Maximize Sharpe ratio about gurobi-optimods HOT 7 OPEN

I like it. I think it won't harm much if the nup function allows for either the variance-covariance matrix, or its factor.

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Maybe we should complement this Nup with a minimum variance portfolio selection (you'd minimize "just" x @ Q @ X), or can this be covered by some paramters in this Nup already?

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I think we (@etowle, @silkehorn, and myself) should team up and create a small variety of base models in the financial space. This one and #9 are the first two on the list, but they would share the interface (and implementation) of the extra gadgets (min. buy-in, max. allocations, etc.). We may be even able to integrate the online-problem (you start with an existing allocation) into each formulation. A third variation may be needed for minimizing a tracking error.

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I would love to see the best way to include these in a multi-objective problem. Sharpe, TE, MV, etc...How would you link the y world and x in an efficient and convex way using the built in multi-objective method?

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Hi @ChinSquared, could you please elaborate on what you mean here? Gurobi allows you to combine objectives either as a weighted sum, or in a hierarchical manner using priorities. Which are you looking for, and for which metrics?

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Sure, for example, if you specify a hierarchical objective, first is to max Sharpe with a budget of 20 bps. Then minimize tracking error as the second objective. Other constraints in the portfolio are active like max trade, step size, max positions. Thanks!

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To incorporate other performance metrics into the Sharpe ratio model and retain convexity, these other metrics would have to be modeled in the space of the y variables (the reformulated variable space used in the Sharpe ratio model). This is because:

• The Sharpe ratio model is only convex in the space of the y variables
• We can't simultaneously model some metrics in the x-variable space and others in the y- variable space, unless we link together the x and y variables with the non-convex constraints x = y / (e^T y)

At any rate, I fear a multi-objective, multiple-metric model with side constraints is outside the scope of what this Mod is trying to accomplish. That said, you could always use the Sharpe ratio model-building code as a starting point for building a more complex model:

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