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Chapter Thirteen

Chapter Thirteen. Duration and Reinvestment Concepts. Learning Objectives. 1. Understand that duration is a better measure of the life of a bond than maturity. 2. Be able to use present value techniques to compute duration.

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Chapter Thirteen

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  1. Chapter Thirteen Duration and Reinvestment Concepts

  2. Learning Objectives 1. Understand that duration is a better measure of the life of a bond than maturity. 2. Be able to use present value techniques to compute duration. 3. Explain the effect that duration has on bond price sensitivity to interest rate changes 4. Describe the uses of duration in protecting the value of a portfolio. 5. Relate zero-coupon bonds to the concept of duration. 6. Explain how the reinvestment rate for inflows may materially affect the final value of an investment.

  3. Review of Basic Bond Valuation Concepts. • From Chapter 12:

  4. Bond Investment Decision. • As market interest rates rise, bond prices decline. • L-T bonds are more responsive to changes in yield than S-T bonds. • Which of the following two bonds is more risky? Bond Coupon Maturity Ghazi Corp. 8% 20 years Talal Inc. 12% 25 years Bond Valuation formula: (12-1)

  5. Weighted Average Life • What is the effective life of a bond? Is it determined by its maturity date or by its weighted average life? • Weighted Average Life refers to the time period over which the coupon payments and maturity payment on a bond are recovered. • Weights are based on the sum of the undiscounted individual cash flows.

  6. Weighted Average Life of the 5 yr. bond

  7. Duration • Duration represents theweighted average life of a bond where the weights are based on the present value of the individual cash flows relative to the present value of total cash flows. • It is the economic life of a bond which accounts for yield-to-maturity, timing and size of cash flows.

  8. (13-1) Duration = MaCaulay Duration Where: CF = Yearly cash flow for each time period PV = Present value factor for each time period (from Appendix C) V = Total present value or market price of the bond n = number of periods to maturity

  9. Duration of the 5 yr. bond

  10. Table 13-3 Duration for an 8 Percent Coupon Rate Bond With Maturities of 1 & 5 years Discounted at 12%.

  11. Table 13-3 Duration for an 8 Percent Coupon Rate Bond With Maturities of 10 years Discounted at 12%. Duration

  12. Duration and Price Sensitivity • Duration is determined by maturity, coupon rate and market rate of interest. • A bond will have different duration values, for the same maturity under different market rates. • The longer the maturity or duration, the greater the impact of a given change in interest rates on price. • Duration increases at a decreasing rate as maturity increases.

  13. Change in interest rates = Duration x Approx. change bond value Duration and Bond Price Changes • Percentage change in price parallels the change in duration much more closely than it does maturity. The sign of the final answer is reversed because interest rate changes and bond prices move in opposite directions. The approximation gets progressively rougher as the term of the bond increases. Market rates of interest (YTM) and duration are inversely related. Duration decreases at a decreasing rate as YTM increases.

  14. Table 13-4 Duration and Price Sensitivity (8 Percent Coupon Rate Bond) x 2% =

  15. Duration and Coupon Rates • As the coupon rates rise, duration decreases. • High coupon (low coupon) rate bonds tend to produce higher (lower) annual cash flows prior to maturity and have more (less) influence on duration. • Duration for a given YTM decreases at a decreasing rate as coupon rates increase. • To attain the maximum bond price volatility, the bond investor should buy low coupon rate bonds.

  16. Figure 13-1. The Effects of coupon rates on Duration Duration Zero-coupon bond 4% coupon bond 8% Coupon bond 12% Coupon bond 45O Years to maturity

  17. Bringing Together the Influences on Duration • Assume a YTM of 12% which will drop to 10% PercentageBond Maturity Coupon Duration Change in _____ _______ Rate _______ Price a • Ghazi 20 Yrs 8.0% 8.939 +18.5% ACorp. • Talal 25 Yrs 12.0% 8.784 +17.6% AInc. • Now you know how to make your investment decision.

  18. Duration and Zero-Coupon Bonds • Zero-coupon bonds do not make any interest payments prior to maturity. Therefore, the duration of a zero-coupon equals the number of years it has to maturity. • Zero-coupon bonds have the greatest duration and therefore the greatest price volatility, holding risk and maturity constant.

  19. Uses of Duration • Duration is used as measure of bond price sensitivity to interest rate changes. • A strategy based on duration involves the timing of investment inflows to provide a needed cash outlay at a known future date. • Suppose $10 million is needed after eight years. You need to invest an amount today to realize a future cash flow of $10 million. If interest rates go down (up), there will be capital appreciation (depreciation) for the portfolio but a lower (higher) reinvestment rate opportunity.

  20. 7% bond value if interest reinvested at same rate. 12% bond value if interest reinvested at same rate. Compound Interest

  21. Zero-coupon Bonds and Duration 13-17

  22. Truncated table

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