I'm currently taking a course in Financial Econometrics and there is a question in the lecture notes regarding back-testing of VaR which I'm have difficulty with.
First of all the procedure for back-testing of VaR using a rolling scheme is described as follows:
assume we have returns data $r_{t}, t=1,...,T$ for some large enough $T$. We take the first 60 observations and calculate their sample mean $\mu_{1-60}$ and variance $\sigma_{1-60}^{2}$ and then calculate: $$\mbox{VaR}_{1-60}\left(\alpha\right)=-\mu_{1-60}+\Phi^{-1}\left(\alpha\right)\cdot\sigma_{1-60}$$ Where $\alpha$ is our confidence parameter (usually $\alpha=0.05$) and $\Phi^{-1}$ is the inverse standard normal CDF. If $r_{61}<-\mbox{VaR}_{1-60}\left(\alpha\right)$ we mark $1$ and otherwise $0$. We proceed doing the same thing for observations $2...62$ compared to $63$ and so on and in the end we count the number of times in which the result was $1$. while under the null hypothesis we expect that the proportion of times we got $1$ to be at most $\alpha$. In particular it's important to notice we had an assumption here that the returns are all normally distributed, $r_{t}\sim N\left(\mu_{t},\sigma_{t}^{2}\right)$.
Now for the actual question, suppose $r_{t}, t=1,...,T$ are the returns using a WML investment strategy (momentum trading strategy). Is the procedure described above suitable for testing the VaR in such a case and if not why?
Usually the phrasing of the question would hint towards there being some sort of problem with using the procedure in such a case but I don't see why that would be the case... Help would very much be appreciated!