CPLEX solver in MATLAB: maximizing Sharpe Ratio

[Tommy Lavertes]

Hello, I was wondering if you can help me implement a Sharpe ratio optimization problem in CPLEX for matlab.

I read your post for YALMIP portfolio optimization but I can't seem to reproduce the same results when I try to change my Sharpe ratio optimization problem into the convex version you utilized.

This is my code:

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function [weights_new] = max_sharpe_ratio(asset_init, exp_ret, Q, risk_free)

% Computes the maximum Sharpe Ratio using CPLEX solver

% Set variable upper and lower bounds

n = length(asset_init);

k = 1;

lb = k*ones(n,1);

ub = lb;

% Set linear aspect of objective function

c = zeros(n,1);

% Set linear constraints

A1 = exp_ret - risk_free;

A2 = ones(1,n);

lhs = 1;

rhs = lhs;

% Compute optimal portfolio weights

cplex1.Cplex('Sharpe');

cplex1.Model.sense = 'minimize';

cplex1.addcols(c, [], lb, ub);

cplex1.addrows(k, A2, k);

cplex1.addrows(lhs, A1', rhs);

cplex1.Model.Q = 2*Q;

cplex1.solve();

% New optimal weights

weights_new = cplex1.Solution.x / sum(cplex1.Solution.x);

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My function tries to solve the optimization problem for:

min        (y^T)*Q*y

s.t.         sum((exp_ret - risk_free)*y) = 1

              sum(y) = k

              k*lower bound <= y <= k*upper bound

              k >= 0

whereby my optimal weights = y/k

My CPLEX solver always gives me an error string of "Infeasible" and so I cannot compute properly

[Johan Löfberg]

No idea, There's a reason we use modeling layers

[Tommy Lavertes]

Then is there a way to implement your portfolio example into a form CPLEX understands?

So CPLEX takes in optimization problems in the following form:

minimize      (c^T)*x + 0.5*(x^T)*Q*x       % Objective quadratic/linear function 

s.t               bl <= A*x <= bu                  % Linear constraints (equalities has bl = bu)

                   (d^T)*x + (x^T)*Q*x <= r      % Quadratic constraints

                   l <= x <= u                         % Variable bounds

[Johan Löfberg]

Not sure what you mean. 

Via YALMIP, you can export the model to cplex format if you want (using the command export)