Optimisation, with 20 variable program?

So I am creating a portfolio of 20 assets and their returns, and then I am trying to minimize them with the optimisation app. I have managed to get it to work with 3 assets (variables) but I don't have a clue how to get the right line of code for 20.

The is the code that I have so far.

function Ret = PRet(x)
Return = xlsread('Data.xlsx','Sheet1', 'V3:AO254'); % I change the amount of data coming in depending on the formula, this is bringing in 20 assets.

Ret = x(1)* Return(:,1) + x(2)*Return(:,2) + (1-x(1)-x(2))*Return(:,3); % This is the line I have to change to 20 variables and I cannot work it out.
end

The other code is in a function GetVar, which works fine, by sorting the data then getting the correct percentile and I apply this to the Optimisation app.

@(x)GetVar(PRet(x),0.05,-1) %where the 0.05 is the percentile, the -1 is just the left tail, and it is the x value that I am trying to work out.

I have tried using

Ret = x(1)*Return(:,1) + x(2)*Return(:,2) + x(3)*Return(:,3) +x(4)*Return(:,4) +x(5)*Return(:,5) +x(6)*Return(:,6)+x(7)*Return(:,7)+x(8)*Return(:,8)+x(9)*Return(:,9)+x(10)*Return(:,10)+x(11)*Return(:,11)+x(12)*Return(:,12)+x(13)*Return(:,13)+x(14)*Return(:,14)+x(15)*Return(:,15)+x(16)*Return(:,16)+x(17)*Return(:,17)+x(18)*Return(:,18)+x(19)*Return(:,19)+x(20)*Return(:,20);

but that doesn't really help unless i give an x of [0.05....0.05] but then i don't need the optimisation tool.

the x matrix is the weightings of each individual asset returns, and i am trying to find the x values that add up to one that will give me the lowest value of VaR.

there error i get whenever I try to change the code to add more data in is:

Index exceeds matrix dimensions.

Any help would be great thanks.

Edit:

So I think by changing the line of code to

Ret = x(1)*Return(:,1) + x(2)*Return(:,2) + x(3)*Return(:,3) +(1-x(2)-x(3)-x(1))*Return(:,4);

for 4 sets of data, then changing the optimisation tool start points, linear inequalities and bounds to a 3 column matrix would work for the 4 variables? it seems too anyway, would changing this to 20 variables in a a similar way work too? or would that just take forever :S

Answer 1

[Walter Roberson]

Ret = Return * [x(:); 1-sum(x)];

Here x would be a vector with one fewer entries than the number of columns in Return.

Note you should avoid doing the xlsread there. See https://www.mathworks.com/help/matlab/math/parameterizing-functions.html