[When agents can learn about their abilities as active investors, they rationally "trade to learn" even if they expect to lose from active investing. The model used to develop this insight draws conclusions that are consistent with empirical study of household trading behavior: Households' portfolios underperform passive investments; their trading intensity depends on past performance; and they begin by trading small sums of money. Using household data from Finland, the article estimates a structural model of learning and trading. The estimated model shows that investors trade to learn even if they are pessimistic about their abilities as traders. It also demonstrates that realized returns are significantly downward-biased measures of investors' true abilities.]

When agents can learn about their abilities as active investors, they rationally “trade to learn ” even if they expect to lose from active investing. The model used to develop this insight draws conclusions that are consistent with empirical study of household trading behavior: Households ’ portfolios underperform passive investments; their trading inten-sity depends on past performance; and they begin by trading small sums of money. Using household data from Finland, the article estimates a structural model of learning and trad-ing. The estimated model shows that investors trade to learn even if they are pessimistic about their abilities as traders. It also demonstrates that realized returns are significantly downward-biased measures of investors ’ true abilities. (JEL D10, G11) While most households adjust their stock portfolios only infrequently, some trade very actively and underperform passive investments.1 I ask whether a model in which investors rationally learn from experience can explain this be-havior, and, if so, what the model tells us about households ’ beliefs. In my model, investors are uncertain about their abilities and learn as they trade. If the value of observing another signal is high, then an investor trades even if she expects to lose money, thus apparently trading “too much. ” If a trade is successful, the investor infers skill and subsequently trades more. If an investor loses money, she will infer less skill and subsequently trade less. After enough losses, she stops trading altogether. Investors who are especially uncertain about their abilities trade small amounts early in their careers until

Classical approaches to estimation and decisions requiring estimation often are at odds. When values critical to the decision are convex or concave functions of unknown parameters, the statistician's estimation error adjustments are the opposite of what is appropriate for the decision. We illustrate the conflict by studying multi-period investment problems. The proper application of Jensen's inequality to the decision turns finance intuition on its head: Multi-period investments with negative risk premia can be profitable, risk-averse investors can have infinite demand for risky securities, settings exist in which risk-averse investors should not diversify, and demand for mutual funds with negative alphas may be rational.

Stock market participation is monotonically related to IQ, controlling for wealth, income, age, and other demographic and occupational information. The high correlation between IQ and participation exists even among the affluent. Supplemental data from siblings, studied with an instrumental variables approach and regressions that control for family effects, demonstrate that IQ's influence on participation extends to females and does not arise from omitted familial and nonfamilial variables. High‐IQ investors are more likely to hold mutual funds and larger numbers of stocks, experience lower risk, and earn higher Sharpe ratios. We discuss implications for policy and finance research.