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Term Structure of Interest Rate

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Explain the term structure of interest rates. What are the effects of rise in risk and expectations on the formation of long term rates?

Interest rate within an economy is subject to many factors and as a result varies in relativity of those. The major factors are time period: short term Vs. long term investments, the degree of risk to which its exposed (AAA rated, mortgages, default, zero coupon…).
Term structure of Interest rate is a significant tool for investors of bonds but also for policy makers, in terms of having an overview of whether to invest in short or longer term securities. This essay will go on to explain the term structure of interest rate how it is used by investors, the different theories and hypothesis behind it but also how the creation of long term rates effects its relation to risk.

The term structure of interest rates also called the yield curve shows the relationship between interest rate and time to maturity of bonds, it is a common method of bond valuation. A graph is used to represent this relationship in relation to long term interest rates and short term interest rates where the maturity of an investment (x axis ) is compared to the interest rate (y axis) showing the yield (rate return) on bonds with the different maturity length. Term structure of interest usually refers to zero coupon bonds which are bonds without coupons (weekly interest rate payments on the bond) which are sold at its face value requiring as a result a fixed interest rate.

The yield curve usually indicates that holding long term bonds generates a higher yield in comparison to holding short term assets which are highly liquid e.g. money short term bonds such as bills etc. This previous statement is demonstrated by the typical yield curve (fig1) which slopes upward but flattens out eventually showing the usual pattern of long term bonds which generate higher interest rates.
This curves represents normal market conditions where investors behaviours indicate their beliefs of no changes in the economy e.g. stability of inflation rates etc. this is where investors are drawn to invest in long term bonds assuming their yield will be higher due to future market looking stable. This links to the known factor which is: the higher the risk the higher the return meaning that holding long term therefore more risky investments generates higher returns as the maturity prolongs the liquidity premium increases (as well as the maturity/risk premium).

However an upward slope is not always the case we notice that the upward slope is not steep and is not reflective of the market in all cases which brings us to the flat yield curve showing numerous movements within the markets. Uncertainty about the future then becomes stronger which encourages risk aversion meaning short term interest rate will rise as a result. This last result can lead to an inverted yield curve even though this is a rare condition which would most likely occur when future interest rate is known to drop which lead to investors opting for short term assets giving higher yield than those in the long term as the price of the bond is known to drop in the future.

Such a measure implements a projection of future performances since future spot interest rates are unknown the yield curve serves as a benchmark or an approximation of expected returns on these types of securities thus appeases the uncertainties dreaded by most investors.

The degree of risk will also affect investor’s decisions. Since the information about future of Interest rate is incomplete and it is known that the further into the future we try to forecast the more wrong we are, long term bonds hence present a greater risk. The term premium theories assume that most investors are risk averse and as we know interest rate is known increase as the maturity increases a premium on the return is generated. This addition to interest rate is needed to persuade risk adverse investors and savers to lend more long term securities.

The expectation theory suggests that observing the term structure is indeed a tool for market participants to forecast the future and therefore a cause of the different expectations. This theory represents an important tool as it has a major influence over the relationship between yield and the term to maturity of bonds. It shows how future changes affect the current structure if the yield curve shows stability it means that borrowers and lenders are at equilibrium of current patterns of IR in other word they are both lending and borrowing as much as each other .

The theory looks into future rates:

If long term is for 2years it will be demonstrated as:

Where iL= long term interest rate

As short term loans are of 1 year lenders might want to renew at the expected rate of 1 year by comparing it with the earning on the investment at today’s rate over a two year term. In order to seek whether renewing investment to longer term is beneficial. This can be represented as:

is = short term interest rate

î = expected rate

now that the expected rate has been put in relation to the current short term rate we can derive it which will generate a result representing the average long term interest rate by using the expectation we can see what the future will hold for interest rate through relative to the progression of short run.
This is expressed through deriving average rate:

Therefore a rise in the long term bonds in comparison to short run bonds will cause the yield curve to slope upward as the current rate encourages investors willing to lend for longer periods. To illustrate this last statement we can look at an example: if current interest rate for short run = 4% and current interest rate for long term bonds = 7% 1+ îs + 4 = 1+ 2(7) 5+ îs = 15

So expected rate at the beginning of each stated period will be 10%
Since long term rate (7%) is higher than the short term (4%)

However if future long term rates were expected to fall the yield would slope downward relatively bringing long run IR to a decrease as well.
We have also have to note the fact these expectation are to some extent determined by monetary authorities, thus if we look at today’s economy we know that a main objective would be to stay out of the recession which brings to monetary authorities bringing the interest rate down drawing the yield curve to a downward slope. In other words expected short term rates to fall as well as long term interest rate as we know they move together but which leads to a rise in long term bond prices. Another factor which affects the yield curve is debt enhancement financed by central bank which will then increase bank deposits and lead to a rise in money supply as the amount of lending will increase. This process then creates inflation and IR to rise in future which will then show on the yield curve which will become steeper.

Another theory attempting to explain term structure is segmentation theory which assumes that markets are highly segmented as opposed to expectation theory. It bases its theory on the investors’ preferences to hold certain level of maturity of bonds. This links to the liquidity preference theory risk adverse investors will tend to minimise their risk by investing in short term bonds whether risk loving investors such as hedge funders will tend to hold on more the long run. From this point it is concluded that this is why the demand for long term bonds is lower than short term this could also be linked to diversification of portfolios where the risk is being minimised through investing in various instruments with different level of maturity. The theory is seen as a critic of the expectation theory, as they believe bonds with different maturity levels cannot affect each other. However the theory itself does not attempt to explain why the both have a tendency of moving alongside each other.

The liquidity preference theory gives an understanding of why investors are drawn to certain investments which was what segmented theory based its hypothesis on. This theory assumes that most investors prefer holding short term highly liquid assets (short term bonds) as to avoid long term assets losing their capital value over time. Short-term lending is more appealing as it is more flexible and can lead to re-investment. If there is a certainty about the future investors will opt to invest in long term assets in which they will receive a higher return in contrast uncertainty about the future will have the opposite effect on investments. It is therefore concluded that investors are willing to hold long term assets only if they are compensated by a higher return on their investments. The premium demanded will depend on degree of uncertainty as well as the level of interest rate. This goes back to the term premium theory.
If interest rates are relatively low for example close to 0 investors believe that interest rates are more likely to increase.

Finally we conclude that many theories attempt to explain the term structure of interest rate. How the relationship will affect rise in long term rate which was done by looking at investors’ behaviour, interest rate of different maturity bonds and risk in relativity to the movement of the yield curve. Some of the theories present flaws in terms of whether they give a valid explanation however these gives investors a good sneak peak of the future rates Even though the uncertainty of the future and the stability of certain markets can never be fully predicted.


* John C.Cox, Jonathan E. Ingersoll (1985). Econometrica Vol 53. USA: the econometric society. 385-407.

* Miskin, F.S. (2010) The Economics of Money, Banking, and Financial Markets, 9th Edition, Addison-Wesley.

* Miskin. (2010). Money and Banking . Available: [Last accessed 12th Dec 2011]

* Miskin, F.S. and Eakins, S.G. (2000) Financial Markets and Institutions, 3rd Edition, Addison Wesley, Reading, Ch.5

* ROLAND RICART PIERRE SICSIC. (). Estimation d'une Structure par Terme. Available: . [Last accessed 9th Dec 2011] * Studynet

* Phillipe Priaulet & Moez. (2006). Modelisation de la Courbe des Taux .Available: [Last accessed 14th Dec 2011]

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