I have recently been developing a method of generating portfolio weights via the Omega ratio.  Other than the calculation of the Omega function itself, the technique is very simple to implement and visualize, and thus I will attempt to explain it.

1. Define a range of return thresholds over which you would like to calculate the weights on.  Wider ranges reduce the portfolio variance, but also seem to reduce the portfolio return.
2. For each asset N, calculate the integral of asset N's Omega curve over the specified range
3. For each asset N, let the Nth element in a vector V be the sum of the differences between its Omega integral and all other Omega integrals
4. Divide the vector V by the scalar sum of the absolute values of its elements.  Let this be W, the weighting vector for the generated portfolio. 

    Note that the portfolio weighting has a special properties. Since the weights are the difference of areas under the Omega curves over an interval, and these differences are additive inverses symmetric over each pair of assets, the sum of the portfolio weights must be 0 (under strict, not FP arithmetic).  Any probabilistic profit is therefore arbitrage.

    As an example, I have calculate such a weighting over the Select SPDR ETFs.  The Omega curves have been calculate over plus-or-minus twice the average return of the Russell 2000, and the integral evaluated as simple Riemann sums over 64 steps.  The Omega curves themselves look very similar to the ones I calculate earlier this week in another Omega ratio post.

 Here is V, the sum of the integrals of the Omega differences for each respective ETF:

And likewise W, the portfolio weighting for each respective ETF: 

Lastly, here is a comparison of the SPY with the Omega portfolio in weighting vector W.

Here as well is a table summarizing the moment estimations of the log-return distributions of each portfolio.  Note the order of magnitude bettering in mean and variance, but the left-leaning skewness and doubled kurtosis commonly seen among hedge fund return distributions.

Note that this return distribution is calculated over the same time periods as the training data, and so is not to be taken as a representation of this strategy's predictive abilities.  The point of the graph and moments is to exhibit the risk reduction of the portfolio with bettered return.