Hello I have a question in the VaR calculation problem here. What yield should I use to solve this?
Q: An investor is considering the portfolio impact of a new 12-year corporate bond position with a $75 million face value, a 3.25% coupon, current YTM of 2.85%, modified duration of 9.887, and a price of 104.0175 per 100 of face value.
What is the approximate VaR for the bond position at a 99% confidence interval (equal to 2.33 std.deviation) for one month (with 21 trading days) if daily yield volatility is 1.5bps and returns are normally distributed?
My calcuation
- Change the daily volatility to 21 days’ at 99% confidence: 0.00015*Square root of 21 * 2.33=0.0016
- Calculate the impact on the portfolio: (-Modify duration 9.887 * change in yield) * 0.0016 * 75M bond face value
Here I put the YTM given in the problem above, but in the answer, it uses 1.040175 which is the bond price/100. Why is that so? I cannot understand. which yield should I use here for VaR calculation and why?
Thanks for your generous help in advance!