Engle et al. (2019) marry two previously separate strands of the literature—time-series GARCH dynamics and cross-sectional nonlinear shrinkage—into the DCC-NL framework for large dynamic covariance matrices. We extend this marriage along two orthogonal dimen- sions, one for each step of the DCC-NL pipeline: (i) replacing the standard GARCH (1, 1) in Step 1 with asymmetric GARCH variants—EGARCH (1, 1, 1), which captures the lever- age effect, and GARCH (2, 1) -DCC-NL, which allows richer short-term dynamics—building on the direction suggested by De Nard et al. (2022, Remark 2. 1) ; (ii) replacing the an- alytical QuESTimate shrinkage in Step 2 with a learned eigenvalue autoencoder trained via a two-phase curriculum of unsupervised denoising and QuESTimate-supervised distil- lation. Both modifications are independent and can be combined. Using the same CRSP data and portfolio-construction rules as De Nard et al. (2022) (with two minor implementa- tion deviations documented in Section 6), we evaluate all models on unconstrained Global Minimum Variance (GMV) portfolios across universe sizes N ∈100, 500, 1, 000, and on Markowitz-momentum portfolios at N=1, 000, over the period 12/18/1998–12/31/2018. At N=1, 000, the eigenvalue autoencoder achieves the lowest annualised portfolio standard de- viation (6. 99% vs. 7. 37% for DCC-NL) and the highest net-of-cost information ratio (0. 75 vs. 0. 70), while maintaining the lowest turnover and maximum drawdown. EGARCH de- livers the highest gross Sharpe ratio (0. 87 in GMV, 1. 01 with momentum) at the cost of substantially higher turnover; net of transaction costs it is dominated by the standalone au- toencoder. The autoencoder Pareto-dominates DCC-NL on all practical metrics: lower SD, higher net IR, lower turnover, and lower maximum drawdown. The combined EGARCH- DCC-AE model matches the standalone autoencoder’s risk metrics. The improvements are concentrated at N = 1, 000, where the high concentration ratio (c = N/T ≈0. 8) makes covariance estimation most challenging; at smaller universe sizes the gains are marginal.
Hermann Chung (Thu,) studied this question.