How to Combine a Billion Alphas

Abstract

We give an explicit algorithm and source code for computing optimal weights for combining a large number N of alphas. This algorithm does not cost O(N^3) or even O(N^2) operations but is much cheaper, in fact, the number of required operations scales linearly with N. We discuss how in the absence of binary or quasi-binary "clustering" of alphas, which is not observed in practice, the optimization problem simplifies when N is large. Our algorithm does not require computing principal components or inverting large matrices, nor does it require iterations. The number of risk factors it employs, which typically is limited by the number of historical observations, can be sizably enlarged via using position data for the underlying tradables.

Keywords: alpha, optimization, regression, risk factor, factor model, style factor, principal component, volatility, turnover, momentum, correlation, covariance, variance, equities, Sharpe ratio

JEL Classification: G00