# Need help pls: R14 (VaR) EOC 21 and BB example 20

I’ve seen the errata for BB20 btw and still can’t make sense of this.

In blue box eg.20 they multiply the daily yield volatility by the YTM of the bond. (0.0175 x 3.528% = 0.0617 % = 6.174 bps) then solve for the expected change in YTM based on a 99% confidence interval for the
bond and a 1.75% yield volatility over 21 trading days, which equals 65.9 bps = (6.174 bps ×
2.33 standard deviations × √21).

In EOC 21 they do not multiply by the YTM of 2.85%? Solution reads “The expected change in yield based on a 99% confidence interval
for the bond and a 1.50% yield volatility over 21 trading days equals 16 bps =
(1.50% × 2.33 standard deviations × √21).”

Hi, the only aspect that I am aware where they multiply volatility with yield is in finding volatility of portfolio for two different foreign assets. Can you post this question?

Sure this is BB eg. 20

Consider the earlier case of an investor holding \$50 million face value of a 15-year bond with a coupon of 2.75%, a current YTM of 3.528%, and a price of 91 per 100 of face value. What is the VaR for the full bond price at a 99% confidence interval for one month (assuming 21 trading days in the month) if daily yield volatility is 1.75% and we assume a normal distribution?

Solution:
First, we solve for the expected change in YTM based on a 99% confidence interval for the bond and a 1.75% yield volatility over 21 trading days, which equals 65.9 bps = (6.174 bps × 2.33 standard deviations × √21).We can quantify the bond’s market value change using either a duration approximation or the actual price change as follows. We can use the Excel MDURATION function to solve for the bond’s duration as 12.025. We can therefore approximate the change in bond value using the familiar (−ModDur × ΔYield) expression as \$3,605,636 = (\$50 million × 0.91 × (−12.025 × .00659)). We can also use the Excel PRICE function to directly calculate the new price of 84.113 and multiply the price change of 6.887 by the face value to get \$3,443,500.

Rely on EOC. It is more closely aligned to mean+/-std dev*t statistics.Concept from prior levels.