Covariance appears throughout investment management, e.g., in risk reporting and control, portfolio construction, risk parity, smart beta, algorithmic trading, and hedging. It is usually represented via multi-factor model. The form’s fewer parameters and structure—comovement through...

We develop and implement methods for determining whether relaxing sparsity constraints on portfolios improves the investment opportunity set for risk-averse investors. We formulate a new estimation procedure for sparse second-order stochastic spanning based on a greedy algorithm and Linear...