GA Multiobjective, Consider reducing the number of outputs

I'm trying to make maximize the portfolio return and the sharpe ratio at the same time using a genetic algorithm.

So, I'm using gamultiobj function, but my code don't archive a result.

Could someone help me fix my code or help me find where the error is.

Thanks

format long g
filename = 'Returns.xlsx';

data = readmatrix(filename);

nAssets = size(data, 2);

%Returns and covariance
mu = mean(data);
mu.'

sigma = cov(data);

%formulate the problem/optimization
f = zeros(nAssets, 1);    %there is no constant
A = -eye(nAssets) %besides the returns we forbid short selling
b = zeros(nAssets, 1) % required return and weights greater/eqauls 0
Aeq = ones(1, nAssets)   %All weights should sum up...
beq = 1                  %... to one (1)

%solve the optimization
fcn = @(w)MultipleMax(w,mu,sigma);

[w, fval, flag, output] = gamultiobj(fcn, nAssets, A, b, Aeq, beq)

if isempty(w)
   warning('could not find any solution')
else
    %print the solution
    fprintf(2, 'Risk: %.3f%%\n', sqrt(w*sigma*w')*100);
    fprintf(2, 'Ret: %.3f%%\n', w*mu'*100);
    fprintf(2, 'Sharpe: %.3f%%\n', (w * mu')/sqrt(w*sigma*w'));
    w.'
end

function f = MultipleMax(w,mu,sigma)
  f(1) = -(w * mu');
  f(2) = -((w * mu')/sqrt(w*sigma*w'))
end

[Matt J]

We cannot run it. Returns.xlsx is not attached.

[Santiago]

I already uploaded it. Thank you

Answer 1

[Matt J]

format long g
filename = 'Returns.xlsx';

data = readmatrix(filename);

nAssets = size(data, 2);

%Returns and covariance
mu = mean(data);


sigma = cov(data);

%formulate the problem/optimization
f = zeros(nAssets, 1);    %there is no constant
A = -eye(nAssets); %besides the returns we forbid short selling
b = zeros(nAssets, 1); % required return and weights greater/eqauls 0
Aeq = ones(1, nAssets) ;  %All weights should sum up...
beq = 1  ;                %... to one (1)

%solve the optimization
fcn = @(w)MultipleMax(w,mu,sigma);

[w, fval, flag, output] = gamultiobj(fcn, nAssets, A, b, Aeq, beq);

Optimization terminated: average change in the spread of Pareto solutions less than options.FunctionTolerance.

if isempty(w)
   warning('could not find any solution')
else
    
    
    Risk=sqrt(sum( (w*sigma).*w  ,2));
    Ret=w*mu';
   
    
    %print the solution
   T=table(Risk*100,Ret*100, Ret./Risk,'Var',{'Risk', 'Ret','Sharpe'})

end

T = 70×3 table
          Risk                    Ret                    Sharpe       
    _________________    _____________________    ____________________

     1.82270580599563       0.0414442638688286      0.0227377691630221
      5.5975747702471        0.134827088101126      0.0240866971206485
     5.23178853842043        0.120862342189557      0.0231015342653829
    0.461935673562308    -0.000674686488551271    -0.00146056372600171
    0.528634985441716      0.00767769295854254      0.0145236186971758
      5.9032491046392        0.299494602724574      0.0507338581543525
    0.704199038638267        0.013492243327366      0.0191597014296645
      5.9076423218751        0.306218706756716      0.0518343342525722
     5.95204520612309          0.2388704234092      0.0401324948210181
     5.99154527935198        0.347974879239879      0.0580776515933322
     5.88977561886967        0.313547919299954      0.0532359701947574
     6.15988585509584        0.194051150537262      0.0315023938920445
    0.767128657407251       0.0155247157962803      0.0202374342900327
    0.459904609958335       0.0058126967149091      0.0126389181344273
     6.00395224177566        0.230234228469682      0.0383471119020078
    0.537608842709213      0.00968018020495565      0.0180059914122201

function f = MultipleMax(w,mu,sigma)
  f(1) = -(w * mu');
  f(2) = -(f(1)/sqrt(w*sigma*w'));
end

[Santiago]

Hi Matt, thank you for your answer.

I have a question, Is it possible to put the percentages (w) of each of the rows of the table you made?

Thanks for your help

[Matt J]

Sure.

T=table(Risk*100,Ret*100, Ret./Risk,w,'Var',{'Risk', 'Ret','Sharpe','Percentages'})