Question

An annual corporate bond is priced to yield 7.5% annually and has a price of $972.18. Its Macaulay duration is 5.8215. If the rate decreases to 7.4%, estimate the price of the bond using

(a) first-order modified approximation;

(b) first-order Macaulay approximation.

Answer 1

(a) P0 = $ 972.18,Macaulay's Duration = M = 5.8215, Change in Interest Rate = - 7.4 % and Initial Rate = i1 = 7.5 %, New Interest Rate = i2 = -7.4+7.5 = 0.1 %

Modified Duration = D = M / (1+i1) = 5.8215 / (1.075) = 5.41535

Approximate Price at New Interest Rate (using First Order Modified Approximation) = P0 x [1-(i2-i1) x D] = 972.18 x [1-(0.001 - 0.075) x 5.41535] ~ $ 1361.77

(b) Macaulay's Duration = M = 5.8215, Initial Interest Rate = i1 = 7.5 %, New Interest Rate = i2 = 0.1 %, P0 = $ 972.18

Approximate Price at New Interest Rate (using First Order Macaulay's Approximation) = P0 x [(1+i1)/(1+i2)]^(M) = 972.18 x [(1.075)/(1.001)]^(5.8215) = $ 1472.53