If the daily volatility of interest rates is 2%, what is the 1-day VaR of the portfolio at a 95% confidence level?

An investor holds a bond portfolio with three bonds with a modified duration of 5, 10 and 12 years respectively. The bonds are currently valued at $100, $120 and $150.

If the daily volatility of interest rates is 2%, what is the 1-day VaR of the portfolio at a 95% confidence level?
A . 115.51
B . 163.11
C . 370
D . 165

Answer: A

Explanation:

The total value of the portfolio is $370 (=$100 + $120 + $150). The modified duration of the portfolio is the weighted average of the MDs of the different bonds, ie =(5 * 100/370) + (10 * 120/370) + (12 * 150/370) = 9.46.

This means that for every 1% change in interest rates, the value of the portfolio changes by 9.46%. Since the daily volatility of interest rates is 2%, the 95% confidence level move will be 1.65 * 2% = 3.30%. Thus, the VaR of the portfolio at the 95% confidence level will be 3.3 * 9.46% * $370 = $115.51.

All other answers are incorrect.