  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 occurred
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
three well known and publicly available market variables to construct 1000
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.
