Multifactor Alpha Models

A single factor's IC of 3–5% is far too small to run a business on; the craft of alpha modelling is combining factors so the whole exceeds the parts. This note derives the IC of a linear factor combination, then poses and solves the central design problem — choose the factor weights $v$ to maximise the model's IR — and discovers something elegant: the answer is mean–variance optimisation all over again, but in IC space, with $\overline{IC}$ playing the role of expected returns and the IC covariance matrix playing the role of risk. Two structural results close the note: a positive-semidefiniteness bound showing that highly correlated factors cannot both carry large independent information, and the orthogonalisation procedure that makes a factor's incremental contribution transparent.

Learning objectives. By the end of this note you should be able to: