# Tag Info

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 $$\epsilon_i = r_i - ( ... 2 Each of these can be used, but each has serious drawbacks. No. 1 is inaccurate unless you use N>>10 years of data. But decades of data may not be available or may no longer be relevant to today's economy. No. 2 is good except that the CAPM has been rejected by empirical tests. More advanced models from Asset Pricing Theory may be helpful (FF3, FF5, ... 2 How about letting the FX rates remain fixed, and recalculate the portfolio volatility. That seems very obvious - am i missing something? 2 The 0.5813 is correct. I won't post the formulas here given it is to basic. I am attaching picture with all the numbers you need. If you have a question on how any of those numbers is computed just ask, but should be very straightforward. 1 Maybe. Certainly you shouldn't use their realized return ("past return") because that does not reflect expectations, it reflects events that became known after the client decided on their asset allocation. On the other hand: with a lot of (unrealistic?) assumptions, you CAN discern the client's risk aversion from their allocation. Suppose for example that ... 1 There is no solution. If w is a solution to the original problem, then consider aw with a>1$$\beta_i(aw) = a(\beta_i w) = 0$$and$$(aw)^T\Sigma(aw) = a^2 (w^T\Sigma w) > w^T\Sigma w so the original solution $w$ was not a maximum.