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Let us ignore the riskless rate for simplicity of the presentation. If you have (historical or simulated) return series $r_i$ for the portfolio and $r_i^M$ for the market, then the beta is the OLS regression beta: $$ \beta = cov(r_i,r_i^M)/var(r_i^M). $$ Then if you write $r_i = \alpha + \beta r_i^M + \epsilon_i$ on the other hand $$ \epsilon_i = r_i - ( ...


How about letting the FX rates remain fixed, and recalculate the portfolio volatility. That seems very obvious - am i missing something?


It doesn't make sense to use the (co)variance(s) of asset values; if you did, by cutting an investment's share of the allocation by half, you would also cut its variance by a factor of 4. In a meaningful portfolio design, the volatility (variance) of an asset, by itself, is the same no matter how much or how little of your portfolio you put in it. Why ...


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 ...

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