Assume that an asset has the following end-of-year cash payments
What is this asset’s duration if the interest rate is 8%? Using duration, estimate the percentage change in the price of the asset if the interest rate decreased to 7%.
First, compute the present value of the cash payments using the given rate of 8%. Then we assign weight to these present values out of the total present value. Lastly, multiply these weights with life/ years and we would get the duration.
|Year||Payment||PVF@8%||Present Value||Weight||Weight x Year|
Duration = 2.3969 yrs
To compute the estimate change in price, we need modified duration. It is computed as follows –
Modified Duration = Duration / (1+r) = 2.3969 / (1.08) = 2.2194
Modified duration denotes that for every 1% change in rates, the asset price will change by 2.2194%. So, if the rate decrease to 7%, the bond price will increase by 2.2194% (inverse relation between bond price and interest rates)