Optimal Shrinkage-Based Portfolio Allocation with Banded-Toeplitz Target

The optimal portfolio solution in the Markowitz framework relies on a well-conditioned covariance matrix estimator. This paper deals with the problem of large portfolio allocation by improving the covariance matrix estimator via shrinkage strategy. The banding technique is adopted to produce a positive-definite target matrix and to utilize the information of the sample structure as much as possible. For the Toeplitz target with a fixed band, we derive the closed expression of the shrinkage estimator. Then, we obtain the optimal portfolio allocation from a quadratic problem with a finite band parameter. Empirical analysis reveals that the proposed shrinkage estimator has a satisfactory performance compared to the existing covariance estimators in the large portfolio.