The Term Structure of Interest Rates

The term structure of interest rates is the relationship between interest rates and term to maturity. However, financial instruments differ not only in terms of their maturity characteristic, but also other characteristics, most notably the risk. Therefore, the term structure is best estimated through yields on the default risk free government securities. A yield curve that charts yield-to-maturity (YTM) for Treasury securities (on the vertical axis) of various maturities (on the horizontal axis) as of a particular date captures the term structure. The yield curve changes from day to day as the YTM changes. While yields on other money market instruments, such as those on commercial papers of varying maturity could also be considered for the term structure, the risk element in these instruments would need to be considered. Yield curves, today, are popularly estimated in parametric forms using the methodology of Nelson and Siegel (1987) or its extension by Svensson (1994).

Three alternative paradigms are usually used to explain the term structure of interest rates. The unbiased expectations theory (or the pure expectations theory) suggests that the expected future spot rate equals the forward rate. If, say, current economic conditions (say rise in current inflation or a speculative pressure on domestic currency) make short-term spot rates high, then the term structure represented by the yield curve should turn downward sloping in accordance with the expectations theory.

The liquidity preference theory is based on the premise that investors prefer short-term securities because of the interest rate risk or because the investors fear that if needed, they may not be able to realise their funds earlier than anticipated because of liquidity problems. Investors, therefore, prefer short-term securities and try to roll over these securities. Rollovers, however, involve transaction costs. The investors, therefore, evaluate the expected returns from holding long-term bonds and compare them with those on the short-term bonds. They generally tend to charge a liquidity premium for holding long-term bonds, which is the difference between the forward rate and the expected future spot rate. In this case downward sloping yield curves would occur only when the market expectations are that interest rates would decline substantially. A flat term structure in itself indicates that interest rates are expected to decline somewhat. The upward sloping yield curve would indicate an expected rise or fall in interest rates depending upon the steepness of the slope. Steeper the slope, more likely is that market expects interest rates to rise in future.

Another alternative explanation for observed term structure is provided by the market segmentation theory. It points to institutional and legal constraints that often exist in markets so that some investors and borrowers are restricted to certain maturities alone. Psychological factors, customs and habits may also restrict them from investing only in certain classes of maturities. For example, pension and insurance funds generally prefer longer maturity debt instruments in relation to banks and other financial institutions. Besides, trading restrictions, lack of instruments and institutional structures may also result in the term structure getting disjointed. It is possible that the short-end, the long-end and the intermediate-term of the markets may be segmented. With spot rates in each of these segments getting determined by respective demand and supply conditions, the yields in each segment may remain misaligned. The yield curve could be upward or downward sloping depending upon whether the intersection of short-end demand and supply curves are lower or higher than that for the long-end.

The term structure or the yield curves have considerable information content. They could be used to value a wide range of fixed income instruments, including coupon paying bonds, interest rate forwards and swaps and other derivative instruments. The coupon paying bonds, for example, can be stripped into zero coupon instruments corresponding to various cash flows, with the redemption amount getting added to the terminal coupon. The underlying price of this fixed income security can then be calculated as the net present value of the stream of all these cash flows using this zero coupon yield curve. In practice, however, yields of various securities of various maturities are affected by several factors, other than coupon rates and maturity period. The risk factor, marketability and tax rates are important considerations in pricing that a yield curve may not easily capture.

The term structure also has information content on future inflation and future real economic activity. The value of this information content to a large extent depends upon the stability and predictability of the yield curve with respect to non-financial activity. The information content in the yield curve depends largely on the Fisher equation and the expectations theory of the yield curve. Fisher equation decomposes one period nominal interest rate roughly into one period ex ante real interest rate and the one period ahead expected inflation. Combining this with expectations theory, the YTM could be explained by the expected real interest rate and the expected inflation. Following liquidity preference theory, a risk premium could be added to the two expected variables determining YTM if investors are believed to charge the same for holding the bond of a certain maturity. Under the expectations theory, however, the risk premium is constant for all maturities. The yield spread or the slope of the yield curve provides information on expected real interest rate spread and on market's inflation expectations. The yield curve provides the best measure of market's expected inflation path if expectations are formed rationally, risk premium is constant over time and the real term structure is flat denoting constant expected real interest rate for all maturities. If prices are fixed, nominal yield spreads capture the expectations regarding the future real economic activity. However, in practice, the information content of the yield spread for the future real economic activity depends on the nature of macroeconomic shocks. If the shocks are largely of a monetary nature, a positive yield spread could indicate expectations of an economic slowdown. If shocks are real and price rigidities exist, a positive yield spread could indicate a future economic upswing.

In India, the predictive power of the yield curve is yet to be established. The term structure was largely segmented and though a great deal of integration has taken place over the last few years, yields of various maturities are still not perfectly correlated with one another or with the movements in expected inflation. As a result, the predictive power of the yield spread is curtailed by the noise in the forecasts. Nag and Ghose (2000) find that the term structure is segmented, with liquidity considerations affecting the short-end and expectations dominating the long-end of the market and interpret that the yield curve movements during 1996-99 were subject to the segmentation. The growing integration of the term structure is, however, reflected in the co movement of interest rates. The correlation coefficients among the set of interest rates is positive (Report on Currency and Finance, 1998-99). For the banking sector, the short-term deposit rates, long-term deposit rates and the prime lending rates have shown strong co-movement with the Bank Rate in the recent years (Chart.III.4, RBI Annual Report, 1998-99). More importantly, the inter-linkages across the term structure for gilts in India is reflected in cointegration between call money rates and cut off yield on short term 91 day T-bills, medium term 364 days T-bills and redemption yield on long-term Government of India securities (Joshi, 1998). However, as unique common stochastic trend is not observed in this set, the complete integration of the term structure or the efficiency of trading across maturities is still to evolve. As such, it is difficult to identify a reference rate that could be used as a policy instrument to guide the course of the entire term structure. Bhoi and Dhal (1998), on the other hand, observe that the cut off yield on 91 day T-bills could qualify as a reference rate for India among the set of other available rate variables. They find that excluding call money rates and return on equity, all other interest rates exhibited co-movement with the 91 days Treasury bills. It is possible that with further widening and deepening of the gilt market, a smooth yield curve may emerge in the years ahead. The term structure ranging from the overnight call rate to the long-end may get aligned, so that the central bank can more effectively operate at the short-end for its monetary policy objectives. The yield curve could then have a considerable predictive power.