Dynamic Portfolio Management with Machine Learning

We present a structured portfolio optimization framework with sparse inverse covariance estimation and an attention-based LSTM network that exploits machine learning (deep learning) techniques. We shrink Wishart volatility towards a Graphical Lasso initial covariance estimator and solve the portfolio optimization using a fast coordinate descent algorithm with regularization determined using a genetic algorithm. We further introduce a novel portfolio shrinkage rule using an attention-based Long-Short-Term-Memory (LSTM) network, allowing a formal selection of reference portfolios where the network forecasts future performance based on predetermined out-of-sample monthly certainty equivalent return. We reduce the dimension of successful candidates and then linearly combine them. When nested within a minimum-variance, Bayes-Stein shrinkage, Black-Litterman portfolio framework with four types of weight constraints based on no-short-selling, upper, lower-generalized variance-based restrictions, our approach delivers a clear improvement over the baseline sample-based minimum-variance portfolio and claims superiority over 11 GARCH models used to forecast covariances, as well as a minimum-variance combination of all dynamic optimization models. We provide an illustrative example based on optimal diversification across hedge fund strategies. Robustness checks show our application of sparse covariance dominates the use of a dimension reduction algorithm for Wishart covariance forecasting.