# Explaining the term structure

What determines the term structure of interest rates? This question has long puzzled academicians and practitioners. Four principle explanations have been offered: the expectations theory, the liquidity preference theory, the preferred theory, the preferred habitat theory, and the market segmentation theory.

Expectations Theory:

This theory holds that the shape of the yield curve can be explained by the interest rate expectations of those who participate in the market. More precisely the expectations theory holds that any long term rate is equal the geometric mean of current future one year rates expected by the market participants.

In general terms, the expectations theory may be expressed as follows:

(1+ tRn) = [ (1 + tR1) ( 1 + t+1R1) … ( 1 + t+n-1R1)]1/n ———-eq1
where

tRn = actual long term rate
n= term to maturity (in years) of the long issue
tR1= current year rate
t+iR1=expected one year rate during some future period (i= 1,… n-1)

Clearly, the expectations hypothesis can explain any shape of yield curve:
Yield Curve: Explanation
Ascending: Short term rates are expected to rise in future
Descending: Short term rates are expected to fall in future
Humped: Short term rates are expected to rise for a while and then fall
Flat: Short term rates are expected to remain changed in future

Liquidity Preference Theory:

An important criticism leveled against the expectations theory is that it assumes that investors know with certainty what lies ahead of them. The future, however, is not known. There is uncertainty about the one year period return from a bond whose maturity is greater than one period. And this uncertainty regarding the one period return increases with the maturity of the bond.

Since investors risk averse, J R Hicks argued that they require an inducement to hold long term bonds. They will ask for a long term rate which is higher than the average of expected future rates. Put differently, forward rate should incorporate interest rate expectations as well as a risk (or liquidity) premium.

In formal terms, the liquidity preference hypothesis may be expressed as a variation of Eg 1:

(1+ t Rn ) = [(1+tR1 ) ( 1 + t+1R1+ L2) … (1 +t+n-1R1 + Ln)]1/n —eq2

where

tRn= actual long term rate
n= term t maturity (in years) of the long issue
tR1= current one year rate
t+iR1 = expected one year rate during some future period (i= 1, …, n-1)
Li = risk (liquidity) premium for year i(I = 2,…,n)

Thus according to the liquidity preference theory an upward sloping yield curve suggest that future interest rates will rise (or will be flat) or even fall if the liquidity premium increases fast enough to compensate for the decline in the future interest rates.

Preferred Habitat Theory:

The liquidity preferences theory assumes that risk premium must necessarily rise with maturity because investors wish to liquidate their investments at the earliest and borrowers want to borrow log. This assumption, however, may not be realistic.

According to Modigliani and Sutch who originally formulated the habitat theory , risk aversion implies that investors will prefer to match the maturity of investments to their investment objective. Investors with long investment horizons would like to invest in instruments of longer maturities; otherwise they will be exposed to a reinvestment. Likewise, short term investors would like to invest in instruments of shorter maturity; otherwise they will be exposed to a price risk, i.e. the risk that the price of an asset will fall when it is sold prematurely because of a rise in interest rates. Similar considerations apply to borrowers risk aversion implies that borrowers would like to match the maturity of their borrowings to the length of time for which they need funds.

If there is a mismatch between the demand and supply of funds in certain maturity range, the preferred habitat theory asserts that some lenders and borrowers may have to be induced o shift out of their preferred maturity ranges. Ofcourse, they will have to be compensated for this in form of a suitable risk premium which depends on the degree of risk aversion.

The shape of the yield curve, according to the preferred habitat theory, is influenced by expectations of further interest rates as well as risk premia, positive or negative, required to move market participants out of the preferred habitats. Clearly, all types of yield curves, viz. upward, sloping, downward sloping , flat or humped are possible.

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