We study a natural experiment in which 1.5 million investors participate in allocation lotteries for Indian IPO stocks. Randomized IPO gains cause winning investors to increase applications to future IPOs and substantially increase portfolio trading volume in non-IPO stocks relative to lottery losers; the effects are symmetrically negative for experienced losses. Investors who have received multiple past IPO allocations show smaller responses, suggesting learning/selection moderates responses to noise shocks. The evidence is most consistent with investors learning about their own ability from experienced noise, drawing inferences about their skill from luck.