Historical VaR Backtests Depend on Portfolio and Model Design

Summary

The document frames a research question about how historical Value at Risk settings—confidence level and holding period—perform for equity portfolios. It mentions common backtesting approaches, including counting VaR exceptions, convergence checks, and Kupiec-style tests, as well as evaluating realized risk for portfolios constructed around a VaR objective. The motivating case seeks evidence relevant to larger US equity portfolios and longer holding periods, while noting that cited examples cover a small Greek equity sample or foreign exchange instead.

The response cautions that VaR results depend on the portfolio, data window, return construction, weights, and variance-covariance estimation. A failed backtest therefore calls for examining how the VaR estimate was built, rather than relying on conclusions from unrelated studies. It recommends starting with a stable subset and adding complexity gradually so the effects remain interpretable. This is methodological guidance, not a review of empirical findings or a specific validated choice of confidence level or horizon; the response also questions the value of studies detached from the target portfolio and model.

Key ideas

• Historical VaR backtests commonly examine exceptions and statistical tests of violation frequency.
• VaR performance depends on portfolio composition, data, returns, weights, and risk estimation choices.
• A backtest failure should prompt review of the VaR construction process.
• Building a model incrementally can make the impact of added complexity easier to understand.
• Evidence from small or unrelated markets may not transfer directly to a larger US equity portfolio.

Tags

# performance of historical VaR parameters


# performance of historical VaR parameters












An historical VaR measure is parameterized in terms of the confidence level and also number of periods. Specifically, the $\alpha$% T-period VaR is defined as the portfolio loss x in market value over time T that is not expected to be exceeded with probability (1 - $ \alpha$).

I am looking for empirical backtesting research on the choice of T-period and $\alpha$% for producing stock portfolios. Usually this backtest research involves looking at the # of "exceptions" (violations of the predicted risk), convergence tests, the Kupiec, and Kupier test, or involves looking at the realized risk of a portfolio constructed to minimize the VaR measure.

An illustrative example of this research is here -- however, this study involves the Greek equity market and the sample consists of only 5 equities and my focus market is U.S. equity portfolios consisting of say 25+ securities for 3-month to 1-year holding periods. Another VaR study covering the Forex market is here.

## Answer by user12348 (score 1)

https://quant.stackexchange.com/a/21435

By very nature of VaR, CVAR etc they are dependent on the portfolio, data window, variance-covariance estimation, returns, portfolio weights etc. Backtesting failure requires you to review how you create VaR, for example. I do not see how you can gain much insight from some studies. May be you can start out with a stable sub set and add non linearity incrementally. Developing a very complex model, right of the top, may inhibit comprehension of results. If there was an close form analytical solution then you have some good research that you can use. I do not believe, random studies can do any good. Just realized that this is a very old question, anyways.

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