Given twenty days of desk P and L that include one very large loss, compute the 95% historical VaR, the normal VaR and the expected shortfall, and say which the risk committee should see.

Historical VaR is Rs 12 lakh, normal VaR is about Rs 22 lakh, and expected shortfall is Rs 48 lakh. With 20 days, one day in twenty is worse than the VaR, so the VaR is the second-worst day and the tail beyond it is the single minus 48. The committee should see expected shortfall beside VaR, with the minus 48 named, because Rs 12 lakh says nothing about how bad the bad day was.

Sort the days from worst to best: -48, -12, -8, -6, -5 and so on up to +9. A 95% VaR is a loss exceeded on only 5% of days; with 20 days that is one day, so the historical VaR is the second-worst loss, Rs 12 lakh, and the expected shortfallThe average loss on the days worse than the VaR. It answers how bad the bad days are, which VaR does not. is the average of the days beyond it, here the single Rs 48 lakh loss. Conventions differ on whether to interpolate or take the worst day itself, so state the one you use. The normal VaR instead fits a bell curve: the mean is -1.95 and the standard deviation 12.19, so VaR is 1.645 x 12.19 minus the mean, about Rs 22.0 lakh, and the normal expected shortfall is about Rs 27.1 lakh.

Picture a flood barrier. VaR tells you the height of the water on the worst day out of twenty you choose to ignore; it says nothing about the one you ignored. Expected shortfall tells you how deep that ignored day was. One outlier moves the measures very differently: historical VaR does not see it at all, the normal VaR sees it only through an inflated standard deviation, and expected shortfall is made of it. Change the -48 to -20 and historical VaR stays at 12, normal VaR drops to 12.4 and expected shortfall drops to 20. The normal VaR is the oddest of the three: the outlier pushes it to 22, a level in the empty gap between the desk's -12 and -48 days, while a bell curve with that mean and spread says a -48 day should come about once in 50 years.

Recommend a short set, not one number. Report the historical VaR of Rs 12 lakh and the expected shortfall of Rs 48 lakh together, name the profit warning day explicitly, and stop using the normal VaR for this desk, because its returns are visibly not bell-shaped. Then flag the sample: 20 days give one observation in the tail, so the expected shortfall is a single data point, not an estimate. A committee should see the same measures on a year or more of history, plus a stress scenario for the desk's largest single-name holdings, since the -48 came from concentration, not from the market.

Close with why the desk head's choice is tempting and wrong. Rs 12 lakh is a true number on the chosen convention. It is also the one measure that is unchanged by the only event the committee needs to hear about. Reporting it alone meets the letter of a VaR limit while hiding the risk that actually hurt.