Description
Documentation aims to test the Liquidity Preference Theory in the Indian money market.
Liquidity Preference Theory
Does it work in India?
7/19/2010
Liquidity Preference Theory July2010
Table of Contents
Executive Summary ................................................................................................................................................................................ 3 Introduction ............................................................................................................................................................................................... 4 Term Structure of Interest Rates...................................................................................................................................................... 5 Market expectations (pure expectations) hypothesis ............................................................................................................ 8 Liquidity Preference Theory .............................................................................................................................................................. 8 Deriving Expected Future Rates: Liquidity Preference Theory ................................................................................ 9 Liquidity Premium in Term Structure .............................................................................................................................. 10 Liquidity Vs Expectation theory .......................................................................................................................................... 10 Market Segmentation Theory ......................................................................................................................................................... 10 Estimating the Zero Coupon Yield Curve ................................................................................................................................... 11 Nelson & Siegel equation ............................................................................................................................................................. 11 Spot rates ............................................................................................................................................................................................ 12 Indian Government Bond 10 year Yield Curve ....................................................................................................................... 13 Indian Interest Rate ............................................................................................................................................................................ 13 Calculating the Forward rates & Liquidity Premium using the spot rates ................................................................. 13 Conclusion ............................................................................................................................................................................................... 16
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Liquidity Preference Theory July2010
Executive Summary
Characterizing the properties of the term structure in markets where a given asset is offered at different maturities is a central issue in financial economics. The complex relationship between time to maturity and yield on securities is of widespread interest to both economists and financial market participants. It provides useful information regarding the presence of inter-temporal arbitrage opportunities present in the market. At the macroeconomic level, it also gives the monetary authorities information regarding the extent to which the interest rate term structure can be altered to desirably affect short-term international capital flows, while simultaneously encouraging long-term local investment. Apart from its relevance for monetary policy implementation, or from the possible ability of the term structure slope to predict future changes in economic activity, it has been discussed for a number of years that some characteristics of the term structure contain significant information on future interest rate changes. This paper aims to test the Liquidity Preference Theory in the Indian money market. The liquidity preference theory has received a lot of attention in previous literature in addressing hypothesis that account for yield curve behaviour. The empirical results have often been contradictory and the ability of the liquidity preference theory to explain the behaviour of interest rates over the term structure has been controversial for a long time.
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Liquidity Preference Theory July2010
Introduction
Indian market for gilt securities has, for the past few decades, predominantly been a market dominated by the banks and institutions. Investments were being done primarily with the objective of holding till maturity. As a result, activity in the secondary market used to be very subdued and consequently, volumes very low. Existence of high coupon rates usually assured adequate returns on investments even without any churning of portfolio. Appetite for trading was almost non-existent. Moreover, lack of depth and non availability of timely and reliable market information worked as a barrier against the development of this market. However, with the liberalization taking hold on the Indian financial market during the past decade, complexion of the market started changing rapidly. While interest rates continued to be more or less regulated for the larger part of the decade, Forex market started getting driven more and more by demand and supply. Rupee/Dollar swap market started having significant impact on the short term Rupee rates so much so that a large segment of the market started considering Swap rate driven term money rates as reference rates. Equity market also saw major move towards transparent pricing, leading to the development of a trading culture in the market. Market for gilt securities also did not remain isolated from this development. Reserve Bank of India, as a regulator, took many steps for market development (e.g. bringing about strict Capital Adequacy norms, enforcing Asset Liability Management requirements for banks, allowing simple Rupee Derivatives like Interest Rate Swaps, slow but steady deregulation of Rupee interest rates) which resulted in a significant shift in the nature of the market. Many of these changes forced financial service providers to access gilt market for reasons like reducing mismatches in their books. This provided others with trading opportunities. Regulatory changes on the modes of holding investments (e.g. categorisation of investments into Trading, AFS and HTM) and its valuation methodologies added further impetus to churn securities in the portfolio for the purpose of realignment. Moreover, allowing Foreign Institutional Investors to invest in G-sec market and allowing them to hedge their forex risk by way of taking forward covers brought in another important group of players with appetite for trading in the market. Increased availability of reliable market information, large scale computerization, availability of efficient analytical tools and trained manpower contributed positively to the development process. Trading volumes, as a result showed sharp increase - SGL volumes (Central Government securities & T-Bills) increased by about 145% and 198% in 2001-02 and 2002-03 respectively as compared to the volumes in 2000-01. However, increase in volume did not result in any significant improvement of market liquidity in the real sense. Indian market is still characterized by lack of depth & shallow liquidity except for about 8-10 securities at a time (with average daily trading of about Rs. 100 crore) for which two way quotes are available in the market. Activity is concentrated in these securities due to the market confidence & ability to liquidate positions quickly at a fair value. Absence of market making activity in other securities (almost non-availability of any reasonable quote) discourages trading in such securities. Perceived inability to offload holdings at around the stop loss levels, if required, works as an effective deterrent. This trade dynamics appear to work against expansion of the market in terms of number of securities traded. Moreover, in a bullish phase, the market volume shows a tendency to increase rapidly and traders are less hesitant take positions even in relatively illiquid securities. In a bearish market, traders however avoid taking positions in such securities. Moreover, there are cases of quick shifts of market preference making certain securities illiquid in a short span of time (e.g. 7.95% GS 2032 were liquid up to January ’03 but are now traded thinly). This phenomena is also a constant source of worry for the traders and acts as a restraint from being a contrarian.Dominance of a few traders over the market, as it exists today, again ensures that other players also trade in the securities preferred by these traders. Market participants also cite some more reasons for the inadequate liquidity in the Indian Gilt market: a) Lack of reference yields come in the way of estimating fair price of a security i. In the shorter end, 4 to 5 T-bills are traded per day on an average and money market is concentrated mostly in overnight trade.
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Liquidity Preference Theory July2010
In the medium to long term, securities are not available for all maturities (e.g. there are no outstanding securities in the maturity range of 24 years to 29 years i.e. after 10.18% GS 2026 next maturity is for 7.95% GS 2032) and absence of long term zero coupon instrument/STRIPS makes estimating zero rates less reliable. b) Non availability of proper hedging instruments like rupee derivatives (e.g. interest rate swaps, futures and options) restricts the possibility of hedging positions in the derivatives market c) Concentration of securities amongst few players and lack of reliable market information related to floating stock leads to difficulty in pricing illiquidity d) Absence of speculators at retail level deprives the market of the cushioning effect in cases of movements without adequate change in fundamentals ii.
Term Structure of Interest Rates
A yield curve displaying the relationship between spot rates of zero-coupon securities and their term to maturity.
The resulting curve allows an interest rate pattern to be determined, which can then be used to discount cash flows appropriately. Unfortunately, most bonds carry coupons, so the term structure must be determined using the prices of these securities. Term structures are continuously changing, and though the resulting yield curve is usually normal, it can also be flat or inverted. The exact shape of the curve can be different at any point in time. So if the normal yield curve changes shape, it tells investors that they may need to change their outlook on the economy .
There are three main patterns created by the term structure of interest rates: 1) Normal Yield Curve: As its name indicates, this is the yield curve shape that forms during normal
market conditions, wherein investors generally believe that there will be no significant changes in the economy, such as in inflation rates, and that the economy will continue to grow at a normal rate. During such conditions, investors expect higher yields for fixed income instruments with long-term maturities that occur farther into the future. In other words, the market expects long-term fixed income securities to offer higher yields than short-term fixed income securities. This is a normal expectation of the market because short-term instruments generally hold less risk than long-term instruments; the farther into the future the bond's maturity, the more time and, therefore, uncertainty the bondholder faces before being paid back the principal. To invest in one instrument for a longer period of time, an investor needs to be compensated for undertaking the additional risk. Remember that as general current interest rates increase, the price of a bond will decrease and its yield will increase.
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Liquidity Preference Theory July2010
2) Flat Yield Curve: These curves indicate that the market environment is sending mixed signals to
investors, who are interpreting interest rate movements in various ways. During such an environment, it is difficult for the market to determine whether interest rates will move significantly in either direction farther into the future. A flat yield curve usually occurs when the market is making a transition that emits different but simultaneous indications of what interest rates will do. In other words, there may be some signals that short-term interest rates will rise and other signals that long-term interest rates will fall. This condition will create a curve that is flatter than its normal positive slope. When the yield curve is flat, investors can maximize their risk/return trade-off by choosing fixed-income securities with the least risk, or highest credit quality. In the rare instances where-in long-term interest rates decline, a flat curve can sometimes lead to an inverted curve.
3) Inverted Yield Curve: These yield curves are rare, and they form during extraordinary market conditions wherein the expectations of investors are completely the inverse of those demonstrated by the normal yield curve. In such abnormal market environments, bonds with maturity dates further into the future are expected to offer lower yields than bonds with shorter maturities. The inverted yield curve indicates that the market currently expects interest rates to decline as time moves farther into the future, which in turn means the market expects yields of long-term bonds to decline. Remember, also, that as interest rates decrease, bond prices increase and yields decline.
You may be wondering why investors would choose to purchase long-term fixed-income investments when there is an inverted yield curve, which indicates that investors expect to receive less compensation
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Liquidity Preference Theory July2010
for taking on more risk. Some investors, however, interpret an inverted curve as an indication that the economy will soon experience a slowdown, which causes future interest rates to give even lower yields. Before a slowdown, it is better to lock money into long-term investments at present prevailing yields, because future yields will be even lower.
The Theoretical Spot Rate Curve:
Unfortunately, the basic yield curve does not account for securities that have varying coupon rates. When the yield to maturity was calculated, we assumed that the coupons were reinvested at an interest rate equal to the coupon rate, therefore, the bond was priced at par as though prevailing interest rates were equal to the bond's coupon rate. The spot-rate curve addresses this assumption and accounts for the fact that many Treasuries offer varying coupons and would therefore not accurately represent similar non-callable fixed-income securities. If for instance you compared a 10-year bond paying a 7% coupon with a 10-year Treasury bond that currently has a coupon of 4%, your comparison wouldn't mean much. Both of the bonds have the same term to maturity, but the 4% coupon of the Treasury bond would not be an appropriate benchmark for the bond paying 7%. The spot-rate curve, however, offers a more accurate measure as it adjusts the yield curve so it reflects any variations in the interest rate of the plotted benchmark. The interest rate taken from the plot is known as the spot rate.
The spot-rate curve is created by plotting the yields of zero-coupon Treasury bills and their corresponding maturities. The spot rate given by each zero-coupon security and the spot-rate curve are used
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Liquidity Preference Theory July2010
together for determining the value of each zero-coupon component of a non-callable fixed-income security.
Remember, in this case, that the term structure of interest rates is graphed as though each coupon payment of a non-callable fixed-income security were a zero-coupon bond. T-bills are issued by the government, but they do not have maturities greater than one year. As a result, the bootstrapping method is used to fill in interest rates for zero-coupon securities greater than one year. Bootstrapping is a complicated and involved process and will not be detailed in this section (to your relief!); however, it is important to remember that the bootstrapping method equates a T-bill's value to the value of all zero-coupon components that form the security. There are four main economic theories attempting to explain how yields vary with maturity:
Market expectations (pure expectations) hypothesis
The pure expectations theory simply sates that forward rates are the market’s expectation of the level of future interest rates. Forward Rate = Expected Future Interest Rate – – This means that the shape of the term structure reflects the markets expectation of future shortterm rates. The pure expectations theory is based on the assumption that market participants who buy and sell treasury bonds are willing and able to exploit profit opportunities whenever forward rates differ form expected future rates.
Liquidity Preference Theory
The theory of liquidity preference holds that long-term securities should provide higher returns than short-term obligations because investors are willing to sacrifice some yields to invest in short-maturity obligations to avoid the higher price volatility of long-maturity bonds. Another way to interpret the liquidity preference hypothesis is to say that lenders prefer short-term loans, and, to induce them to lend long term, it is necessary to offer higher yields. The liquidity preference theory contends that uncertainty and volatility cause investors to favour shortterm issues over bonds with longer maturities because short-term bonds are less volatile and can easily be converted into predictable amounts of cash should unforeseen events occur. This theory argues that the yield curve should slope upward and that any other shape should be viewed as a temporary aberration.
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Liquidity Preference Theory July2010
This theory can be considered an extension of the expectations hypothesis because the formal liquidity preference position contends that the liquidity premium inherent in the yields for longer maturity bonds should be added to the expected future rate in arriving at long-term yields. Specifically, the liquidity premium (L) compensates the investor in long-term bonds for the added volatility inherent in long-term bonds compared to short-maturity securities. Because the liquidity premium (L) is provided to compensate the long-term investor, it is simply as follows: (1 + t RN) = [(1 + t R1)(1 + t+1r1 + L2) . . . (1 + t+N–1r1 + Ln)]1/N In this specification, the Ls are not the same but would be expected to increase with maturity because the price volatility increases with maturity. The liquidity preference theory has been found to possess some strong empirical support. To see how the liquidity preference theory predicts future yields and how it compares with the pure expectations hypothesis, let us predict future long-term rates from a single set of one- year rates: 6 percent, 7.5 percent, and 8.5 percent. The liquidity preference theory suggests that investors add increasing liquidity premiums to successive rates to derive actual market rates. As n example, they might arrive at rates of 6.3 percent, 7.9 percent, and 9.0 percent. As a matter of historical fact, the yield curve shows an upward bias, which implies that some combination of the expectations theory and the liquidity preference theory will more accurately explain the shape of the yield curve than either of them alone. Specifically, actual long-term rates consistently tend to be above what is envisioned from the price expectations hypothesis. This tendency implies the existence of a liquidity premium. A hypothesis about the term structure of interest rates (the relationship between interest rates and term to maturity) holding that investors demand a premium for bearing interest rate risk. The extent of the premium increases with term to maturity but at a decreasing rate. The two reasons behind the decreasing rate of increase are that duration, a measure of a bond's price sensitivity to interest rate changes, increases at a decreasing rate with term to maturity and that long term interest rates are typically less volatile than short term interest rates. ? Prices of longer term bonds are more sensitive to changes in interest rate--as measured by duration-- therefore they are more susceptible to interest rate risk. – If investors are averse to this risk they will prefer to hold short-term bonds unless they are adequately compensated for bearing the interest rate risk inherent in longer-term bonds. Forward Rate = Expected Rate + Liquidity Premium Expected Rate = Forward Rate – Liquidity Premium
– –
Deriving Expected Future Rates: Liquidity Preference Theory
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Liquidity Preference Theory July2010
Liquidity Premium in Term Structure
Liquidity Vs Expectation theory
Market Segmentation Theory
A modern theory pertaining to interest rates stipulating that there is no necessary relationship between long and short-term interest rates. Furthermore, short and long-term markets fall into two different categories. Therefore, the yield curve is shaped according to the supply and demand of securities within each maturity length. The yield curve reflects the actions and preferences of the major participants in the market. Institutions have strong maturity preferences:
a) Commercial banks dominate demand for short-term securities
b) Insurance Companies dominate demand for long term securities. c) Insurance demand is stable over time
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Liquidity Preference Theory July2010
d) Commercial bank demand is less stable, e) During strong business activity, banks sell short-term bond to accommodate loans--so short-term spot rates rise. f) During weak business activity, banks buy short term bond --so short term spot rates decline
Estimating the Zero Coupon Yield Curve
The term structure of the interest rates forms the basis of valuation of all fixed income securities. Modelled as a series of cash-flows due at different points in time in the future, the underlying price of a fixed income security can be calculated as the net present value of the stream of cash-flows. Each cash flow has to be discounted using the interest rate for the associated term to maturity. Arriving at the appropriate set of interest rates- term structure or Zero coupon yield curve – for the Indian debt market is the objective of this section.
Nelson & Siegel equation
The Nelson & Siegel equation is as under:
Spot Rate = ß0 + (ß1+ß2) * where, ß0 is the contribution of long term component
[(1-exp
(-m/
t)]/(m/t)–
ß2*exp
(-m/
t)
ß1 is the contribution of short term component ß2 indicates the contribution of medium term component t is the decay factor and m is the maturity ß2 & t determine the shape of the curve
The present exercise uses the data from the NSE-WDM, which constitutes about 70 percent of secondary market volume. The result of the model is as following:
beta 0 beta 1 beta 2 tau
16-Jul07 10.5030 -3.1726 -0.7166 15.5000
15-Jul08 11.9901 -2.4912 -3.7937 5.5194
16-Jul08 19.1424 -9.4000 12.9728 11.9868
15-Jul09 9.5540 -5.5438 -0.0412 4.1271
16-Jul09 10.2146 -5.9592 -0.0184 5.8687
15-Jul10 9.1150 -3.7740 0.0190 2.8015
16-Jul10 9.2352 -3.2667 -0.0122 3.9433
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Liquidity Preference Theory July2010
Spot rates
The estimated term structure/ spot rates are as follows:
Time to Spot Rate ( As Spot Rate ( Maturity on 16-07As on 15(In years) 2007) 07-2008) 0.5 7.3696 9.4467 1 7.4082 9.4069 1.5 7.4463 9.3779 2 7.4837 9.3587 2.5 7.5206 9.3479 3 7.5569 9.3446 3.5 7.5927 9.3479 4 7.6293 9.3573 4.5 7.6640 9.3715 5 7.6981 9.3900 5.5 7.7318 9.4140 6 7.7649 9.4375 6.5 7.7975 9.4656 7 7.8297 9.4959 7.5 7.8613 9.5281 8 7.8925 9.5619 8.5 7.9232 9.5969 9 7.9545 9.6329 9.5 7.9831 9.6697 10 8.0136 9.7070
Spot Rate ( As on 16-072008)
9.6728 9.6122 9.5601 9.5161 9.4797 9.4505 9.4281 9.4115 9.4017 9.3976 9.3991 9.4049 9.4158 9.4311 9.4505 9.4738 9.5008 9.5311 9.5646 9.6010
Spot Rate ( As on 15-072009)
4.3297 4.6249 4.8979 5.1505 5.3844 5.6013 5.8025 5.9963 6.1695 6.3306 6.4806 6.6204 6.7508 6.8726 6.9864 7.0928 7.1925 7.2859 7.3735 7.4557
Spot Rate ( As on 1607-2009)
4.5008 4.7328 4.9523 5.1599 5.3565 5.5427 5.7191 5.8925 6.0507 6.2008 6.3432 6.4785 6.6069 6.7290 6.8451 6.9555 7.0606 7.1607 7.2559 7.3467
Spot Rate ( As on 15-072010)
5.6593 5.9423 6.1944 6.4194 6.6206 6.8009 6.9627 7.1135 7.2442 7.3622 7.4690 7.5659 7.6540 7.7342 7.8073 7.8742 7.9355 7.9918 8.0436 8.0914
Spot Rate ( As on 16-072010)
6.1659 6.3475 6.5149 6.6691 6.8115 6.9429 7.0645 7.1811 7.2850 7.3814 7.4708 7.5539 7.6312 7.7032 7.7702 7.8328 7.8912 7.9458 7.9969 8.0448
12.0000 10.0000 8.0000 6.0000 4.0000 2.0000 0.0000 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 Time to Maturity ( In Years) Spot Rate ( As on 1607-2007) Spot Rate ( As on 1607-2010) Spot Rate ( As on 1607-2009) Spot Rate ( As on 1607-2008)
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Liquidity Preference Theory July2010
Indian Government Bond 10 year Yield Curve
Indian Interest Rate
Calculating the Forward rates & Liquidity Premium using the spot rates
16-07-2007 Maturity (Years) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Half Year One Year forward Liquidity Spot Rates Forward Rates rates YTMs Premium 7.369605616 7.408219676 7.182184404 7.446250599 7.385971411 7.483706724 7.45713144 7.559246825 7.2619 -0.005186958 7.520596323 7.526655031 7.556927591 7.594574264 7.703518999 7.361 -0.000684509 7.592708649 7.660920836 7.629292164 7.736106926 7.846678138 7.3621 -0.004812781 7.663976468 7.790137959 7.69813476 7.851916016 7.97394576 7.398 -0.004322257
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Liquidity Preference Theory July2010
5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 7.731774843 7.764904438 7.797531185 7.829662639 7.861306273 7.892469474 7.923159545 7.954536965 7.983149083 8.013581249 7.912245079 7.971154811 8.028674455 8.084832831 8.139658335 8.193178933 8.245422162 8.316442961 8.32615382 8.41633784 8.099374271 8.21902987 8.333142827 8.452364019 8.546435139 7.542 7.6543 7.689 7.8113 7.9108 0.001655271 0.001115371 -0.004009295 0.003423494 0.002640074
16-07-2008 Maturity (Years) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
Spot Rates 9.672773432 9.612173751 9.560106518 9.516100556 9.479706906 9.45049784 9.428065913 9.411528553 9.401729625 9.397585187 9.399062494 9.404938613 9.415815449 9.431103304 9.450528092 9.47382913 9.500758532 9.53108063 9.564571421 9.601018034
Half Year Forward Rates 9.110934065 9.242487309 9.173792522 9.126041619 9.097651215 9.087130994 9.089298614 9.115632878 9.150942925 9.20213829 9.255438884 9.328853097 9.408729433 9.497338839 9.593836329 9.697430588 9.807381062 9.922995194 10.0436258
One Year forward rates
YTMs
Liquidity Premium
9.420111568 9.319410276 9.294703922 9.341829492 9.441713159 9.588222902 9.77337737 9.990171817 10.23246762
9.3916 9.3656 9.4132 9.4609 9.5085 9.5562 9.5819 9.3691 9.35
-0.001528706 -0.001016033 0.002614204 0.003100786 0.003050975 0.002546137 -0.000114085 -0.023086623 -0.010542176
16-07-2009 Maturity Half Year One Year forward (Years) Spot Rates Forward Rates rates 0.5 4.500799842 1 4.73281919 4.855568821
YTMs
Liquidity Premium
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Liquidity Preference Theory July2010
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 4.952276553 5.159937071 5.356516174 5.542682946 5.719063252 5.89249644 6.050700567 6.200783718 6.343224857 6.478472489 6.606946696 6.729041021 6.845124233 6.955541963 7.060618237 7.16065689 7.2559429 7.346743619 5.321768741 5.704046791 6.054860834 6.376803774 6.672254904 6.992291144 7.195436431 7.423360448 7.632546866 7.824538747 8.000751822 8.162484997 8.310929997 8.447180228 8.572238895 8.687026464 8.7923875 8.889096942 5.588796811 6.312358953 6.948908896 7.442934235 7.877845703 8.244883451 8.554564921 8.815800845 9.036133183 5.3876 5.766 6.1519 6.4988 6.592 6.9382 6.9917 6.9899 6.9536 0.00026959 0.006489563 0.003691597 0.004548394 -0.008186208 0.007942577 -0.011876147 -0.018402998 -0.024086795
Liquidity Premium Graphs
0.01 0.005 Liquidity premium 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Liquidity Premium from16-07-09
-0.005 -0.01
-0.015 -0.02
Liquidity Premium
-0.025 -0.03 Time to Maturity
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Liquidity Preference Theory July2010 Liquidity Premium 16-07-2007
0.004 0.003 0.002 0.001 0 -0.001 -0.002 -0.003 -0.004 -0.005 -0.006
Liquidity Premium
1
3
5
7
9
11 13 15 17
Liquidity Premium 1607-2007
Maturity ( Years)
Liquidity Premium 16-07-2008
0.005 0 Liquidity Premium 1 -0.005 -0.01 -0.015 -0.02 -0.025 Maturity (Years) Liquidity Premium 1607-2008 3 5 7 9 11 13 15 17
Conclusion
From the zero coupon yield curves it could be seen that there is a upward trend in the spot rates. This clearly shows, that for higher maturity zero coupon yield increases. If lenders know that short-term rates will remain constant in the future, current long-term rates must be equal to current short-term rates, so that the yield curve will be perfectly flat. If there is no uncertainty about future interest rates, current long-term rates must be an appropriately weighted average of current and future short -term rates. A two-year rate, for instance, must be a weighted average of current and future one-year rates, while a six-month rate must be a weighted average of current and future three-month rates, etc. Yield curves tend to be steeply upward-sloping when short-term interest rates are low and often slope downward when short-term rates are high. During the last century at least, it has been distinctly upwardsloping.” The simple expectations theory could explain this only by assuming that lenders usually expect
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Liquidity Preference Theory July2010
rates to rise persistently over time. This assumption does not seem plausible, unless you believe that lenders were extremely poor forecasters. While interest rates have varied considerably during the past century there is little evidence that they have increased on average, or that market participants had any reason to expect them to do so. Indeed, the evidence suggests that people usually expect future shortterm interest rates to remain near current levels. Any alternative explanation for the fact that yield curves are normally upward-sloping must be based on something about long-term securities that makes them systematically less attractive to lenders than short-term securities. If the risk of capital loss on securities tends to increase in proportion to their remaining terms, lenders who demand interest compensation for bearing this risk will demand more compensation on long-term securities than on short-term securities. This will tend to make the yields on longer-term securities higher than those on securities with shorter terms—that is, it will tend to make the yield curve upward sloping. When lenders expect interest rates to change in the future, In this case, the actual yield should be given by the sum of the term-adjusted rate (that is, the weighted-average base rate) and the appropriate term premium. This can produce curves that slope in one direction along one part of their range. but in the opposite direction along another part. If lenders expect interest rates to remain constant for a shoit period, and then fall sharply, for example, the yield curve will appear humped, sloping upward at very short terms, peaking near the term corresponding to the date at which rates are expected to decline, and sloping downward for a range of terms thereafter. Curves with this shape are frequently observed shortly before economic recessions begin, presumably because interest rates tend to fall sharply during recessions. Yield Curve when base rate is constant
Yield Curve when base rate will fall
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Liquidity Preference Theory July2010
From the above analysis, it could be seen that for year 2007 & 2008 the interest rate may remained constant. The estimators also assumed it to remain constant in the future. Market participants expected future short-term interest rates to remain near current levels. So a flat zero coupon yield curve could be in the year 2007 & 2008. In 2009, due to recession the risk free rate dropped from 8-9 percent to 4-5 percent. Because of this drop in interest rate, the net yield of the bonds went down. This could be seen in the zero coupon yield curve for the year 2009. The starting point is around 4 percent. It is an upward sloping curve with long term maturities having a higher yield. The liquidity preference theory works in India. It could be easily seen that apart from the short term interest rates, the long term securities have a premium attached to it to make them attractive to invest. The liquidity premium increases as the term to maturity increases.
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doc_223240247.docx
Documentation aims to test the Liquidity Preference Theory in the Indian money market.
Liquidity Preference Theory
Does it work in India?
7/19/2010
Liquidity Preference Theory July2010
Table of Contents
Executive Summary ................................................................................................................................................................................ 3 Introduction ............................................................................................................................................................................................... 4 Term Structure of Interest Rates...................................................................................................................................................... 5 Market expectations (pure expectations) hypothesis ............................................................................................................ 8 Liquidity Preference Theory .............................................................................................................................................................. 8 Deriving Expected Future Rates: Liquidity Preference Theory ................................................................................ 9 Liquidity Premium in Term Structure .............................................................................................................................. 10 Liquidity Vs Expectation theory .......................................................................................................................................... 10 Market Segmentation Theory ......................................................................................................................................................... 10 Estimating the Zero Coupon Yield Curve ................................................................................................................................... 11 Nelson & Siegel equation ............................................................................................................................................................. 11 Spot rates ............................................................................................................................................................................................ 12 Indian Government Bond 10 year Yield Curve ....................................................................................................................... 13 Indian Interest Rate ............................................................................................................................................................................ 13 Calculating the Forward rates & Liquidity Premium using the spot rates ................................................................. 13 Conclusion ............................................................................................................................................................................................... 16
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Liquidity Preference Theory July2010
Executive Summary
Characterizing the properties of the term structure in markets where a given asset is offered at different maturities is a central issue in financial economics. The complex relationship between time to maturity and yield on securities is of widespread interest to both economists and financial market participants. It provides useful information regarding the presence of inter-temporal arbitrage opportunities present in the market. At the macroeconomic level, it also gives the monetary authorities information regarding the extent to which the interest rate term structure can be altered to desirably affect short-term international capital flows, while simultaneously encouraging long-term local investment. Apart from its relevance for monetary policy implementation, or from the possible ability of the term structure slope to predict future changes in economic activity, it has been discussed for a number of years that some characteristics of the term structure contain significant information on future interest rate changes. This paper aims to test the Liquidity Preference Theory in the Indian money market. The liquidity preference theory has received a lot of attention in previous literature in addressing hypothesis that account for yield curve behaviour. The empirical results have often been contradictory and the ability of the liquidity preference theory to explain the behaviour of interest rates over the term structure has been controversial for a long time.
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Liquidity Preference Theory July2010
Introduction
Indian market for gilt securities has, for the past few decades, predominantly been a market dominated by the banks and institutions. Investments were being done primarily with the objective of holding till maturity. As a result, activity in the secondary market used to be very subdued and consequently, volumes very low. Existence of high coupon rates usually assured adequate returns on investments even without any churning of portfolio. Appetite for trading was almost non-existent. Moreover, lack of depth and non availability of timely and reliable market information worked as a barrier against the development of this market. However, with the liberalization taking hold on the Indian financial market during the past decade, complexion of the market started changing rapidly. While interest rates continued to be more or less regulated for the larger part of the decade, Forex market started getting driven more and more by demand and supply. Rupee/Dollar swap market started having significant impact on the short term Rupee rates so much so that a large segment of the market started considering Swap rate driven term money rates as reference rates. Equity market also saw major move towards transparent pricing, leading to the development of a trading culture in the market. Market for gilt securities also did not remain isolated from this development. Reserve Bank of India, as a regulator, took many steps for market development (e.g. bringing about strict Capital Adequacy norms, enforcing Asset Liability Management requirements for banks, allowing simple Rupee Derivatives like Interest Rate Swaps, slow but steady deregulation of Rupee interest rates) which resulted in a significant shift in the nature of the market. Many of these changes forced financial service providers to access gilt market for reasons like reducing mismatches in their books. This provided others with trading opportunities. Regulatory changes on the modes of holding investments (e.g. categorisation of investments into Trading, AFS and HTM) and its valuation methodologies added further impetus to churn securities in the portfolio for the purpose of realignment. Moreover, allowing Foreign Institutional Investors to invest in G-sec market and allowing them to hedge their forex risk by way of taking forward covers brought in another important group of players with appetite for trading in the market. Increased availability of reliable market information, large scale computerization, availability of efficient analytical tools and trained manpower contributed positively to the development process. Trading volumes, as a result showed sharp increase - SGL volumes (Central Government securities & T-Bills) increased by about 145% and 198% in 2001-02 and 2002-03 respectively as compared to the volumes in 2000-01. However, increase in volume did not result in any significant improvement of market liquidity in the real sense. Indian market is still characterized by lack of depth & shallow liquidity except for about 8-10 securities at a time (with average daily trading of about Rs. 100 crore) for which two way quotes are available in the market. Activity is concentrated in these securities due to the market confidence & ability to liquidate positions quickly at a fair value. Absence of market making activity in other securities (almost non-availability of any reasonable quote) discourages trading in such securities. Perceived inability to offload holdings at around the stop loss levels, if required, works as an effective deterrent. This trade dynamics appear to work against expansion of the market in terms of number of securities traded. Moreover, in a bullish phase, the market volume shows a tendency to increase rapidly and traders are less hesitant take positions even in relatively illiquid securities. In a bearish market, traders however avoid taking positions in such securities. Moreover, there are cases of quick shifts of market preference making certain securities illiquid in a short span of time (e.g. 7.95% GS 2032 were liquid up to January ’03 but are now traded thinly). This phenomena is also a constant source of worry for the traders and acts as a restraint from being a contrarian.Dominance of a few traders over the market, as it exists today, again ensures that other players also trade in the securities preferred by these traders. Market participants also cite some more reasons for the inadequate liquidity in the Indian Gilt market: a) Lack of reference yields come in the way of estimating fair price of a security i. In the shorter end, 4 to 5 T-bills are traded per day on an average and money market is concentrated mostly in overnight trade.
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Liquidity Preference Theory July2010
In the medium to long term, securities are not available for all maturities (e.g. there are no outstanding securities in the maturity range of 24 years to 29 years i.e. after 10.18% GS 2026 next maturity is for 7.95% GS 2032) and absence of long term zero coupon instrument/STRIPS makes estimating zero rates less reliable. b) Non availability of proper hedging instruments like rupee derivatives (e.g. interest rate swaps, futures and options) restricts the possibility of hedging positions in the derivatives market c) Concentration of securities amongst few players and lack of reliable market information related to floating stock leads to difficulty in pricing illiquidity d) Absence of speculators at retail level deprives the market of the cushioning effect in cases of movements without adequate change in fundamentals ii.
Term Structure of Interest Rates
A yield curve displaying the relationship between spot rates of zero-coupon securities and their term to maturity.
The resulting curve allows an interest rate pattern to be determined, which can then be used to discount cash flows appropriately. Unfortunately, most bonds carry coupons, so the term structure must be determined using the prices of these securities. Term structures are continuously changing, and though the resulting yield curve is usually normal, it can also be flat or inverted. The exact shape of the curve can be different at any point in time. So if the normal yield curve changes shape, it tells investors that they may need to change their outlook on the economy .
There are three main patterns created by the term structure of interest rates: 1) Normal Yield Curve: As its name indicates, this is the yield curve shape that forms during normal
market conditions, wherein investors generally believe that there will be no significant changes in the economy, such as in inflation rates, and that the economy will continue to grow at a normal rate. During such conditions, investors expect higher yields for fixed income instruments with long-term maturities that occur farther into the future. In other words, the market expects long-term fixed income securities to offer higher yields than short-term fixed income securities. This is a normal expectation of the market because short-term instruments generally hold less risk than long-term instruments; the farther into the future the bond's maturity, the more time and, therefore, uncertainty the bondholder faces before being paid back the principal. To invest in one instrument for a longer period of time, an investor needs to be compensated for undertaking the additional risk. Remember that as general current interest rates increase, the price of a bond will decrease and its yield will increase.
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Liquidity Preference Theory July2010
2) Flat Yield Curve: These curves indicate that the market environment is sending mixed signals to
investors, who are interpreting interest rate movements in various ways. During such an environment, it is difficult for the market to determine whether interest rates will move significantly in either direction farther into the future. A flat yield curve usually occurs when the market is making a transition that emits different but simultaneous indications of what interest rates will do. In other words, there may be some signals that short-term interest rates will rise and other signals that long-term interest rates will fall. This condition will create a curve that is flatter than its normal positive slope. When the yield curve is flat, investors can maximize their risk/return trade-off by choosing fixed-income securities with the least risk, or highest credit quality. In the rare instances where-in long-term interest rates decline, a flat curve can sometimes lead to an inverted curve.
3) Inverted Yield Curve: These yield curves are rare, and they form during extraordinary market conditions wherein the expectations of investors are completely the inverse of those demonstrated by the normal yield curve. In such abnormal market environments, bonds with maturity dates further into the future are expected to offer lower yields than bonds with shorter maturities. The inverted yield curve indicates that the market currently expects interest rates to decline as time moves farther into the future, which in turn means the market expects yields of long-term bonds to decline. Remember, also, that as interest rates decrease, bond prices increase and yields decline.
You may be wondering why investors would choose to purchase long-term fixed-income investments when there is an inverted yield curve, which indicates that investors expect to receive less compensation
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Liquidity Preference Theory July2010
for taking on more risk. Some investors, however, interpret an inverted curve as an indication that the economy will soon experience a slowdown, which causes future interest rates to give even lower yields. Before a slowdown, it is better to lock money into long-term investments at present prevailing yields, because future yields will be even lower.
The Theoretical Spot Rate Curve:
Unfortunately, the basic yield curve does not account for securities that have varying coupon rates. When the yield to maturity was calculated, we assumed that the coupons were reinvested at an interest rate equal to the coupon rate, therefore, the bond was priced at par as though prevailing interest rates were equal to the bond's coupon rate. The spot-rate curve addresses this assumption and accounts for the fact that many Treasuries offer varying coupons and would therefore not accurately represent similar non-callable fixed-income securities. If for instance you compared a 10-year bond paying a 7% coupon with a 10-year Treasury bond that currently has a coupon of 4%, your comparison wouldn't mean much. Both of the bonds have the same term to maturity, but the 4% coupon of the Treasury bond would not be an appropriate benchmark for the bond paying 7%. The spot-rate curve, however, offers a more accurate measure as it adjusts the yield curve so it reflects any variations in the interest rate of the plotted benchmark. The interest rate taken from the plot is known as the spot rate.
The spot-rate curve is created by plotting the yields of zero-coupon Treasury bills and their corresponding maturities. The spot rate given by each zero-coupon security and the spot-rate curve are used
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Liquidity Preference Theory July2010
together for determining the value of each zero-coupon component of a non-callable fixed-income security.
Remember, in this case, that the term structure of interest rates is graphed as though each coupon payment of a non-callable fixed-income security were a zero-coupon bond. T-bills are issued by the government, but they do not have maturities greater than one year. As a result, the bootstrapping method is used to fill in interest rates for zero-coupon securities greater than one year. Bootstrapping is a complicated and involved process and will not be detailed in this section (to your relief!); however, it is important to remember that the bootstrapping method equates a T-bill's value to the value of all zero-coupon components that form the security. There are four main economic theories attempting to explain how yields vary with maturity:
Market expectations (pure expectations) hypothesis
The pure expectations theory simply sates that forward rates are the market’s expectation of the level of future interest rates. Forward Rate = Expected Future Interest Rate – – This means that the shape of the term structure reflects the markets expectation of future shortterm rates. The pure expectations theory is based on the assumption that market participants who buy and sell treasury bonds are willing and able to exploit profit opportunities whenever forward rates differ form expected future rates.
Liquidity Preference Theory
The theory of liquidity preference holds that long-term securities should provide higher returns than short-term obligations because investors are willing to sacrifice some yields to invest in short-maturity obligations to avoid the higher price volatility of long-maturity bonds. Another way to interpret the liquidity preference hypothesis is to say that lenders prefer short-term loans, and, to induce them to lend long term, it is necessary to offer higher yields. The liquidity preference theory contends that uncertainty and volatility cause investors to favour shortterm issues over bonds with longer maturities because short-term bonds are less volatile and can easily be converted into predictable amounts of cash should unforeseen events occur. This theory argues that the yield curve should slope upward and that any other shape should be viewed as a temporary aberration.
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Liquidity Preference Theory July2010
This theory can be considered an extension of the expectations hypothesis because the formal liquidity preference position contends that the liquidity premium inherent in the yields for longer maturity bonds should be added to the expected future rate in arriving at long-term yields. Specifically, the liquidity premium (L) compensates the investor in long-term bonds for the added volatility inherent in long-term bonds compared to short-maturity securities. Because the liquidity premium (L) is provided to compensate the long-term investor, it is simply as follows: (1 + t RN) = [(1 + t R1)(1 + t+1r1 + L2) . . . (1 + t+N–1r1 + Ln)]1/N In this specification, the Ls are not the same but would be expected to increase with maturity because the price volatility increases with maturity. The liquidity preference theory has been found to possess some strong empirical support. To see how the liquidity preference theory predicts future yields and how it compares with the pure expectations hypothesis, let us predict future long-term rates from a single set of one- year rates: 6 percent, 7.5 percent, and 8.5 percent. The liquidity preference theory suggests that investors add increasing liquidity premiums to successive rates to derive actual market rates. As n example, they might arrive at rates of 6.3 percent, 7.9 percent, and 9.0 percent. As a matter of historical fact, the yield curve shows an upward bias, which implies that some combination of the expectations theory and the liquidity preference theory will more accurately explain the shape of the yield curve than either of them alone. Specifically, actual long-term rates consistently tend to be above what is envisioned from the price expectations hypothesis. This tendency implies the existence of a liquidity premium. A hypothesis about the term structure of interest rates (the relationship between interest rates and term to maturity) holding that investors demand a premium for bearing interest rate risk. The extent of the premium increases with term to maturity but at a decreasing rate. The two reasons behind the decreasing rate of increase are that duration, a measure of a bond's price sensitivity to interest rate changes, increases at a decreasing rate with term to maturity and that long term interest rates are typically less volatile than short term interest rates. ? Prices of longer term bonds are more sensitive to changes in interest rate--as measured by duration-- therefore they are more susceptible to interest rate risk. – If investors are averse to this risk they will prefer to hold short-term bonds unless they are adequately compensated for bearing the interest rate risk inherent in longer-term bonds. Forward Rate = Expected Rate + Liquidity Premium Expected Rate = Forward Rate – Liquidity Premium
– –
Deriving Expected Future Rates: Liquidity Preference Theory
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Liquidity Preference Theory July2010
Liquidity Premium in Term Structure
Liquidity Vs Expectation theory
Market Segmentation Theory
A modern theory pertaining to interest rates stipulating that there is no necessary relationship between long and short-term interest rates. Furthermore, short and long-term markets fall into two different categories. Therefore, the yield curve is shaped according to the supply and demand of securities within each maturity length. The yield curve reflects the actions and preferences of the major participants in the market. Institutions have strong maturity preferences:
a) Commercial banks dominate demand for short-term securities
b) Insurance Companies dominate demand for long term securities. c) Insurance demand is stable over time
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Liquidity Preference Theory July2010
d) Commercial bank demand is less stable, e) During strong business activity, banks sell short-term bond to accommodate loans--so short-term spot rates rise. f) During weak business activity, banks buy short term bond --so short term spot rates decline
Estimating the Zero Coupon Yield Curve
The term structure of the interest rates forms the basis of valuation of all fixed income securities. Modelled as a series of cash-flows due at different points in time in the future, the underlying price of a fixed income security can be calculated as the net present value of the stream of cash-flows. Each cash flow has to be discounted using the interest rate for the associated term to maturity. Arriving at the appropriate set of interest rates- term structure or Zero coupon yield curve – for the Indian debt market is the objective of this section.
Nelson & Siegel equation
The Nelson & Siegel equation is as under:
Spot Rate = ß0 + (ß1+ß2) * where, ß0 is the contribution of long term component
[(1-exp
(-m/
t)]/(m/t)–
ß2*exp
(-m/
t)
ß1 is the contribution of short term component ß2 indicates the contribution of medium term component t is the decay factor and m is the maturity ß2 & t determine the shape of the curve
The present exercise uses the data from the NSE-WDM, which constitutes about 70 percent of secondary market volume. The result of the model is as following:
beta 0 beta 1 beta 2 tau
16-Jul07 10.5030 -3.1726 -0.7166 15.5000
15-Jul08 11.9901 -2.4912 -3.7937 5.5194
16-Jul08 19.1424 -9.4000 12.9728 11.9868
15-Jul09 9.5540 -5.5438 -0.0412 4.1271
16-Jul09 10.2146 -5.9592 -0.0184 5.8687
15-Jul10 9.1150 -3.7740 0.0190 2.8015
16-Jul10 9.2352 -3.2667 -0.0122 3.9433
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Liquidity Preference Theory July2010
Spot rates
The estimated term structure/ spot rates are as follows:
Time to Spot Rate ( As Spot Rate ( Maturity on 16-07As on 15(In years) 2007) 07-2008) 0.5 7.3696 9.4467 1 7.4082 9.4069 1.5 7.4463 9.3779 2 7.4837 9.3587 2.5 7.5206 9.3479 3 7.5569 9.3446 3.5 7.5927 9.3479 4 7.6293 9.3573 4.5 7.6640 9.3715 5 7.6981 9.3900 5.5 7.7318 9.4140 6 7.7649 9.4375 6.5 7.7975 9.4656 7 7.8297 9.4959 7.5 7.8613 9.5281 8 7.8925 9.5619 8.5 7.9232 9.5969 9 7.9545 9.6329 9.5 7.9831 9.6697 10 8.0136 9.7070
Spot Rate ( As on 16-072008)
9.6728 9.6122 9.5601 9.5161 9.4797 9.4505 9.4281 9.4115 9.4017 9.3976 9.3991 9.4049 9.4158 9.4311 9.4505 9.4738 9.5008 9.5311 9.5646 9.6010
Spot Rate ( As on 15-072009)
4.3297 4.6249 4.8979 5.1505 5.3844 5.6013 5.8025 5.9963 6.1695 6.3306 6.4806 6.6204 6.7508 6.8726 6.9864 7.0928 7.1925 7.2859 7.3735 7.4557
Spot Rate ( As on 1607-2009)
4.5008 4.7328 4.9523 5.1599 5.3565 5.5427 5.7191 5.8925 6.0507 6.2008 6.3432 6.4785 6.6069 6.7290 6.8451 6.9555 7.0606 7.1607 7.2559 7.3467
Spot Rate ( As on 15-072010)
5.6593 5.9423 6.1944 6.4194 6.6206 6.8009 6.9627 7.1135 7.2442 7.3622 7.4690 7.5659 7.6540 7.7342 7.8073 7.8742 7.9355 7.9918 8.0436 8.0914
Spot Rate ( As on 16-072010)
6.1659 6.3475 6.5149 6.6691 6.8115 6.9429 7.0645 7.1811 7.2850 7.3814 7.4708 7.5539 7.6312 7.7032 7.7702 7.8328 7.8912 7.9458 7.9969 8.0448
12.0000 10.0000 8.0000 6.0000 4.0000 2.0000 0.0000 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 Time to Maturity ( In Years) Spot Rate ( As on 1607-2007) Spot Rate ( As on 1607-2010) Spot Rate ( As on 1607-2009) Spot Rate ( As on 1607-2008)
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Liquidity Preference Theory July2010
Indian Government Bond 10 year Yield Curve
Indian Interest Rate
Calculating the Forward rates & Liquidity Premium using the spot rates
16-07-2007 Maturity (Years) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Half Year One Year forward Liquidity Spot Rates Forward Rates rates YTMs Premium 7.369605616 7.408219676 7.182184404 7.446250599 7.385971411 7.483706724 7.45713144 7.559246825 7.2619 -0.005186958 7.520596323 7.526655031 7.556927591 7.594574264 7.703518999 7.361 -0.000684509 7.592708649 7.660920836 7.629292164 7.736106926 7.846678138 7.3621 -0.004812781 7.663976468 7.790137959 7.69813476 7.851916016 7.97394576 7.398 -0.004322257
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Liquidity Preference Theory July2010
5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 7.731774843 7.764904438 7.797531185 7.829662639 7.861306273 7.892469474 7.923159545 7.954536965 7.983149083 8.013581249 7.912245079 7.971154811 8.028674455 8.084832831 8.139658335 8.193178933 8.245422162 8.316442961 8.32615382 8.41633784 8.099374271 8.21902987 8.333142827 8.452364019 8.546435139 7.542 7.6543 7.689 7.8113 7.9108 0.001655271 0.001115371 -0.004009295 0.003423494 0.002640074
16-07-2008 Maturity (Years) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
Spot Rates 9.672773432 9.612173751 9.560106518 9.516100556 9.479706906 9.45049784 9.428065913 9.411528553 9.401729625 9.397585187 9.399062494 9.404938613 9.415815449 9.431103304 9.450528092 9.47382913 9.500758532 9.53108063 9.564571421 9.601018034
Half Year Forward Rates 9.110934065 9.242487309 9.173792522 9.126041619 9.097651215 9.087130994 9.089298614 9.115632878 9.150942925 9.20213829 9.255438884 9.328853097 9.408729433 9.497338839 9.593836329 9.697430588 9.807381062 9.922995194 10.0436258
One Year forward rates
YTMs
Liquidity Premium
9.420111568 9.319410276 9.294703922 9.341829492 9.441713159 9.588222902 9.77337737 9.990171817 10.23246762
9.3916 9.3656 9.4132 9.4609 9.5085 9.5562 9.5819 9.3691 9.35
-0.001528706 -0.001016033 0.002614204 0.003100786 0.003050975 0.002546137 -0.000114085 -0.023086623 -0.010542176
16-07-2009 Maturity Half Year One Year forward (Years) Spot Rates Forward Rates rates 0.5 4.500799842 1 4.73281919 4.855568821
YTMs
Liquidity Premium
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Liquidity Preference Theory July2010
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 4.952276553 5.159937071 5.356516174 5.542682946 5.719063252 5.89249644 6.050700567 6.200783718 6.343224857 6.478472489 6.606946696 6.729041021 6.845124233 6.955541963 7.060618237 7.16065689 7.2559429 7.346743619 5.321768741 5.704046791 6.054860834 6.376803774 6.672254904 6.992291144 7.195436431 7.423360448 7.632546866 7.824538747 8.000751822 8.162484997 8.310929997 8.447180228 8.572238895 8.687026464 8.7923875 8.889096942 5.588796811 6.312358953 6.948908896 7.442934235 7.877845703 8.244883451 8.554564921 8.815800845 9.036133183 5.3876 5.766 6.1519 6.4988 6.592 6.9382 6.9917 6.9899 6.9536 0.00026959 0.006489563 0.003691597 0.004548394 -0.008186208 0.007942577 -0.011876147 -0.018402998 -0.024086795
Liquidity Premium Graphs
0.01 0.005 Liquidity premium 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Liquidity Premium from16-07-09
-0.005 -0.01
-0.015 -0.02
Liquidity Premium
-0.025 -0.03 Time to Maturity
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Liquidity Preference Theory July2010 Liquidity Premium 16-07-2007
0.004 0.003 0.002 0.001 0 -0.001 -0.002 -0.003 -0.004 -0.005 -0.006
Liquidity Premium
1
3
5
7
9
11 13 15 17
Liquidity Premium 1607-2007
Maturity ( Years)
Liquidity Premium 16-07-2008
0.005 0 Liquidity Premium 1 -0.005 -0.01 -0.015 -0.02 -0.025 Maturity (Years) Liquidity Premium 1607-2008 3 5 7 9 11 13 15 17
Conclusion
From the zero coupon yield curves it could be seen that there is a upward trend in the spot rates. This clearly shows, that for higher maturity zero coupon yield increases. If lenders know that short-term rates will remain constant in the future, current long-term rates must be equal to current short-term rates, so that the yield curve will be perfectly flat. If there is no uncertainty about future interest rates, current long-term rates must be an appropriately weighted average of current and future short -term rates. A two-year rate, for instance, must be a weighted average of current and future one-year rates, while a six-month rate must be a weighted average of current and future three-month rates, etc. Yield curves tend to be steeply upward-sloping when short-term interest rates are low and often slope downward when short-term rates are high. During the last century at least, it has been distinctly upwardsloping.” The simple expectations theory could explain this only by assuming that lenders usually expect
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Liquidity Preference Theory July2010
rates to rise persistently over time. This assumption does not seem plausible, unless you believe that lenders were extremely poor forecasters. While interest rates have varied considerably during the past century there is little evidence that they have increased on average, or that market participants had any reason to expect them to do so. Indeed, the evidence suggests that people usually expect future shortterm interest rates to remain near current levels. Any alternative explanation for the fact that yield curves are normally upward-sloping must be based on something about long-term securities that makes them systematically less attractive to lenders than short-term securities. If the risk of capital loss on securities tends to increase in proportion to their remaining terms, lenders who demand interest compensation for bearing this risk will demand more compensation on long-term securities than on short-term securities. This will tend to make the yields on longer-term securities higher than those on securities with shorter terms—that is, it will tend to make the yield curve upward sloping. When lenders expect interest rates to change in the future, In this case, the actual yield should be given by the sum of the term-adjusted rate (that is, the weighted-average base rate) and the appropriate term premium. This can produce curves that slope in one direction along one part of their range. but in the opposite direction along another part. If lenders expect interest rates to remain constant for a shoit period, and then fall sharply, for example, the yield curve will appear humped, sloping upward at very short terms, peaking near the term corresponding to the date at which rates are expected to decline, and sloping downward for a range of terms thereafter. Curves with this shape are frequently observed shortly before economic recessions begin, presumably because interest rates tend to fall sharply during recessions. Yield Curve when base rate is constant
Yield Curve when base rate will fall
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Liquidity Preference Theory July2010
From the above analysis, it could be seen that for year 2007 & 2008 the interest rate may remained constant. The estimators also assumed it to remain constant in the future. Market participants expected future short-term interest rates to remain near current levels. So a flat zero coupon yield curve could be in the year 2007 & 2008. In 2009, due to recession the risk free rate dropped from 8-9 percent to 4-5 percent. Because of this drop in interest rate, the net yield of the bonds went down. This could be seen in the zero coupon yield curve for the year 2009. The starting point is around 4 percent. It is an upward sloping curve with long term maturities having a higher yield. The liquidity preference theory works in India. It could be easily seen that apart from the short term interest rates, the long term securities have a premium attached to it to make them attractive to invest. The liquidity premium increases as the term to maturity increases.
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