Price Path Continuity and the Cross-Section of Cryptocurrency Returns

Abstract

This paper examines whether the continuity of past price trajectories predicts the cross-section of cryptocurrency returns. The Frog-in-the-Pan hypothesis argues that investors underreact more strongly when information arrives gradually rather than discretely. I extend this logic to cryptocurrency markets, where conventional cash-flow anchors are limited and price movements themselves play a central informational role. To measure the structure of return formation, I construct a short-term Rank-Weighted Price Path Continuity measure (PPC) using daily returns over the prior 14 days and apply it to a broad, survivorship-bias-mitigated cryptocurrency sample from January 2020 to April 2026. Weekly Fama-MacBeth regressions show that short-term past returns exhibit reversal on average, but become increasingly associated with continuation when accumulated through smoother, more continuous price paths. The effect persists across alternative horizons, alternative continuity measures, size-exclusion samples, market states, abnormal-volume states, and cryptocurrency-policy-uncertainty regimes. Overall, the evidence shows that the path of past returns contains incremental information about delayed price adjustment in cryptocurrency markets, consistent with limited-attention interpretations of the Frog-in-the-Pan hypothesis.

Keywords: cryptocurrency, Momentum, Investor Attention, Price Path Continuity, Behavioral Finance