Question

Both Bond Sam and Bond Dave have 7 percent coupons, make semi-annual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam? Of Bond Dave? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds?

Answer 1

Semi-annual coupon payment = $1,000 x 7% x (6/12) = $35

Periods to maturity Bond Sam = 6 (3x2)

Bond Dave = 40 (20x2) If r rises by 2 %,

Price of bond Sam = 35 ({1-[1/(1+0.045)]^6} / 0.045) + 1,000 [1/(1+0.045)^6] =$948.40 % change in the price of bond Sam = ($948.40 - $1,000)/$1,000 = -5.16%

Price of Bond Dave = 35 ({1-[1/(1+0.045)]^40} / 0.045) + 1,000 [1/(1+0.045)^40] = $816.00 Percentage change in price of Bond Dave = ($816 - $1,000)/$1,000

Answer: Bond Bill Compounding = Semianually Priced = Par Value 1000 Coupon Rate = 0.045 Market Rate = 0.055...