Bond Yields

1. Bond Yields Fixed Income Securities

2. Outline • Sources of Return for a Bond Investor • Measures of Return/Yield • Nominal Yield • Current Yield • Yield to Maturity • Impact of Reinvestment Assumption • Yield to Maturity for a Zero Coupon Bond • Yield to Call and the Yield to Worse • Yield Measures of a Portfolio of Bonds • Yield Measure for a Floating Rate Security • Total Return

3. Sources of Bond Return • Three sources of return: • Periodic coupon interest payments • Any capital gain (or capital loss)) when the bond matures or is called back or is sold • Income from reinvestment of the periodic coupon interest • Any measure of bond yield should be based on the above three potential sources of return

4. Nominal Yield • Nominal yield of a bond is the coupon rate on the bond • A bond with 8 percent coupon has a 8% nominal yield • Does not consider capital gain or capital loss • Does not consider reinvestment income

5. Current Yield • Current yield relates the annual coupon interest to the current market price of the bond • Considers only coupon interest income • Does not consider capital gain or loss • Does not consider reinvestment income

6. Yield to Maturity • Also called the internal rate of return of a bond • The interest rate that will make the present value of the cash flows equal to the price (or initial investment) • Rate of return promised to an investor if you purchased the bond at the current market price given coupon and maturity of the bond

7. Yield to maturity will equal the actual rate of return to a bond investor if and only if • The investor holds the bond to its maturity and • All interim cash flows in the form of coupon payments are reinvested at the computed yield to maturity

8. YTM Contd… • The YTM takes into account • Coupon interest income • Capital gain or capital loss • Interest on interest income • How much YTM tells us about a bond’s actual return? • Depends on reinvestment risk and • Interest rate risk

9. Reinvestment Risk and YTM • Higher the reinvestment risk, less we will know from the YTM about the actual yield of a bond • When will reinvestment risk be high? • For a given YTM and coupon, higher maturity bonds have a high reinvestment risk • For a given YTM and maturity, high coupon bonds have a high reinvestment risk • Which type of bonds will face higher reinvestment risk? • Premium Bonds • Discount Bonds • Zero Coupon Bonds

10. Interest Rate Risk and YTM • Inverse relationship between bond prices and bond yields • For an investor who plans to hold the bond to maturity will not face interest rate risk and YTM may be a good measure of actual yield of bond assuming other things are held constant • If you plan to trade bond before maturity, you will face price risk and YTM may not be closer to the actual yield of a bond • Impact of price will differ from bond to bond

11. YTM for a Zero Coupon Bond • A zero-coupon bond has only one cash inflow • The rate at which maturity value of a zero-coupon bond equals the current market price of the bond

12. Yield to Call • Usually, bond market participants compute both the yield to maturity and the yield to call for a callable bond and use the lower of the two to price bonds • When bonds are trading at or above a specified crossover point, which is approximates the bond’s par value plus one year’s interest, the YTC will normally provide the lowest yield measure

13. When is the bond issuer most likely to call back callable bonds? • When the bond price rises to the price above par and the computed YTM becomes low enough that it would be profitable for the issuer to call the bond and finance the call by selling new bonds in the market.

14. Total Return of a Bond • An investor can make explicit assumption about the reinvestment rate instead of assuming that the coupon interest will be reinvested at the YTM • Total return is a measure of yield that makes explicit assumptions about the reinvestment rate

15. Total Return • Why Total Return? • Suppose an investor who has a 5-year investment horizon is considering the following 4-bonds: Coupon Maturity YTM Bond A 5% 3 years 9.0% Bond B 6% 20 years 8.6% Bond C 11% 15 years 9.2% Bond D 8% 5 years 8.0% Assuming that all the four bonds are of equal credit quality, which is the most attractive to this investor?

16. How do we find out the best bonds? • It depends on investor’s expectations. • Depends on the interest rate at which coupon income can be reinvested until the investor’s planned investment horizon. • Also, for bonds with maturity higher than investment horizon, it depends on the required yield in the market at the end of the planned investment horizon. • Consequently, any of the bonds can be the best alternative, depending upon some reinvestment rate and some future required yield a

17. How to Compute Total Return? • Compute the total future dollars that will result from investing in a bond assuming a particular reinvestment rate • The total return is the interest rate that will make the initial investment in the bond grow to the computed total future dollars • Total return requires an investor to specify: • An investment horizon • A reinvestment rate, and • A selling price for the bond at the end of the investment horizon (which depends on the assumed yield to maturity for the bond at the end of the investment horizon)