McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 15 The Term Structure of Interest Rates

15-2 The relationship between yield to maturity and maturity. Information on expected future short term rates can be implied from yield curve. The yield curve is a graph that displays the relationship between yield and maturity. Three major theories are proposed to explain the observed yield curve. Overview of Term Structure

15-3 Yields Maturity Upward Sloping Downward Sloping Flat Yield Curves

15-4 Expected Interest Rates (Table 15.1) Expected One-Year Rates in Coming Years YearInterest Rate 0 (today) 8% 110% 211% 311%

15-5 Pricing of Bonds using Expected Rates PV n = Present Value of $1 in n periods r 1 = One-year rate for period 1 r 2 = One-year rate for period 2 r n = One-year rate for period n

15-6 Bond Prices using Expected Rates Time to Maturity Price of Zero*Yield to Maturity 1$ % * $1,000 Par value zero

15-7 f n = one-year forward rate for period n y n = yield for a security with a maturity of n Forward Rates from Observed Rates

15-8 Example of Forward Rates using Table yr = yr = 9.660fn = ? (1.0993) 4 = (1.0966) 3 (1+f n ) ( ) / ( ) = (1+f n ) f n = or 11% Note: this is expected rate that was used in the prior example.

15-9 Downward Sloping Spot Yield Curve Zero-Coupon RatesBond Maturity 12% % % %4 9.25%5

15-10 Forward Rates Downward Sloping Y C 1yr Forward Rates 1yr[(1.1175) 2 / 1.12] - 1 = yrs[(1.1125) 3 / (1.1175) 2 ] - 1 = yrs[(1.1) 4 / (1.1125) 3 ] - 1 = yrs[(1.0925) 5 / (1.1) 4 ] - 1 =

15-11 Expectations Liquidity Preference Upward bias over expectations Market Segmentation Preferred Habitat Theories of Term Structure

15-12 Expectations Theory Observed long-term rate is a function of today’s short-term rate and expected future short-term rates. Long-term and short-term securities are perfect substitutes. Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates.

15-13 Long-term bonds are more risky. Investors will demand a premium for the risk associated with long-term bonds. The yield curve has an upward bias built into the long-term rates because of the risk premium. Forward rates contain a liquidity premium and are not equal to expected future short-term rates. Liquidity Premium Theory

15-14 Liquidity Premiums and Yield Curves Yields Maturity Liquidity Premium Forward Rates Observed Yield Curve

15-15 Liquidity Premiums and Yield Curves Yields Maturity Liquidity Premium Forward Rates Observed Yield Curve

15-16 Short- and long-term bonds are traded in distinct markets. Trading in the distinct segments determines the various rates. Observed rates are not directly influenced by expectations. Preferred Habitat: Modification of market segmentation Investors will switch out of preferred maturity segments if premiums are adequate. Market Segmentation and Preferred Habitat

15-17 Using Spot Rates to Price Coupon Bonds A coupon bond can be viewed as a series of zero coupon bonds. To find the value each payment is discount at the zero coupon rate. Once the bond value is found, one can solve for the yield. It’s the reason that similar maturity and default risk bonds sell at different yields to maturity.

15-18 Sample Bonds A B Maturity4 years 4 years Coupon Rate6%8% Par Value 1,0001,000 Cash Flow in Cash Flow in 4 1,0601,080 Assuming Annual compounding

15-19 Price Using Spot Rates Bond A Period Spot Rate Cash Flow PV of Flow , Total978.54

15-20 Price Using Spot Rates Bond B Period Spot Rate Cash Flow PV of Flow , Total1,047.56

15-21 Solving For Yield to Maturity Bond A Bond Price YTM6.63% Bond B Price1, YTM6.61%