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What are typical values for risk aversion parameters $\lambda$ used in mean-variance optimization? Please provide references.

Just to be clear, I'm talking about the $\lambda$ in $U(w) = w'\mu - \frac{\lambda}{2} w' \Sigma w$, the utility function in mean-variance optimization.

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  • $\begingroup$ Shouldn't it be "-" the variance term?!? $\endgroup$ – vonjd Jul 7 '13 at 18:33
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    $\begingroup$ @vonjd You are right. Just edited. $\endgroup$ – Slow Learner Jul 9 '13 at 0:45
  • $\begingroup$ I have a somewhat related question on Economics SE. $\endgroup$ – Richard Hardy Aug 16 at 6:41
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Typical risk aversion levels lie between one and ten.

See pages 11f. in the following paper:
Preferences by Andrew Ang

EDIT: Unfortunately the paper doesn't seem to be available online anymore. The final source is the following book:

Asset Management: A Systematic Approach to Factor Investing (Financial Management Association Survey and Synthesis) 1st Edition by Andrew Ang

If you know a way to access the above chapter legally please let me know in the comments, I will update the post accordingly (I leave the original link for now).

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  • $\begingroup$ Thanks for the response. That is the risk aversion parameter for CARA utility though, not for mean-variance utility. Unless you are suggesting there is a direct way to transform into the latter? (I don't think so. The latter is not unitless and depends on the unit in which you measure returns) $\endgroup$ – Slow Learner Jul 9 '13 at 1:05
  • $\begingroup$ Please read the paper first: On page 29 it e.g. says: "The mean-variance solution in equation (10) turns out to be the same as CRRA utility (see equation (1)) if returns are log-normally distributed. This is one sense that mean-variance and CRRA are the same." $\endgroup$ – vonjd Jul 9 '13 at 8:02
  • $\begingroup$ The link has gone dead. $\endgroup$ – Richard Hardy Aug 14 at 12:32
  • $\begingroup$ @RichardHardy: Will have a look... Thank you! $\endgroup$ – vonjd Aug 14 at 15:25
  • $\begingroup$ Is it perhaps Ang "Asset Management: A Systematic Approach to Factor Investing" (2014)? See also my somewhat related question on Economics SE. $\endgroup$ – Richard Hardy Aug 16 at 6:39
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The risk aversion coefficient is also referred to as the Arrow-Pratt risk aversion index. When λ is small (i.e., the aversion to risk is low), the pen- alty from the contribution of the portfolio risk is also small, leading to more risky portfolios. Conversely, when λ is large, portfolios with more exposures to risk become more highly penalized. If we gradually increase λ from zero and for each instance solve the optimization problem, we end up calculating each portfolio along the efficient frontier. It is a common practice to calibrate λ such that a particular portfolio has the desired risk profile. The calibration is often performed via backtests with historical data. For most portfolio allocation decisions in investment management applications, the risk aversion is somewhere between 2 and 4.----BY petter kolm's book

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