Study On Term Structure Of Interest Rates Finance Essay

Study On Term Structure Of Interest Rates Finance Essay

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The term structure of interest rates is an extremely important element in Finance. It is one of the most important indicators for pricing contingent claims, determining the cost of capital and managing financial risk. Interest rates may be used in an extensive variety of applications; such as investments, long term debt, determination of the cost of capital, measurement of credit risk, valuation of contingent claims as well as pricing, hedging and managing the risk of interest rate derivatives. Furthermore; interest rates are used in the establishment of fiscal and monetary policies.

Maturity plays also an important role as a determinant on interest rates; since this factor determines the length on a loan. Longer term loans imply higher interest rates than shorter term loans since a longer term implies higher future uncertainty of expected outcomes. Financial theory and asset pricing models state that as maturity increases the risk involved or assumed by investors is higher. Therefore; the expected returns should be greater. Consequently; investors would be interested in knowing elasticity estimates according to specific frequencies. As maturity increases the mean increases accordingly suggesting the existence of a term premium built on the term structure.

Interest rates are frequently used in several additional applications; such as fixed income securities and interest rate derivatives. In both cases interest rates play a key role; since this component is utilized to determine the present value. Within the area of financial risk management, it is important to determine how a change in the level of interest rates will affect a specific asset. Interest rate derivatives allow for the possibility of hedging risk as a result of unpredictable shocks. Financial instruments are widely applied since they are able to explain how risk management maximizes shareholders wealth.

Interest rate fluctuations create one of the most important determinants on bond prices. As interest rates fluctuate; bondholders are exposed to capital losses and gains. However; this exposure is only experienced when bondholders hold bonds only for a determined period of time. In the case when bonds are hold until maturity; there is no exposure to risk. In addition; it has been shown empirically that long term bonds are more sensitive to interest rate movements than short term bonds.

THEORY AND LITERATURE REVIEW

The price of a bond depends on the stochastic behavior of the current and future spot rates in the economy. As a result; bond prices must be a function of the current and future spot rates. Additionally; interest rates can not be constant, since that would imply predictability on bond prices. Moreover; constant interest rates may imply no volatility on the underlying assets. Consequently; the demand for any interest rate derivatives would reduce completely since all possible risk could be vanished. Therefore it is important to model the term structure of interest rate.

Theories of Term Structure

In order to be able to evaluate and understand correctly the term structure of interest rates; it is important to comprehend the different theories involved. It is required to understand how the spot rates or discount factors are determined; as well as to comprehend the explanations that determine the shape of the term structure of interest rates. According to Nelson (1972); the term structure of interest rates is determined mainly by two different theories, which are the liquidity preference theory and the preferred habitat theory.

Moreover; Gibson, Lhabitant and Talay (2001) agree that the term structure of interest rates is mainly explained by three theories which analyze the relationship between interest rates of various maturities and the value of the term premium. These theories include the expectations hypothesis, the liquidity preference theory and the segmented market hypothesis.

Liquidity Preference Hypothesis

This theory was developed by Hicks. It predicts that a term premium may be obtained by capital invested in long term bonds because bond holders will require compensation for exposure to capital fluctuations. (Nelson; 1972) According to the liquidity preference theory, investors are risk averse, prefer short term maturities and will require a premium in order to commit in long term securities.

Liquidity Preference Theory admits the importance of expected future spot rates but gives more importance to the effects of the risk preferences of market participants. This hypothesis states that risk aversion will cause forward rates to be greater than expected spot rates by an amount which increases with maturity. The term premium is the increment given to investors in order to hold longer term securities since those imply higher risk.

Expectations hypothesis

This theory gives increasing importance on the expected values of future spot rates. This theory states that bonds are priced so that the implied forward rates are equal to the expected spot rates. This hypothesis is characterized by two propositions. The first proposition states that the return on holding a long term bond to maturity is equal to the expected return on repeated investment in a series of short term bonds. On the second proposition; it is mentioned that the expected rate of return over the next holding period is the same for bonds of all maturities.

According to the expectations theory, it is argued that the term structure of interest rates is driven by the investors’ expectations on future spot rates; where the forward rate is an unbiased estimator of the future spot rate. The rate of return on a bond maturing at time should be equivalent to the geometric average of the expected short term rate from t to T.

Preferred habitat theory

This theory was developed by Modigliani and Sutch (1966). It states that market participants are assumed to have preferred maturity ranges but will decide to change their selected habitat if a enough term premium is offered. (Nelson; 1972) According to the preferred habitat theory, investors and borrowers have different specific time horizons .The institutional investors have different maturity needs that lead them to confine their security selections to specify maturity segments.

This theory contends that the business environment along , with the legal and regulatory limitations tends to direct each type of financial institutions to allocate its resources to particular types of bonds with specific maturity characteristics.

DATA CONSIDERATION

For determining the term structure of interest rates we have taken most actively traded wholesale bond market data from NSE website using the bhavcopy. The data was taken from 9th August, 2010 to 23rd August, 2010.

Firstly we have taken all the bonds the bonds from bhav copy of WDM from NSE website. This comprised of around 4300 bond list.

Then we excluded all those bonds which have not been traded in last 15 days.

The bonds have improper or incomplete data have also been removed.

We were left with 132 different bonds which have been included in our study.

Then those observations which have been found as outliers are further removed from our data sample.

The final sample after removing outliers was of 99 bonds.

METHODOLOGY

Yield to maturity of all these government Coupon paying bonds is calculated. The term to maturity is also calculated. This is done by using the “yieldâ€Â function of excel. The term to maturity is calculated using the Day360 function of excel.

Test for Normality was done for both YTM and TTM series. The Jacques Bera statistics was used to check the normality of data.

Cook's distance is a commonly used estimate of the influence of a data point when doing least squares regression. Cook's distance measures the effect of deleting a given observation. Data points with large residuals (outliers) and/or high leverage may distort the outcome and accuracy of a regression. A large Cook's D indicates that excluding a case from computation of the regression statistics changes the coefficients substantially.

There are different opinions regarding what cut-off values to use for spotting outliers:

A simple operational guideline of Di > 1 has been suggested.

All values greater than 4/n where n is the number of our data sample can be removed as outliers. This method is used to remove the outliers in our regression.

The outlier was removed using the SPSS software. (Files attached)

The regressions using various models have been run between yield to maturity data and time to maturity data. The dependent variable was Yeild to maturity and independent variable was time to maturity. This was done in EVIEWS. (Files attached )

ANALYSIS

Model

Equation

R2

White hetroscadacity Test

Residual normality

Linear

Y = b0 + (b1 * t)

0.357

0.017

0.008

Log

Y = b0 + (b1 * ln(t)).

0.553

0.28

0.034

Inverse

Y = b0 + (b1 / t).

0.377

0.011

0.057

Quadratic

Y = b0 + (b1 * t) + (b2 * t**2).

0.57

0.34

0.023

Cubic

Y = b0 + (b1 * t) + (b2 * t**2) + (b3 * t**3).

0.57

0.607

0.024

Power

ln(Y) = ln(b0) + (b1 * ln(t))

0.545

0.078

0.001

Growth

ln(Y) = b0 + (b1 * t).

0.34

0.01

0.00047

Sqrt YTM

Y1/2 = b0 + (b1 * t)

0.35

0.013

0.0009

Sqrt TTM

Y = b0 + (b1 * t1/2)

0.47

0.111

0.0275

Analysis

Cubic and quadratic models both have an R2 of 0.57 and the power and log model have an R2 of 0.55.

Quadratic model has white heteroscedasticity value of 0.34, cubic has 0.607 and log has 0.28.

Considering the R2 and white heteroscedasticity, the best model is cubic model.The equation found out to be as: YTM = 0.06-0.0028*ttm+0.015*ttm^2+0.00014*ttm6^3

RESULT

The equation of term structure of interest rates can help us to determine the coupon interest of new bonds which are to be raised by issuing authorities.

This can also help us to compare and estimate the coupon payments for other corporate bonds by adding the additional risk premium to the ytm at that maturity.

This also helps us to get a better idea of which all bonds needs to be used for investment portfolio.

GRAPHS AND PLOTS

Scatter Plot

Linear Model

Logarithmic Model

Power Model

Quadratic Model

Cubic Model

Power 4 Model

LIMITATION

Inflation rate, volatility, mean, spread between long and short term rates could have a significant impact on the term structure equations but we have considered that the price of bond have included all these effects, which can be further debated.

There is no common and unified frame-work which could nest all available equations. The high end models like Nelson Siegel etc were tough to implement due to knowledge and exposure constraints.

Corporate bonds though have been considered to have a certain risk premium over and above the government bonds which we have included in our study but this can be a further explored.

SCOPE FOR FURTHER IMPROVEMENT

The term structure for Interest rates equation can be improved using Splines and Knots. We have done some work on Splines in SAS but due to constraints of knowledge, the scope of improvement remains.

There are few other models like Nelson-Seigel Model and Cox-Ingersoll-Ross model which can help us determine these equation better can also be implemented.