I have computed VaR for a portfolio of assets ( commodities: oil and derivatives). The problem is the VaR value is quite volatile. It can be one value today and double that the next day. ( The assets prices are volatile too). I managed to compute a different and more stable VaR that is basically a weighted average of the last 5 VaRs (the VaR is daily). The new VaR seems to be as good as the old one if back-tested on 5000 historical values. Is there something I am missing? Does this method seem ok?

used to work on VaR models before- you cannot do window average to pass regulators since you are underestimate your risks...- try some statistical models which will give better stable VaRs

Statistical models such as...? Any suggestions? Thanks!

How long is your window? And how non-Gaussian are your portfolio returns? If you have fat tails (or if your second moments don't even exist), small sample VaR calculations can be VERY unstable. If you haven't, you should read a few of Mandelbrot's papers, just so you are made to be properly worried about these issues: "The variation of certain speculative prices" Journal of Business, 36, 1963 394-419"The variation of the prices of cotton, wheat, and railroad stocks, and of some financial rates" Journal of Business 40, 1967 393-413

I have a window of 5000 observations and the distribution is indeed quite fat tailed

5000 observations doesn't sound like a small window - that's 20 years of daily observations - especially if you are computing day-to-day VaR changes with overlapping windows. Are you sure your calculations are correct? For your VaR to be unstable with this sort of window, you'd need absolutely humungous returns to be dropping in or out of your sample.You should be able to figure out some idea of how unstable your VaR ought to be: bootstrap your return distribution and calculate the VaR on a sample of size 5000 via MC simulation. This will get you a distribution for your VaR numbers. If your observed VaR instability is much higher or lower than what this would lead you to think, you might want to check your calculations more carefully.

The problem is not the VaR, I have used the bootstrap method actually. The problem is the series. The portfolio is mainly benzene, the series is really volatile and the quality of the data I have is dubious.

Ah. In that case, I'd be inclined not to use sample VaR at all.Unless you have a model for the fat-tailedness (i.e. stochastic vol of some sort) so you can calculate some kind of conditional variance VaR measure, I'd be inclined to calculate VaR from the full bootstrapped distribution and use that. That way at least you wouldn't exclude any of the tails that you have actually observed. Or, to be more conservative, you could compute your sample VaR for all possible size 5000 subsamples and pick the biggest of these.And, with such non-Gaussian distributions, you should be looking at stress-tests and worst-cases as well as just VaR - but you are probably doing that, already.

my 2-cent.you're of the kind to work in the commodities area! then, your difficult might arise from (say annual) seasonality of your original series (the seasonal variations of volatility).thus, remove the seasonality of your original data, and compute your VaR from that new series.

Last edited by tagoma on September 24th, 2012, 10:00 pm, edited 1 time in total.

In the spirit of VaR maybe if you have n daily samples you should not use the mean() at all but the 90th percentile, for example.

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