We show that retail trading activity has a positive effect on the volatility of stock returns. To identify this effect, we use a reform of the French stock market that triggers a drop in retail trading activity by raising the relative cost of speculative trading for retail investors. The daily return volatility of the stocks affected by the reform falls by twenty basis points (a quarter of the sample standard deviation of the return volatility) relative to other stocks. For affected stocks, we also find a significant decrease in the magnitude of return reversals and the price impact of trades. We argue that these findings are consistent with the view that some retail investors behave as noise traders.