How to Combine a Billion Alphas

TL;DR

This paper presents an efficient algorithm for optimally combining a vast number of alphas, significantly reducing computational complexity and avoiding traditional matrix operations, thereby enabling scalable portfolio optimization.

Contribution

The authors introduce a linear-scaling algorithm for alpha combination that bypasses matrix inversion and principal component analysis, suitable for large N without binary clustering assumptions.

Findings

Algorithm scales linearly with N

No need for matrix inversion or PCA

Enables larger risk factor models using position data

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.