Equal Weights vs Optimised Blends
Optimising blend weights from historical correlations often looks better in-sample and worse out-of-sample than just averaging signals equally — a recurring, humbling result in research.
Prerequisites: Combining Many Weak Signals
Given ten signals and their historical correlations and IC's, the obvious move is to solve for the weights that maximise historical performance. That's usually a mistake. Equal weighting — averaging every signal with the same weight — routinely beats an optimised blend out of sample, and understanding why is one of the more useful humility lessons in signal research.
Why the "obvious" answer underperforms
An optimiser given historical returns will find weights that fit the sample perfectly, including the noise in it. If two signals happened to be slightly negatively correlated over the estimation window by chance, the optimiser will lever one against the other to exploit that — a relationship that had nothing to do with the true underlying structure and won't repeat. The more signals there are relative to the length of history, the worse this gets, because the number of covariance parameters to estimate grows roughly with the square of the number of signals, while the amount of data to estimate them from doesn't.
Equal weighting makes no claim about which signal is better or how they relate — and so it can't be wrong about a relationship it never assumed. It trades away a small amount of achievable in-sample improvement for a large amount of robustness.
The gap between "optimal on the training window" and "optimal out of sample" is estimation error, not signal quality — and it grows with the number of signals and shrinks with the length of clean history. Equal weighting is a reasonable default until there's a lot of stable data to justify deviating from it.
A worked example
A researcher has five signals, each with a similar standalone IC, estimated over three years of daily data. An in-sample mean-variance optimiser produces a blend with a backtested Sharpe of 2.4 — noticeably better than the equal-weighted blend's in-sample Sharpe of 1.6. Run both blends forward on the next year of data: the optimised blend's Sharpe falls to 0.9, while the equal-weighted blend's Sharpe holds at 1.5. The optimiser spent its extra apparent skill on fitting sample noise, and most of that "skill" evaporated the moment the sample changed.
A middle ground exists: shrink the optimised weights partway toward equal weight rather than choosing one extreme. The right amount of shrinkage depends on how much history backs the correlation estimates — more history justifies trusting the optimiser more.
Related concepts
Practice in interviews
Further reading
- DeMiguel, Garlappi & Uppal (2009), Optimal Versus Naive Diversification