Introduction to Corporate Finance

4: Valuing Bonds

the same period, the two-year bond offers just 2.5% per year or 5% total (5.06% after compounding).

In this scenario, Russell earns more by investing in two one-year bonds than in one two-year bond. But

what if the yield on a one-year bond is just 2% next year? In that case, Russell earns 4% over two years

(or 4.04% after compounding), and he is better off buying the two-year bond. If next year’s yield on the

one-year bond is about 3%, then Russell will earn approximately the same return over the two years no

matter which investment strategy he chooses.

This example illustrates the expectations theory (or expectations hypothesis): in equilibrium, investors

should expect to earn the same return whether they invest in long-term Treasury bonds or a series of

short-term Treasury bonds. If the yield on two-year bonds is 2.5% when the yield on one-year bonds is

2%, then investors must expect next year’s yield on a one-year bond to be 3%. Suppose not. If they expect

a higher yield than 3%, investors are better off purchasing a series of one-year bonds than the two-year

bond. Conversely, if investors expect next year’s bond rate to be less than 3%, they will flock to the two-

year bond. Equilibrium occurs when investors’ expectations are such that the expected return on a two-

year bond equals the expected return on two one-year bonds. In this example, equilibrium occurs when

investors believe that next year’s interest rate will be 3%.

Figure 4.6 illustrates this idea. The first part of the figure shows that the value of $1 invested in one

two-year bond will grow to (1 + r)^2. In this expression, r represents the current interest rate on a two-

year bond. Next, the figure shows that investors expect $1 invested in a sequence of two one-year bonds

to grow to (1 + r 1 ) [1 + E(r 2 )]. Here, r 1 represents the current one-year bond rate, and E(r 2 ) represents

the expected one-year bond rate in the second year. Equilibrium occurs when the two strategies have

identical expected returns, or when the expected one-year interest rate is about 3%.

The expectations theory implies that when the yield curve is sloping upward – that is, when long-term

bond yields exceed short-term bond yields – investors must expect short-term yields to rise. According to

the theory, only if investors expect short-term rates to rise will they be willing to forgo the higher current

expectations theory

In equilibrium, investors

should expect to earn the

same return whether they

invest in long-term Treasury

bonds or a series of short-term

Treasury bonds

FIGUre 4.6 THE EXPECTATIONS THEORY

The expectations theory says that investors should earn the same expected return by purchasing one two-year bond or two
one-year bonds. In this example, equilibrium occurs when the expected return on a one-year bond next year, E(r 2 ), is 6%.
Only then do the two investment strategies provide the same expected return.

2-year investment

(1 r )^2

(1 r 1 ) [1 E (r 2 )] (1 r )^2

(1 0.02) [1 E (r 2 )] (1 0.025)^2

E (r 2 ) 0.03003 3%

T wo 1-year investments

Equilibrium occurs when

(1 r 1 ) [1 E (r 2 )]

First year Second year