Fmincon with Nested Optimization

I have to maximize the sharpe ratio, but my weights are given by an equation. I am not knowing how to connect that with fmincon

function [y] = w2(a) %function for weight

global avrcc avrco avroc avroo avrrvp avrtvl rcc rco roc roo tvl rvp i j n

y = a(1)*(rcc(i-1,j)-avrcc(i-1))./n...
    + a(2)*(roo(i,j)-avroo(i))./n...
    + a(3)*(roc(i-1,j)-avroc(i-1))./n ...
    + a(4)*(rco(i,j)-avrco(i))./n...
    + a(5)*(tvl(i-1,j)/avrtvl(i-1,j))*(rcc(i-1,j)-avrcc(i-1))./n...
    + a(6)*(tvl(i-1,j)/avrtvl(i-1, j))*(roo(i,j)-avroo(i))./n...
    + a(7)*(tvl(i-1,j)/avrtvl(i-1,j))*(roc(i,j)-avroc(i-1))./n...
    + a(8)*(tvl(i-1,j)/avrtvl(i-1,j))*(rco(i,j)-avrco(i))./n...
    + a(9)*(rvp(i-1,j)/avrrvp(i-1,j))*(rcc(i-1,j)-avrcc(i-1))./n...
    + a(10)*(rvp(i-1,j)/avrrvp(i-1,j))*(roo(i,j)-avroo(i))./n...
    + a(11)*(rvp(i-1,j)/avrrvp(i-1,j))*(roc(i-1,j)-avroc(i-1))./n...
    + a(12)*(rvp(i-1,j)/avrrvp(i-1,j))*(rco(i,j)-avrco(i))./n;

end

My function for sharpe ratio is as follows

function [y] = msharper(mu,Q,rf)

y = mu-rf/sqrt(w2(a)'*Q*w2(a));

end

I do not know how to apply fmincon such a way that I find the values of a vector.

[Walter Roberson]

It is not clear which variable you are optimizing over? Is it a ? If so then it should be an input to msharper()

http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[motleyfool]

Thank you for your response Walter, I am need to find values of a(1) through a(12). Such that that long equation is what I must plug-in for my weights in the second function.

Answer 1

[Matt J]

My approach would be to modify the functions as follows, taking into account Walter's remarks and also getting rid of the global variables,

    function [y] = w2(a,   avrcc, avrco, avroc, avroo, avrrvp,...
                           avrtvl, rcc, rco, roc, roo, tvl, rvp, i, j, n)

    y = a(1)*(rcc(i-1,j)-avrcc(i-1))./n...
        + a(2)*(roo(i,j)-avroo(i))./n...
        + a(3)*(roc(i-1,j)-avroc(i-1))./n ...
        + a(4)*(rco(i,j)-avrco(i))./n...
        + a(5)*(tvl(i-1,j)/avrtvl(i-1,j))*(rcc(i-1,j)-avrcc(i-1))./n...
        + a(6)*(tvl(i-1,j)/avrtvl(i-1, j))*(roo(i,j)-avroo(i))./n...
        + a(7)*(tvl(i-1,j)/avrtvl(i-1,j))*(roc(i,j)-avroc(i-1))./n...
        + a(8)*(tvl(i-1,j)/avrtvl(i-1,j))*(rco(i,j)-avrco(i))./n...
        + a(9)*(rvp(i-1,j)/avrrvp(i-1,j))*(rcc(i-1,j)-avrcc(i-1))./n...
        + a(10)*(rvp(i-1,j)/avrrvp(i-1,j))*(roo(i,j)-avroo(i))./n...
        + a(11)*(rvp(i-1,j)/avrrvp(i-1,j))*(roc(i-1,j)-avroc(i-1))./n...
        + a(12)*(rvp(i-1,j)/avrrvp(i-1,j))*(rco(i,j)-avrco(i))./n;

    end

    function [y] = msharper(a, mu,Q,rf,weightfun)

       y = mu-rf/sqrt(weightfun(a)'*Q*weightfun(a));

    end

and then in the main workspace,

   weightfun=@(a) w2(a,   avrcc, avrco, avroc, avroo, avrrvp,...
                           avrtvl, rcc, rco, roc, roo, tvl, rvp, i, j, n);

   a_opt = fmincon @(a)  msharper(a, mu,Q,rf,weightfun),    __________  );

[motleyfool]

Made a few mods, but the idea of eliminating the global variables helped for sure! Thank you