Hi

@Laely It's important to understand that, no, VaR is most definitely

**not** premised on the mean-variance framework that assumes normality. CLT tells us the

**average of a sequence of i.i.d. variables** tends to be normal, so it might apply: for example, it is a decent justification for assuming daily P/L is

*approximately *normal, but importantly CLT assumes

*independent and identical variables* which is often unrealistic.

VaR is the quantile of a distribution; e.g., where does the 5.0% tail "start" in the distribution, such that 5.0% of the time the loss is worse (what is that 0.05 quantile on the distribution)? It has no requirement as to how the distribution is generated, it can be a function (parametric), a histogram based on collected data (non-parametric) or a simulation. VaR is just a property of the distribution. Instead of asking, what is the median (which is the 50%), VaR asks, what is the %ile?

Parametric versus non-parametric refers to the method by which we generate the distribution, and consequently, how it appears. If we use a function (e.g., normal, mixture, Poisson), that's parametric and it appears as a "coherent" pattern, like a bell shaped curve or a unimodal binomial. Non-parametric methods collect a historical window of data, which is "messy;" this is what it means that non-parametric methods do not make distributional assumption. Instead, they generate a possibly incoherent histogram. Unlike a normal which is well-behaved because it's a function, a non-parametric histogram can have all sort of shapes (like a shoreline on a map).

A normal distribution is parametric and there are many other parametric distributions, normal is just popular for learning and sometimes justified by CLT. VaR is a feature of any valid probability distribution, which itself can be parametric, non-parametric or some combination.

All of this has a world of further depth. I hope that's helpful.

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