Choosing and Calibrating Risk Aversion in Mean-Variance Optimization
Summary
The document explains how the risk-aversion coefficient in mean-variance utility affects portfolio choice. A low coefficient places less weight on variance and permits greater risk exposure; a high coefficient penalizes risk more heavily. Varying the coefficient traces portfolios along the efficient frontier.
It reports two ranges from cited sources: one to ten as a typical span, and two to four for many investment-management allocation decisions. These are reference points rather than universal settings. The suggested practical approach is to calibrate the coefficient to a target portfolio risk profile, often by using historical backtests. The document does not provide a specific calibration procedure, compare the cited ranges, or discuss how estimates of expected returns and covariance affect the result. Therefore, the ranges should be treated as context, with the chosen value tied to the investor and application.
Key ideas
- A larger risk-aversion coefficient places a greater penalty on portfolio variance.
- A smaller coefficient generally permits portfolios with greater risk exposure.
- Changing the coefficient traces different portfolios along the efficient frontier.
- The cited sources give typical ranges of one to ten and, for many allocation applications, two to four.
- Calibration can match the coefficient to a desired risk profile, often using historical backtests.
Tags
Full text
# Typical risk aversion parameter value for mean-variance optimization?
# Typical risk aversion parameter value for mean-variance optimization?
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.
## Answer by vonjd (score 7, accepted)
https://quant.stackexchange.com/a/8413
Typical risk aversion levels lie between one and ten.
See pages 11f. in the following paper: Preferences by Andrew Ang
EDIT: The paper was a preprint, 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
## Answer by user6494 (score 4)
https://quant.stackexchange.com/a/9431
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 bookShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.