Large (and Deep) Factor Models

Bryan T. Kelly, Boris Kuznetsov, Semyon Malamud and Teng Andrea Xu
Additional contact information
Bryan T. Kelly: Yale SOM; AQR Capital Management, LLC; National Bureau of Economic Research (NBER)
Boris Kuznetsov: Swiss Finance Institute; EPFL
Semyon Malamud: Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute
Teng Andrea Xu: École Polytechnique Fédérale de Lausanne

No 23-121, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: 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 DNNSDF is increasing in the NN depth, saturating at huge depths of around 100 hidden layers.

Pages: 52 pages
Date: 2023-12
New Economics Papers: this item is included in nep-big, nep-cmp and nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp23121

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