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A zero coupon bond with 2.5 years to maturity has a annualized yield to maturity of...

A zero coupon bond with 2.5 years to maturity has a annualized yield to maturity of 5%. A 3-year maturity annual-pay coupon bond has as face value of $1000 and a 5% coupon rate. The coupon bond also has a yield to maturity of 5%.

Please calculate the duration of each bond. Which bond has the higher duration and why?

Using the formula that approximates bond price change as a function of the duration, please calculate the price change of both bonds if yields drop from 5% to 4%.

Solutions

Expert Solution

Macaulay Duration is calculated as the weighted average of the number of years until each of the bond’s promised cash flow is to be paid, where the weights are the present value of each cash flows as a percentage of bond’s full value.

Modified Duration = Mac Duration / (1+ YTM)

% Change in Bond Price = - ModDur * Change in YTM

Higher maturity bond are more sensitive to the interest rate changes, hence the 3 year bond has a higher duration than zero coupon bond.

jeff jeffy answered 2 years ago
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