Interpreting Risk Aversion in Power and Exponential Utility

Summary

The document asks whether commonly accepted ranges exist for risk-aversion parameters in power and exponential utility functions. Its author describes simulating stock returns over multiple weeks and comparing optimal portfolios across different values of the power utility parameter, gamma. Some tested values produce no clear pattern, while a higher sequence appears to associate greater risk aversion with larger losses.

The post does not provide an answer, empirical results, or a recommended parameter range. It raises a useful distinction between how a utility parameter is defined and calibrated, and how portfolio outcomes behave under a particular return simulation and optimization setup. The observed pattern cannot be generalized from the description alone: it may depend on the utility specification, return assumptions, constraints, horizon, and what “lose money” measures. Readers should treat the reported behavior as a question about one study rather than a general law linking risk aversion to losses.

Key ideas

• The post asks whether typical risk-aversion parameter ranges are established for power and exponential utility.
• It reports inconsistent portfolio patterns across the tested gamma values in one simulated stock-return study.
• Greater risk aversion does not by itself imply greater losses without specifying the utility model and investment setup.
• Parameter calibration and outcome comparisons depend on assumptions that the post does not detail.

Tags

# Risk-aversion parameters estimation in utility functions


# Risk-aversion parameters estimation in utility functions












Are there any "typical" risk-aversion parameters for power utility function and exponential utility function? Once I've seen an articel, in which author stated that for extremely risky person gamma in power utility function is approximately 40 and there is virtually no upper bound for risk-aversive individuals (up to 200+). But since than I have not seen any paper devoted to this with some kind of a range for a parameter.

In my study I have simulated 10,000 returns of some stocks for each of 50 weeks ahead. I am using power utility function. Computing optimal portfolio, I have arrived at strange results: for values of gamma(risk-aversion parameter) 2,6,10 there is no pattern. For values, for example, 10,20,30 - there is a pattern: more risky individual lose money more. So, the second question is about the pattern. Is there any common pattern for returns in the context of utility function? Like "the more risky you are, the more you lose"?

Any help would be greatly appreciated! Thank you in advance!

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