Zero Variance Portfolio
Jinyuan Chang, Yi Ding, Zhentao Shi, Bo Zhang
TL;DR
The paper addresses high-dimensional minimum-variance portfolio optimization in regimes where the number of assets ($N$) far exceeds the sample size ($T$). It introduces Ridgelet, a tiny ridge-regularized estimator that yields a zero-variance portfolio on training data while enabling strong out-of-sample generalization, exhibiting a double-descent risk pattern. The authors show Ridgelet1 approximates the exact minimum-norm ZVP, whereas Ridgelet2 employs a consistent idiosyncratic covariance estimator (e.g., POET) to achieve oracle out-of-sample variance under $N\gg T$. Through extensive simulations and empirical applications to S&P 500 and Nikkei 225 data, Ridgelet2 consistently improves risk performance over standard benchmarks, offering a tuning-free, high-dimensional MVP approach with practical impact for asset management.
Abstract
When the number of assets is larger than the sample size, the minimum variance portfolio interpolates the training data, delivering pathological zero in-sample variance. We show that if the weights of the zero variance portfolio are learned by a novel ``Ridgelet'' estimator, in a new test data this portfolio enjoys out-of-sample generalizability. It exhibits the double descent phenomenon and can achieve optimal risk in the overparametrized regime when the number of assets dominates the sample size. In contrast, a ``Ridgeless'' estimator which invokes the pseudoinverse fails in-sample interpolation and diverges away from out-of-sample optimality. Extensive simulations and empirical studies demonstrate that the Ridgelet method performs competitively in high-dimensional portfolio optimization.