Backtesting VaR

Backtesting attempts to verify whether actual losses are reasonably consistent with projected losses. It compares the history of value at risk (VaR) forecasts to actual (realised) portfolio returns. It is important to backtest VaR models because Backtesting gives a “reality check” on whether VaR forecasts are well-calibrated. Backtesting is central to Basel Committee’s groundbreaking decision to allow internal VaR models for capital requirements.

We can backtest a VAR model with relative ease. When the VaR model is perfectly calibrated, the number of observations falling outside VAR should align with the confidence level.

Specifically, the percentage of observed exceptions should be approximately the same as the VaR significance level, where significance is one minus the confidence level. The number of exceptions is also known as the number of exceedances, and this is simply the number of days during which the VaR level is exceeded. When too many exceptions are observed, the model is “bad” and underestimates risk. This is a significant problem because too little capital may be allocated to risk-taking units; the regulator may impose penalties. This is also problematic when too few exceptions are observed because it leads to an inefficient allocation of capital across units.

Example of Backtesting VaR

A 95.0% daily VaR should be exceeded by about 13 days per year; 5% * 250 days = 12.5 days (or 12.6 days if 252 days per year is assumed).

Why Backtesting VaR is Important?

A good (aka, accurate) model will produce approximately the number of expected exceptions. For example, over 500 days, a good (aka, accurate) 95.0% VaR model will produce approximately 5.0% * 500 days = 25 exceptions. Over 100 days, a good 99.0% VaR model is expected to produce only 1.0% * 100 = 1 exception.