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Ding, Yi and Li, Yingying and Zheng, Xinghua, “High dimensional minimum variance portfolio under factor model” (2020), 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.
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Ding, Yi and Li, Yingying and Song, Rui, “Statistical learning for individualized asset allocation” (2022), Journal of the American Statistical Association
Abstract: We establish a high-dimensional statistical learning framework for individualized asset allocation. Our proposed methodology addresses continuous-action decision-making with a large number of characteristics. We develop a discretization approach to model the effect from continuous actions and allow the discretization frequency to be large and diverge with the number of observations. The value function of continuous-action is estimated using penalized regression with our proposed generalized penalties that are imposed on linear trans-formations of the model coefficients. We show that our proposed Discretization and Regression with generalized fOlded concaVe penalty on Effect discontinuity (DROVE) approach enjoys desirable theoretical properties and allows for statistical inference of the optimal value associated with optimal decision- making. Empirically, the proposed framework is exercised with the Health and Retirement Study data in finding individualized optimal asset allocation. The results show that our individualized optimal strategy improves individual financial well-being.
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Ding, Yi and Engle, Robert and Li, Yingying and Zheng, Xinghua, “Factor modeling for volatility” (2021), 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.