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Bond Yields and Interest Rates (chapter 17)

Bond Yields and Interest Rates (chapter 17). KEY TERMS. 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

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Bond Yields and Interest Rates (chapter 17)

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  1. Bond Yields and Interest Rates (chapter 17)

  2. KEY TERMS • 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

  3. Interest Rates • 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

  4. Determinants of Interest Rates • 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

  5. Determinants of Interest Rates • 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

  6. The Term Structure of Interest Rates • 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

  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. 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. 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. An example:Observed Treasury rates and the PEH MaturityYield 1 year 6.0% 2 years 6.2% If expectations hypothesis holds, what does the market expect will be the interest rate on one-year securities, one year from now?

  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. Measuring Bond Yields • 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

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

  16. Realized Compound Yield • 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

  17. What is interest rate (or price) risk? (no calculations for the exam) • Interest rate risk is the concern that rising kd will cause the value of a bond to fall. % change 1 yr rd 10yr % change +4.8% $1,048 5% $1,386 +38.6% $1,000 10% $1,000 -4.4% $956 15% $749 -25.1% The 10-year bond is more sensitive to interest rate changes, and hence has more interest rate risk.

  18. What is reinvestment rate risk? (no calculations for the exam) • Reinvestment rate risk is the concern that kd 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. Conclusions about interest rate and reinvestment rate risk • CONCLUSION: Nothing is riskless!

  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. 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

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