Question

How do you find the dollar duration of a zero coupon bond

Answer 1

Dollar duration = - change in dollar value/change in interest rates

The above formula, however, is not applicable for a zero coupon bond. For a zero-coupon bond there is another formula that relates the zero price to the zero rate.

From the formula given at top we can say that dollar duration of a zero coupon bond is directly related to the slope of the price-rate function. Here we will have to make use of calculus to get the slope of the price-rate function and an explicit formula for the dollar duration of a zero coupon bond.

Thus dollar duration of a zero coupon bond = -dt (rt) = t/[(1+(ri/2))^(2t+1)]

Where t is the number of years and r is the discount rate.