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  • Ding, Yi and Li, Yingying and Zheng, Xinghua, “High dimensional minimum variance portfolio under factor model” (2021), Journal of Econometrics

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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

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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 Liu, Guoli and Li, Yingying and Zheng, Xinghua, “Stock co-jump networks" (2023), Journal of Econometrics

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Abstract: We propose a network model with communities to study the stock co-jump dependency. To estimate the community structure, we extend the SCORE algorithm in Jin (2015) and develop a Spectral Clustering On Ratios-of-Eigenvectors for networks with Dependent Multivariate Poisson edges (SCORE-DMP) algorithm. We prove that SCORE-DMP enjoys strong consistency in community detection for the proposed co-jump network with dependent edges. Empirically, using high-frequency data of S&P 500 constituents, we identity two co-jump networks according to whether the market jumps or not and show that the identified community structure helps in predicting stock returns.

 

 

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  • Ding, Yi and Engle, Robert and Li, Yingying and Zheng, Xinghua, “Factor modeling for volatility” (2021), working paper

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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.

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  • Ding, Yi and Zheng, Xinghua, “High dimensional covariance matrices under dynamic volatility models: asymptotics and shrinkage estimation” (2023), R&R under Annals of Statistics

 

​Abstract: We study the estimation of unconditional covariance matrix and its spectral distribution under high-dimensional dynamic volatility models. Data under such models have nonlinear dependency both cross-sectionally and temporally. We first investigate the empirical spectral distribution (ESD) of the sample covariance matrix under scalar BEKK models and establish conditions under which the limiting spectral distribution (LSD) is either the same as or different from the i.i.d. case. We then propose a time-variation adjusted (TV-adj) sample covariance matrix and prove that its LSD follows the same Marcenko-Pastur law as the i.i.d. case. Based on the LSD of the TV-adj sample covariance matrix, we obtain a consistent population spectrum estimator. We further develop a TV-adj nonlinear shrinkage estimator that consistently estimates the asymptotically optimal shrinkage estimator.

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  • Andersen, Torben and Ding, Yi and Todorov, Viktor, “Granular origin of tail risk in asset prices” (2023), working paper

Abstract: We study the cross-sectional jump tail risk and asset pricing implications. We develop estimators of the power law tail index for the cross section of systematic jumps and idiosyncratic jumps using high-frequency returns from a large cross-section and establish their asymptotic distributions. Moreover, we propose a goodness-of-fit test for the fitting of the power law in systematic and idiosyncratic jump tails. Empirically, we find that the systematic jump tail risk and idiosyncratic jump tails risk both behave differently than the volatilities and they exhibit different features in their time-series. Finally, we find that both the jump tail risks carry significant risk premium but with opposite signs.

  • Ding, Yi and Zheng, Xinghua, “High-dimensional covariance matrix estimation under elliptical factor model with 2 + εth moment” (2023), working paper

​Abstract: We study the estimation of the high-dimensional covariance matrix under elliptical factor models with 2 + εth moment. For such heavy-tailed data, robust estimators like the Huber-type estimator in Fan et al. (2018) can not achieve sub-Gaussian optimal convergence rates. We develop a idiosyncratic-projected self-normalization (IPSN) method to remove the effect of the heavy-tailed elliptical parameter. Based on IPSN, we propose robust pilot estimators for the scatter matrix and show that our estimators enjoy the optimal sub-Gaussian rates. We further develop a consistent generic POET estimator of the covariance matrix based on our proposed pilot estimators.

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