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What are the underlying assumptions for doing this Assumption: Historical returns are lognormally distributed with no autocorrelation. can those assumptions be tested statistically Testing: $\sqrt{xy} = \sqrt{x} \sqrt{y}$ Substitute time $t$ and variance $\sigma^2$ for $x$ and $y$ respectively $\sqrt{t\sigma^2} = \sqrt{t} \sqrt{\sigma^2} = \sigma\...


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VeV is simply the scale parameter $\sigma$ such that the returns follow the $N(-\dfrac{1}{2} \sigma T, \sigma^2T)$ distribution and is obtained by inverting the VaR formula under this assumption. Have a look at this question where the full derivation of VeV is covered.


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Practically, I can tell you the sqare root assumption doesn't actually hold in practice--vol is not actually homoskedastic as a result of underlying returns not being iid (the scale tends to fall just short of the square of 12 in equities as a result of heterskedasticity). A quick google turned up this, which seems to walk through precisely what you're ...


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