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Sharpe Ratios, Tail-Risk Measures, and Investor Preferences

Article Quant Q&A · Author: Gcube
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Summary

The document asks how to choose portfolio objectives for investors with different risk preferences. It questions whether the Sharpe ratio suits a risk-neutral investor and whether replacing standard deviation in its denominator with value at risk or conditional value at risk would better reflect fat-tailed returns.

The replies distinguish the Sharpe ratio, which relates excess return to a chosen measure of risk, from VaR, which describes a loss threshold at a confidence level. They also caution that the Sharpe ratio alone does not show portfolio drawdowns, and that VaR offers limited information. The answers do not provide a formal utility-function framework, settle the proposed use of CVaR in a modified ratio, or give empirical comparisons. The discussion therefore serves as a conceptual reminder to match performance criteria and risk measures to investor preferences, while evaluating drawdowns and tail behavior separately.

Key ideas

  • The Sharpe ratio combines excess return with a selected denominator representing portfolio risk.
  • Risk-neutral preferences raise a question about whether a risk-adjusted return objective is appropriate.
  • VaR and the Sharpe ratio describe different aspects of portfolio performance and risk.
  • A Sharpe ratio should be considered alongside drawdowns and other risk information.
  • The discussion does not establish a preferred utility function or validate a CVaR-based Sharpe ratio.

Tags

Risk managementPortfolio constructionStatistics
Full text
# Sharpe ratio with CVaR for denominator and different investor utility functions


# Sharpe ratio with CVaR for denominator and different investor utility functions












I would like to model different type of investors, hence I need to find some kind of utility functions to optimize. Apart from very abstract exponential utility function, I couldn't find any proper one. Frankly speaking, I would like to find some kind of more realistic criteria rather than type of abstract utility function. For example, for risk-neutral investor I have two questions:

1)Is it possible to use Sharpe ratio? (Can it be named as a criterion for risk-neutral?)

2)Can I use CVaR/VaR in denominator of SR (instead of StdDev)? If no, why not? I think, this will better account for fat tails.

If there are papers on this topic (utility functions for different investing styles), I would really appreciate it!

Thank you in advance!

## Answer by David Nguyen (score 0)

https://quant.stackexchange.com/a/45286

- For the first question: Let me ask you a question. Do the risk-neutral investor have a feeling of risk?

- For the second question: Sharpe Ratio tries to capture the excess return over the risk free rate. But you need to adjust it with the risk associated with your portfolio. So it depends on the type of risk measure you employ.

## Answer by user24980 (score 0)

https://quant.stackexchange.com/a/54182

SR and VaR are very different things.

The Sharpe ratio gives an idea of the performance of a given investment strategy, but it is nothing without looking at the corresponding drawdown.

VaR just gives limited information based on the volatility of a portfolio within a certain confidence interval.

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.