In typical mean-variance analysis, the risk-adjusted relative value of an individual asset takes the general form


with further weighting and normalization depending on the particular optimization conditions.

In economics books, I have also read the suggestion that this structure is a consequence of assuming a quadratic utility function in combination with the assumption of gaussian returns. (Is that sufficient?)

I have seen some examples of expectation value computations, but I have not seen the general connection between utility functions, distributions, and the form of risk derived explicitly. What is the proper procedure to derive the form of risk-adjusted value from an arbitrary utility function and distribution? Or is there a good reference that shows this?

  • $\begingroup$ Related: quant.stackexchange.com/questions/79292 $\endgroup$ Commented May 7 at 12:50
  • $\begingroup$ @RichardHardy the word you are looking for is "cross-posted". $\endgroup$
    – Giskard
    Commented May 7 at 16:10
  • $\begingroup$ @Giskard, right. I was in a rush and got this one a bit wrong. $\endgroup$ Commented May 7 at 20:04


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