justified, with the conditional covariance coefficients
significant for all frequencies of data and sample periods. GARCH(1,1) seems to
represent the futures price changes well for denser data only, with the coefficients in
the variance equation mostly insignificant for weekly and monthly samples.


The results are not shown here but I also relaxed the assumption of constant
conditional correlations for daily data in favour of the Diagonal VECH form of
multivariate GARCH, to allow for the non-constant correlation after 2003 suggested
by figure 6.1. There was no improvement in hedging performance.



CONCLUSIONS

I have thoroughly assessed the tenge-dollar exchange rate hedging potential of oil
futures with an extensive arsenal of hedge ratio estimation procedures. The only
conclusion that I can draw is that this particular commodity-currency cross hedge,
appropriate as it might appear in theory, is likely ineffective in practice. As a general
rule hedging performance seems to increase with data frequency, suggesting errors in
variables bias. However, neither covariance nor correlation between the monthly
series is ever found to be significant, and I must therefore consign this to a side effect
of estimating with a smaller sample.


30


That the minimum variance hedge increases risk in sample can be attributed to the imposed structure
pushing the covariance estimate away from its sample value


40
HEDGING TENGE with OIL FUTURES



One potential reason for my theory's failure, consistent with Habib's and Kalmova's
(2007) observations on the relationship between the real NWK rate and the real oil
price, might be tied (ironically) to the lack of domestic investment assets. Though
Kazakhstan is hardly as frugal as Norway in the use of its "currency gift" - to which its
glittering new capital Astana is testament - the National Fund for the Republic of
Kazakhstan was founded in 2001 with the express aim of ".reducing the impact of
volatile market prices for natural resources and smoothing the distribution of oil
wealth over generations". By acting to prolong the gains of high oil prices through
reinvesting abroad
31
some of those excess oil revenues taxed from the six
32
principal
petroleum companies (all those above a baseline price of $19/bbl), the fund might
well sterilise any effect of such high revenues on the domestic economy.
Unfortunately data on the actions of the fund - at a relevant frequency - is likely
unavailable, and its future behaviour prohibitively unpredictable for hedgers to
compensate (Najman, Pomfret, Raballand, Sourdin, 2005).


Such public insulation of the economy against oil revenue fluctuations could also be
significantly enhanced by private retention, through the informal economy rather than
workers' salaries, and subsequent investment abroad. For anecdotal evidence of such
practices, one need look no further than Baker Hughes's shaming 2007 admission of
making illegal payments (under the US Foreign Corrupt Practices Act) to a
commercial agent in Kazakhstan, who in turn made payments to an executive of
KazakhOil
33
. However, such "leakages" of oil revenues are very difficult to track,
particularly since local employee quota negotiations were decentralised, and it would
be very hard to verify the extent of such an effect (Najman, Pomfret, Raballand,
Sourdin, 2005).

It should not be forgotten either that my chosen exchange rate model, linking the
tenge to the price of oil, is founded on the assumptions of competitive wage rate
determination and perfect labour mobility. The breakdown of either of these
assumptions could serve to sever any commodity-currency link that might otherwise
exist. Hence, another explanation for Kazakhstan's insulation against its greatest
export's price swings might be the nature of the region and the oil industry itself.
Within the Middle East and Central Asia there is a long history of large immigrant
labour pools and remittances paid between countries (Billmeier and Massa, 2007). It
is possible that this labour source could make the elasticity of labour so great as to

31
32
33

$5 billion, or 17% of GDP, of foreign equities had been accumulated in late 2004
As of 2004
"Baker Hughes Settles Previously Disclosed FCPA Investigations", Media Release, April 26, 2007;
Nikola Krastev, "Kazakhstan: U.S. Firm Pleads Guilty In Bribery Case", Radio Free Europe, April 30,
2007



41
HEDGING TENGE with OIL FUTURES


remove any inflationary pressures caused by increased oil revenues (Habib and
Kalmova, 2007). Complementing this excess of labour would be the minimal
requirements of the oil industry, with less than 50,000 people or 1% of Kazakhstan's
working population employed directly by the oil sector as of 2004. Meanwhile, the
assumption of perfect competition is further eroded through the domination of the oil
industry by a few key players, and the capital barriers against other entrants. The
labour mobility assumption suffers from the apparent lack of a national labour market
in Kazakhstan, evidenced by large regional differences in household expenditure
(Najman, Pomfret, Raballand, Sourdin, 2005).


On an empirical note; all those methods tested here were based around Least Squares
procedures vulnerable to lead-lag errors when the response of one market to another
might be delayed. As the weekly and monthly series were subsets of the daily series,
and not averages, lead-lag errors would not have been controlled for by my working
with multiple frequencies. Sercu and Wu (1999) find an improvement in hedging
performance using the less well established Scholes-Williams instrumental variables
estimator, which is not vulnerable to lead-lag errors, to estimate hedge ratios. The
gains in risk reduction seen in their study do not amount to anything that would
correct the poor performance seen above, but a repeat of this study using the
instrumental variables estimator might prove interesting nevertheless.


Perhaps the strongest alternative to an oil-tenge cross hedge might be to use a basket
of foreign currency futures to hedge tenge positions. International Financial Series
data shows that Kazakhstan's foreign trade is well spread between European
countries, for which liquid futures markets exist, and FSU/Middle eastern states, for
which they do not, presenting an obstacle against the construction of such a basket.
However, the former group could be said to dominate, and investigation of the
effectiveness of currency-currency cross hedging would be merited.




















42
REFERENCES

Adrangia B, Chatrath A, Dhandaa K K, Raffieeb K, 2001. Chaos in oil prices?
Evidence from futures markets, Energy Economics pp. 405 - 425
Anderson R, Danthine JP, 1981. Cross hedging, J. Political Economy Vol. 89, No. 6,
pp. 1182-1196, University of Chicago Press
Benet B A, 1990. Commodity futures cross hedging of foreign exchange exposure, J.
Futures Markets Vol. 10, No. 3, pp. 287
Billmeier A, Massa I, 2007. What Drives Stock Market Development in the Middle
East and Central Asia--Institutions, Remittances, or Natural Resources? IMF
Working Papers 07/157, International Monetary Fund
Bowman C, 2005. Effective cross-hedging for commodity currencies, International
and Development Economics Working Papers idec05-6, International and
Development Economics
Cashin P, Cespedes L, Sahay R, 2004. Commodity currencies and the real exchange
rate, J. Development Economics, Vol. 75, 239 - 268
Chakraborty A, Barkoulas J T, 1999. Dynamic futures hedging in currency markets,
European J. Finance Vol. 5, No. 4, pp. 299-314
Chen S-S, Lee C-F, Shrestha K, 2003. Futures hedge ratios: a review, Quarterly
Review of Economics and Finance, Vol. 43, pp. 433-465
Chen Y, Rogoff K, 2003. Commodity currencies, J. International Economics, Vol. 60,
pp.133-160
Eaker M, Grant D, 1987. Cross-hedging foreign currency risk, J. International Money
and Finance, Vol. 6, pp. 85-105
Ederington L H, 1979. Hedging performance of the new futures markets, J. Finance,
Vol. 34, No. 1, pp. 157-170
Frankel J, 2005. On the tenge: Monetary and exchange rate policy for Kazakhstan,
Short-term consultancy for government of Kazakhstan, Centre for International
Development, Apr.11, 2005
Habib M M, Kalmova M M, 2007. Are there oil currencies? The real exchange rate
of oil exporting countries, European Central Bank, working paper series No. 839
Hubricht K, Lutkepohl H, Saikonnen P, 2001. A review of systems cointegration tests,
Econometric Reviews, Vol. 20, No. 3, pp. 247-318
Kroner K F, Sultan J, 1993. Time-varying distributions and dynamic hedging with
foreign currency futures, J. Financial and Quantitative Analysis, Vol. 28, No. 4,
pp.993
Levine R, Zervos S, 1996. Stock market development and long-run growth, World
Bank Economic Review, 10(2), 323-339
Lien D, Tse Y K, 2002. Some recent developments in futures hedging, J. Economic
Surveys, Vol. 16, No. 3
Lloyd K, 1994. Kazakhstan economic report, World Bank report no. 12856
McCurdy T H, Morgan I G, 1988. Testing the martingale hypothesis in deutsche mark
futures with models specifying the form of heteroskedasticity, J. Applied
Econometrics, Vol. 3, pp. 187-202
Meese R A, Rogoff K, 1983. Empirical exchange rate models of the seventies: Do
they fit out of sample? Journal of International Economics, Vol. 14, pp. 3-24
Najman B, Pomfret R, Raballand G, Sourdin P, 2006. How are oil revenues
redistributed in an oil economy? The case of Kazakhstan, Development and
Comp Systems 0512012, EconWPA



43
HEDGING TENGE with OIL FUTURES


Palmer E, 2004. Pension reform and the development of pension systems: An
evaluation of World Bank assistance: Background paper Kazakhstan country
study, World Bank 39144
Rogoff K, 1996. The purchasing power parity puzzle, J. Economic Literature, Vol. 34,
No. 2, pp. 647-668
Sercu P, Wu X, 1999. Cross- and Delta-hedges: Regression- versus price-based
hedge ratios, J. Business Finance & Accounting, Vol. 35, No 1-2, pp. 250-280
Stein J L, 1961. The simultaneous determination of spot and futures prices, American
Economic Review, Vol. 51, No. 5, pp. 1012-1025
Telser L G, 1955. Safety first and hedging, The Review of Economic Studies, Vol. 23,
No. 1, pp. 1-16
Working H, 1953. Futures trading and hedging, American Economic Review, June,
pp. 314-343
Working H, 1962. New concepts concerning futures markets and prices, American
Economic Review, June, pp. 431-459.

2004. Republic of Kazakhstan - Financial sector Assessment program update -
Technical note - Investment opportunities for pension funds, IMF Country Report No.
04/337

CPC Blend Assay and Composition, Chevron

2003. Datastream Data - the facts, Thompson Financial


































44
APPENDIX ROLLING HEDGE RATIO ESTIMATES





01/06/1999 - 28/09/2007 01/01/2003 - 28/09/2007

Daily Weekly Monthly Daily Weekly Monthly
2004 Dec 0.00249 0.00197 -0.00072 0.01251 0.01937 0.01055
2005 Jan 0.00241 0.00172 -0.00067 0.01183 0.01724 0.00931
2005 Feb 0.00233 0.00140 -0.00068 0.01136 0.01544 0.00919
2005 Mar 0.00213 0.00122 -0.00160 0.01054 0.01436 0.00329
2005 Apr 0.00197 0.00042 -0.00198 0.00990 0.01198 0.00296
2005 May 0.00227 -0.00026 -0.00166 0.01063 0.01017 0.00484
2005 Jun 0.00271 -0.00164 -0.00505 0.01143 0.00585 -0.00575
2005 Jul 0.00247 -0.00175 -0.00508 0.01061 0.00523 -0.00510
2005 Aug 0.00255 -0.00117 -0.00488 0.01052 0.00607 -0.00565
2005 Sep 0.00226 -0.00191 -0.00495 0.00956 0.00423 -0.00590
2005 Oct 0.00217 -0.00238 -0.00490 0.00926 0.00316 -0.00495
2005 Nov 0.00223 -0.00202 -0.00477 0.00934 0.00416 -0.00353
2005 Dec 0.00223 -0.00219 -0.00470 0.00915 0.00355 -0.00373
2006 Jan 0.00225 -0.00201 -0.00465 0.00904 0.00362 -0.00383
2006 Feb 0.00237 -0.00224 -0.00446 0.00926 0.00324 -0.00359
2006 Mar 0.00232 -0.00230 -0.00424 0.00898 0.00274 -0.00342
2006 Apr 0.00274 -0.00053 -0.00259 0.00988 0.00667 -0.00010
2006 May 0.00220 -0.00027 -0.00288 0.00845 0.00721 -0.00072
2006 Jun 0.00209 0.00030 -0.00357 0.00809 0.00840 -0.00238
2006 Jul 0.00191 -0.00052 -0.00296 0.00761 0.00639 -0.00140
2006 Aug 0.00205 0.00041 -0.00032 0.00795 0.00878 0.00641
2006 Sep 0.00216 0.00084 0.00259 0.00817 0.00989 0.01471
2006 Oct 0.00220 0.00099 0.00347 0.00816 0.01026 0.01739
2006 Nov 0.00219 0.00112 0.00344 0.00803 0.01014 0.01707
2006 Dec 0.00218 0.00090 0.00343 0.00801 0.00976 0.01702
2007 Jan 0.00206 -0.00093 0.00129 0.00755 0.00576 0.01245
2007 Feb 0.00224 -0.00088 0.00126 0.00784 0.00556 0.01227
2007 Mar 0.00256 -0.00087 0.00249 0.00846 0.00526 0.01370
2007 Apr 0.00252 -0.00084 0.00206 0.00832 0.00532 0.01275
2007 May 0.00201 -0.00051 0.00206 0.00716 0.00596 0.01251
2007 Jun 0.00239 0.00020 0.00248 0.00792 0.00737 0.01372
2007 Jul 0.00224 0.00057 0.00298 0.00754 0.00797 0.01409
2007 Aug 0.00247 0.00129 0.00631 0.00798 0.00946 0.02217
2007 Sep 0.00275 0.00272 0.00873 0.00851 0.01218 0.02661

Table A Shows the month-by-month minimum variance hedge ratio estimates, produced by the rolling
estimation procedure, over the period to which they are applied out of sample











45

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