Cd

Time to maturity

Yield curve

Yield curve sP°t rates sP°t rates

| Liquidity | premium o

Time to maturity

Figure 20.4 Yield curves with liquidity premiums.

of investors interested in long-term debt, a premium will have to be offered on long-term debt. If many firms and institutions wish to issue short-term debt and there are few investors who wish to invest short terms, a premium will have to be offered on short-term debt.

What is meant by a premium? For simplicity consider two periods. Let SQl be the spot interest rate in the first period and S,2 be the expected one-period spot rate in the second. If the expectations theory holds, the two-period rate expressed as a rate per period is

\ssume that there is a surplus of short-term investors and therefore an extra return is necessary to induce investors to hold the two-period bond. If P is the size of the premium, then

In this case, preferred habitat theoiy would result in a set of spot rates that could have been derived equally well from the liquidity premium theory. If, on the other hand, there is a need to move investors to the short term, holding the two-period bond will be less profitable than holding two one-period bonds or

with

With the preferred habitat theory, the premiums can be positive or negative. Without an idea of the sign and size of the premiums, nothing can be concluded about future one-period rates from observing the yield curve.

Term Structure and Coupon Bonds In the last section we examined the term structure for pure discount bonds. We will now examine the term structure for coupon paying bonds. A coupon paying bond can be considered a portfolio of pure discount bonds. Consider a three-period bond with a coupon of $75 and a principal repayment of $1000. Its price is calculated as follows.

Price =

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