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CHAPTER - 3
TERM STRUCTURE OF INTEREST RATES – A
THEORETICAL FRAMEWORK
The concept of rate of interest occupies an important place not only in economic literature but also in economic activities. “Interest rate has diverse roles in the economy
such as reward to capital which is a factor of production, a return to saving and a cost to investment, and an instrument of monetary policy for credit. These and other aspects are relevant for policy makers” (Avadhani, 2009). One of the main objectives of a monetary and financial policy in a developing country like India is to have an appropriate interest rate structure. Inter-relationship between different interest rates is of crucial importance in so far as it can be explained in terms of difference in the period of maturity of different loans (Roy, 1975). In discussing the „term structure of interest rates‟, it has to be recognised that instead of a single rate of interest, there may be a spectrum of interest rates observable in the financial system at a given point of time. In what sense are these different „interest rates‟ functionally „related to each other‟ may be referred as structure of interest rates.
The structure of interest rates may be determined primarily by a number of factors:
- Maturity Structure of the financial claim: The differences in the interest rates may exist on account of varying maturity structure of debt obligations. If the maturity structure is longer, the degree of risk is also higher and vice-versa. As a consequence, the long-term debt may involve higher rates and vice-versa.
- Taxation characteristic of the financial claim: Interest rates on certain securities carry high tax liability, whereas the tax liability on some other securities may be low or nil. Accordingly, the interest return on them must be higher or lower, otherwise people may be averse in respect of holding those securities.
- Degree of default risk of the financial claim: The degree of risk of default on the various debt contracts varies. The creditors want to compensate themselves against such a risk. Therefore, higher interest rates are charged on the funds involving greater risk and vice-versa.
- Marketability of the financial claim: The marketability of debt instruments also determines higher or lower rates of interest. If the securities are non-marketable, the investors will have to hold them till their maturity. That may involve greater risk of loss and, therefore, the interest rate on them may be higher. On the contrary, in case of marketability of debt instruments, risk – aversion can be possible through their disposal in the market. Such instruments carry lower rates of interest. The relationship between maturity and the interest rate is referred to as “the term structure of interest rates”. It is the interest rate difference on fixed income securities due
to difference in time of maturity. It is, therefore, also known as time structure or maturity structure of interest rates, which explains the relationship between yields and maturity of same type of security. Government securities are the best example of a financial claim to see the effect of maturity „on the structure of interest rates‟. In general, rates on the securities which mature within one year of issue are called short term rates and those which mature after one year are long-term rates.
3.1 YIELD CURVE “A diagrammatic representation of this relationship is known as the yield curve, which illustrates the relationship between maturity and yield at any given time, assuming all other factors to be constant. The yield curve can be constructed by plotting the yield to maturity (YTM) along the vertical axis, while the horizontal axis shows the term to maturity (measured in years)”(Oster, 2003). It can be considered as an economic forecasting tool whereby the market`s prediction of future interest rates is being made. According to Oster (2003), “yield curves change their shape over time in response to factors such as changes in interest rate expectations and fluctuations in liquidity in the economy”. The yield or the interest rates on financial claims tends to increase as the maturity gets longer. There are four possible patterns in explaining the yield curve.
Figure 3.1 (A) shows an upward sloping yield curve, which indicates that as the maturity of the security increases, rate of interest also increases. On the contrary in Figure 3.1 (B), the yield curve is downward sloping, depicting that the rate of interest declines as the maturity period increases. A flat yield curve as evident from Figure 3.1(C) that shows constant interest rates across securities of different maturities. In Figure 3.1 (D) humped yield curve is observed, which shows that interest rates at first increase and then decline as maturity increases. “The upward sloping curves prevail mostly during the periods of moderate economic growth and periods of recession. Flat and downward sloping curves, perhaps with humps, are usually observed during the periods of vigorous economic expansion and near the peaks of economic activity” (Henning et al, 1978). Although the above four forms of yield curves are theoretically possible and different theories have been propounded to explain them; but of all these, the upward sloping yield curve is most likely to be encountered. Mishkin (2001) stated “that besides explaining different shapes of the yield curve, a good theory of the term structure of interest must explain the following three empirical observations” : (a) “Interest rates on bonds of different maturities move together over time”. (b) “When short term interest rates are low, long term interest rates tend to be high, such that yield curves are upward sloped and vice-versa”. (c) “Yield curves are usually upward sloped”.
3.2 THEORIES OF TERM STRUCTURE OF INTEREST RATES A considerable effort has been devoted to determine the forces behind the shape of the yield curve. Despite extensive empirical and theoretical work in this area, no definite conclusion has been drawn. As per Cargill (1979), “there are four important and well-known theories which compete for explaining the term structure of interest rates”: 3.2.1 „Expectations Theory‟ 3.2.2 „Liquidity Premium Theory‟ 3.2.3 „Market Segmentation Theory‟ 3.2.4 „Preferred Habitat Theory‟
A brief discussion of the three theories is given below :- 3.2.1 Expectations Theory The expectations theory of the term structure was one of the earliest of theories advanced to explain the shape of yield curve. According to the expectations theory, the expectations regarding future interest rates determine the present structure of interest rates. The theory originated with Irving Fisher, was perfected by Hicks (1946) in his Value and Capital, and is closely identified with Lutz (Paul, 1996). The main proposition of this theory is that the interest rate structure is determined by the expectations of the lenders and borrowers concerning the future rate of interest. According to Paul(1996), “this theory is based on certain assumptions”: (a) “There is a perfect competition in financial markets”. (b) “The investors are rational, i.e., they wish to maximise the yield of their holding period”. (c) “Investors have a perfect foresight, and they hold uniform expectations about the future level and changes of short term interest rates and security prices”. (d) “There are no transaction costs of shifting funds from one maturity period to another”. (e) “Securities of different maturities are perfect substitutes for each other”. For the purpose of simplification, the yield can be calculated by using the simple averaging method, for which the equation is: r 1 +r 2 +r3……………………….+rn Rn = n Where Rn is the current „long term rate of interest‟ and r 1 , r 2 …….. rn are the expected future short term rates of interest. On the basis of above assumptions, it is posited that long term rate equals „average of the short-term rates of interest‟ that market participants expect to prevail over the long term period. “The long term rate will be higher than the short-term rate (i.e. the yield curve will be upward sloping) only if investors expect future short term rates to be higher than the current short-term rate. Similarly, the long term rate will be lower than the short-term rate (the yield curve will be downward sloping) when investors expect future short-term spot rates to fall below the current short-term spot rate” (Bhole,2004).
3.2.2 Liquidity Premium Theory The liquidity premium theory is based on the expectations theory but rejects the assumption that market participants are indifferent to short-term versus long-term obligations. According to Bhole (2004) views, “Some people viewed it as an extension or modification of the pure expectations theory and, therefore, it is sometimes called a biased expectations theory”. “It accepts the expectations approach that expectations of changes in the interest rates affect the term structure of interest rates. But, it maintains that the expectations are not the only factor influencing the term structure; liquidity factor also explains part of this structure”(Paul, 1996). According to this theory, the degree of liquidity of a financing instrument is the determinant of the structure of rate of interest. The higher the degree of liquidity, the lower is the rate of interest and the lower the degree of liquidity, the higher is the rate of interest. “While the expectations theory ignores risk, it assumes that investors wish to maximise return. In contrast to this, the liquidity preference theory assumes that investors are risk-return traders; they do not want to maximise return, whatever be the risk. Similarly, they do not want to minimise risk even if it entails a very low return”(Bhole, 2004). Further, he argued that “long term securities are more risky as compared with short term securities. Because of the higher risk on long term securities, other things being equal, the investors prefer to lend for short term. Borrowers, on the other hand, prefer to borrow long in order to reduce the risk of inability to meet the principal payments, i.e., in order to reduce the financial risk”. As regards their reluctance to hold long term securities, which are poor substitutes of money and are not readily marketable, a positive liquidity or risk premium must be offered to investors to induce them to purchase long term securities. “This premium concept introduces the compensation to investors for the added risk of having their money tied up for a longer period”(Irturk,2006) According to the liquidity premium theory, the long term rate is equal to the mean of the current short-term rate, the expected short-term rate and the liquidity premium. All the four shapes of the yield curve are consistent with liquidity premium theory. However, because the liquidity premium added to the long term rate positively, the upward sloping
curve is the most common shape predicted by the liquidity premium theory. In case of liquidity theory, the yield curve would be upward sloping, because as the maturity period is lengthened, the yield will rise. A descending yield curve could arise if participants expected short-term rates to decline significantly below long-term rates so as to more than offset the liquidity premium. Irturk (2006) further opined that, “as a complete explanation of the term structure of interest rates, however, this theory comes up quite short. Taken alone, the liquidity preference theory‟s main problem is that it explains only one shape of the yield curve- a rising one. By itself, it does not explain yield curves that are falling, flat or humped in shape”. 3.2.3 Market Segmentation Theory This is another theory for explanation of „term structure of interest rates‟ , mainly propounded „by Culbertson‟. Lutz has called it the „theory of risk avoidance‟. This approach differs sharply from the expectations and liquidity premium theories. “The market segmentation theory has been developed as an alternative to the expectations theory. It denies the basic assumption of expectations theory that a great deal of substitution can occur between securities with different maturities. According to this theory, investors are assumed to be risk minimisers or risk-averters” (Robinson and Wrightsman, 1981). The only way to hedge against risks is „by matching the maturity of both assets and liabilities‟. If the maturity of an investor‟s assets is longer than that of the liabilities, he incurs a capital loss when he is forced to sell his assets before they are due for redemption. On the other hand, if the maturity of an investor‟s assets is shorter than that of his liabilities, he runs the risk of income loss. In order to avoid the two kinds of risks, investors must „match the maturities of their assets and liabilities‟ of both the markets. The segmented market theory holds that „short-term and long-term interest rates‟ are determined in several separated or segmented markets. Some investors prefer short- term securities, while others such as insurance companies prefer long term securities. Thus, securities of different maturities are imperfect substitutes for buyers and sellers of securities in the market. In such segmented markets, the term structure of interest rates is determined exclusively by the supply of and demand for securities. Consequently, the yield curve is the result of several demand and supply curves for securities of different
four theories, the two major ones are market segmentation theory and pure expectations theory. Market Segmentation Theory (MST) is important because it establishes how market forces governing supply and demand of assets determine interest rates. Pure Expectations Theory (PET), in turn, extends MST to show how expectations impact the structure of interest rates. The preferred habitat theory and liquidity premium theory are just extensions of MST and PET. These theories help to understand how supply and demand, economic conditions, monetary policy, maturity preferences and expectations affect the bond market in general and structure of interest rates in particular”.
3.3 EMPIRICAL EVIDENCE ON THE THEORIES OF TERM STRUCTURE OF INTEREST RATES The „term structure of interest rates‟ has been a much researched area in the field of economics and finance. There has been a considerable empirical research to analyse the determinants of the term structure and to evaluate which of the four theories have been consistent with the quantitative evidence. “The expectations hypothesis stated that the long term yield can be expressed as the average of expected future short term yields. This theory is the most popular and most empirically tested. However, not all authors show the support for this theory by data”(Longstaff, 2000). Much of the empirical work on the expectations hypothesis has been concerned with developed countries. The evidence relating to smaller and less developed countries is considerably thinner. The „expectations theory‟, however, always had a very „little empirical support‟. Campbell and Shiller (1991) argued “that they saw an apparent paradox in the hypothesis, i.e. that the slope of the term structure always gives a forecast in the wrong direction for the short term change in the yields on longer bonds, but gives a forecast in the right direction for long term changes in short term rates”. A large volume of research into the term structure of interest rates has tested the expectations hypothesis where, in the majority of the cases, it has been rejected. Some of the studies which rejected the expectations hypothesis included Culbertson (1957), Roll (1970), Shiller et al. (1983), Mankiw and Summers (1984), Fama (1984), Mankiw (1986), Fama and Bliss (1987), Stambaugh (1988), Froot (1989), Cook and Hahn (1990), Campbell and Shiller (1991), Taylor (1992), Campbell et al. (1996), Buser et al. (1996), Bekaert et al. (1997), Balduzzi
et al. (1997) and Backus et al. (1998). The rejection may be on the basis that the term premium in the interest rates cannot be zero. Opposite to above findings, Van Horne (1965) gave support to the expectations hypothesis. Mac Donald and Speight (1988) have also found evidence in favour of this hypothesis. Tease (1988) supported the unbiased expectation theory in the Australian bill market. Based on the weekly market expectation of the 90 and 180 day treasury bills, he verified the accuracy of forward rate, also existence of zero risk premium. Choi and Wohar (1991) re-examined the validity of expectations theory for 5 different sub-periods. Their findings supported the predictive power of the yield curve and concluded that expectations hypothesis cannot be rejected. The empirical tests conducted in the study by Ghazali (1993) proved the validity of expectations hypothesis in the Malaysian Treasury- bill market. Holmes et al. (2010) tested the applicability of expectations hypothesis for a sample of seven Asian countries namely Hong Kong, Korea, Japan, Malaysia, Philippines, Singapore and Thailand. They found evidence supportive of the expectations hypothesis for each country. “Liquidity Premium Theory developed by Hicks (1946) allows the long term rate to deviate from the expected short-term rates. The return on short-term bonds is assumed to be more or less certain while the return on long term bonds is not. Therefore, the investors would like to get additional interest called liquidity premium for this uncertainty” (Mikalai, 2006). “The idea of liquidity premium hypothesis is quite natural and is supported by data. A lot of empirical tests done by Kessel (1965) and Mc Culluch (1975) showed the existence of premium. However, there is no unique view about what factors influence the liquidity premium and whether it varies over time. The opinions of different authors are mutually exclusive. For example, Cagan (1969) states the positive correlation between liquidity premium and the level of interest rates whereas Mc Culloch (1975) found no relation”(Fernandez, 2002). The available empirical evidence regarding Liquidity Premium Hypothesis (LPH) is mixed. Studies by Kessel (1965), Cagan (1969), Kane (1983), Kiely (1995) and Pelaez (1997) reported evidence in support of this hypothesis. But Mc Culluch (1975) and Olsen (1974) found no significant relationship between liquidity premium and market interest
Vayanos(2009)). They further insisted “on funding liquidity to the investors and discussed the relevance of preferred habitat for central bank policies during 2007- financial crisis”. Even though the preferred habitat theory is relevant in practice, it has not entered into academic mainstream
3.4 CONCLUSION Much research has been conducted in the area of term structure of interest rates and has offered considerable insight into the various theories. Although this issue has been widely talked about in research papers in case of developed countries, not much empirical work in this context has been conducted for developing countries. The empirical evidence for economies with well developed financial markets has so far generally favoured the expectations theory and preferred habitat hypothesis over the segmented hypothesis. Since credit markets for such economies are not seriously segmented, so borrowers and lenders do generally substitute between assets of different maturities. If we consider the „day-to-day changes in the term structure‟, then preferred habitat theory has been considered. On the other hand, if we consider the long run, expectations regarding future interest rates and liquidity premium become relevant. Although much discussed, empirical implementation of the market segmentation hypothesis has been elusive. The failure of empirical research may be due to lack in econometric sophistication. Though there is still controversy over which theory is correct, there is widespread acceptance of the role of expectations of interest rates as being an important component to any interpretation of the term structure. Therefore, validity of expectations hypothesis is of interest since it has important implications for economic policy.
