Nonlinear shrinkage of Eigenvalues in Integrated Covolatility Matrix for Portfolio Allocation in High Frequency Data

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• Clifford Lam (LSE)
• Friday 22 January 2016, 16:00-17:00
• MR12, Centre for Mathematical Sciences, Wilberforce Road, Cambridge..

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In portfolio allocation of a large pool of assets, the use of high frequency data allows the corresponding high-dimensional integrated covolatility matrix estimator to be more adaptive to local volatility features, while sample size is significantly increased. To ameliorate the bias contributed from the extreme eigenvalues of the sample covolatility matrix when the dimension p of the matrix is large relative to the average daily sample size n, and the contamination by microstructure noise, various researchers attempted regularization with specific assumptions on the true matrix itself, like sparsity or factor structure, which can be restrictive at times. With non-synchronous trading and contamination of microstructure noise, we propose a nonparametrically eigenvalue-regularized integrated covolatility matrix estimator which does not assume specific structures for the underlying matrix. We show that our estimator is almost surely positive definite, with extreme eigenvalues shrunk nonlinearly under the high dimensional framework where the ratio p/n goes to c>0. We also prove that almost surely, the optimal weight vector constructed has maximum weight magnitude of order p^{-1/2}, which is supported by our data analysis. The practical performance of our estimator is illustrated by comparing to the usual two-scale realized covariance matrix as well as some other nonparametric alternatives using different simulation settings and a real data set.

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