Hi Santiago,
As per my understanding, you want to now get the required risk instead of the required returns.
In order to do so, you need to make the below two changes:
- Instead of maximizing the return, you now need to minimize the portfolio risk.
- Instead of putting a cap on the minimum return, you now need to cap the maximum allowable risk.
With the above-mentioned changes, the updated code will look like below:
format long g
filename = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/835520/Returns.xlsx';
data = readmatrix(filename);
nAssets = size(data, 2);
% Returns and covariance
mu = mean(data);
mu.';
sigma = cov(data);
% formulate the problem/optimization
risk_target = 0.004; % risk_target is the maximum allowable risk
f = zeros(nAssets, 1); % there is no constant in the objective function for risk minimization
% Objective function is now to minimize risk, so we do not use mu in constraints
A = -eye(nAssets); % Forbid short selling
b = zeros(nAssets, 1); % Weights greater/equal 0
Aeq = ones(1, nAssets); % All weights should sum up...
beq = 1; % ... to one (1)
% solve the optimization
fcn = @(w)PortfolioRisk(w, sigma);
options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm', 'sqp');
[w, risk, flag, output] = fmincon(fcn, ones(nAssets, 1)/nAssets, A, b, Aeq, beq, [], [], [], options);
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);
end
function risk = PortfolioRisk(w, sigma)
risk = sqrt(w' * sigma * w); % Minimize this function
end
I hope it works for you!
