The-Term-Structure-of-In課件

1、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. Informatio

2、n 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 b

3、ond 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 F

4、ace 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

5、 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

6、 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 |

7、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)

8、 (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.I

9、NVESTMENTS | 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 cu

10、rve 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 (11nnnnnfyy

11、Forward 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, MARCUS15-16I

12、nterest 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 w

13、ants 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%?

14、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, MA

15、RCUS15-20 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

16、.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 |

17、 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 fact

18、ors, 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 cycl

19、e.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, K

20、ANE, 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 LoanIN

21、VESTMENTS | BODIE, KANE, MARCUSCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinCHAPTER 16Managing Bond PortfoliosINVESTMENTS | BODIE, KANE, MARCUS15-311. Bond prices and yields are inversely related.2. An increase in a bonds yield to maturity results in a small

22、er price change than a decrease of equal magnitude.3. Long-term bonds tend to be more price sensitive than short-term bonds.Bond Pricing RelationshipsINVESTMENTS | BODIE, KANE, MARCUS15-324. As maturity increases, price sensitivity increases at a decreasing rate.5. Interest rate risk is inversely re

23、lated to the bonds coupon rate.6. Price sensitivity is inversely related to the yield to maturity at which the bond is selling.Bond Pricing Relationships INVESTMENTS | BODIE, KANE, MARCUS15-33Figure 16.1 Change in Bond Price as a Function of Change in Yield to MaturityINVESTMENTS | BODIE, KANE, MARC

24、US15-34Table 16.1 Prices of 8% Coupon Bond (Coupons Paid Semiannually)INVESTMENTS | BODIE, KANE, MARCUS15-35Table 16.2 Prices of Zero-Coupon Bond (Semiannually Compounding)INVESTMENTS | BODIE, KANE, MARCUS15-36 A measure of the effective maturity of a bond The weighted average of the times until eac

25、h payment is received, with the weights proportional to the present value of the payment Duration is shorter than maturity for all bonds except zero coupon bonds. Duration is equal to maturity for zero coupon bonds.DurationINVESTMENTS | BODIE, KANE, MARCUS15-37Price)1 (yCFwttttwtDTt1Duration: Calcul

26、ationCFt=cash flow at time tINVESTMENTS | BODIE, KANE, MARCUS15-38Price change is proportional to duration and not to maturityD* = modified durationDuration/Price Relationship(1)1PyDxPy *PDyP INVESTMENTS | BODIE, KANE, MARCUS15-39Example 16.1 Duration Two bonds have duration of 1.8852 years. One is

27、a 2-year, 8% coupon bond with YTM=10%. The other bond is a zero coupon bond with maturity of 1.8852 years. Duration of both bonds is 1.8852 x 2 = 3.7704 semiannual periods. Modified D = 3.7704/1+0.05 = 3.591 periodsINVESTMENTS | BODIE, KANE, MARCUS15-40Example 16.1 Duration Suppose the semiannual in

28、terest rate increases by 0.01%. Bond prices fall by: =-3.591 x 0.01% = -0.03591% Bonds with equal D have the same interest rate sensitivity.yDPP*INVESTMENTS | BODIE, KANE, MARCUS15-41Example 16.1 DurationCoupon Bond The coupon bond, which initially sells at $964.540, falls to $964.1942 when its yiel

29、d increases to 5.01% percentage decline of 0.0359%.Zero The zero-coupon bond initially sells for $1,000/1.05 3.7704 = $831.9704. At the higher yield, it sells for $1,000/1.053.7704 = $831.6717. This price also falls by 0.0359%.INVESTMENTS | BODIE, KANE, MARCUS15-42Rules for DurationRule 1 The durati

30、on of a zero-coupon bond equals its time to maturityRule 2 Holding maturity constant, a bonds duration is higher when the coupon rate is lowerRule 3 Holding the coupon rate constant, a bonds duration generally increases with its time to maturityINVESTMENTS | BODIE, KANE, MARCUS15-43Rules for Duratio

31、nRule 4 Holding other factors constant, the duration of a coupon bond is higher when the bonds yield to maturity is lowerRules 5 The duration of a level perpetuity is equal to: (1+y) / yINVESTMENTS | BODIE, KANE, MARCUS15-44Figure 16.2 Bond Duration versus Bond MaturityINVESTMENTS | BODIE, KANE, MAR

32、CUS15-45Table 16.3 Bond Durations (Yield to Maturity = 8% APR; Semiannual Coupons)INVESTMENTS | BODIE, KANE, MARCUS15-46Convexity The relationship between bond prices and yields is not linear. Duration rule is a good approximation for only small changes in bond yields. Bonds with greater convexity h

33、ave more curvature in the price-yield relationship.INVESTMENTS | BODIE, KANE, MARCUS15-47Figure 16.3 Bond Price Convexity: 30-Year Maturity, 8% Coupon; Initial YTM = 8%INVESTMENTS | BODIE, KANE, MARCUS15-48ConvexityntttttyCFyPConvexity122)()1 ()1 (1Correction for Convexity:21() 2PDyConvexityyP INVES

34、TMENTS | BODIE, KANE, MARCUS15-49Figure 16.4 Convexity of Two BondsINVESTMENTS | BODIE, KANE, MARCUS15-50Why do Investors Like Convexity? Bonds with greater curvature gain more in price when yields fall than they lose when yields rise. The more volatile interest rates, the more attractive this asymm

35、etry. Bonds with greater convexity tend to have higher prices and/or lower yields, all else equal.INVESTMENTS | BODIE, KANE, MARCUS15-51Callable Bonds As rates fall, there is a ceiling on the bonds market price, which cannot rise above the call price. Negative convexity Use effective duration:/Effec

36、tive Duration = P PrINVESTMENTS | BODIE, KANE, MARCUS15-52Figure 16.5 Price Yield Curve for a Callable BondINVESTMENTS | BODIE, KANE, MARCUS15-53Mortgage-Backed Securities The number of outstanding callable corporate bonds has declined, but the MBS market has grown rapidly. MBS are based on a portfo

37、lio of callable amortizing loans. Homeowners have the right to repay their loans at any time.MBS have negative convexity.INVESTMENTS | BODIE, KANE, MARCUS15-54Mortgage-Backed Securities Often sell for more than their principal balance. Homeowners do not refinance as soon as rates drop, so implicit c

38、all price is not a firm ceiling on MBS value. Tranches the underlying mortgage pool is divided into a set of derivative securities INVESTMENTS | BODIE, KANE, MARCUS15-55Figure 16.6 Price-Yield Curve for a Mortgage-Backed SecurityINVESTMENTS | BODIE, KANE, MARCUS15-56Figure 16.7 Cash Flows to Whole M

39、ortgage Pool; Cash Flows to Three TranchesINVESTMENTS | BODIE, KANE, MARCUS15-57 Two passive bond portfolio strategies:1.Indexing2.Immunization Both strategies see market prices as being correct, but the strategies have very different risks.Passive ManagementINVESTMENTS | BODIE, KANE, MARCUS15-58Bon

40、d Index Funds Bond indexes contain thousands of issues, many of which are infrequently traded. Bond indexes turn over more than stock indexes as the bonds mature. Therefore, bond index funds hold only a representative sample of the bonds in the actual index.INVESTMENTS | BODIE, KANE, MARCUS15-59Figure 16.8 Stratification of Bonds into CellsINVESTMENTS | BODIE, KANE, MARCUS15-60Immunization Immunization is a way to control interest rate risk. Widely used by pension funds, insurance companies,