Question

An insurance company is analyzing the following three bonds, each with five years to maturity, and is using duration as its measure of interest rate risk:

a. $10,000 par value, coupon rate = 8%, rb = 0.10
b. $10,000 par value, coupon rate = 10%, rb = 0.10
c. $10,000 par value, coupon rate = 12%, rb = 0.10

Answer 1

To calculate the duration of each bond, use the formula Duration = (1/r) * [((1-c) / r) - (n(1+c) / (r(1+r)^n))] + n * (1+c) / (1+r)^n, where r is the required yield, c is the coupon rate, and n is the number of periods until maturity.

Duration is a measure of interest rate risk for bonds. It calculates the weighted average time it takes to receive the bond's cash flows. To calculate the duration, you need to determine the present value of each cash flow and the bond price. Using the given information, you can calculate the duration for each bond using the formula:

Duration = (1/r) * [((1-c) / r) - (n(1+c) / (r(1+r)^n))] + n * (1+c) / (1+r)^n

where r is the required yield, c is the coupon rate, and n is the number of periods until maturity.

For each bond, substitute the given values into the formula to calculate the duration.

J11