We propose new tests to examine whether stock index futures affect stock market volatility. These tests decompose spot portfolio volatility into the cross-sectional dispersiona nd the average volatility of returns on the portfolio's constituent securities. Examining shifts in both cross-sectional dispersion and spot portfolio volatility facilitates focus on the unique implications of futures-related "basket" trading strategies. Using average volatility mitigates extraneous influences on these other volatiity measures. Applied to the Tokyo Stock Exchange, our tests show that, for Nikkei stocks, spot volatility increased and cross-sectional dispersion decreased after Nikei futures trading began on the Osaka Stock Exchange (OSE), but not on the Singapore International Monetary Exchange(SIMEX). For non-Nikkei stocks, no structural shift occurred when futures began trading on either exchange. These findings are consistent with the hypotheses that, absent the trading restrictions discussed by Brenner, Subrahmanyam, and Uno (1989), futures trading increases spot portfolio volatility but that the volatility impact does not "spillover" to stocks against which futures are not traded. The absence of a volatility spillover from Nikkei to non-Nikkei stocks also suggests that the volatility impact of futures trading on Nikkei stocks is not spuriously caused by extraneous economic disturbances.