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The usual answer is that most risk assets tend to exhibit left-skew, with correlations ->1 into the left tail (ie diversification breaks down). And so positively skewed assets have attractive portfolio features, over and above their own intrinsic fundamentals. The more formal answer is that for two distributions with the same mean and standard deviation, ...

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It's a little simplistic to say that positive skew is better, you could for example have a return distribution which is negatively skewed but has a mean of 10%, versus a positively skewed one with a mean of 5%. That said, negative skew has a serious downside when it comes to risk and estimation. At any given point in time, you will generally only have a ...

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Consider the definition of VaR with respect to Jorion's FRM Handbook: $$VaR_{\alpha} = \mathbb{E}_t[S_T] - Q_t(S_T,\alpha)$$ where $S_T$ is the value of portfolio/asset at time $T$, $\mathbb{E}_t$ is the conditional expectation of the process at time $t$, and $Q_t(S_T,\alpha)$ is the conditional $\alpha$th percentile of the ...

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