Decision focused learning and portfolio selection

One of the more interesting papers on portfolio management links prediction with optimization. Rather than a two-step process, the authors focus on how optimization should be managed alongside prediction. The paper, “Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models”, provides insights on how decision-focused learning (DFL) can be used to improve overall portfolio returns. 

The usual process for building a portfolio is through mean-variance optimization. This process is two-staged. It is a predict-then-optimize method. In the first stage, a set of expected returns is generated, and in the second stage, the optimization selects the set of assets that maximizes return subject to a set of constraints. The problem with MVO has been studied extensively. The issue is that if the expected returns are poorly defined, the MVO will choose the “best" returns, yet the portfolio may be optimized on the forecast errors. The classic answer from Markowitz is that estimating expected returns is the investor’s job, not the optimizer’s.

The DFL framework will integrate the prediction and optimization to improve the outcomes. The issue is whether the MSE of forecasts for each asset is treated independently and equally or integrated with asset correlations. With DFL, the optimization accounts for prediction errors when finding the weights via a loss or regret function.

It is found that DFL identifies fewer assets than a standard MVO and exhibits a bias toward positively returning assets, given the optimization for a long-only portfolio. Still, it offers a better way to optimize a portfolio.