Optimal weights in portfolio optimization

Hi guys!

I'm trying to calculate the optimal weights for 2 riskt assets and a riskfree asset. I would like to do this based on a volatility timing strategy, which means that the weigths should only vary based on the conditional volatility. I have calculated the conditional covariance between the two risky assets and the sample means of the risky assets returns. For each day I should solve the following quadratic program:

 Min. wt'SIGMAwt

S.T. wt'ut + (1-wt'1)Rf = up

were SIGMA is the 2x2 conditional covariance matrix, ut is the 2x1 risky asset returns, up is the expected return on the portfolio and wt is the 2x1 weight matrix. I have tried to set up a loop based on the quadratic optimization routine provided by Matlab, which plugs in the relevant conditional covariance matrix. Since the weights are determined solely on the conditional covariance, I assume that the expected return of the assets are constant and equal to the sample mean. My problem is that i'm not sure if I have written the code correctly or if there is a easier way to tackle the overall problem.

My code so far looks like the following:

for i=1:10

aeg = Dagligeafkast(1,1:2); beg = r;

lb = zeros(2,1); ub = ones (2,1);

c = zeros(2,1);

options = optimoptions('quadprog', 'algorithm','interior-point-convex');

options = optimoptions(options, 'Display', 'iter', 'tolfun',1e-10);

tic

[x1] = quadprog(Betingetkovariansmatricedaglige(i:i+1,i:i+1), c, aeg,beg,lb,ub);

toc

Plotportfdemostandardmodel(x1);

end

I know that my constrain in this setting is equivalent to wt'ut = up, but I just thought that the weight in the riskless asset should be 1-wt'1.

I have searched around and not been able to find something useful, so I would really appreciate to hear your thoughts about my approach to this problem.

Best regards,

Kristian