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If the information from a 3rd factor can be derived from the information in the other 2 factors, then the 3rd factor is redundant and is not necessary. But as others have commented, probably not a great risk model. If one is uncomfortable with the risk in those sectors, it might be best to use a filter to screen those industries out of your portfolio.

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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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For a very nice reference on this matter, I recommend Pykhtin and Zhu’s Guide to Modelling Counterparty Credit Exposure, a short paper that thoroughly defines these concepts. Expected Exposure $EE(t)$ (also known as Expected Positive Exposure) for a trade with value $V(t)$ is given by: $$EE(t)=\mathbb{E}[\max(0,V(t))]$$ It is effectively “what you could ...

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