Correcting In-Sample Optimism Bias: Realized Volatility of Large Optimal Portfolios

Jianqing Fan Alex Furger Dacheng Xiu

Statistics Theory and Methods mathscidoc:1912.43444

Using high-frequency data, we estimate the risk of a large portfolio with weights being the solution of an optimization problem subject to some linear inequality constraints. We propose a fully nonparametric approach as a benchmark, as well as a factor-based semiparametric approach with observable factors to attack the curse of dimensionality. We provide in-fill asymptotic distributions of the realized volatility estimators of the optimal portfolio, while taking into account the estimation error in the optimal portfolio weights as a result of the covariance matrix estimation. Our theoretical findings suggest that ignoring such an error leads to a first-order asymptotic bias which undermines the statistical inference. Such a bias is related to in-sample optimism in portfolio allocation. Our simulation results suggest satisfactory finite sample performance after bias correction, and that the factor-based approach becomes increasingly superior with a growing cross-sectional dimension. Empirically, using a large cross-section of high-frequency stock returns, we find our estimator successfully addresses the issue of in-sample optimism.
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@inproceedings{jianqingcorrecting,
  title={Correcting In-Sample Optimism Bias: Realized Volatility of Large Optimal Portfolios},
  author={Jianqing Fan, Alex Furger, and Dacheng Xiu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114455000394004},
}
Jianqing Fan, Alex Furger, and Dacheng Xiu. Correcting In-Sample Optimism Bias: Realized Volatility of Large Optimal Portfolios. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114455000394004.
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