Portfolio Construction Using Stratified Models

Abstract

In this paper we develop models of asset return mean and covariance that depend on some observable market conditions, and use these to construct a trading policy that depends on these conditions, and the current portfolio holdings. After discretizing the market conditions, we fit Laplacian regularized stratified models for the return mean and covariance. These models have a different mean and covariance for each market condition, but are regularized so that nearby market conditions have similar models. This technique allows us to fit models for market conditions that have not occured in the training data, by borrowing strength from nearby market conditions for which we do have data. These models are combined with a Markowitz-inspired optimization method to yield a trading policy that is based on market conditions. We illustrate our method on a small universe of 18 ETFs, using four well known and publicly available market variables to construct 10000 market conditions, and show that it performs well out of sample. The method, however, is general, and scales to much larger problems, that presumably would use proprietary data sources and forecasts along with publicly available data.

Covariance Prediction via Convex Optimization

“…Laplacian regularized stratified covariance predictor. Laplacian regularized stratified models, described in [41,42,43], can be used to develop a covariance predictor. To do this, one bins x into K categories, and gives a (possibly different) covariance matrix for each of the K bins.…”