## Value At Risk (VaR)

swarnendupathak
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### Value At Risk (VaR)

A large international benk has a trading book whose size depend on he oppertunities perceived by the traders. The market ris manager estimates the One-Day VaR, at 95% confidence level to be USD 50 million. You are asked to evaluate how good of a job the manager is doing in estimating the one-day VaR. Which of the following would be the more convincing evidence that the manager is doing a poor job?? assuming the losses are i.i.d.
(a) Over the last 250 days there are 8 exceedences
(b) Over the last 250 days there is a largest loss of USD 500 MN.
(c) Over the last 250 days, the mean loss is USD 60 MN.
(d) Over the last 250 days there is no exceedences.

content.pristine
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### Re: Value At Risk (VaR)

The concept of VaR, is that 95% of the time, your maximum loss is \$50Mn.
5% of the time, your loss is more than \$50Mn. The Loss can be very high on these days and still be consistent with the VaR as long as it occurs less than 5% of the time
An exceedence means that you have lost more than \$50Mn on a particular day.
Consider Option:
A. 8 exceedences = 8/250 = 3.2% Since this is less than 5%, our VaR estimate is fine.
B. Largest loss is \$500. Well, this is bad. However, this is only 1 occurence. With VaR we cannot explain the extreme tail (Note: such a high loss looks like there is an operational error) This is consistent with the VaR.
C. Mean Loss is 60Mn. That mean 60Mn is the peak of the bell curve! We are looking for the 95% of the tail!! This is highly inconsistent!
D. 250 days no exceedence. That means the manager has overestimated the VaR. However, overestimating the VaR is better than underestimating the VaR!!

swarnendupathak
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### Re: Value At Risk (VaR)

Thanks,But i have little doubt in the concept.
With 95% confidence interval with 250 trading days we can have at max 12.5 exceedences. I think the mean loss of USD 60 mn can occur below 5% level with some high loss days with less than equal to 12.5 days..... so can we take it as consistent .... & the last option is with Zero exceedences, means that the market risk manager calculated VaR on very high side.which may not be required at all, so with no use he has calculated VaR on a higher side... so i feel answer would be (d).
This is my thinking....though i am not sure...is it is a correct approach???

Swarnendu

content.pristine
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### Re: Value At Risk (VaR)

Hi Swarnendu,

I understand your point. But they said 60Mn was the mean. Unless there is an outlier soo high, that it shifts the mean to the left side of the 95%VaR, 60Mn can be the mean loss. Perhaps if a value is 10000Mn Loss, then 60Mn can be the mean loss and the VaR is 50Mn..
I would be a little more convinced of (D), if (C) said the Mean Excess Loss, or Mean Shortfall, or Tail VaR or something along those lines.
But I guess, D is a sure way that he is OVER estimating the VaR..