Portfolio Optimization with LASSO
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I have to find the optimal portfolio adding the "l-1 norm" constraint to the classical mean-variance model. How can i write this optimization in matricial form ?回答（2 个）
Ameer Hamza
2020-10-12
编辑：Ameer Hamza
2020-10-12
This shows an example for the case of 5 portfolios
mu = rand(1, 5);
eta = 0.5;
Sigma = ones(5);
Aeq = [mu; ones(1, 5)];
Beq = [eta; 1];
x0 = rand(5,1); % initial guess
sol = fmincon(@(x) x.'*Sigma*x, x0, [], [], Aeq, Beq, [], [], @nlcon);
function [c, ceq] = nlcon(x)
c = sum(abs(x))-1;
ceq = [];
end
4 个评论
ANDREA MUZI
2020-10-12
Ameer Hamza
2020-10-12
You want the weighted sum to be equal to eta or less than eta? I have corrected a mistake in my code, and now it implements the constraints as written in the question.
ANDREA MUZI
2020-10-12
Ameer Hamza
2020-10-12
Then the code in my answer satisfies all the constraints. You can verify
mu = rand(1, 5);
eta = 0.5;
Sigma = ones(5);
Aeq = [mu; ones(1, 5)];
Beq = [eta; 1];
x0 = rand(5,1); % initial guess
sol = fmincon(@(x) x.'*Sigma*x, x0, [], [], Aeq, Beq, [], [], @nlcon);
function [c, ceq] = nlcon(x)
c = sum(abs(x))-1;
ceq = [];
end
Results
>> mu*sol % output is eta
ans =
0.5000
>> sum(sol) % sum is 1
ans =
1
>> sum(abs(sol)) % sum of absolute values is 1
ans =
1
ANDREA MUZI
2020-10-12
0 个投票
I thank you but it is not the result I expected; I try to rephrase the question. I found a way to linearize the constraint on the weights norm (photo). Basically I have to find the vector between tmin and tmax, in which tmin penalizes all the weights of the assets, bringing them to zero, except one whose weight will be equal to 1 and tmax, whose value will not penalize any asset
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2020-10-12
2020-10-12
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