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How are an investors risk preferences related to $\alpha \in (0,1)$ in a mean CVaR optimization?

Would a risk averse investor choose a higher value of $\alpha$, and if so why?

My understanding is, yes. CVaR is the average value of the worst case scenarios (in this case, the portfolio returns). So by choosing a higher $\alpha$ (i.e. closer to one), the investor wants to essentially minimize CVaR (minimize losses) even for scenarios which are very likely to occur.

If someone could provide a second opinion on my understanding, and/or provide a different perspective that would be great. Thanks

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  • $\begingroup$ Defining your terms might help give you an answer. For example how do you define mean(?) CVaR on level $\alpha$? I ask because you write on the one hand "worst case scenarios" on the other hand "even for scenarios which are very likely to occur". So what is it? $\endgroup$
    – g g
    Commented Dec 12, 2019 at 18:34
  • $\begingroup$ @gg mean CVaR optimization as an alternative to mean variance optimization. So by mean I mean asset returns. Correct me if I am wrong but CVaR is the average value of the worst case scenarios. So a 1% CVaR will average the worst 1% of the cases. A 60% CVaR will average the worst 60% of the cases; these will include the worst 1% of the cases as well, the other 59% are more likely to occur. Ofcourse an assumption here is that the more worse a loss is, the more unlikely it is to occur, which is a fair assumption I would say $\endgroup$
    – OvermanZarathustra
    Commented Dec 12, 2019 at 18:46

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