Risk Structure of Long-Term Bonds in the United States © 2004 Pearson Addison-Wesley. All rights reserved

Increase in Default Risk on Corporate Bonds © 2004 Pearson Addison-Wesley. All rights reserved

© 2004 Pearson Addison-Wesley. All rights reserved

1. Riskier corporate bonds Dc , Dc shifts left Corporate Bond Market 1. Riskier corporate bonds Dc , Dc shifts left 2. Less liquid corporate bonds Dc , Dc shifts left 3. Pc , ic  Treasury Bond Market 1. Relatively more liquid Treasury bonds, DT , DT shifts right 2. PT , iT  Outcome: Risk premium, ic – iT, rises Risk premium reflects not only corporate bonds’ default risk, but also lower liquidity © 2004 Pearson Addison-Wesley. All rights reserved

Tax Advantages of Municipal Bonds © 2004 Pearson Addison-Wesley. All rights reserved

Term Structure: Facts to be Explained 1. Interest rates for different maturities move together over time 2. Yield curves tend to have steep upward slope when short rates are low and downward slope when short rates are high 3. Yield curve is typically upward sloping Theories of Term Structure Expectations Theory Expectations Theory explains 1 and 2, but not 3 Segmented Markets Theory Segmented Markets explains 3, but not 1 and 2 Liquidity Premium (Preferred Habitat) Theory Combines features of Expectations Theory and Segmented Markets Theory to get Liquidity Premium (Preferred Habitat) Theory and explains all facts

Interest Rates on Different Maturity Bonds Move Together © 2004 Pearson Addison-Wesley. All rights reserved

© 2004 Pearson Addison-Wesley. All rights reserved

Expectations Hypothesis Key Assumption: Bonds of different maturities are perfect substitutes Implication: RETe on bonds of different maturities are equal Investment strategies for two-period horizon 1. Buy $1 of one-year bond and when it matures buy another one-year bond 2. Buy $1 of two-year bond and hold it Expected return from 1 = Expected return from 2 (1 + it)(1 + iet+1) = (1 + i2t)2 1 + it + iet+1+ it iet+1 = 1 + 2 i2t + i2t2 i2t = (it + iet+1) / 2 © 2004 Pearson Addison-Wesley. All rights reserved

More generally for n-period bond: it + iet+1 + iet+2 + ... + iet+(n–1) int = n In words: Interest rate on long bond = average short rates now and those expected to occur over the life of long bond Numerical example: One-year interest rate now and expected over the next five years: 5%, 6%, 7%, 8% and 9%: Interest rate on two-year bond: (5% + 6%)/2 = 5.5% Interest rate for five-year bond: (5% + 6% + 7% + 8% + 9%)/5 = 7% Interest rate for one to five year bonds: 5%, 5.5%, 6%, 6.5% and 7%.

Expectations Hypothesis and Term Structure Facts Explains why yield curve has different slopes: 1. When short rates are expected to rise in future, average of future short rates = int is above today’s short rate yield curve is upward sloping 2. When short rates are expected to stay same in future, average of future short rates are same as today’s  yield curve is flat 3. When short rates are expected to fall yield curve is downward sloping Expectations Hypothesis explains Fact 1: short rates and long rates move together If short rate rises are persistent it  today, iet+1, iet+2 etc.   average of future rates   int  Therefore: it   int , i.e., short and long rates move together © 2004 Pearson Addison-Wesley. All rights reserved

Expectations Hypothesis explains Fact 2: yield curves tend to have steep slope when short rates are low and downward slope when short rates are high When short rates are “low”, they are expected to rise to normal level. Long rate (= average of future short rates) will be well above today’s short rate  yield curve will have steep upward slope When short rates are high, they are expected to fall to normal. Long rate (= average of future short rates) will be below current short rate  yield curve will have downward slope But the expectations hypothesis doesn’t explain Fact 3: the yield curve usually has upward slope Short rates are as likely to fall in the future as to rise Average of future short rates should not be higher than current short rate Yield curve should not usually slope upward On average, yield curve should be flat © 2004 Pearson Addison-Wesley. All rights reserved

Segmented Markets Theory Key Assumption: Bonds of different maturities are not substitutes Implication: Markets are completely segmented Interest rate at each maturity is determined separately Explains Fact 3: yield curve is usually upward sloping People typically prefer short holding periods and thus have higher demand for short-term bonds, which have higher price and lower interest rates than long bonds Does not explain Facts 1 or 2: segmented market theory assumes long and short rates separately determined Rates shouldn’t move together Yield curve shouldn’t slope steeply upward when short rate is low. © 2004 Pearson Addison-Wesley. All rights reserved

Liquidity Premium (Preferred Habitat) Theory Key Assumption: Bonds of different maturities are substitutes, but are not perfect substitutes Modifies Expectations Theory with Segmented Markets Theory: Investors prefer short bonds to long bonds  must be paid liquidity (term) premium, lnt, to hold long bonds Results in following modification of Expectations Theory it + iet+1 + iet+2 + ... + iet+(n–1) int = + lnt n © 2004 Pearson Addison-Wesley. All rights reserved

Relationship Between the Liquidity Premium (Preferred Habitat) and Expectations Theories © 2004 Pearson Addison-Wesley. All rights reserved

Numerical Example 1. One-year interest rate now and expected over the next five years: 5%, 6%, 7%, 8% and 9% 2. Investors’ preferences for holding short-term bonds  liquidity premiums for one to five-year bonds: 0%, 0.25%, 0.5%, 0.75% and 1.0%. Interest rate on the two-year bond: (5% + 6%)/2 + 0.25% = 5.75% Interest rate on the five-year bond: (5% + 6% + 7% + 8% + 9%)/5 + 1.0% = 8% Interest rates on one to five-year bonds: 5%, 5.75%, 6.5%, 7.25% and 8%. Compared to yield curves for the expectations theory, liquidity premium (preferred habitat) theories produce yield curves that are more steeply upward sloped explains all facts © 2004 Pearson Addison-Wesley. All rights reserved

Market Predictions of Future Short Rates © 2004 Pearson Addison-Wesley. All rights reserved

Interpreting Yield Curves 1980–2000 © 2004 Pearson Addison-Wesley. All rights reserved