Question

A manager is holding a $1 million bond portfolio with a modified duration of eight years. She would like to hedge the risk of the portfolio by short-selling Treasury bonds. The modified duration of T-bonds is 10 years. How many dollars’ worth of T-bonds should she sell to minimize the risk of her position?

Short answer

0.8 million T bonds

Step-by-step solution

Given information:

Portfolio value: $1 million

Modified Duration of Portfolio= 8 years

Modified duration of T-bonds = 10 years

Calculation of worth of T-bonds sell

The T-Bonds of sell = Portfolio value x Modified durationof Portfolio/ Modified duration of T-bonds

= $1 million x 8 /10

=.8 million