Large (and Deep) Factor Models
This provides a theoretical foundation for using deep learning in finance, making it interpretable for portfolio managers, though it is incremental in linking existing methods.
The paper tackles the problem of understanding deep learning for portfolio optimization by proving that a deep neural network trained to maximize the Sharpe ratio of the Stochastic Discount Factor is equivalent to a large factor model, enabling closed-form derivations and showing that out-of-sample performance increases with depth up to about 100 layers.
We open up the black box behind Deep Learning for portfolio optimization and prove that a sufficiently wide and arbitrarily deep neural network (DNN) trained to maximize the Sharpe ratio of the Stochastic Discount Factor (SDF) is equivalent to a large factor model (LFM): A linear factor pricing model that uses many non-linear characteristics. The nature of these characteristics depends on the architecture of the DNN in an explicit, tractable fashion. This makes it possible to derive end-to-end trained DNN-based SDFs in closed form for the first time. We evaluate LFMs empirically and show how various architectural choices impact SDF performance. We document the virtue of depth complexity: With enough data, the out-of-sample performance of DNN-SDF is increasing in the NN depth, saturating at huge depths of around 100 hidden layers.