VAR estimate on negatively skewed of analytical method

In Book 7, 3PM, Q23.4 If the distribution of returns is negatively skewed, the VAR estimate using the analytical method will underestimate the probability of a very large loss. The VAR estimate will be biased downward (ie, would be too low) rather than upward. I don’t understand why it’s biased downward? I though the estimate VAR number is too large (ie, My calculation is losing 20 million. But instead, I should have lost 30 million). So my estimate is biased upward. Can someone please help me on this? Thanks !

you’re not reading it right. they are estimating a low Value at risk, the Value at risk is biased downward, the potential loss would be higher.

florinpop, thanks… But I still don’t understand what you mean. I thought they have estimated a HIGH value at risk number, which is wrong given that the distribution is negatively skewed.

sorry I misread

Here is what I understand 1. the VAR using analytical method assumes normal distribution, if you draw it, VAR is some left area in the graph starting at 2. when you have negative Kurtosis, the whole graph shifts to the left, therefore you have a huge potential loss, because that left area (VAR) is larger–> VAR in 1 underetimates the true VAR (in 2) Another similar statement that I have learned in one of the question “Two characteristics of alternative investment returns that reduce the downside risk are positive skewness and low kursosis” In this case they meant the real VAR is smaller than the analytical VAR

Yea… I also think that the real VAR is smaller than the analytical VAR too. That’s why I thought it’s biased upward, instead of biased downward. Any thought?