Value at Risk

Communities Bank has a $17 million par position in a bond with the following characteristics: The bond is a 7-year, zero-coupon bond. The market value is $12,358,674. The bond is trading at a yield to maturity of 4.6%. The historical mean change in daily yield is 0.0%. The standard deviation in yield is 15 basis points. The one-day VAR for this bond is closest to: A) $105,257. B) $260,654. C) $339,487. D) $206,390


I could be way off on this, but Im hoping the reasoning will help guide you in the right direction. VAR is the max loss you are x% certain you will not exceed over a certain period of time. Generally it is 99% (credit risk), 99.9% (market risk) or 99.97% (economic capital). 99.9% CI is 3 std. dev-s or 45bps, i.e. the portfolio starts losing $$ as soon as YTM hits 5% (4.5% + 45bps). Discount back 7 yrs using YTM of 5% to find the new market price, subtract that from the given market value and the difference you get is VAR. The answer depends on CI and it is not specified in the problem what exactly they expect you to assume. Personally I’d go with 99% (as per the basel regulations for market risk and also how a risk mgmt team would most likely look at this), so answer B. This is just a quick calc and Im sure I’m missing something here but this is the general line of reasoning. HTH a bit.

Friends the official answer is the following: The correct answer was D) $206,390. VAR is the market value of the position times the price volatility of the position, which in this case equals ($12,358,674) × (0.0167) = $206,390. How did they calculate the price volatility of the position as 0.0167? Thanks again for your replies.

like I said the answer depends on the CI you choose. To get D, CI would have to be 95% (just follow the same logic). I can almost guarantee you though, that if a risk manager at a BB looks at this, they will most likely come up with B ($284,630 to be exact). Bottom line: this question is ambiguous and incomplete. Just make sure you understand the concept behind it (which is pretty straightforward) and move on.

Its August

Thanks Lola, I am new to this material and somehow did not quite get the correct answer. I followed the following comutations: N=7 I/Y = 1.65*.15 + 4.6 = 4.8475 (1.65 because the confidence level is 95%) FV = 17000000 PMT = 0 This gives the PV = 12,205,128.74 Now I subtract the PV from market value = $12,358,674 So 12,358,674 - 12,205,128 = 153,545 Where did I mess up?


BA Wrote: ------------------------------------------------------- > Its August +1

BA Wrote: ------------------------------------------------------- > Its August And you are already on AF!!

read about duration

I can’t get the exact answer as D. But it goes like this: Assume the 95% confidence interval. The duration is 7 because it’s a zero coupon bond. So: VaR (90.0%) = VaR (95.0%) = NORMINV(95.0%, 0, 1) * 0.0015 * 7 * 12358674 = 213446.2024 VaR (97.5%) = NORMINV(97.5%, 0, 1) * 0.0015 * 7 * 12358674 = 254336.8373 any comments?

i agree with your calculation, lxwgh. However, I would use 1.65 instead of NORMINV(95.%, 0, 1) and 1.96 for NORMINV(97.5%, 0,1) because those are the typical quantiles of normal distribution worth remembering.