Question

Consider a 3-year maturity annual 9% coupon paying bond with a YTM of 12%.

A. What is the Duration of this bond?

B. What will be the predicted price of this bond if the market yield increases by 100 basis points?

Answer 1

1.
Price=(1000*9%/1.12+1000*9%/1.12^2+1000*9%/1.12^3+1000/1.12^3)=927.9450620

Macaulay Duration TxC NxM (1 + Y)T + (1 + YJN Price

Duration=(1*1000*9%/1.12+2*1000*9%/1.12^2+3*1000*9%/1.12^3+3*1000/1.12^3)/927.9450620=2.7494876

2.
% change in price=-Duration/(1+yield)*% change in yield=-2.7494876/1.12*1%=-2.4549%

New Price=Old Price*(1+% change)=927.9450620*(1-2.4549%)=905.1649387