Question

Consider a bond with maturity 4 year, 100 face value, coupon 5%, and yield 5%. Compute a dollar duration numerically using a dy =0.001%. Recall that $Dur is approximately equal to [P(y+dy)-P(y)]/dy when dy is small and P(y) is the price of the bond at the yield y. Report you result rounded to the closest integer and the correct sign.

Answer 1

Solution :

Face value = 100, Coupon = 5% , Yield = 5% Dy = 0.001%

Assuming coupon is paid annually

P(Y) = 100 because yield = coupon

P( Y +dY ) = P (5.001%) = 99.99645413 ( See excel image for price calculation

Dollar duration =( P( Y +dY ) - P(Y) ) / dY = 0.003545868 / 0.001 % = 355