  We propose a novel method to improve estimation of asset returns for
portfolio optimization. This approach first performs a monthly directional
market forecast using an online decision tree. The decision tree is trained on
a novel set of features engineered from portfolio theory: the efficient
frontier functional coefficients. Efficient frontiers can be decomposed to
their functional form, a square-root second-order polynomial, and the
coefficients of this function captures the information of all the constituents
that compose the market in the current time period. To make these forecasts
actionable, these directional forecasts are integrated to a portfolio
optimization framework using expected returns conditional on the market
forecast as an estimate for the return vector. This conditional expectation is
calculated using the inverse Mills ratio, and the Capital Asset Pricing Model
is used to translate the market forecast to individual asset forecasts. This
novel method outperforms baseline portfolios, as well as other feature sets
including technical indicators and the Fama-French factors. To empirically
validate the proposed model, we employ a set of market sector ETFs.
