Question

An investor has two bonds in his portfolio that have a face value of 1,000 and pay an 11% annual coupon. Bond L matures in 12 years, while Bond S matures in 1 year. a. What will the value of each bond be if the going interest rate is 6%, 8%, and 12%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 12 more payments are to be made on bond L. b. Why does the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change? (Without using Excel or Calculator).

Answer 1

Bond L Soln Bonds F loor Coupon rate = 11% c = 11% h = l year 4TM/8 = 61, 64 ,121 YTM/- 61.4), 121. c+F-p YTM = EtP Ft P when re 6% (or YTM = 6-1.) Bond s 6000 &op= rox200 + 1000x200 - Loop 206 P - S 216ooo P 532 P = 1048.541 Bond L Se ( 1004 = 10 +(0007 12 12 (6000 + 6P) = 12x110xzoot 100x200-2001 2721 - 392000 P 1441.17)

when r= 8 %. Bonds llow tel 110 t lovop 1 8000 + op = llox200 tlow X 200 2001 208 p = 214000 Bond Te = 1023.84] y 3 (1000+P) - lot 100-p. 12 1600x200 - 200 p 12 8000 + 8P) = 12x110x 200+ 296 P = 363000 Te = 1203.24 when r= 12 % Bands 110 + 1000-P 1000- 110 + 12 (1000+P) = 2-) = Too = 110X200t lovox 200 200 p 12x1000 +12P TP = 99o.56 110 t1ooo -p Bond L 12 121009p) - 110 + lovo -P loop 12 flooo 12 + 12PX12 = 12x110x200 + 1000 x 200 - 2000

Generally, bonds with long maturities and low coupons have the longest durations. These bonds are more sensitive to a change in market interest rates and thus are more volatile in a changing rate environment. Conversely, bonds with shorter maturity dates or higher coupons will have shorter durations. There is a greater probability that interest rates will rise (and thus negatively affect a bond's market price) within a longer time period than within a shorter period. With short-term bonds, this risk is not as significant because interest rates are less likely to substantially change in the short term.