利率的期限结构

1、The Risk and Term Structure of Interest Rates-一、Risk structure of Interest Rates(一）Default Risk(二) Liquidity(三）Income Tax ConsiderationRisk Structure of Long Bonds in the United States(一）Default RiskIncrease in Default Risk on Corporate BondsAnalysis of Figure 2: Increase inDefault Risk on Corporate

2、 BondsCorporate Bond Market1.RETe on corporate bonds , Dc , Dc shifts left2.Risk of corporate bonds , Dc , Dc shifts left3.Pc , ic Treasury Bond Market4.Relative RETe on Treasury bonds , DT , DT shifts right5.Relative risk of Treasury bonds , DT , DT shifts right6.PT , iT Outcome:Risk premium, ic iT

3、, rises(Risk premium: The spread between the interest rates on bonds with default risk and default-free bonds)Bond Ratings(二) Liquidity Corporate Bonds Become Less LiquidCorporate Bond Market1.Less liquid corporate bonds Dc , Dc shifts left2.Pc , ic Treasury Bond Market1.Relatively more liquid Treas

4、ury bonds, DT , DT shiftsright2.PT , iT Outcome:Risk premium, ic iT, risesRisk premium reflects not only corporate bonds default risk, but also lower liquidity(三）Income Tax ConsiderationTax Advantages of Municipal BondsAnalysis of Figure 3: Tax Advantages of Municipal BondsMunicipal Bond Market1.Tax

5、 exemption raises relative RETe on municipal bonds, Dm , Dm shifts right2.Pm , im Treasury Bond Market1.Relative RETe on Treasury bonds , DT , DT shifts left2.PT , iT Outcome:im iT二Term Structure of Interest Rates Facts to be Explained1.Interest rates for different maturities move together2.Yield cu

6、rves tend to have steep slope when short rates are low and downward slope when short rates are high3.Yield curve is typically upward slopingThree Theories of Term Structure（一）Expectations Theory（二）Segmented Markets Theory（三）Liquidity Premium TheoryA.Expectations Theory explains 1 and 2, but not 3B.S

7、egmented Markets explains 3, but not 1 and 2C.Solution: Combine features of both Expectations Theory and Segmented Markets Theory to get Liquidity Premium Theory and explain all factsInterest Rates on Different Maturity Bonds Move TogetherYield Curves（一）Expectations HypothesisKey Assumption: Bonds o

8、f 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 another one-year bond2.Buy $1 of two-year bond and hold itExpected return from strategy 2(1 + i2t)(1

9、 + i2t) 11 + 2(i2t) + (i2t)2 1=11Since (i2t)2 is extremely small, expected return is approximately 2(i2t)Expected return from strategy 1(1 + it)(1 + iet+1) 11 + it + iet+1 + it(iet+1) 1=1 1Since it(iet+1) is also extremely small, expected return is approximatelyit + iet+1From implication above expec

10、ted returns of two strategies are equal: Therefore2(i2t) = it + iet+1Solving for i2t it + iet+1 i2t =2More generally for n-period bond: it + iet+1 + iet+2 + . + iet+(n1)int =nIn words: Interest rate on long bond = average short rates expected to occur over life of long bondNumerical example:One-year

11、 interest rate 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%.Expected return from strategy 1Expectations Hypothesis and

12、 Term Structure FactsExplains why yield curve has different slopes:1.When short rates expected to rise in future, average of future short rates = int is above todays short rate: therefore yield curve is upward sloping2.When short rates expected to stay same in future, average of future short rates a

13、re same as todays, and yield curve is flat3.Only when short rates expected to fall will yield curve be downward slopingExpectations Hypothesis explains Fact 1 that short and long rates move together1.Short rate rises are persistent2.If it today, iet+1, iet+2 etc. average of future rates int 3.Theref

14、ore: it int , i.e., short and long rates move together1.When short rates are low, they are expected to rise to normal level, and long rate = average of future short rates will be well above todays short rate: yield curve will have steep upward slope2.When short rates are high, they will be expected

15、to fall in future, and long rate will be below current short rate: yield curve will have downward slopeDoesnt explain Fact 3 that yield curve usually has upward slopeShort rates as likely to fall in future as rise, so average of future short rates will not usually be higher than current short rate:

16、therefore, yield curve will not usually slope upwardExplains Fact 2 that yield curves tend to have steep slope when short rates are low and downward slope when short rates are high（二）Segmented Markets TheoryKey Assumption: Bonds of different maturities are not substitutes at allImplication: Markets

17、are completely segmented: interest rate at each maturity determined separatelyExplains Fact 3 that 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

18、 not explain Fact 1 or Fact 2 because assumes long and short rates determined independently（三）Liquidity Premium TheoryKey Assumption: Bonds of different maturities are substitutes, but are not perfect substitutesImplication: Modifies Expectations Theory with features of Segmented Markets TheoryInves

19、tors prefer short rather than long bonds must be paid positive liquidity (term) premium, lnt, to hold long-term bondsResults in following modification of Expectations Theory it + iet+1 + iet+2 + . + iet+(n1)int = + lnt nRelationship Between the Liquidity Premium and Expectations TheoriesNumerical Example:1.One-year interest rate 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%