1、INVESTMENTS | BODIE, KANE, MARCUS Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 15 The Term Structure of Interest Rates INVESTMENTS | BODIE, KANE, MARCUS 15-2 The yield curve is a graph that displays the relationship between yield and maturity. Info
2、rmation on expected future short term rates can be implied from the yield curve. Overview of Term Structure INVESTMENTS | BODIE, KANE, MARCUS 15-3 Figure 15.1 Treasury Yield Curves INVESTMENTS | BODIE, KANE, MARCUS 15-4 Bond Pricing Yields on different maturity bonds are not all equal. We need to co
3、nsider 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, MARCUS 15-5 Table 15.1 Prices and Yields to Maturities on Zero-Coupon
4、 Bonds ($1,000 Face Value) INVESTMENTS | BODIE, KANE, MARCUS 15-6 Example 15.1 Valuing Coupon Bonds Value a 3 year, 10% coupon bond using discount rates from Table 15.1: Price = $1082.17 and YTM = 6.88% 6.88% is less than the 3-year rate of 7%. 32 07. 1 1100$ 06. 1 100$ 05. 1 100$ Price INVESTMENTS
5、| BODIE, KANE, MARCUS 15-7 Two Types of Yield Curves Pure 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 selli
6、ng at or near par. The financial press typically publishes on- the-run yield curves. INVESTMENTS | BODIE, KANE, MARCUS 15-8 Yield 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
7、provide the same return. INVESTMENTS | BODIE, KANE, MARCUS 15-9 Figure 15.2 Two 2-Year Investment Programs INVESTMENTS | BODIE, KANE, MARCUS 15-10 Yield 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
8、investing in the 2-year bond. 2 212 1 2 212 (1)(1) (1) 1(1) (1) yr xr yr xr INVESTMENTS | BODIE, KANE, MARCUS 15-11 Spot 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
9、 is the geometric average of its component short rates. INVESTMENTS | BODIE, KANE, MARCUS 15-12 Short 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
10、, r2 , is less than this years short rate, r1, the yield curve slopes down. May indicate rates are expected to fall. INVESTMENTS | BODIE, KANE, MARCUS 15-13 Figure 15.3 Short Rates versus Spot Rates INVESTMENTS | BODIE, KANE, MARCUS 15-14 1 1 )1( )1( )1( n n n n n y y f fn = one-year forward rate fo
11、r period n yn = yield for a security with a maturity of n )1 ()1 ()1 ( 1 1n n n n n fyy Forward Rates from Observed Rates INVESTMENTS | BODIE, KANE, MARCUS 15-15 Example 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
12、 maturity = 7%. 1106. 1 07. 1 08. 1 1 1 1 3 4 3 3 4 4 4 y y f %.f0611 4 INVESTMENTS | BODIE, KANE, MARCUS 15-16 Interest 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.
13、898$ 06. 105. 1 1000$ 38.952$ 05. 1 1000$ INVESTMENTS | BODIE, KANE, MARCUS 15-17 Interest 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.
14、 INVESTMENTS | BODIE, KANE, MARCUS 15-18 Interest 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, MARCUS 15-19 Interest Rate Uncertainty Investors require a risk premium to hold a longer-term b
15、ond. This liquidity premium compensates short-term investors for the uncertainty about future prices. INVESTMENTS | BODIE, KANE, MARCUS 15-20 Expectations Liquidity Preference Upward bias over expectations Theories of Term Structure INVESTMENTS | BODIE, KANE, MARCUS 15-21 Expectations Theory Observe
16、d 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, MARCUS 15-22 Long-term bonds are more risky; therefore, fn generally exceeds E(rn) The excess of fn over E(rn) is the liquidity premiu
17、m. The yield curve has an upward bias built into the long-term rates because of the liquidity premium. Liquidity Premium Theory INVESTMENTS | BODIE, KANE, MARCUS 15-23 Figure 15.4 Yield Curves INVESTMENTS | BODIE, KANE, MARCUS 15-24 Figure 15.4 Yield Curves INVESTMENTS | BODIE, KANE, MARCUS 15-25 In
18、terpreting 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 t
19、o hold long term bonds. INVESTMENTS | BODIE, KANE, MARCUS 15-26 Interpreting 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 an
20、d signal a recession. INVESTMENTS | BODIE, KANE, MARCUS 15-27 Figure 15.6 Term Spread: Yields on 10-year vs. 90-day Treasury Securities INVESTMENTS | BODIE, KANE, MARCUS 15-28 Forward Rates as Forward Contracts In general, forward rates will not equal the eventually realized short rate Still an important consideration when trying to make decisions : Locking in loan rates INVESTMENTS | BODIE, KANE, MARCUS 15-29 Figure 15.7 Engineering a Synthetic Forward Loan
