Question

how to compare the VAR results to backtesting results.

Answer 1

Value at risk(VaR) gives the maximum dollar-losses on a portfolio over a specific time period for a certain level of confidence.For example based on VaR calculation,an investor may be 95% confident that the maximum loss in one day on a $100 equity investment will not exceed $3.

Backtesting is the process of comparing losses prdicted by a VaR model to those actually experienced over the testing period.It is done to ensure that VaR model are reasonably accurate.

Backtesting involves the comparison of the calculated VaR measure to the actual losses or gains achieved on the portfolio.A backtesting relies on the level of confidence that is assumed in the calculation.For example,the investor who calculated a one day VaR of $3 on a $100 investment with 95% confidence will expect the one day loss on his portfolio to exceed $3 only 5% of the time.If the investor recorded the actual losses over 100 days,the loss would exceed $3 on exactly five of those days if the VaR model is accurate.A simple backtest stacks up the actual return distribution against the model return distribution by comparing the proportion of actual loss exceptions to the expected number of exceptions.The backtest must be performed over a sufficiently long period to ensure that ther are enough actual return distribution.