Maximise Sharpe ratio subject to contraints in Jul

Question

I want to maximize the value of q[1](Sharpe Ratio), subject to following constraints in julia.

1. Value elements of W is positive. ( W[i] >0 )

2. Sum of values of W is 1. ( sum(W[1:5]) == 1 )

   function getSharpeRatio(W,ex_mu,S)
     q = ( W'*ex_mu ) / sqrt((W'*S*W))
     return q[1]
   end
   

For Reference :: W is (5X1) vector,ex_mu is (5x1) vector and S is (5x5) matrix. I found out two julia libraries to use JuMP and Optim.jl , but not able to translate the function getSharpeRatio as required by the libraries.

Update : I have done so far but seems like transpose is not implemented yet in JuMP library using JuMP

function getSharpeRatio(W,ex_mu,S)
   return dot(W', ex_mu) / sqrt(dot(W',S*W))
end

items  = [1;2;3;4;5]
m = Model()
@variable(m, 0 <= W[items] <= 1)
@constraint(m, sum{ W[item] , item in items} == 1)
@objective(m, Max, getSharpeRatio(W,ex_mu,S))
solve(m)
println(getvalue(W))

Any suggestions how to go about this.

Answer 1

I believe your function needs to be on one array. Make a 25+5+5 length vector, and make getSharpeRatio(v) start W,ex_mu,S=translate(v) function which gets your temporary arrays out using views.

translate(v) = (view(v,1:5),view(v,6:10),reshape(view(11:35),5,5))

That won't allocate, but it means your new function can be

function getSharpeRatio(v)
  W,ex_mu,S=translate(v)
  dot(W,ex_mu)/ sqrt(dot(W,S*W))
end

which matches what JuMP/Optim expect. From there, you need to re-do your constraints to match the indices from here... though I think I set this up (with W first) so that way it'll work.