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I would like to model different type of investors, hence I need to find some kind of utility functions to optimize. Apart from very abstract exponential utility function, I couldn't find any proper one. Frankly speaking, I would like to find some kind of more realistic criteria rather than type of abstract utility function. For example, for risk-neutral investor I have two questions:

1)Is it possible to use Sharpe ratio? (Can it be named as a criterion for risk-neutral?)

2)Can I use CVaR/VaR in denominator of SR (instead of StdDev)? If no, why not? I think, this will better account for fat tails.

If there are papers on this topic (utility functions for different investing styles), I would really appreciate it!

Thank you in advance!

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  • $\begingroup$ A common utility function used in the literature is CRRA with a parameter $\eta$ between 2 and 5 en.wikipedia.org/wiki/Isoelastic_utility $\endgroup$
    – Alex C
    Commented Apr 24, 2019 at 14:43
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    $\begingroup$ I found this article about using CVaR in the Sharpe ratio denominator instead of standard deviation. scielo.org.za/… $\endgroup$
    – algoquant
    Commented Sep 12, 2021 at 21:56

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  • For the first question: Let me ask you a question. Do the risk-neutral investor have a feeling of risk?
  • For the second question: Sharpe Ratio tries to capture the excess return over the risk free rate. But you need to adjust it with the risk associated with your portfolio. So it depends on the type of risk measure you employ.
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  • $\begingroup$ 1) Well, I guess, no. However, in my opinion it is worth considering someone with risk feeling between risk-aversive and gambling, which means that a this type of person has some preferences about risks 2) I think I didn't get your point here. Do you mean that there are no practical limitations on risk measure to employ here? $\endgroup$
    – Gcube
    Commented Apr 25, 2019 at 15:28
  • $\begingroup$ 2) As I remember there exist modified versions of Sharpe Ratio using other measures of risk. The reasoning behind the ratio as I guess is the trade-off between return (reward) and risk. $\endgroup$
    – David Nguyen
    Commented Apr 25, 2019 at 16:01
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SR and VaR are very different things.

The Sharpe ratio gives an idea of the performance of a given investment strategy, but it is nothing without looking at the corresponding drawdown.

VaR just gives limited information based on the volatility of a portfolio within a certain confidence interval.

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  • $\begingroup$ Hi. It is quite outdated for a year, but anyway, thanks for answering. My question was not about definitions of these concepts and the difference between them. Sorry if the question is not clearly stated. The idea was to use something more finance-related instead of utility function to solve optimization problem. That's why I came to the idea of SR as one can use it to find optimal expected return given risk. And I was wondering whether any VaR modifications exsist. For me SR with VaR in denominator makes sense - you return normalized by just another risk measure (not StDev). $\endgroup$
    – Gcube
    Commented May 24, 2020 at 9:03

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