Risk Structure of Long-Term Bonds in the United States

Increase in Default Risk on Corporate Bonds

Corporate Bond Market1. Riskier corporate bonds Dc , Dc shifts left2.Less liquid corporate bonds Dc , Dc shifts left3.Pc , ic Treasury Bond Market1.Relatively more liquid Treasury bonds, DT , DT shiftsright2.PT , iT Outcome:Risk premium, ic iT, risesRisk premium reflects not only corporate bonds default risk, but also lower liquidity

Tax Advantages of Municipal Bonds

Term Structure: Facts to be Explained1.Interest rates for different maturities move together over time2.Yield curves tend to have steep upward slope when short rates are low and downward slope when short rates are high3.Yield curve is typically upward slopingTheories of Term StructureExpectations TheoryExpectations Theory explains 1 and 2, but not 3Segmented Markets TheorySegmented Markets explains 3, but not 1 and 2Liquidity Premium (Preferred Habitat) TheoryCombines 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

Expectations HypothesisKey Assumption: Bonds of different maturities are perfect substitutesImplication: RETe on bonds of different maturities are equalInvestment strategies for two-period horizon1.Buy $1 of one-year bond and when it matures buy anotherone-year bond2.Buy $1 of two-year bond and hold itExpected return from 1 = Expected return from 2(1 + it)(1 + iet+1) = (1 + i2t)21 + it + iet+1+ it iet+1 = 1 + 2 i2t + i2t2i2t = (it + iet+1) / 2

More generally for n-period bond: it + iet+1 + iet+2 + ... + iet+(n1)int = nIn words: Interest rate on long bond = average short rates now and those expected to occur over the life of long bondNumerical 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 FactsExplains why yield curve has different slopes:1.When short rates are expected to rise in future, average of future short rates = int is above todays short rate yield curve is upward sloping2.When short rates are expected to stay same in future, average of future short rates are same as todays yield curve is flat3.When short rates are expected to fall yield curve is downward slopingExpectations Hypothesis explains Fact 1: short rates and long rates move togetherIf 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

When short rates are low, they are expected to rise to normal level. Long rate (= average of future short rates) will be well above todays short rate yield curve will have steep upward slopeWhen 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 doesnt explain Fact 3: the yield curve usually has upward slopeShort rates are as likely to fall in the future as to riseAverage of future short rates should not be higher than current short rate Yield curve should not usually slope upwardOn average, yield curve should be flatExpectations Hypothesis explains Fact 2: yield curves tend to have steep slope when short rates are low and downward slope when short rates are high

Segmented Markets TheoryKey Assumption: Bonds of different maturities are not substitutesImplication: Markets are completely segmentedInterest rate at each maturity is determined separatelyExplains Fact 3: yield curve is usually upward slopingPeople typically prefer short holding periods and thus have higher demand for short-term bonds, which have higher price and lower interest rates than long bondsDoes not explain Facts 1 or 2: segmented market theory assumes long and short rates separately determined Rates shouldnt move togetherYield curve shouldnt slope steeply upward when short rate is low.

Liquidity Premium (Preferred Habitat) TheoryKey Assumption: Bonds of different maturities are substitutes, but are not perfect substitutesModifies Expectations Theory with Segmented Markets Theory: Investors prefer short bonds to long bonds must be paid liquidity (term) premium, lnt, to hold long bondsResults in following modification of Expectations Theory it + iet+1 + iet+2 + ... + iet+(n1)int = + lnt n

Relationship Between the Liquidity Premium (Preferred Habitat) and Expectations Theories

Numerical Example1.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

Market Predictions of Future Short Rates

Interpreting Yield Curves 19802000