How to Combine a Billion Alphas

Journal of Asset Management 18(1) (2017) 64-80

23 Pages Posted: 29 Feb 2016 Last revised: 15 Dec 2016

See all articles by Zura Kakushadze

Zura Kakushadze

Quantigic Solutions LLC; Free University of Tbilisi

Willie Yu

Duke-NUS Medical School - Centre for Computational Biology

Date Written: February 27, 2016


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

Suggested Citation

Kakushadze, Zura and Yu, Willie, How to Combine a Billion Alphas (February 27, 2016). Journal of Asset Management 18(1) (2017) 64-80, Available at SSRN: or

Zura Kakushadze (Contact Author)

Quantigic Solutions LLC ( email )

680 E Main St #543
Stamford, CT 06901
United States
6462210440 (Phone)
6467923264 (Fax)


Free University of Tbilisi ( email )

Business School and School of Physics
240, David Agmashenebeli Alley
Tbilisi, 0159

Willie Yu

Duke-NUS Medical School - Centre for Computational Biology ( email )

8 College Road
Singapore, 169857

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