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?
- 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.
- Use the empirical distribution, but discard the returns when there is no exposure.