There are about 10 ETF as assets. I am comparing the following strategiesA. mean-variance allocation strategy: 1. Forecast asset return; 2.Forecast asset covariance; 3 Minimize portfolio volatility ? portfolio return to calculate ETF weights. Result: portfolio return annual 5.5%, volatility 3.6%, Sharpe ratio 1.52B. Equal weighting strategy: 1. Forecast asset return; 2 long ETF if forecasted return is positive; long the inverse ETF if forecasted return is negative; 3.Assign each ETF the same weight.Result: portfolio return annual 9.4%, volatility 5%, Sharpe ratio 1.85I think the equal weighting strategy is practically more satisfactory. But theoretically the mean-variance allocation strategy should beat the equal weighting strategy by offering a higher Sharpe ratio.I am using matlab fmincon for portfolio optimization in mean-variance allocation strategy, when I switch to matlab ga algorithm, the portfolio return is negative. So at this stage the mean-variance allocation strategy does not make sense to me. My target is to get my portfolio return higher than 10%, and volatility around 4%. Any suggestions to do this?Tank you in advance.

You can check by first assuming perfect forecasting ability. In the that case, it would seem to me the ex-post mean-variance Sharpe ratio must behigher under A, assuming freely allowed short sales (negative weights).Assuming that check works out, then you can attribute your described results to the inability to forecast well enough to get any value out ofunconstrained mean-variance portfolio theory, a well-known problem. You could, in principle, be able to forecast the sign of return with enough accuracy toearn some 'alpha', but with not enough precision to significantly improve upon simple weighting schemes. One suggestion that might get around the issue. You might try the mean-variance allocation with highly constrained weights, say within some [$]\epsilon[$] of strategy B and see how it does. This might get you to your target, with all the usual caveats, of course, about past performance ...

Or you may just forecast higher returns...

haha!

>> I think the equal weighting strategy is practically more satisfactory.It is indeed very difficult to beat the equal weight strategy in this type of applications (I always recommend to use the equal weight as a benchmark). I would avoid using forecasted returns, unless you have a very good statistical model for "alpha". You can also try to use minimum variance and risk-parity allocations. The equal weight portfolio will have a higher ex-ante volatility than the minimum variance portfolio, and the volatility of the risk parity portfolio is inbetween.>> My target is to get my portfolio return higher than 10%, and volatility around 4%.Ex-ante or ex-post?It is a very ambitious target anyway - Sharpe ratio of 2.5 with volatility of 4%. It is impossible unless you have a good "alpha" model for expected asset returns. A robust allocator will then of course help...

Thank you all for your suggestions.Alan, I have tried adding constrains to the mean-variance strategy. If there are n ETF, then each ETF's weight is in the range [0,1/n] if forecasted return is positive, or [-1/n,0] if forecasted return is negative. The after minimization, the weight of each ETF is very close to the equal weighting scheme, as expected. And actually, by adding more constrains, the upper and lower bounds are frequently touched.Engy, I think risk-parity allocations should be a good consideration. At least in the back testing, I have to set a high sharpe ratio as my target.

I take it this was a backtesting ?