Why Realized Returns Cannot Reveal an Investor’s Risk Aversion

Summary

The discussion asks whether a client's past investing history can identify their risk aversion for portfolio optimization. Its central point is that realized returns are a poor basis for inference: they reflect outcomes that occurred after the allocation decision, not the investor's expectations or preferences at the time. Past performance alone therefore does not isolate risk tolerance.

Under restrictive assumptions, portfolio allocation may contain information about risk aversion. The example assumes two asset classes, shared beliefs about expected returns, volatilities, and correlations, and a known power utility model. Within some ranges, an optimal allocation then corresponds to a utility exponent. This is a conceptual illustration, not a practical estimation recipe. The assumptions are strong, and the response cautions that real-world use would require much more than observing a client's historical returns or allocation. It provides no empirical test, estimation procedure, or guidance for handling changing beliefs and constraints.

Key ideas

• Realized returns reflect subsequent market events and do not directly reveal an investor's expectations.
• Historical returns alone are not a sound measure of risk aversion.
• Under a specified utility model and common return assumptions, portfolio allocation can be linked to risk aversion.
• The example uses two asset classes and assumes known return statistics.
• The proposed inference is conceptual and its assumptions limit practical application.

Tags

# given someone's past investing history, is there a way to calculate his risk aversion?


# given someone's past investing history, is there a way to calculate his risk aversion?












given someone's past investing history, is there a way to calculate his risk aversion? Say, we know this client's investment history for example his past return, is there a way to calculate his risk aversion and use this parameter to portfolio optimization?

## Answer by user20429 (score 1)

https://quant.stackexchange.com/a/25571

Maybe. Certainly you shouldn't use their realized return ("past return") because that does not reflect expectations, it reflects events that became known after the client decided on their asset allocation.

On the other hand: with a lot of (unrealistic?) assumptions, you CAN discern the client's risk aversion from their allocation. Suppose for example that there are just two asset classes, "stocks" and "bonds," there is agreement on the statistics of future returns, such as expected returns, standard deviations, and correlations of asset class returns, and suppose also that somehow you know a client has power utility of expected wealth. There is a one-to-one correspondence between the possible exponents for the utility function and the corresponding optimal allocation of investment portfolio between "stocks" and "bonds," at least within some intervals for the exponent and for the optimal allocations.

However, this is only good to help understand the concepts; anyone trying to apply this in real life should have their head checked.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.