I am researching optimal asset allocations and am wondering if I am making mistake(s) in calculating the portfolio return. I have three assets, of which I have monthly return data. I have calculated the returns by log(pt/pt-1) (because I was told to do this). Next, I calculate the variance-covariance matrix, from which I get the portfolio variance etc. Then I multiply the weights by the realized returns to get the portfolio return. I use an algorithm to get the Sharpe-maximizing weights.
Is it even correct to calculate the return of the assets as the arithmetic mean of the log returns? How should it be done?
How should the portfolio return be calculated? Is it wrong to multiply weights by expected returns because the log returns aren't cross asset additive?