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15 Managing Bond Portfolios

# 15 Managing Bond Portfolios - Managing Bond Portfolios 1...

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Comm367 1 COMM 367 Managing Bond Portfolios

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Comm367 2 u Inverse relationship between price and yield u An increase in a bond’s yield results in a smaller price decline than the gain associated with a decrease of equal magnitude in yield u Long-term bonds are more price sensitive than short-term bonds u As maturity increases, price sensitivity increases at a decreasing rate u Price sensitivity is inversely related to a bond’s coupon rate u Price sensitivity is inversely related to the yield to maturity at which the bond is selling Interest Rate Sensitivity
Comm367 3 Interest Rate Sensitivity Bond Coupon Maturity Initial  YTM A 12% 5 years 10% B 12% 30 years 10% C 3% 30 years 10% D 3% 30 years 6% A B C D Change in yield to maturity (%) Pe rce nta ge ch an ge in bo nd pri ce 0

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Comm367 4 Example u Bond J is a 4% coupon bond. Bond K is a 10% coupon bond. Both bonds have 8 years to maturity, make semiannual payments, and have a YTM of 9%. If interest rates suddenly rise by 2%, what is the percentage price change of these bonds? What if rates suddenly fall by 2% instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?
Comm367 5 u Percentage Changes in Bond Prices Example Bond Prices and Market Rates 7% 9% 11% Bond J \$818.59 \$719.15 \$633.82 % chg. ( +13.83% ) ( –11.87% ) Bond K \$1,181.41 \$1,056.17 \$947.69 % chg. ( +11.86% ) ( –10.27% ) All else equal, the price of the lower-coupon bond changes more (in percentage terms) than the price of the higher- coupon bond when market rates change.

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Comm367 6 u Different effects of yield changes on the prices for different bonds u Maturity inadequate measure of a bond’s economic lifetime u A measure is needed that accounts for both size and timing of cash flows Motivation of Duration
Comm367 7 Duration u A measure of the effective maturity of a bond u The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment = × = T t t w t D 1 t   time   at   Flow   Cash   CF ) 1 ( , ) 1 (   where t 1 = + = + = = T t t B B t t y CF P P y CF w t t

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Comm367 8 Duration Calculation: Example 1 8 % Bon d Ti me ( Y r) Paymen t PV of CF (10 %) Weig ht C1 X C 4 .
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15 Managing Bond Portfolios - Managing Bond Portfolios 1...

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