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Chapter 15

Chapter 15. The Term Structure of Interest Rates. Overview of Term Structure of Interest Rates. Relationship between yield to maturity and maturity Information on expected future short term rates can be implied from yield curve

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Chapter 15

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  1. Chapter 15 The Term StructureofInterest Rates 15-1

  2. Overview of Term Structure of Interest Rates • 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 15-2

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

  4. Expected Interest Rates in Coming Years (Table 15.1) Expected One-Year Rates in Coming Years YearInterest Rate 0 (today) 8% 1 10% 2 11% 3 11% 15-4

  5. Pricing of Bonds using Expected Rates PVn = Present Value of $1 in n periods r1 = One-year rate for period 1 r2 = One-year rate for period 2 rn = One-year rate for period n 15-5

  6. Long-Term Rates and Bond Prices using Expected Rates Time to Maturity Price of Zero* Yield to Maturity 1 $925.93 8.00% 2 841.75 8.995 3 758.33 9.660 4 683.18 9.993 * $1,000 Par value zero 15-6

  7. Forward Rates from Observed Long-Term Rates fn = one-year forward rate for period n yn = yield for a security with a maturity of n 15-7

  8. Example of Forward Rates using Table 15.2 Numbers 4 yr = 9.993 3yr = 9.660 fn = ? (1.0993)4 = (1.0966)3 (1+fn) (1.46373) / (1.31870) = (1+fn) fn = .10998 or 11% Note: this is expected rate that was used in the prior example 15-8

  9. Downward Sloping Spot Yield Curve Zero-Coupon RatesBond Maturity 12% 1 11.75% 2 11.25% 3 10.00% 4 9.25% 5 15-9

  10. Forward Rates for Downward Sloping Yield Curve 1yr Forward Rates 1yr [(1.1175)2 / 1.12] - 1 = 0.115006 2yrs [(1.1125)3 / (1.1175)2] - 1 = 0.102567 3yrs [(1.1)4 / (1.1125)3] - 1 = 0.063336 4yrs [(1.0925)5 / (1.1)4] - 1 = 0.063008 15-10

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

  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 15-12

  13. Liquidity Premium Theory • Long-term bonds are more risky • Investors will demand a premium for the risk associated with long-term bonds • 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 15-13

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

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

  16. Market Segmentation and Preferred Habitat • 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 15-16

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