A0378
Title: A nonparametric eigenvalue-regularized integrated covariance matrix estimator for asset return data
Authors: Clifford Lam - London School of Economics and Political Science (United Kingdom)
Phoenix Feng - London School of Economics (United Kingdom) [presenting]
Abstract: The estimation of an integrated covariance matrix is important in finance for portfolio allocation. To ameliorate the bias contributed from the extreme eigenvalues of the realized covariance 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 covariance matrix estimator (NERIVE) which does not assume specific structures for the underlying integrated covariance matrix. We show that NERIVE is almost surely positive definite, with extreme eigenvalues shrunk nonlinearly under the high dimensional framework $p/n \rightarrow c > 0$. We also prove that almost surely, the minimum variance optimal weight vector constructed using NERIVE has maximum exposure and actual risk upper bounds of order $p^{-1/2}$. Incidentally, the same maximum exposure bound is also satisfied by the theoretical minimum variance portfolio weights. All these results hold true also under a jump diffusion model for the log-price processes with jumps removed using the wavelet method.
