Does anyone happen to know a closed form method for solving for the optimal asset weights in a long only portfolio given: 1. Vector of Asset Mean Returns 2. Variance Covariance Matrix Solver is giving me strange results which seem to be influenced by the starting weights of the portfolio.
There is no closed form solution for the problem you described. For long-short, the answer is: Vector of weights x = labmda*(B^-1)*mu, where mu is the vector of mean returns, B - covariance matrix, labmda - normalization parameter so that the sum of weights will equal to 1.
Really, really REALLY, why use Excel to these kind of calculations ?
AntonioY Wrote: ------------------------------------------------------- > Really, really REALLY, why use Excel to these kind > of calculations ? 1. Because I hate how inflexible Allocation Advisor is when it comes to formatting the charts 2. It’s what I have at my finger tips 3. My company is too cheap to buy MatLab or any other hard core number crunching software
maratikus Wrote: ------------------------------------------------------- > There is no closed form solution for the problem > you described. For long-short, the answer is: > > Vector of weights x = labmda*(B^-1)*mu, where mu > is the vector of mean returns, B - covariance > matrix, labmda - normalization parameter so that > the sum of weights will equal to 1. Thanks for this. I think I may modify my code to first calculate a solution based on the above formula and then use that as my starting point for solver.
How many assets do you have in your optimization?
maratikus Wrote: ------------------------------------------------------- > How many assets do you have in your optimization? 8 assets (asset classes)
then here is what you can do. calculate x = (B)^-1*mu, then if nobody has negative weigths, that’s the optimal allocation. otherwise, if say, x1 and x2 are negative (then no interior solution, the final solution will have at least one of them = 0), re-run smaller dimension problem without x1 (7 assets), and then without x2 (7 assets). If you run several iterations like that, you can get the optimal solution. Does that make sense to you?
Absolutely! Pretty slick way to do it. Thanks for the assist!
One more question. The formula above will give me the minimum variance portfolio. Is it possible to find other points on the efficient frontier by modifying that formula?
jg1996business Wrote: ------------------------------------------------------- > One more question. The formula above will give me > the minimum variance portfolio. Is it possible to > find other points on the efficient frontier by > modifying that formula? Not sure. You might have to play with it.