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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?

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  • $\begingroup$ Just speaking for myself, no. I'm all over the place as far as types of mutual funds I invest in, and that depends on how I think the economy will go in the next 12 months. So my "average risk tolerance" would not be accurate at all. $\endgroup$
    – Bulrush
    Apr 22, 2016 at 21:25

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Generally speaking no. You wouldn't be able to distinguish re-balancing for risk aversion reasons from re-balancing motivated by changes in expected returns or the co-variance of returns.

Consider the simple case of a household periodically re-balancing their investments in across both a fixed index fund and an equity index fund. The econometrician sees the investor reduce their equity holdings and increase the fixed income investment. Any of the following could induce such a change:

  1. An increase in risk aversion
  2. Lower expected returns for the equity index
  3. Higher expected returns for fixed income index
  4. Greater positive co-variation of the two funds

And in reality, the situation is much worse because there are many investments, taxes, transaction costs, behavioral issues, and rational-inattention.

I'm sure you could simplify and cook up a theoretical setting where you could do this (for one, just assume that all the other things cannot change), but in general this won't be possible.

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  • $\begingroup$ I guess you have a few good points. However, from my point of view each reason might result in a slightly different pattern in the portfolio history as each factor creates a different and perhaps distinctive characteristic to the time series. Probably assuming these are independent from utility maximization, it should be possible to capture other factors in an error term if they are orthogonal to the utility factor, which we are interested here. If we use some general maximum likelihood approach, it is possible I think.. But it requires a model and stoch. process for sure.. $\endgroup$
    – T123
    Jan 15, 2023 at 8:43
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adding to the previous answer, i found this paper here where the authors just did that. They controlled for other effects and the shape of the utility function so i guess its possible..

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2845338

Hope this helps (well, the Question as asked nearly 7 yrs ago by now..)

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