Revisiting the 1/N-strategy: a neural network framework for optimal strategies

This work has two main objectives. First, we design a data-driven neural network approach to portfolio optimization within expected utility theory. The methodology is inspired by Li and Forsyth (Insur Math Econ 86:189–204, 2019. https://doi.org/10.1016/j.insmatheco.2019.03.001), who worked on target based defined contribution plans. Our proposal and the architecture of the model is flexible enough to address a variety of specific portfolio problems, from standard optimal utility allocation with constraints, to optimal deviations from a benchmark. Using the celebrated 1/N-Strategy (see DeMiguel et al. in Rev Financ Stud 22(5):1915–1953, 2007. https://doi.org/10.1093/rfs/hhm075) as benchmark constitutes the second objective of the paper. We consider two assets on a single path of historical return data for an investor whose utility is represented by a constant relative risk aversion function. Across several levels of risk aversion, we revisit the literature claims that it is essentially impossible to significantly outperform 1/N. Using our advanced method, we confirm that this is only true for high levels of risk aversion, but the 1/N can be consistently outperformed for low and moderate risk aversion levels.