Independent solution

How to solve this Macaulay Duration from Price Sensitivity question

Setup

Setup

Let P(i) be price as a function of annual yield. At i = 8%, the supplied price is 100 and the supplied derivative is −700.

P=100,i=0.08,dP/di=−700P=100,\quad i=0.08,\quad dP/di=-700

Model

Model

Macaulay duration and the price derivative satisfy D = −(1 + i)P′(i)/P(i). This converts the local price sensitivity into a time-weighted duration.

DM=−1+iPdPdiD_M=-\frac{1+i}{P}\frac{dP}{di}

Compute

Compute

Substitution gives −1.08(−700)/100 = 7.56 years.

DM=−1.08100(−700)=7.56D_M=-\frac{1.08}{100}(-700)=7.56

Answer

Answer

The calculation gives 7.56 for macaulay duration from price sensitivity, matching published choice C.

DM=7.56(C)\boxed{D_M=7.56\quad\text{(C)}}