1. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. Chapter 5 The Term and Risk Structure of Interest Rates

2. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-2 Learning Objectives Envision and draw the yield curve and describe the determinants of its slope Explain how risk is important in influencing interest rates Comprehend the impact on interest rates of income taxes

3. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-3 The Term Structure of Rates and the Yield Curve Term Structure—Relationship among Yields of different maturities of the same type of security Yield Curve (Figure 5.1) –Graphical relationship between yield and maturity –Yield is measured on the vertical axis and term to maturity is on the horizontal

4. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-4 The Term Structure of Rates and the Yield Curve (Cont.) Yield Curve (Figure 5.1) (Cont.) –The basic question—does the curve slope upward, downward, or horizontal (Figure 5.1) –In the real world yields on all maturities tend to move together while there are distinct, divergent patterns between movements in short-term and long- term yields.

5. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-5 FIGURE 5.1 Three alternative yield curves.

6. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-6 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve –Supply and Demand Determined by relative supply/demand of different maturities Deals with each maturity by itself and ignores the interrelationships between different maturities of the same security

7. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-7 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –The Pure Expectations Approach Short-term and long-term securities are very good substitutes for each other within investor’s portfolios who collectively impact the market Therefore, there are not separate markets for short-term and long-term securities, there is a single market

8. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-8 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –The Pure Expectations Approach (Cont.) These investors are interested in the return over the period and not the maturity date of the final payment Implies that expectation of future short-term rates determines how long-term rates are related to short-term rates Buying and selling pressure maintains the long-term rate as an average of current short-term rate and the expected future short-term rates

9. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-9 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –The Pure Expectations Approach (Cont.) If expected future short-term rates are above current short- term rates—yield curve will be upward sloping Alternatively, lower expected short-term rates will cause the curve to be downward sloping The key to expectations theory is that short-term securities and long-term securities are good substitutes for each other

10. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-10 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –The Liquidity Premium Modification Prices of long-term securities are more volatile Possibly suffer capital loss if owner needs to sell security prior to maturity Prefer to hold short-term securities for liquidity Demand liquidity (risk) premium for exposure to price uncertainty with long-term securities Suggests long-term rates will always be higher than short- term

11. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-11 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –The Preferred Habitat Approach Different investors actually have a preference for different maturities—depends on their liquidity needs This suggests the supply/demand concept for different maturities will establish the specific rates for each maturity range Changes in supply/demand can cause the rates to get out of line with expectations.

12. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-12 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –The Preferred Habitat Approach (Cont.) However, Investors will drop preferred habitat if rates get out of line with expectations and switch portfolio holdings This portfolio adjustment will cause the rates to become more in line with the expectations theory

13. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-13 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –Real-World Observations When interest rates are high relative to past rates, investors expect them to decline and the price of bonds to rise in the future resulting in big capital gains Investors would then favor long-term securities, which drives up price and lowers yield—downward sloping yield curve (Figure 5.2)

14. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-14 FIGURE 5.2 Yields on U.S. government securities.

15. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-15 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –Real-World Observations (cont.) Opposite if interest rates are low relative to past—results in an upward sloping curve Historically, over the business cycle short-term rates fluctuate more than longer-term rates (Figure 5.3) Yield curves tend to be upward sloping more often, suggesting the liquidity premium is the dominant theory

16. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-16 FIGURE 5.3 Three different Treasury rates.

17. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-17 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –Summary of term structure theory Expectations theory forms the foundation of the slope of the curve Liquidity premium theory makes a long-term permanent modification that suggests an upward sloping curve Over short periods, relative supplies of securities have an impact on yields, altering the shape of the curve

18. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-18 The Term Structure of Rates and the Yield Curve (Cont.) Different Theories of the Shape of the Yield Curve (Cont.) –An Aside on Marketability Recently issued government bonds (current coupon—“on the run”) are more marketable as compared to older issues (“off the run”) Because these newly issued bonds are highly marketable, they carry somewhat lower yields to maturity as compared to older issues

19. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-19 Risk and Tax Structure of Rates Default Risk –Other than US Federal government securities, bonds carry a risk of default –Risk on municipal bonds used to be considered very low –However, experience of New York City (1975), Cleveland (1978) and Orange Country, California (1995) suggest these bonds are becoming riskier –Corporate bonds generally have a higher default risk than municipal bonds –Investors will expect higher return to compensate for increased default risk

20. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-20 Risk and Tax Structure of Rates (Cont.) Default Risk (Cont.) –Standard and Poor’s and Moody’s Investors Service rate the default risk on bonds which serve as a guide to investors –The introduction of risk in the yield curve will cause the curve to shift since another variable other than “maturity” has changed –The higher the perceived risk, the greater the upward shift of the curve for that particular security (Figure 5.4)

21. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-21 FIGURE 5.4 Riskier securities carry higher yields.

22. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-22 Risk and Tax Structure of Rates (Cont.) Tax Structure –Investors are concerned about the after tax return on bonds –Although municipal bonds are riskier than federal government bonds, tax exempt status of municipal bonds will generally result in a lower yield (downward shift of the curve) (Figure 5.4)

23. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-23 TABLE 5.1 A Guide to Bond Ratings

24. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. Appendix BOND PRICE VOLATILITY: DURATION VERSUS MATURITY

25. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-25 APPENDIX—BOND PRICE VOLATILITY: DURATION VERSUS MATURITY Problem with relationship between bond price volatility and maturity stems from the way maturity is defined –Maturity is typically the date of final repayment of principal –This ignores the fact that the bond makes coupon payments before principal is repaid

26. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-26 APPENDIX—BOND PRICE VOLATILITY: DURATION VERSUS MATURITY (cont.) More comprehensive measure of maturity is duration –Duration is defined as a weighted average of the time periods when a bond’s payments are made –Takes into account the timing of coupon and principal payments –A bond with longer duration has greater price volatility than a bond with short duration –The higher the yield to maturity, the lower the duration of a bond –Lower coupon payments mean longer duration –Duration always equals maturity for zero-coupon bond (and is less than maturity for bonds with coupons

27. Copyright © 2009 Pearson Addison-Wesley. All rights reserved. 5-27 TABLE 5A.1 Duration of Bonds with Different Maturities