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Scaling volatility (standard deviation) is not the best option while calculating long term VaR. This has been discussed extensively in this post. See this page for the paper by Diebold et al. (1996). Keep in mind that long term volatility is believed to mean revert to its long term average. So if an investment is currently in high volatility regime, then ...


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Let's $\Phi$ represent the standard normal CDF, and q the required var quantile (e.g., 95%) so your $z=\Phi^{-1}\left(q\right)$. Now assume the return x is normally distributed with annualised mean $\mu$ and annualised standard deviation $\sigma$. By the way you can annualise your daily volatility by scaling it by $\sqrt{258}$ because we are in simple ...


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