The Bounce Has No Direction: Sign, Magnitude, and the Microstructure of Equity Return Predictability

Victoria Portnaya

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Abstract: SPY's lag-1 return autocorrelation ($\hat\rho(1)=-0.081$, $z=-7.4$) is among the most significant regularities in empirical equity finance, yet the standard variance-ratio (VR) test cannot determine whether it reflects directional reversal or magnitude shrinkage - phenomena with entirely different trading implications. We develop the Fourier-Residue Identity (FRI), which decomposes return autocorrelation into a sign ($k=2$) and a magnitude ($k=4$) channel, each independently testable and neither redundant. Applied to six US instruments over 1993--2026 and a 21-instrument cross-asset panel, the FRI delivers a sharp microstructure diagnosis. The lag-1 autocorrelation in SPY is driven entirely by magnitude: the FRI sign test is insignificant ($p=0.11$) while the full test achieves $p 1) rather than sampling noise (R_N->sqrt(2)). The cross-asset panel shows mean reversion confined to exchange-traded equities and sovereign bonds; credit ETFs, commodities, FX, and crypto are indistinguishable from random walks. All estimators pass 27 unit tests; Monte Carlo confirms correct 5% size under GARCH.

Date: 2026-06
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