Maximizing sharpe ratio of a portfolio with shorting allowed, where sum of absolute weights must be one.

Hi!

I am attempting to solve a problem in which I have a portfolio with 10 assets and their respective means and covariances, and I am trying to maximize the sharpe ratio. Shorting is allowed, but the sum of absolute weights of the assets must be 1. I have tried it but am not able to implement the constraint which limits the sum of absolute value of the weights to 1. Any help would be appreciated!

Thanks!

Answer 1

[Mukul Rao]

Hello,

Have you tried specifying bounds to be negative with "setBounds"

https://www.mathworks.com/help/finance/setbounds.html

You can specify the constraint that the weights add up to 1 with "addEquality"

https://www.mathworks.com/help/finance/addequality.html

I also found a similar thread, that might be helpful

Long-Short-Portfolio

You could also try to write your own portfolio optimization problem similar to what is described here

Mixed Integer Quadratic Programming Portfolio Optimization

While the example above has the weights restricted to be greater than zero, I would assume for the case of shorting, your use case would involve negative weights. The objective function can then be formulated to maximize the Sharpe Ratio.