Long-Short Spread Versus Single-Leg Inference

A common way to test a stock-picking signal is to sort names into deciles, go long the top decile and short the bottom decile, and check whether the spread's return is significantly positive. It's tempting to think this is equivalent to testing the long leg and short leg separately and combining the results, but it isn't, because the two legs share market-wide shocks that mostly cancel out in the spread and would otherwise inflate each leg's own variance.

Suppose the long decile returns 12% a year with a standard deviation of 20%, and the short decile (as a return, before flipping sign) returns 4% with the same 20% standard deviation, and the two are 70% correlated because both move with the market. Tested alone, neither leg's t-statistic looks overwhelming. But the spread's variance is $\sigma_L^2 + \sigma_S^2 - 2\rho\sigma_L\sigma_S$, which with 70% correlation shrinks the spread's standard deviation to well under either leg's — around 15.5% instead of 20% — concentrating the same mean difference into a much tighter distribution and producing a far higher t-statistic on the spread than either leg would show.

Because of this, correctly reporting the significance of a long-short strategy means running the test on the realized spread return series itself (with proper autocorrelation-robust standard errors), not on decile-level statistics computed separately and stitched together after the fact.