Portfolio Sharpe opt with ismember constraints

[Tal Shir]

Hello,

Using your advise I transformed the Sharpe ratio maximization to a linear eq. The problem I seems to have is that in this case adding a ismember constraint don't do the job.

z = sdpvar(N,1);

d = binvar(N,1);  

Sharpe = [0 <= z, z'*(r) == 1]

 Sharpe=Sharpe+ismember(z,sum(z)*(0:0.1:1)) 

I'm getting

Error using lmi/plus (line 25)

Both arguments must be constraints

Any idea of how to work around this?

Thanks a lot,

Tal

[Johan Löfberg]

nfortunately ismember(sdpvar,sdpvar)  is not a modelling construct but a low level check to see if a varaible appears among the others (i.e. it returns a list of true/false)

You have to implement it manually, which is rather simple by defining a binary matrix T where T(i,j) says that variable i uses the prescribed ratio j

N = 10;

M = 11;

z = sdpvar(N,1);

d = binvar(N,1);  

r = rand(N,1)

Sharpe = [0 <= z, z'*(r) == 1]

T = binvar(N,M,'full');

levels = linspace(0,1,M);

Sharpe = [Sharpe, implies(T,repmat(z,1,M) == sum(z)*repmat(levels,N,1))];

Sharpe = [Sharpe, sum(T,2)==1]

Q = randn(N);Q=Q*Q';

optimize(Sharpe,z'*Q*z)

value(z)/value(sum(z))