I have an honours economics degree from a top UK university and am currently in the selection process for a number of graduate schemes. I have undertaken a policy-based internship at a government institution and extensive entrepreneurial activities while at university. I speak three European languages fluently and have a working level of another two.

Outline the main theories of the term structure of interest rates.

Studies on the term structure of interest rates deal with the reasons why yields to maturity may differ between zero coupon bonds of different maturities. This is shown graphically by yield curves, which are simply the relationship between yield and time – that is, yield to maturity and term to maturity. Observations of the yield curve have given rise to theories about the 'term structure' of interest rates. There are different theories about it which try to explain why the rate of return on bonds varies with time as they approach maturity. The four main theories regarding the term structure are: pure expectations theory (also referred to as expectations theory), segmented markets theory, liquidity premium hypothesis and preferred habitat hypothesis. For the purpose of analysing these theories we will assume all bonds are zero coupon bonds (pure discount), and that there is no default risk (which is normally the case with government bonds). We will also assume there is no possibility of early redemption, so to finally keep constant the factors of risk, tax liabilities and redemption possibilities1. With such instruments, spot rates (the price of a commodity quoted for immediate purchase) are taken to be equivalent to the yield to maturity. Yield to maturity is the rate of return from holding a bond to maturity.

The pure expectations theory suggests that future interest rates, and therefore the shape of yield curves, will be determined by expected interest rates. These expectations are based on forward rates. It argues that the return on a long-term bond must come to equate the return on several short-term bonds which add up to the same time period, through arbitrage opportunities. If long-term (say, for simplicity, two-year) investors see that the return for a two-year investment is higher on long-term bonds than short-term (one-year) bonds, they will invest in long-term bonds. Short-term investors will also prefer to buy long-term bonds and sell them before maturity. The high level of preference for long-term bonds will cause prices to change until there is no difference in the rates of return. Long-term bonds and short-term bonds adding up to the same time period would therefore be perfect substitutes for each other. Advocates of this theory believe yield curves can be derived simply from expected future interest rates, by compounding the present interest rate with all subsequent interest rates prior to the future date we wish to predict the interest rate for. In other words, long-term interest rates are a geometric mean of the previous short-term interest rates, or expected future interest rates (which forward rates are normally assumed to be). Under this theory, if interest rates were expected to remain constant, the yield curve would be horizontal. If they were expected to increase, the yield curve would be upward-sloping, and so on.

In reality, it has been observed that long-term interest rates are not determined by expectations so plainly. In fact, these observations gave rise to an alternative hypothesis – the 'tail-wags-dog' theory, proposed by Tversky and Kahneman, 1974. It says that "long-term interest rates may overreact to information only relevant to short-term interest rates"2 . Actually, the assumptions in the framework of the pure expectations theory are quite strong. We must assume all investors are risk neutral and interested in obtaining the highest possible return on their investment, regardless of their time horizon. However, individuals are generally not risk neutral, and it has been observed that many investors strongly prefer to invest in bonds of their time horizon maturity. Yakov Amihud (1979) points out that a large problem with this theory is its taking of forward rates as unbiased estimates of expected future interest rates. In accordance with the tail-wags-dog theory, he argues that due to the fact that in reality investors are not risk neutral and due to the existence of transaction costs, forward rates are downward biased predictions of the value of future spot rates3.

In contrast to the expectations theory, the segmented markets theory (or market segmentation theory) suggests that investors have very strong preferences for bonds of certain maturities, according to their time horizons. It goes on to assume that this preference is so strong investors will be willing to give up higher return bonds in order to remain on their preferred maturity. As opposed to the expectations hypothesis, this theory does not regard bonds of different maturities as substitutes. This means that the price of short-term bonds cannot possibly be the determinant for the price of long-term bonds and therefore cannot determine the shape of the yield. If individuals and firms will only be willing to invest in their preferred maturity bonds, then short-term rates will be determined only by supply and demand of short-term funds and long-term rates will be determined only by supply and demand of long-term funds. In order to try and predict future directions of the yield curve under this theory, we need to analyse fund flows into these market segments. Evidence for this theory includes the stylised fact that long-term yields usually exceed short-term yields. Normally, short-term bonds will have lower returns than long-term bonds because investors give a higher value to a liquid portfolio (that is, one that can be easily converted into cash).

This is in compliance with this is the liquidity premium theory. The similarity is that it is also based on the importance investors' attribute to bonds of different maturities. However, this theory starts to differ from the segmented markets theory in that it sees investors as persuadable to change from their preferred maturity, if offered a higher expected return – a premium. This theory assumes a relatively low number of long-term investors, so that long-term bonds must offer premiums to encourage investors to hold them. As opposed to the previous two theories outlined, under the liquidity premium hypothesis, the yield curve will also have a more positive slope than the spot rates curve (and expected spot rates, or forward rates). At the present time, the yield curve and spot rates will be at the same point, but they will begin to diverge as the yield curve takes a higher rate of increase than spot rates. This difference between the two is the liquidity premium, and it increases with time. The only possible way of obtaining a horizontal or negatively sloped yield curve is to have a negatively sloped spot rates curve.

A problem with this theory is that unless the liquidity premium is known, yield curves cannot be estimated for future dates. It is very difficult to name a value for liquidity premium because different investors have different maturity preferences, and may require different premiums in order to change from their preferred maturities. Additionally, it must not be forgotten that some investors (for example, for pension funds) prefer long-term to short-term bonds and some would be willing to hold long-term bonds without a premium. To some extent, this theory is also similar to the pure expectations theory in that it also sees expected interest rates as determinants of future interest rates, but combined with a liquidity premium which accounts not only for less liquidity in long-term bonds but also for higher price uncertainty and risk. It is in perfect compliance with the tail-wags-dog theory, since long-term rates will be higher than short-term rates. We can see how this theory provides a combination of factors from the rather extreme pure expectations and segmented markets theories.

Another theory which provides 'middle ground' is the preferred habitat theory4 , and it accounts for the fault in the liquidity premium theory which does not reognise some investors as actually preferring long-term bonds. However, it tends more towards the segmented markets theory than the pure expectations theory. Instead of predetermining short-term bonds as largely preferred, it is more flexible in that it sees premiums as required not necessarily for long-term maturities, but for maturities where there is insufficient demand. The function of higher return premiums is to induce investors to hold bonds outside their preferred maturity – not necessarily longer than their preferred maturity. In addition, premiums do not have to be positive. Negative premiums on popular maturities can also serve the purpose of inducing investors to leave their 'preferred habitat'. Without knowledge of the premium size and whether it is positive or negative, we cannot estimate future one-period rates from the yield curve. However, it may be useful to analyse fund flows for short-term and long-term periods, as in the segmented markets theory, and expected future rates, since the preferred habitat theory combines elements from the first two theories outlined.

The previous four theories have shown different perspectives on the term structure of interest rates and the determination of future interest rate estimates. The pure expectations theory and the segmented markets theory are opposite approaches in many aspects, and are then combined in the liquidity premium theory and preferred habitat theory, although the latter is more flexible in its analysis of yield curves. Basically, it adds to the liquidity premium theory the possibility of different preferred maturities and a larger variety of premium types, to finally match ultimate lenders and ultimate borrowers. Long-term rates do normally exceed short-term rates, and advocates of the preferred habitat theory attribute this to the overall preference for short-term bonds in fixed-income markets. Each one of these theories, however, make assumptions which are inconsistent with reality, such as risk neutrality, zero transaction costs, no possibility of early bond redemption, and perfect information of market conditions. Although these assumptions are often necessary in order to fairly analyse the term structure of interest rates, when considering a real case study, they must be taken into consideration.

References
Yakov Amihud, “A Possible Error in the Expectations Theory: Note”, Journal of Money, Credit and Banking, Vol. 11, No. 2 (May, 1979).

Michael Brett, How to Read the Financial Pages, Hutchinson, 5th edition, 2003.

Edwin J. Elton, Martin J. Gruber, “Modern Portfolio Theory and Investment Analysis” (Fourth Edition), John Wiley and Sons Inc., 1991.

Robert J. Shiller et al, « Forward Rates and Future Policy: Interpreting the Term Structure of Interest Rates », Brookings Papers on Economic Activity, Vol. 1983, No. 1. (1983).

Stephen J. Turnovsky, “The Term Structure of Interest Rates and the Effects of Macroeconomic Policy”, Journal of Money, Credit and Banking, Vol. 2, No. 3 (Aug. 1989).