# VaR based position limits - does not consider Correlations ?

SS-14, Reading #39 Schweser Book No. 4 page 102. I was scanning through the pages and saw a paragraph as follows : Regarding VaR based position limits the text says “The drawback is that the measure does not consider the correlation of different positions. This can lead to overestimating VaR…” What I do not understand is that VAR takes into account correlations/covariance, as can be seen in the formula of PF var. But the text says differently !!! Am I missing something from this?

I think they are referring to low or negative correlations between assets. These will cause VAR to be overestimated. Let’s consider an extreme example. You have two assets - asset A and asset B, whose correlation is negative 1. So, whenever you make money on asset A, you lose money on asset B. Assuming, the standard deviation and portfolio weights of each asset are the same, you should be hedged perfectly at all times. However, what is the VAR of this portfolio? If, for instance, both A and B have VARs of \$1 million, simply adding together the VARs will give you a total VAR of \$2 million. This is incorrect, since we know that the portfolio is supposed to be perfectly hedged. VAR has been overestimated, since it did not consider the negative correlation between A and B. In less extreme cases where the correlation between assets is greater than -1 but lower than 1, VAR will still be overestimated. You won’t have a perfect hedge like in the example above. However, you will have a lower portfolio standard deviation than what a naive application of VAR would imply.

Thanks for the detailed explaination. But in your reply, you said "VAR has been overestimated, since it did not consider the negative correlation between A and B. " But what I say is that when there are two assets or more, we do consider correlation in the calculation of VAR. (ofcourse, if we ignore correlations and simply add two VAR figures, I do agree with their statement that VAR overestimates…). However, they are generally saying the drawback of VAR is that it ignores correlations and overestimates the VAR. Does the (normal) VaR calculation ignores correlations between assets??? Anyway, thanks for your reply.

What I think it is saying is the band (upper limit and lower limit) without correlation is larger i.e. in some ways a more “liberal” band. Think of it as an “undiversified limit”.

FRM2cfa Wrote: > Regarding VaR based > position limits the text says > > “The drawback is that the measure does not > consider the correlation of different positions. > This can lead to overestimating VaR…” If you have positions in EUR/USD with VaR limit of \$1 million and GBP/USD with VaR limit of \$1 million, you know that your overall VaR will be below \$2 million (since correlation between EUR/USD and GBP/USD is not 1 or -1). As a result when you consider VaR of portfolio as the sum of VaR of individual positions, portfolio VaR is overstated (due to implied conservative assumption that when markets go against your portfolio, you will get hurt in every market). If you do want to rely on correlations and target portfolio VaR of \$2 million, you will be able to take larger positions in each market. Does that help?