About minimizing variance of a mimicking portfolio
2 次查看(过去 30 天)
显示 更早的评论
I have been working on an assignment and encountered the following problem: I have one-factor model for returns (say CAPM). I regress the returns of fifteen companies on market returns (my factor) and obtain 15x1 vector of betas. My task is to create a 15x1 vector of weights thetaprime that is the mimicking portfolio of the factor. For this vector of weights to be the mimicking portfolios, I need the following conditions:
1. sum(thetaprime) = 1
2. thetaprime*beta' = 1
3. The variance of the resulting mimicking portfolio (constructed with the thetaprime components) to be the minimum variance possible and the variance is given by:
variance_mimicking = thetaprime*SIGMA*thetaprime' (where SIGMA is a 15x15 variance-covariance symmetric matrix that I have calculated)
I am doing the following steps:
1. N = null([ones(15,1) beta].').';
2.thetaprime = thetaa + randn(1,13)*N;
in this way I can generate infinitely many vectors of thetaprime that satisfy conditions 1) and 2) above. When I substitute thetaprime in the formula for the variance, I get the same variance every time independently of the variables in thetaprime which does not make sense for me. I expectted different result for variance for different values of thetaprime that I can minimize with an optimization routine in order to find one unique value for thetaprime. Any suggestions?
Thank you very much in advance!
2 个评论
Matt J
2013-3-3
Don't you mean
thetaa + N*randn(13,1)
You want a random linear combination of the columns of N, I think.
回答(2 个)
Matt J
2013-3-3
编辑:Matt J
2013-3-3
The only reason I can think of why that would happen is if
Aeq=[ones(15,1) beta]
is in the row space of sigma, or equivalently that null(SIGMA) contains null(Aeq). A simple test would be to check whether
SIGMA*N=0
Incidentally, though, you do know that QUADPROG is the more standard way to solve these kinds of problems, right? Do you not have the Optimization Toolbox?
12 个评论
Matt J
2013-3-3
You should re-examine your SIGMA and how it was generated. It does not admit a unique solution.
另请参阅
类别
在 Help Center 和 File Exchange 中查找有关 Financial Toolbox 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!