# Calculating VaR/CVaR on high frequency data and returns

As we converge on the minute time scale and below for our unit time interval, the return distributions tend to be leptokurtotic and more discretized (due to fixed values such as minimum price increment of a security, commission and liquidity rebate). Moreover, if we are analyzing the VaR/CVaR of a model or strategy for a small number of securities, it is common to have no open position (and hence zero exposure and return) for a significant fraction of the total duration of the backtest, resulting in an artificially large peak at zero.

What adjustments can we make to calculate a meaningful VaR/CVaR and improve its out-of-sample accuracy on high frequency data and returns?

1. Avoid the problem altogether by sampling returns in larger intervals, e.g. daily basis and above. Problem: We lack a meaningful measure of intraday risk, which is our main emphasis since we are pursuing strategies whose holding periods are comparable to the unit time interval.
2. Use the empirical distribution, but discard the returns when there is no exposure.
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All comments have been deleted. (Comments should be purged when they have degraded into pointless bickering and / or noise, and the entire set is unsalvageable.) – olaker Feb 7 '13 at 9:32

Your distribution is leptokurtic therefore I suggest using MVaR (with Cornish-Fisher expansion) which is useful for non-normal distributions. In the formula you enter your observed or expected skew and excess kurtosis.

If your strategy does not have exposure all the time I would still stick with the methodology of measuring the VaR during these periods. The explanatory power of the number you calculate then depends on

1. how robust your strategy behaves. E.g. is it out of the market 30% of the time with +/-5% always then the average VaR for your period should have good explanatory power. On the other extreme, if the strategy is not in the market for a year but completely in the market the following year the explanatory power of your VaR is low. Then you should take a very long observation period/interval.
2. your strategy's behavior against the underlying market. Do you aim to be out of the market on the worst days and your strategy just does that, then your VaR should be lower than the VaR of the market.You can test the difference for significance.

I learned you have to be cautious in terms of risk measures for intraday timing strategies because being exposed during the opening and closing hour can have different risk-return character than being exposed during the middle of the day.

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