Feb
25

## VaR Backtesting

A follow-up of my previous post Value at Risk xls, I was asked why not & how to add a

The Backtesting framework developed by the Basel committee is the main methodology to judge the performance of VaR model, it typically consists of a periodic comparison of the portfolio’s or asset’s daily VaR values with the subsequent daily profit and loss (P&L). Obviously, the ideal model should generate the times of VaR exceeding P&L equal to (1-alpha) multiplied by time periods for backtesting. For a single equity case it is obvious what we need to do is comparing daily VaR results with daily return; but for a portfolio we have to be careful with the trading positions.

Basel committee (1996) introduces a three-zone approach, where the green zone means the possibility of erroneously accepting an inaccurate model is low; yellow zone is risk manager should be careful to check the model before take action; red zone means the probability of erroneously rejecting an accurate model is remote. For example, the backtesting three zones boundaries for a sample of 250 observations, source from Basel committee, 1996 look like

Backtesting results can therefore be judged by counting the number of exceptions and seeing intuitively which colour zone it falls into.

Alternatively you can rely on some statistical testing, for instance, the exception testing by Kupiec (1995).

Your final VaR backtesting results will look similar to

by which you are able to tell the performance of your VaR model.

certainly there isn't only one way for VaR backtesting, the above-mentioned one is an example.

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**VaR backtesting**module in that excel file, well, it is straightforward in principle to do that but since we have to calculate daily VaR for multiple periods in order to do backtesting, I simply didn't add that in an excel for speed reason.The Backtesting framework developed by the Basel committee is the main methodology to judge the performance of VaR model, it typically consists of a periodic comparison of the portfolio’s or asset’s daily VaR values with the subsequent daily profit and loss (P&L). Obviously, the ideal model should generate the times of VaR exceeding P&L equal to (1-alpha) multiplied by time periods for backtesting. For a single equity case it is obvious what we need to do is comparing daily VaR results with daily return; but for a portfolio we have to be careful with the trading positions.

Basel committee (1996) introduces a three-zone approach, where the green zone means the possibility of erroneously accepting an inaccurate model is low; yellow zone is risk manager should be careful to check the model before take action; red zone means the probability of erroneously rejecting an accurate model is remote. For example, the backtesting three zones boundaries for a sample of 250 observations, source from Basel committee, 1996 look like

Backtesting results can therefore be judged by counting the number of exceptions and seeing intuitively which colour zone it falls into.

Alternatively you can rely on some statistical testing, for instance, the exception testing by Kupiec (1995).

Your final VaR backtesting results will look similar to

by which you are able to tell the performance of your VaR model.

certainly there isn't only one way for VaR backtesting, the above-mentioned one is an example.

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So,is it right to get the predicted VaR trough computing the standard deviation of each day and then multiply it with the confidence level and the portfolio value ?

thanks

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