Data Preprocessing and Feature Generation
- U.S. Equity data for underlyings in S&P500 between 2010 and 2021
- Assets remvoed when missing more than 1% of observations
- Asset universe consists of 439 potential equities
Parameter Estimation
- Utilizes biased James-Stein Estimator for mean returns
- L2 regularized covariance matrix
Portfolio Optimization
- Portfolio construction via minimization of mean variance objective across efficient frontier
- Includes support for L1 and L2 Regularization via Split Bregman Algorithm
Split-Bregman Algorithm
- Reformulates original objective into two distinct problems
- Iteratively solves constrained QP and LP either in closed-form or numerically
- Performs a grid search for optimal calibration of regularization parameters
Numerical Results
Approaches:
- Minimum Variance Objective
- Mean Variance Objective
- Biased Mean Variance Objective
- Unbiased Mean Variance Objective with Elastic Net Penalty
- Biased Mean Variance Objective with Elastic Net Penalty
All results evaluated on out of sample U.S. equity data