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This is the general solution (where $C$ is the estimated covariance matrix of portfolio returns):

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I'm sorry for the late answer. I hope you passed the exam anyway! TO answer your question, $s_2 = r_2-r_f$, that is the excess return over the risk free rate/asset. However, there seems to be a typo in your formula, I believe it should be $w_1 = \frac{s_1-ps_2}{(s_1+s_2)(1-p)}$, i.e. plus in the denominator. $w_1$ is the weight for asset 1 and \$w_2 = ...

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Use Mean Squared Forecast Error (or any other forecast evaluation metric). Your question appears to complicate the problem: If your goal is to forecast a given parameter you can test the rolling forecast against the actual observed values. This will also give you a metric of uncertainty as you can then create confidence intervals around your forecasts based ...

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