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In an efficient frontier build with sample moments, I'd like to retrieve weights from any portfolio on the efficient frontier knowing only the standard deviation and the return. (Not the GMV, MaxTO or MaxSharpe ones).

How can I retrieve any weights from the portfolio on the EF? Thanks in advance


If the portfolio of risky assets is on the frontier, you need only know the standard deviation OR return because for each return there is a single portfolio that minimizes the standard deviation and for each standard deviation there is a single portfolio that maximizes return.

You said you are using sample moments, so I'm going to assume you have S, the covariance matrix and r, the expected return vector. You want to find w, the set of weights for the desired portfolio.

Let's say you know the target return. Use a numerical solver to find the weights that minimize w'Sw. You will need to impose two constraints: that the sum of the weights equals 1 and that w'r is equal to your target expected return.

Process is similar if you start with a standard deviation (maximize return given standard deviation constraint). You can do this stuff in excel using solver or in a more sophisticated environment if you are working in one. There are many videos on youtube showing how to perform this process. Search for "Portfolio Optimization in Excel" or similar combinations of terms.

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