Question

Assume a 7-year zero coupon bond with $1000 face value with a yield of 7% (continuously compounding). Wherever applicable, use e = 2.71828.

• What is the price of the bond?

• Use the duration to calculate the effect on the bond’s price of a 0.5% decrease on its yield.

• Recalculate the bond’s price on the basis of a 6.5% per annum yield and verify that your result in (b) is a good approximation of the change in the bond’s price using the duration.

Answer 1

1.
=1000*2.71828^(-7*0.07)
=612.63

2.
For continuously compounded, Macaulay Duration=Modified Duration=Maturity=7

% change=-Modified Duration*change in yield=-7*(-0.5%)=3.5000%

New Price=612.63*(1+3.5%)=634.07

Recalculated Price=1000*2.71828^(-7*0.065)=634.45

Hence, the price is good approximation