1. The Risk and Term Structure of Interest Rates Chapter 5

2. 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 –Graphical relationship between yield and maturity.

3. Empirical Facts Interest rates on bonds of different maturities move together over time. When short-term interest rates are low, yield curves are more likely to have an upward slope; when short-term interest rates are high, yield curves are more likely to slope downward and be inverted. Yield curves almost always slope upward.

4. 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

5. Expectations Hypothesis The shape of the yield curve is determined by the investors’ expectations of future interest rate movements. The interest rate on the long-term bond will equal an average of short-term interest rates that people expect to occur over the life of the long-term bond. If the one-year interest rate over the next five years is expected to be 5, 6, 7, 8, 9 percent, –then the interest rate on the two-year bond would be 5.5%. –While for the five-year bond it would be 7%. Investors are indifferent between short and long-term securities.

6. Liquidity Premium Modification Investors know from experience that short-term securities provide greater marketability and have smaller price fluctuations than do long-term securities. The liquidity premium is that premium demanded for holding long-term securities. Therefore, a two-year security would have to yield more than the average of the two one-year securities as a reward for bearing more risk.

7. The Preferred Habitat Approach The interest rate on a long-term bond will equal an average of short-term interest rates expected to occur over the life of the long-term bond plus a term (liquidity) premium that responds to supply and demand conditions for that bond. If investors prefer the habitat of short-term bonds over long-term bonds, they might be willing to hold short-term bonds even though they have a lower expected return. This means that investors would have to be paid a positive term premium to be willing to hold a long-term bond.

8. 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

9. Real-World Observations 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 Yield curves tend to be upward sloping more often, suggesting the liquidity premium is the dominate theory

10. 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

11. Government Bonds Reading the WSJ. Current coupon or on the run issue.

12. Marketability  Recently issued government bonds (current coupon—“on the run”) are more marketable than 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 –Because these newly issued bonds are highly marketable, they carry somewhat lower yields to maturity as compared to older issues

13. 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

14. Default Risk 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

15. Risk and Tax Structure of Rates 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)

16. Duration Example Given two bonds A and B, which has more interest rate risk? Bond A Bond B Coupon8%10% Maturity 8 years 10 years

17. Duration A measure of interest rate risk that considers both coupon rate and maturity. A weighted average of the number of years until each of the bond’s cash flows is received.

18. Duration Formula

19. Properties of Duration Bonds with higher coupon rates have shorter durations than bonds with smaller coupons of the same maturity. There is generally a positive relationship between term to maturity and duration. The longer the maturity, the higher the duration. For bonds with a single payment, duration is equal to term to maturity. All other factors held constant, the higher the market rate of interest, the shorter the duration of the bond.

20. Duration for Bonds Yielding 10 Percent

21. Duration Example Find the duration of a 5-year bond paying an annual coupon of 10%. The yield to maturity is 14%, par value is $1,000 and the current price is $862.69. Duration = 4.10 years

22. Duration Example Given two bonds A and B, which has more interest rate risk? Bond A Bond B Coupon8%10% Maturity 8 years 10 years