博迪投资学第九版课件

INVESTMENTS|BODIE,KANE,MARCUSCopyright 2011 by The McGraw-Hill Companies,Inc.All rights reserved.McGraw-Hill/IrwinCHAPTER 15The Term Structure of Interest RatesINVESTMENTS|BODIE,KANE,MARCUS15-2 The yield curve is a graph that displays the relationship between yield and maturity.Information on expected future short term rates can be implied from the yield curve.Overview of Term StructureINVESTMENTS|BODIE,KANE,MARCUS15-3Figure 15.1 Treasury Yield CurvesINVESTMENTS|BODIE,KANE,MARCUS15-4Bond Pricing Yields on different maturity bonds are not all equal.We need to consider each bond cash flow as a stand-alone zero-coupon bond.Bond stripping and bond reconstitution offer opportunities for arbitrage.The value of the bond should be the sum of the values of its parts.INVESTMENTS|BODIE,KANE,MARCUS15-5Table 15.1 Prices and Yields to Maturities on Zero-Coupon Bonds($1,000 Face Value)INVESTMENTS|BODIE,KANE,MARCUS15-6Example 15.1 Valuing Coupon Bonds Value a 3 year,10%coupon bond using discount rates from Table 15.1:Price=$1082.17 and YTM=6.88%6.88%is less than the 3-year rate of 7%.3207.11100$06.1100$05.1100$PriceINVESTMENTS|BODIE,KANE,MARCUS15-7Two Types of Yield CurvesPure Yield Curve The pure yield curve uses stripped or zero coupon Treasuries.The pure yield curve may differ significantly from the on-the-run yield curve.On-the-run Yield Curve The on-the-run yield curve uses recently issued coupon bonds selling at or near par.The financial press typically publishes on-the-run yield curves.INVESTMENTS|BODIE,KANE,MARCUS15-8Yield Curve Under Certainty Suppose you want to invest for 2 years.Buy and hold a 2-year zero-or-Rollover a series of 1-year bonds Equilibrium requires that both strategies provide the same return.INVESTMENTS|BODIE,KANE,MARCUS15-9Figure 15.2 Two 2-Year Investment ProgramsINVESTMENTS|BODIE,KANE,MARCUS15-10Yield Curve Under Certainty Buy and hold vs.rollover:Next years 1-year rate(r2)is just enough to make rolling over a series of 1-year bonds equal to investing in the 2-year bond.221212212(1)(1)(1)1(1)(1)yr xryr xrINVESTMENTS|BODIE,KANE,MARCUS15-11Spot Rates vs.Short Rates Spot rate the rate that prevails today for a given maturity Short rate the rate for a given maturity(e.g.one year)at different points in time.A spot rate is the geometric average of its component short rates.INVESTMENTS|BODIE,KANE,MARCUS15-12Short Rates and Yield Curve Slope When next years short rate,r2,is greater than this years short rate,r1,the yield curve slopes up.May indicate rates are expected to rise.When next years short rate,r2,is less than this years short rate,r1,the yield curve slopes down.May indicate rates are expected to fall.INVESTMENTS|BODIE,KANE,MARCUS15-13Figure 15.3 Short Rates versus Spot RatesINVESTMENTS|BODIE,KANE,MARCUS15-1411)1()1()1(nnnnnyyffn=one-year forward rate for period nyn=yield for a security with a maturity of n)1()1()1(11nnnnnfyyForward Rates from Observed RatesINVESTMENTS|BODIE,KANE,MARCUS15-15Example 15.4 Forward Rates The forward interest rate is a forecast of a future short rate.Rate for 4-year maturity=8%,rate for 3-year maturity=7%.1106.107.108.11113433444yyf%.f06114INVESTMENTS|BODIE,KANE,MARCUS15-16Interest Rate Uncertainty Suppose that todays rate is 5%and the expected short rate for the following year is E(r2)=6%.The value of a 2-year zero is:The value of a 1-year zero is:47.898$06.105.11000$38.952$05.11000$INVESTMENTS|BODIE,KANE,MARCUS15-17Interest Rate Uncertainty The investor wants to invest for 1 year.Buy the 2-year bond today and plan to sell it at the end of the first year for$1000/1.06=$943.40.0r-Buy the 1-year bond today and hold to maturity.INVESTMENTS|BODIE,KANE,MARCUS15-18Interest Rate Uncertainty What if next years interest rate is more(or less)than 6%?The actual return on the 2-year bond is uncertain!INVESTMENTS|BODIE,KANE,MARCUS15-19Interest Rate Uncertainty Investors require a risk premium to hold a longer-term bond.This liquidity premium compensates short-term investors for the uncertainty about future prices.INVESTMENTS|BODIE,KANE,MARCUS15-20 Expectations Liquidity PreferenceUpward bias over expectationsTheories of Term StructureINVESTMENTS|BODIE,KANE,MARCUS15-21Expectations Theory Observed long-term rate is a function of todays short-term rate and expected future short-term rates.fn=E(rn)and liquidity premiums are zero.INVESTMENTS|BODIE,KANE,MARCUS15-22 Long-term bonds are more risky;therefore,fn generally exceeds E(rn)The excess of fn over E(rn)is the liquidity premium.The yield curve has an upward bias built into the long-term rates because of the liquidity premium.Liquidity Premium TheoryINVESTMENTS|BODIE,KANE,MARCUS15-23Figure 15.4 Yield CurvesINVESTMENTS|BODIE,KANE,MARCUS15-24Figure 15.4 Yield CurvesINVESTMENTS|BODIE,KANE,MARCUS15-25Interpreting the Term Structure The yield curve reflects expectations of future interest rates.The forecasts of future rates are clouded by other factors,such as liquidity premiums.An upward sloping curve could indicate:Rates are expected to rise And/or Investors require large liquidity premiums to hold long term bonds.INVESTMENTS|BODIE,KANE,MARCUS15-26Interpreting the Term Structure The yield curve is a good predictor of the business cycle.Long term rates tend to rise in anticipation of economic expansion.Inverted yield curve may indicate that interest rates are expected to fall and signal a recession.INVESTMENTS|BODIE,KANE,MARCUS15-27Figure 15.6 Term Spread:Yields on 10-year vs.90-day Treasury SecuritiesINVESTMENTS|BODIE,KANE,MARCUS15-28Forward Rates as Forward Contracts In general,forward rates will not equal the eventually realized short rateStill an important consideration when trying to make decisions:Locking in loan ratesINVESTMENTS|BODIE,KANE,MARCUS15-29Figure 15.7 Engineering a Synthetic Forward Loan