FRM: VaR model backtest 

I am not sure if I got you correctly. Case 1: your VaR is estimated based on 500 observations and you still want to backtest only 1 year of data (250 observations), then it is exactly as described in the video. Case 2: you have 1 day VaR (already calculated and we do not care how many observations were used to calculate it). You want to backtest your model with 500 (around 1.5 years) observations. In this case (assume 99% VaR is used) we expect (if the model is good) 500*0.01=5 observations with loss more than VaR. However, since this result is based on random sample (500 days profit&loss are random sample) 5 is just a mean of Binomial distribution. It sounds natural that values around 5 are also plausible, but what about,for example, 10? We also know how to calculate the standard deviation of Binomial distribution and, say, 95% confidence interval. From this theoretical approach, we can find that with 95% of probability the number of days when a bank experiences a loss more than VaR does not exceed 9. Then you can simply calculate how many days the losses were above the VaR (the VaR value comes from your model and actually examined) and if the number of days is more than 9 than the model is not correct with 95% of probability. It is important to understand that the error can occur only in your VaR calculation, since parameters of Binomial distribution are known and the fact that required distribution is Binomial is also obvious.

ARE YOU sure sir ??