Most diversified portfolio optimisation

[Tal Shir]

Hey guys. First time I'm posting here.
I'm looking to maximise the ratio of the sum of standard definition to the total standard variation of a portfolio.
M=(std'×w)./sqrt (w'*V*w)

Where
std :is a standard definition vector
w : the weights
V: covariance matrix

With the constraints w>0 and sum (w)=1

Please let me know if you have an idea as I guess it's not the standard optimisation problem.
Thanks a lot

[Johan Löfberg]

Maximization of Sharpe ratio can be reformulated to a QP, i.e., simple to solve. I'll email you a text on the topic in a YALMIP context

[Tal Shir]

Perfect. Thanks a lot!

[Tal Shir]

Perfect. Thanks a lot!

[Tal Shir]

Perfect. Thanks a lot!

[Tal Shir]

Perfect. Thanks a lot!

[Tal Shir]

Thank again for your replay, it was very helpful.

I have one more question if you don't mind.

How is it possible to add a constraints on the weights using your reformulation.

for example limiting the max weight to 5% I tried this:

Sharpe = [0 <= z, z'*(r) == 1, z./sum(z)<0.05];

optimize(Sharpe, z'*R*z);

wS = value(z)/sum(value(z));

returnSharpe = wS'*r;

varianceSharpe = sqrt(wS'*R*wS);

but it don't seems to like it and the results are strage.

Thanks,

Tal

[Johan Löfberg]

Never write things as nonlinear constraints when they trivially can be written as linear (z <= 0.05*sum(z))

[Tal Shir]

Thanks!