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Abstract:
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Correlation matrix estimation is very important for portfolio management. Fund managers need to know the correlation of stock returns to construct the portfolio which minimizes the unsystematic risk. Unfortunately, traditional MLE is always computational expensive for high-dimensional data, and does not work when the sample size exceeds the dimension. To address this issue, we propose an estimation approach for correlation matrix. We notice that random variables can be divided into groups/blocks naturally by some properties. For example, hundreds of stocks are divided into different sectors. We assume that in most cases, two variables in a block have the same correlation, and two variables from two blocks have the same correlation with any other two variables from the same two blocks. A small deviation of the correlation matrix is allowed. We will use positive definite programming to solve this problem.
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