Introduction to Corporate Finance

PArT 2: VALUATION, rISk AND reTUrN

yield on a long-term instrument by purchasing a short-term bond. Conversely, when the yield curve

inverts, and short-term yields exceed long-term yields, investors must expect short-term rates to fall.

Only then would investors willingly accept the lower yield on long-term bonds.

example

Suppose a one-year bond currently offers a yield of 5%, and a two-year bond offers a 4.5% yield. Under the

expectations theory, what interest rate do investors expect on a one-year bond next year? Remember that the

expectations theory says that investors should earn the same expected return by investing in either two one-

year bonds or one two-year bond. Therefore, the break-even calculation is:

(.)( ())( .)

(())

(.

100511 0 045

1

104

2

2

2

++=+

+=

Er

Er

55

105

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2

2

)

(.)

Er()= .,or %

The term E(r 2 ) refers to the expected return on a one-year bond next year (year 2). On the left-hand side of

the equation, we have the return that an investor expects to earn by purchasing a one-year bond this year and

another one next year. That should equal the return earned by purchasing a two-year bond today and holding

it to maturity. Only when the expected one-year bond rate is 4% are investors indifferent between these two

strategies.

4-5c THe LIQUIDITY PreFereNCe AND PreFerreD HABITAT

THeOrIeS

Unfortunately, the slope of the yield curve does not always provide a reliable signal of future interest

rate movements, perhaps because the expectations theory ignores several factors that are important to

investors and that influence the shape of the yield curve. The first factor is that investors may have a

preference for investing in short-term securities. As we have seen, when market interest rates change,

the prices of long-term bonds fluctuate more than the prices of short-term bonds. This added risk might

deter some investors from investing in long-term bonds. To attract investors, perhaps long-term bonds

must offer a return that exceeds the expected return on a series of short-term bonds. Therefore, when

the yield curve slopes up, we cannot be sure whether this is the result of investors expecting interest

rates to rise in the future, or simply a reflection of compensation for risk. The liquidity preference theory of

the term structure recognises this problem. It says that the slope of the yield curve is influenced not only

by expected interest rate changes but also by the liquidity premium that investors require on long-term

bonds.

A second factor clouds the interpretation of the slope of the yield curve as a signal of interest rate

movements if certain investors always purchase bonds with a particular maturity. For instance, pension

funds that promise retirement income to investors and life insurance companies that provide death

benefits to policyholders have very long-term liabilities. These companies may have a strong desire to

invest in long-term bonds (the longest available in the market) to match their liabilities, even if long-term

bonds offer low expected returns relative to a series of short-term bonds. Economists use the preferred

habitat theory (or the market segmentation theory) to describe the effect of this behaviour on the yield

curve. If short-term bond rates exceed long-term rates, the cause may be that the demand for long-term

bonds is very high relative to their supply. This demand drives up long-term bond prices and drives down

liquidity preference
theory
States that the slope of the
yield curve is influenced not
only by expected interest
rate changes, but also by
the liquidity premium that
investors require on long-term
bonds

preferred habitat theory
A theory that recognises that
the shape of the yield curve
may be influenced by investors
who prefer to purchase
bonds having a particular
maturity; also called market
segmentation theory