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Sample Size and Exceedances in Historical Simulation VaR

Article Quant Q&A · Author: Rafał
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Summary

The discussion addresses frequent Value at Risk exceedances in backtests of portfolios whose VaR was estimated with historical simulation using rolling samples of 250 or 500 daily returns. It frames the issue as potential underestimation of risk and mentions the Kupiec test, which evaluates whether the observed exceedance rate is consistent with the specified VaR coverage. The proposed explanation is limited sample size: with fewer observations, the tail behavior relevant to VaR is estimated less reliably.

The response suggests that a 500-observation sample may reduce this problem relative to 250 observations and proposes allowing the sample to expand over time instead of dropping older observations. A growing window retains information from past volatile periods, but the excerpt does not quantify improvement or examine whether older data remain representative as market conditions change. It offers sample length as a possible remedy, not a full diagnosis; no portfolio details, test results, or alternative tail models are provided.

Key ideas

  • Historical simulation VaR relies on the return sample to represent losses in the tail.
  • Frequent exceedances can indicate that VaR is too low, though the excerpt attributes them to sample size.
  • A longer historical sample may make the estimated tail less sensitive to limited observations.
  • An expanding window preserves older volatile periods but may not reflect current conditions.
  • The discussion gives no empirical comparison or broader diagnosis of the exceedances.

Tags

Risk managementBacktestingStatistics
Full text
# VaR Backtesting. High frequency of exceedances


# VaR Backtesting. High frequency of exceedances












I'm preparing for thesis defense and I've got simple question connected with Value at Risk backtesting. Portfolio VaR was calculated using historical simulation approach (250 days and 500days) and backtested with Kupiec test. In those portfolios where VaR was not properly estimated, there was always high frequency of exceedances so the Value at Risk was underestimated.

Why there was so many exceedances? The statistical important information was included in tails of distribution, because of lack of these tails the VaR was not properly estimated?

What should be done to improve the precision of estimation?

## Answer by steinbitur (score 0, accepted)

https://quant.stackexchange.com/a/35001

I assume that the problem can be boiled down into:

> SAMPLE SIZE

If I am right, this problem should be less where you are using 500 daily returns in you VaR calculation instead of 250. Then the reason is that the statistical parameters become fuzzier and fuzzier with fewer samples.

A simple way to make it better is to make it grow i.e. make it remember. Allow it to grow never to shrink, then it remembers volatile times.

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