Consider the earlier case of an investor holding $50 million face value of a 15-year bond with a semiannual 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 if annualized daily yield volatility is 1.75% (175 bps) and we assume that interest rates are normally distributed?
Duration - 12.025
I think thw issue is that there are 2 examples of this in the text BB20 and EOCq21 (I think EOCq21 is better) and they take different appraoches (and have issues with the quoting of daily interest rate vol.).
Here the 1.75% is assumed to be a proportional volatility is absolute yield vol (requited for the duration part of the calculation) is yiled vol. x actual yield = 1.75% x 3.528% = 0.0617%
The answer Okachiang has given is correct if we assume the quote is absolute vol.
But note it should be 0.0175% x 21^(1/2) x 2.33 = 0.0187%
The end of chapter takes the appraoch use in Okachiang.
Basically it is a mess with no consistency or proper explanation in the text.
Academic text books seem to calcualte the dail yield vol in different ways some propduce a priptionate method and some an absolute.
To do the duration element you need an absolute method.
