Implementing Markowitz Portfolio Optimization in Matlab

7 次查看（过去 30 天）
Tom
Tom 2017-4-3
编辑： Aurele Turnes 2017-5-18
Hi people,
I'm new to Matlab and I'm trying to implement the following Markowitz portfolio optimization problem in Matlab:
As this is a quadratic optimisation problem I figured I should use the Optimization Toolbox's quadprog() function. I'm having trouble formulating the objective function however and I can't entirely picture how many rows and especially columns it should have. Any help would be much appreciated!
Thanks, Tom

请先登录，再回答此问题。

回答（2 个）

Varun Gunda
Varun Gunda 2017-4-6
As given in the example in the following link:
http://in.mathworks.com/help/optim/ug/quadprog.html
H would be a nxn matrix, f - nx1 matrix and A- 1xn matrix and b 1x1 matrix.
Aurele Turnes
Aurele Turnes 2017-5-18
编辑：Aurele Turnes 2017-5-18
As noted in the doc page for quadprog, the objective function that quadprog expects has this form:
obj = (x' * H * x)/2 + f' * x
You need to build the matrices H and f to pass your objective to quadprog.
To see how to do this, expand the matrix multiplications above (using pseudo-math notation below):
obj = sum_(i=1^n) sum_(j=1^n) H_(i,j)/2 * x_i * x_j + \sum_(i=1^n) f_i * x_i
Identifying the coefficient in front of each unknown term with your equation, you can easily see that:
H_(i,i) = 2* \lambda \sigma_i^2, for i = 1..n
H_(i,j) = 2* \lambda \sigma_(i,j) for i,j = 1..n, i \neq j
f_i = -(1-\lambda) * \bar{r}_i

类别

在 Help Center 和 File Exchange 中查找有关 Portfolio Optimization and Asset Allocation 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by