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VaR and CVaR Choices for High-Frequency Strategy Returns

Article Quant Q&A · Author: madilyn
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Summary

The document describes challenges in estimating value at risk and conditional value at risk from high-frequency strategy returns. At short sampling intervals, returns may be heavy-tailed and discrete, while periods with no open position create many zero returns. Sampling at daily or longer intervals can reduce these effects but obscures intraday risk; excluding unexposed periods changes what the resulting risk measure represents.

One response proposes modified VaR using a Cornish-Fisher expansion with observed or expected skewness and excess kurtosis. It advises retaining no-exposure periods when the goal is to measure risk across the full backtest, while recognizing that interpretation depends on how consistently the strategy is active and how its exposure relates to market conditions. The document also cautions that exposure during market opening and closing periods may have different risk-return characteristics from exposure during the middle of the day. It gives considerations rather than an out-of-sample validation method.

Key ideas

  • High-frequency returns can be heavy-tailed and discrete, with zero-return spikes during periods without exposure.
  • Longer sampling intervals may simplify risk estimation but conceal intraday risk.
  • Modified VaR using a Cornish-Fisher expansion can incorporate skewness and excess kurtosis.
  • Including flat periods makes VaR describe the strategy over the full observation period, but interpretation depends on exposure patterns.
  • Intraday risk can vary by time of day, including between market open, close, and midday.

Tags

Risk managementStatisticsHigh-frequency tradingBacktesting
Full text
# Calculating VaR/CVaR on high frequency data and returns


# 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?

- 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.

## Answer by chriscross (score 2)

https://quant.stackexchange.com/a/8864

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

- 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.

- 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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.