Solving high complexity models
In this paper Kelly et al. study the behavior of portfolios in the high model complexity regime, where the number of predictors exceeds the number of observations. They prove that strategies based on extremely high-dimensional models can thrive out-of-sample and outperform strategies based on simpler models under fairly general conditions. The authors compare market timing strategies based on predictions from very simple models with a single parameter to extremely complex models with over 10,000 parameters (applied to training samples with as few as 12 monthly observations). They find:
Timing positions from high-complexity models are remarkable. They behave similarly to long-only strategies, following the Campbell and Thompson (2008) recommendation to impose a non-negativity constraint on expected market returns. But our models learn this behavior as opposed to being handed a constraint. Moreover, machine learning strategies learn to divest leading up to NBER recessions, successfully doing so in 14 out of 15 recessions in our test sample on a purely out-of-sample basis.
The Virtue of Complexity in Return Prediction
Authors: Bryan Kelly, Semyon Malamud, Kangying Zhou
From: Yale University, Swiss Finance Institute
Solving HANC without the Krussel-Smith aggregation
In this paper, Maliar and Maliar use deep learning to solve the Krusell and Smith (1997, 1998) HANC models in which the agents save only through bonds. The main difference between Krusell and Smith and Maliar and Maliar is that the former approximate the decision function of an agent in terms of the individual state variables of that agent and selected moments of aggregate distributions, while the latter approximate decision functions in terms of all individual and aggregate state variables and let the neural network to choose how the information contained in that distribution can be reduced and condensed into smaller set of artificial features.
This model [Krussel and Smith (1998)] has a remarkable feature of approximate aggregation: the mean of wealth distribution can be accurately predicted with the mean of past wealth distribution. However, if savings are done through bonds, the HANC model does not have this feature (because the mean of bond holding is zero). We solve such model using deep learning solution method in which the decision function and price functions are approximated in terms of true state space of individual and aggregate state variables. The problem has high dimensionality (hundreds of state variables) and ill-conditioning but neural network reduces dimensionality and restore numerical stability. Our deep learning method delivers accurate and reliable solutions.
Deep Learning: Solving HANC and HANK Models in the Absence of Krusell-Smith Aggregation
Authors: Lilia Maliar, Serguei Maliar
From: CUNY-Graduate Center and Stanford University, Santa Clara University
