1 / 35

Yield Measures

Yield Measures. Simple Annual Interest Rate and Effective Annual Yield. So far, interest rates have been annualized by multiplying by the number of periods in a year – this gives the simple annual interest rate This procedure is not accurate

Samuel
Download Presentation

Yield Measures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Yield Measures Fixed Income Securities, Xiaohui Gao

  2. Simple Annual Interest Rate and Effective Annual Yield • So far, interest rates have been annualized by multiplying by the number of periods in a year – this gives the simple annual interest rate • This procedure is not accurate • To obtain an effective annual yield associated with a periodic interest rate (m periods per year), the following equation is used Fixed Income Securities, Xiaohui Gao

  3. Effective Annual Yield– Example Calculate the effective annual yield that corresponds to 8% simple annual interest, with interest paid quarterly. 8% ÷ 4 = 2% EAY = (1.02)4 – 1 = 0.0824 = 8.24% Fixed Income Securities, Xiaohui Gao

  4. Potential Sources of a Bond’s Dollar Return • Investors who purchase bonds can expect to receive a dollar return from one or more of these sources • The periodic coupon interest payments made by the issuer • Any capital gain (or capital loss – negative dollar return) when the bond matures, is called, or is sold • Interest income generated from reinvestment of the periodic cash flows Fixed Income Securities, Xiaohui Gao

  5. Different Measures of Yield • Current Yield • Stated Yield • Yield to Maturity • Yield to Call • Yield to Put • Yield to Worst • Yield for a Portfolio (Internal Rate of Return) • Holding-Period Return • Total Return Fixed Income Securities, Xiaohui Gao

  6. Current Yield • Current yield relates the annual coupon interest to the market price • No consideration is given to capital gains/losses • Example: The current yield for a 15-year 7% coupon bond with a par value of $1,000 selling for $769.42 is Fixed Income Securities, Xiaohui Gao

  7. Stated Yield • Stated yield is just the coupon rate Fixed Income Securities, Xiaohui Gao

  8. Yield on an Investment • The yield, y, is the interest rate that satisfies • This is also called the internal rate of return Fixed Income Securities, Xiaohui Gao

  9. Yield to Maturity • The Yield to Maturity for a bond, y, is found in the same way as the yield or internal rate of return on an investment Fixed Income Securities, Xiaohui Gao

  10. Market Convention • For a semiannual paying bond, doubling the periodic interest rate or discount rate (y) gives the yield to maturity. • This understates the effective annual yield • The yield to maturity computed on the basis of this market convention is called the bond-equivalent yield Fixed Income Securities, Xiaohui Gao

  11. Yield to Maturity – Example Calculate the yield to maturity for a 15-year 7% coupon bond with a par value of $1,000 selling for $769.42. • N = 15 × 2 = 30 • I/Y = 5.0% • YTM = 5.0 × 2 = 10% • PV = -769.42 • PMT = 70 ÷ 2 = 35 • FV = 1,000 Fixed Income Securities, Xiaohui Gao

  12. Yield to Maturity for aZero-Coupon Bond • The yield to maturity for a zero-coupon bond (or Treasury strip), y, can be found by solving directly for y in the equation for the price Fixed Income Securities, Xiaohui Gao

  13. Yield to Maturity for a Zero-Coupon Bond – Example Calculate the yield to maturity for a 10-year zero-coupon bond with a maturity value of $1,000 selling for $439.18. • N = 10 × 2 = 20 • I/Y = 4.2% • YTM = 4.2 × 2 = 8.4% • PV = -439.18 • PMT = 0 • FV = 1,000 Fixed Income Securities, Xiaohui Gao

  14. Yield to Call • When a bond is callable, the price at which it may be called is referred to as the call price • For some issues there is a call schedule that specifies a call price for each call date • The yield to first call is computed for an issue that is not currently callable • The yield to next call is computed for an issue that is currently callable Fixed Income Securities, Xiaohui Gao

  15. Yield to Call • The yield to call for a callable bond, y, is found in a similar way to the yield to maturity, but with M* being the call price and n* being the number of periods until the assumed call date Fixed Income Securities, Xiaohui Gao

  16. Yield to Call – Example Calculate the yield to call for an 18-year 11% coupon bond with a maturity value of $1,000 selling for $1,169. Assume that the first call date is 8 years from now and that the call price is $1,055. • N = 8 × 2 = 16 • I/Y = 4.2675% • YTM = 4.2675 × 2 = 8.535% • PV = -1,169 • PMT = 110 ÷ 2 = 55 • FV = 1,055 Fixed Income Securities, Xiaohui Gao

  17. Yield to Put • When a bond is putable, the price at which it may be put back to the issuer is referred to as the put price • The yield to put is the interest rate that makes the present value of the cash flows to the assumed put date plus the put price on that date as set forth in the put schedule equal to the bond’s price Fixed Income Securities, Xiaohui Gao

  18. Yield to Worst • A practice in the industry is for an investor to calculate for a given bond • The yield to maturity • The yield to call for every possible call date • The yield to put for every possible put date • The minimum of all these yields is called the yield to worst Fixed Income Securities, Xiaohui Gao

  19. Yield for a Portfolio • The yield for a portfolio of bonds is not simply the average or weighted average of the yield to maturity of the individual bond issues in the portfolio • The yield is computed by determining the cash flows for the portfolio and determining the interest rate that will make the present value of the cash flows equal to the market value of the portfolio Fixed Income Securities, Xiaohui Gao

  20. Yield for a Portfolio– Example • Consider a three-bond portfolio • To simplify the example, it is assumed that the coupon payments date is the same for each bond • The portfolio’s total market value is $57,259,000 Fixed Income Securities, Xiaohui Gao

  21. Yield for a Portfolio – Example Fixed Income Securities, Xiaohui Gao

  22. Yield for a Portfolio – Example • To find the yield (internal rate of return) for this three-bond portfolio, the interest rate must be found that makes the present value of the cash flows shown in the last column equal to $57,259,000 • An interest rate of 4.77% is calculated • Doubling this gives 9.54%, which is the yield for the portfolio on a bond-equivalent basis Fixed Income Securities, Xiaohui Gao

  23. Holding-Period Return • Yield to maturity is a measure of return if a bond is held to maturity, and all interest income is reinvested at the yield to maturity • The holding-period return measures return for a shorter period of time Fixed Income Securities, Xiaohui Gao

  24. Holding-Period Return • For a single period Fixed Income Securities, Xiaohui Gao

  25. Holding-Period Return • The holding-period return can be decomposed into two parts Fixed Income Securities, Xiaohui Gao

  26. Holding-period Return – Example • Suppose that an investor buys a 10-year bond for $980. The bond has a coupon rate of 9% paid annually and a par value of $1,000. The investor sells the bond exactly one year later for $970. What is the holding-period return? • P0 = $980, P1 = $970, C = $90 • HPR = [970 – 980 + 90] / 980 = 8.16% Fixed Income Securities, Xiaohui Gao

  27. Total Return • Like the holding-period return, the total return on a bond is a measure of the bond’s yield over a shorter period of time than until maturity • The total return incorporates an explicit assumption about the reinvestment rate Fixed Income Securities, Xiaohui Gao

  28. Computing the Total Return for a Bond • Step 1 – Compute the total coupon payments plus the interest on interest based on the assumed reinvestment rate (use the equation for the future value of an annuity) • Step 2 – Determine the projected sale price at the end of the planned investment horizon • Step 3 – The total future dollars that will be received from the investment, given the reinvestment rate and the projected required yield at the end of the investment horizon is the sum of Steps 1 and 2 Fixed Income Securities, Xiaohui Gao

  29. Computing the Total Return for a Bond (cont) • Step 4 – Obtain the semiannual total return • Step 5 – As interest is assumed to be paid semiannually, double the interest rate in Step 4 – the result is the total return for the investment horizon Fixed Income Securities, Xiaohui Gao

  30. Total Return – Example • Suppose that an investor has a six-year investment horizon, and is considering a 13-year 9% coupon bond selling at par. The investor’s expectations are: • The first four semiannual coupon payments can be reinvested at a simple annual interest rate of 8% • The last eight semiannual coupon payments can be reinvested at a 10% simple annual interest rate • The required yield to maturity on seven-year bonds at the end of the investment horizon will be 10.6% Fixed Income Securities, Xiaohui Gao

  31. Total Return – Example • Step 1A $191.09 (1.04)8 = $261.52 Fixed Income Securities, Xiaohui Gao

  32. Total Return – Example • Step 1B • Total coupon interest plus interest on interest from all 12 coupon payments is $691.23 ($261.52 + $429.71) Fixed Income Securities, Xiaohui Gao

  33. Total Return – Example • Step 2 – Projected sale price of the bond, assuming that the required yield is 10.6%, is $922.31 • Step 3 – The total future dollars are $1613.54 ($691.23 + $922.31) • Step 4 – The semiannual total return is Fixed Income Securities, Xiaohui Gao

  34. Total Return – Example • Step 5 – Doubling 4.07% gives Total return = 8.14% Fixed Income Securities, Xiaohui Gao

  35. Horizon Analysis • When a total return is calculated over an investment horizon, it is referred to as a horizon return. • The horizon analysis framework enables a portfolio manager to analyze the performance of a bond under different scenarios • Using the yield to maturity cannot achieve this. Fixed Income Securities, Xiaohui Gao

More Related