Ding, Yi and Li, Yingying and Zheng, Xinghua, “High dimensional minimum variance portfolio under factor model” (2019), conditionally accepted for Journal of Econometrics
Abstract: We propose a high dimensional minimum variance portfolio (MVP) estimator under statistical factor models, and show that our estimated portfolio enjoys sharp risk consistency. The convergence properties are established under scenarios where the minimum risk either decays to zero as the number of assets increases or is bounded from below. In terms of covariance matrix estimation, we extend the theoretical results of POET (Fan et al. (2013)) to a setting that is coherent with principal component analysis. Simulation and extensive empirical studies on S&P 100 Index stock returns demonstrate favorable performance of our MVP estimator compared with benchmark portfolios.
Ding, Yi and Li, Yingying and Song, Rui, “Statistical learning for individualized asset allocation” (2019), working paper
Abstract: We establish a statistical learning framework for individualized asset allocation. A high-dimensional Q-learning methodology is proposed for continuous decision making. The proposed methodology enjoys desirable theoretical properties and facilitates valid statistical inference for optimal values. Empirically, the proposed statistical learning framework is exercised with Health and Retirement Study data. The results show that our proposed optimal individualized strategy improves individual financial well-being and surpasses benchmark strategies under a consumption-based utility framework.
Ding, Yi and Engle, Robert and Li, Yingying and Zheng, Xinghua, “Factor modeling for volatility” (2019), working paper
Abstract: Under a high-frequency and high-dimensional setup, we establish a framework to estimate the factor structure in idiosyncratic volatility, and more importantly, stock volatility. We provide explicit conditions for the consistency of conducting principal component analysis on realized volatilities in identifying the factor structure in volatility. Empirically, we confirm the factor structure in idiosyncratic volatilities of S&P 500 Index constituents. Furthermore, with strong empirical evidence, we propose a simplified single factor model for stock volatility, where volatility is represented by a common volatility factor and a multiplicative lognormal idiosyncratic component. We further utilize the simplified single factor model for volatility forecasting and show that our proposed approach outperforms various benchmark methods.