Extreme-Return Influence and Volatility Dependence in Bitcoin and Equity Returns

Sensitivity to extreme observations does not by itself establish that a financial return characteristic is episodic rather than persistent. This study separates that interpretation from what an influence experiment actually measures. Daily Bitcoin and SPDR S&P 500 ETF Trust returns are examined in nine fixed calendar years, 2016–2024, using full samples, largest-return deletions, and chronology-preserving winsorization. Marginal influence contrasts are paired with squared-return diagnostics, block resampling, specified-model simulations, and a forward-event comparison against within-year permutations. Median standard-deviation retention after 1st/99th-percentile winsorization is 94.53% for Bitcoin and 96.43% for the equity fund, whereas median excess-kurtosis changes are -1.72 and -1.13. However, lag-one squared-return correlation increases after clipping in four of nine Bitcoin years and seven of nine equity-fund years. Bitcoin in 2020 provides a particularly marked counterexample: excess kurtosis falls from 51.59 to 1.78 while squared-return correlation rises from 0.046 to 0.101. An independent Student-distribution counterexample reproduces strong kurtosis attenuation without temporal dependence. Forward squared returns following extreme episodes exceed the respective permutation reference envelopes for both assets. The findings distinguish moment sensitivity from chronological organization; they do not support a universal attenuation hierarchy or identify separate latent volatility components. Historical-return diagnostics are also distinguished from risk-neutral option-pricing errors. Kaiwei Wang, Mingquan Luo, and Yuan Yao are co-first authors of this manuscript.