1. Vicentiu Covrig 1 Bond Yields and Interest Rates (chapter 17)

2. Vicentiu Covrig 2 Maturity: time when bond principal and all interest will be paid in full - Term-to-Maturity: years remaining until maturity Par Value: face amount, or principle of bond - Discount and Premium to par Coupon Rate: rate promised based on par value of bond principal—determines interest paid Current Yield: rate based on interest paid divided by current bond price KEY TERMS

3. Vicentiu Covrig 3 Rates and basis points - 100 basis points are equal to one percentage point Short-term riskless rate - Provides foundation for other rates - Approximated by rate on Treasury bills - Other rates differ because of  Maturity differentials  Security risk premiums Interest Rates

4. Vicentiu Covrig 4 Real rate of interest - Rate that must be offered to persuade individuals to save rather than consume - Rate at which real capital physically reproduces itself Nominal interest rate - Function of the real rate of interest and expected inflation premium Bonds benefits from a weak economy - Interest rates decline and bond prices increase Important relationship is between bond yields and inflation rates - Investors react to expectations of future inflation rather than current actual inflation Determinants of Interest Rates

5. Vicentiu Covrig 5 Market interest rates on riskless debt  real rate +expected inflation - Fisher Hypothesis Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate Real interest rate is an ex ante concept Determinants of Interest Rates

6. Vicentiu Covrig 6 Term structure of interest rates - Relationship between time to maturity and yields Yield curves - Graphical depiction of the relationship between yields and time for bonds that are identical except for maturity Upward-sloping yield curve - typical, interest rates rise with maturity Downward-sloping yield curves - Unusual, predictor of recession? Term structure theories - Explanations of the shape of the yield curve and why it changes shape over time The Term Structure of Interest Rates

7. Vicentiu Covrig 7 Yield curve and the term structure of interest rates Term structure – relationship between interest rates (or yields) and maturities. The yield curve is a graph of the term structure. The November 2005 Treasury yield curve is shown at the right.

8. Vicentiu Covrig 8 What is the relationship between the Treasury yield curve and the yield curves for corporate issues? Corporate yield curves are higher than that of Treasury securities, though not necessarily parallel to the Treasury curve. The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases.

9. Vicentiu Covrig 9 What determines the yield curve?: Pure (unbiased) Expectations Hypothesis The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates. If interest rates are expected to increase, L-T rates will be higher than S-T rates, and vice-versa. Thus, the yield curve can slope up, down, or even bow. Assumes that the maturity risk premium for Treasury securities is zero. Long-term rates are an average of current and future short-term rates. Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier.

10. Vicentiu Covrig 10 An example: Observed Treasury rates and the PEH MaturityYield 1 year6.0% 2 years6.2% If expectations hypothesis holds, what does the market expect will be the interest rate on one-year securities, one year from now?

11. Vicentiu Covrig 11 Forward rates Forward rates are rates that are expected to prevail in the future For example a two year bond would carry an interest that is an average of the current rate for one year and the forward one year rate one year from now (1+R2)^2= (1+R1)*(1+r1) r1=(1+R2)^2/(1+R1) -1 r1 = (1+0.062)^2/(1+0.06) -1 = 6.4%

12. Vicentiu Covrig 12 Yield to maturity - Most commonly used - Promised compound rate of return received from a bond purchased at the current market price and held to maturity - Equates the present value of the expected future cash flows to the initial investment - Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM Measuring Bond Yields

13. Vicentiu Covrig 13 Yields Yield spread = Yield – Treasury yield Yield spreads are a function of bond characteristics(see previous slide) Yield spread varies inversely to the business cycles Premium bond: if the bond yield is lower than the coupon rate Discount bond: if the bond yield is greater than the coupon rate Current yield: bond’s annual coupon divided by bond price

14. Vicentiu Covrig 14 Factors affecting the Yield spreads Differences in quality Differences in time to maturity Differences in call features Differences in coupon interests Differences in marketability Differences in tax treatments Cross country differences

15. Vicentiu Covrig 15 What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? Must find the ytm that solves this model.

16. Vicentiu Covrig 16 Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates Ex: Total ending wealth = $1,340.1 Purchase price (par) = $1,000 Three years holding, coupon paid semi annual RCY = 0.05 simiannual and 10% bond equivalent annual Realized Compound Yield

17. Vicentiu Covrig 17 What is interest rate (or price) risk? (no calculations for the exam) Interest rate risk is the concern that rising k d will cause the value of a bond to fall. % change 1 yr r d 10yr % change +4.8%$1,048 5% $1,386 +38.6% $1,00010% $1,000 -4.4% $95615% $749 -25.1% The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

18. Vicentiu Covrig 18 What is reinvestment rate risk? (no calculations for the exam) Reinvestment rate risk is the concern that k d will fall, and future CFs will have to be reinvested at lower rates, hence reducing income. EXAMPLE: Suppose you just won $1,000,000 playing the lottery. You intend to invest the money and live off the interest. If you choose to invest in series of 1-year bonds, that pay a 8% coupon you receive $80,000 in income and have $1,000,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $30,000. If you choose a 30-year bond that pay a 10 % coupon you receive $100,000 in income ; you can lock in a 10% interest rate, and $100,000 annual income for 30 years

19. Vicentiu Covrig 19 Conclusions about interest rate and reinvestment rate risk CONCLUSION: Nothing is riskless! Short-term AND/OR High coupon bonds Long-term AND/OR Low coupon bonds Interest rate risk LowHigh Reinvestment rate risk HighLow

20. Vicentiu Covrig 20 Interest Rate Risk : Malkiel’s Theorems  Malkiel’s theorems are a set of relationships among bond prices, time to maturity, and interest rates.  Theorem One : Bond prices move inversely with yields.  Theorem Two : Long-term bonds have more risk.  Theorem Three : Higher coupon bonds have less risk.

21. Vicentiu Covrig 21 Learning objectives Know the key characteristics of a bond Everything except: Sections NOT on the exam: No calculations using the 5 TVM keys to value a bond; Yield to call p. 456; Realized Compound Yield p 457 End of chapter questions 17.1 to 20, 24