Department of Economics
Saint Louis University
Professor: Rapach
Fall 2008
ECON 420
Money and Banking

Chapter Outline for “Chapter 6—The Risk and Term Structure of Interest Rates,” Frederic S. Mishkin, The Economics of Money, Banking, and Financial Markets, Eighth Edition (New York, N.Y.: Addison-Wesley, 2006)

RISK STRUCTURE OF INTEREST RATES

See Figure 1

Default Risk

default: occurs when the issuer of a bond is unable or unwilling to make interest payments when promised or pay off the face value when the bond matures

default-free bonds: bonds with no default risk

risk premium: how much additional interest people must earn in order to be willing to hold that risky bond

See Figure 2

A bond with default risk will always have a positive risk premium, and an increase in its default risk will raise the risk premium

See Table 1

APPLICATION The Enron Bankruptcy and the Baa-Aaa Spread

Liquidity

Income Tax Considerations

See Figure 3

Summary

APPLICATION Effects of the Bush Tax Cut on bond Interest Rates

TERM STRUCTURE OF INTEREST RATES

yield curve: plot of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations

inverted yield curve: downward-sloping yield curve

See Figure 4

1.      Interest rates on bonds of different maturities move together over time.

2.      When short-term interest rates are low, yield curves are more likely to have an upward slope; when short-term interest rates are high, yield curves are more likely to slope downward and be inverted.

3.      Yield curve almost always slope upward.

Expectations Theory

expectations theory: interest rate on a long-term bond will equal an average of short-term interest rates that people expect to occur over the life of the long-term bond

i_t = today’s (time t) interest rate on a one-period bond

i^e_t+1 = interest rate on a one-period bond expected for next period (time t + 1)

i_2t = today’s (time t) interest rate on the two-period bond

(1 + i_2t) (1 + i_2t) – 1 = 1 + 2i_2t + (i_2t)² – 1 = 2i_2t + (i_2t)²

(1 + i_2t) (1 + i_2t) – 1 » 2i_2t

(1 + i_t)(1 + i^e_t+1) –1 = 1 + i_t + i^e_t+1 + (i_t)(i^e_t+1) – 1

(1 + i_t)(1 + i^e_t+1) –1 » i_t + i^e_t+1

Both bonds will be held if: 2i_2t = i_t + i^e_t+1 or i_2t = (i_t + i^e_t+1)/2

In general: i_nt = (i_t + i^e_t+1 + i^e_t+2 + … + i^e_t+(n-1))/n

Examples:

(5% + 6%)/2 = 5.5%

(5% + 6% + 7% + 8% + 9%)/5 = 7%

Segmented Markets Theory

Liquidity Premium and Preferred Habitat Theories

i_nt = [(i_t + i^e_t+1 + i^e_t+2 + … + i^e_t+(n-1))/n] + l_nt

preferred habitat theory: modification of the expectations theory that assumes that investors have a preference for bonds on one maturity over another, a particular bond maturity (preferred habitat) in which they prefer to invest

See Figure 5

Examples:

[(5% + 6%)/2] + 0.25% = 5.75%

[(5% + 6% + 7% + 8% + 9%)/5] + 1% = 8%

See Figure 6

Evidence on the Term Structure

Summary

APPLICATION Interpreting Yield Curves, 1980-2006

See Figure 7

QUESTIONS AND PROBLEMS: 1, 3, 5, 7, 9, 11, 13, 15