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Mean-Variance Optimization with Negative Risk Aversion

Article Quant Q&A · Author: Giovanni Nicolazzo
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Summary

The document asks whether a mean-variance optimization can produce a portfolio with higher variance and lower return as the risk-appetite parameter changes. It also asks whether increasing the parameter could correspond to an inverse relationship between risk and return, and what might explain that result.

The brief answer states that such behavior can arise when the parameter, lambda, is negative, representing a risk-seeking investor. For nonnegative lambda, it says this outcome does not occur. No derivation, assumptions about the optimization setup, numerical example, or supporting analysis is included, so the claim is limited to the stated formulation. Readers should interpret it in the context of the specific objective and constraints used, which are not detailed in the document.

Key ideas

  • The question concerns how a risk-appetite parameter affects mean-variance optimization outcomes.
  • The answer associates negative lambda with risk-seeking behavior.
  • It states that the inverse risk-return outcome does not occur when lambda is nonnegative.
  • The document gives no derivation or details about the optimization constraints.

Tags

Portfolio constructionRisk managementStatistics
Full text
# Risk/Return Paradox in Markowitz Optimization?


# Risk/Return Paradox in Markowitz Optimization?












It is possible that from the efficient frontier obtained varying the "lambda" parameter of the risk-appetite coefficient, in the Mean Variance Parametric Quadratic programming problem, it results that when the variance of the portfolio increases, the return decreases?

So, it is possible that from the Programming Problem, there emerges a inverse relationship between the return and the risk-appetite?

Which could be the reasons justifying that situation?

## Answer by Charles Fox (score 2)

https://quant.stackexchange.com/a/45426

Yes, if you make lambda negative, the investor becomes risk seeking. For lambda >= 0, no.

Shown 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.