# Biased VAR

This is paraphrased from Schweser’s practice exams Vol 2, Exam #3, Question 23. Suppose you have a distribution of returns and generate an average return and standard deviation and then calculate the analytical VAR of the portfolio. You then find out that your returns distribution is negatively skewed (more negative returns). This means that you actually have a higher probability of getting a worse outcome than you expect, right? So, would you say that your VAR estimate is biased upward or downward? I am thinking your estimate is not bad enough so your VAR estimate is biased upward. Schweser’s solution says your estimate is not bad enough so your VAR estimate is biased downward. Am I mixing up terms or is Schweser wrong? I was under the impression that if your estimate is not as far to the left in the distribution as it should be, your estimate is biased upward. Is that correct?

if the estimate is not bad enough, it’s lower than it should actually be => Biased downwards.

Let’s say your 95% VAR estimate based on your assumption of a normal distribution is a \$10M loss. If the distribution is negatively skewed, wouldn’t that mean the VAR is actually a bigger loss than \$10M? If that is the case, is the estimate of 10M biased downwards or upwards? I say upwards since your estimate is further to the right of the distribution than what the 95% VAR actually is.

hezagenius Wrote: ------------------------------------------------------- > Let’s say your 95% VAR estimate based on your > assumption of a normal distribution is a \$10M > loss. If the distribution is negatively skewed, > wouldn’t that mean the VAR is actually a bigger > loss than \$10M? Yes. Actual VaR is higher than the 10M estimate. Hence, the 10M estimate is downward-biased.

Because you are calculating losses when performing VAR I relate losses with negative numbers. If you are underestimating an expected loss you have upwards bias…IMO. Edit OK…but looking at the CFAI materials, they calculate these things on an absolute basis, so in that case then yes there is downward bias. I guess it depends on how you calculate it. I can’t find anywhere where it says to use absolute values, Schweser calculates VAR as a negative number, CFAI as a positive. Go with the CFAI way.

Yeah, I started thinking about it and Schweser’s answer must be in absolute terms. If you say that a worse VAR is “higher”, then the original estimate would have a downward bias. Just something to keep in mind on the exam.