We study a natural experiment in which 1.5 million investors participate in allocation lotteries for Indian IPO stocks. Investors who win the lottery and obtain IPO stocks that rise in value increase portfolio trading volume in non-IPO stocks relative to lottery losers; the effects are negative for lottery winners obtaining IPO stocks that fall in value. A model in which agents learn from random experience about their ability to operate in the market environment best explains the results. Investors who have received multiple past IPO allocations show smaller responses, suggesting that learning/selection moderates these responses to noise shocks.