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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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    $\begingroup$ I think you should focus on the asset allocation between classes, industries, etc. You would have to also make the assumption that the investor is knowledgeable in investing and knowingly allocated assets to match his risk tolerance, which might not always be the case. Using actual volatility can be misleading if higher than normal volatility was were observed for the investments made. Posting this as a comment as I am not an investment professional / quant. $\endgroup$ – ApplePie Apr 21 '16 at 23:55
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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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  • $\begingroup$ To expand on this idea, it would be possible to use more granularity in the Asset Classifications. For example, stocks could be divided by industry and by geographic regions. If it is assumed that an investor is competent and is heavily investing in historically risky assets in regions with historically larger return volatility / expected return volatility, you could infer that they are less risk averse. Again, I think the key lies on historical volatility. $\endgroup$ – ApplePie Apr 24 '16 at 4:47
  • $\begingroup$ That is correct in principle, if not in the details. Here are some points where I hold a different view. Modern finance classifies "stocks" by size (large vs small cap) and P/B and other ratios (growth vs value) rather than industry and geography to "stratify" riskiness. Forecast rather than historical volatility should be used; past returns always reflect unexpected events that did happen. And volatility alone is not normally used (and when it is by practitioners, it is derided by most academics); rather covariance with market returns and other aggregates make more sense as measures of risk. $\endgroup$ – mathguy Apr 24 '16 at 12:02

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