Pruning Redundant Signals
A research library of two hundred signals that all move together is really just one signal wearing two hundred costumes — pruning finds and removes the duplicates so the portfolio isn't quietly making the same bet many times over.
Prerequisites: Alpha Correlation and Effective Breadth, Orthogonalising a Signal Against Known Factors
A research team that has built two hundred signals over the years might reasonably feel well-diversified. But if forty of those signals are all variations on "the stock is cheap relative to earnings" — one uses trailing earnings, another forward estimates, another a five-year average — they are not forty independent sources of edge. They are one economic idea measured forty slightly different ways, and a portfolio combining all forty is really just placing one oversized bet on value while looking, on paper, like it holds many diversified positions.
Redundant signal pruning identifies clusters of highly correlated signals and keeps only the strongest representative (or a single blended version) from each cluster, rather than feeding every near-duplicate into the portfolio separately. The goal is to make the signal count reflect actual independent bets, since — per the Fundamental Law of Active Management — it's independent breadth, not raw signal count, that drives risk-adjusted returns.
Two signals with a correlation above roughly 0.7–0.8 are, for portfolio purposes, close to the same bet — keeping both barely adds diversification but does add estimation noise and turnover, so pruning to one representative per correlated cluster is usually a net improvement, not a loss of information.
Clustering signals by correlation
Worked example
A library contains five signals with the following average pairwise correlations relevant to a new candidate signal, "cash-flow yield": 0.85 with "earnings yield," 0.82 with "book yield," 0.15 with "12-month momentum," and 0.10 with "analyst revision." Cash-flow yield's own standalone IC is 0.035, similar to earnings yield's 0.038.
Because cash-flow yield is correlated 0.85 with a signal already in the library and offers no clear IC improvement, adding it contributes almost no new independent breadth — its inclusion mostly just increases estimation noise and trading costs without meaningfully improving diversification. The momentum and analyst-revision signals, at 0.10–0.15 correlation, are genuinely closer to independent bets and are the ones worth keeping distinct in a blended model; the library is better served by picking the stronger of the two value-family signals and combining it with the two low-correlation ones, rather than keeping all four.
Pruning by unconditional correlation can miss regime-dependent redundancy: two signals might look uncorrelated on average but move together specifically during market stress, which is exactly when correlated losses matter most. Checking correlation conditional on drawdown periods, not just the full-sample average, catches redundancy that a simple pairwise correlation table misses.
Practice in interviews
Further reading
- Grinold and Kahn, Active Portfolio Management (ch. 6)