[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.]

Firms move between growth and value because of changes in either size or book value of equity. The value premium is specific to variation in book-to-market that emanates from size changes. A factor based on this variation earns the entire value premium; one based on the remaining variation earns no premium. Hence, not all high book-to-market firms earn the value premium, and some low book-to-market firms earn value-like returns. Many models price portfolios sorted by size and book-to-market. None distinguish firms that earn the value premium from those that have a high book-to-market but do not earn the premium.

[This article investigates the information content of signals about the identity of investors and their role in price formation. Whereas we document that investors use multiple brokers, broker identity is nevertheless a powerful signal about the identity of investors who initiate trades. The market also correctly processes this signal: the permanent price impact of orders coming from different brokers fits the information profile of the investors associated with these brokers. Our results suggest that an increase in the degree of anonymity may render order flow less informative, which could explain why the literature has documented liquidity improvements in exchanges that reduce transparency.]

[This article shows that individuals' product market choices influence their investment decisions. Using microdata from the brokerage and automotive industries, we find a strong positive relation between customer relationship, ownership of a company, and size of the ownership stake. Investors are also more likely to purchase and less likely to sell shares of companies they frequent as customers. These effects are stronger for individuals with longer customer relationships. A merger-based natural experiment supports a causal interpretation of our results. We also find evidence of causality in the other direction: inheritances and gifts have an effect on individuals' patronage decisions. A setup in which customer-investors regard stocks as consumption goods, not just as investments, seems to best explain our results.]

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

Mutual funds often disappear following poor performance. When this poor performance is partly attributable to negative idiosyncratic shocks, funds' estimated alphas understate their true alphas. This paper estimates a structural model to correct for this bias. Although most funds still have negative alphas, they are not nearly as low as those suggested by the fund‐by‐fund regressions. Approximately 12% of funds have net four‐factor model alphas greater than 2% per year. All studies that run fund‐by‐fund regressions to draw inferences about the prevalence of skill among mutual fund managers are subject to reverse survivorship bias.

Individual investors lose money around earnings announcements, experience poor posttrade returns, exhibit the disposition effect, and make contrarian trades. Using simulations and trading records of all individual investors in Finland, I find that these trading patterns can be explained in large part by investors' use of limit orders. These patterns arise mechanically because limit orders are price‐contingent and suffer from adverse selection. Reverse causality from behavioral biases to order choices does not appear to explain my findings. I propose a simple method for measuring a data set's susceptibility to this limit order effect.

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.

This article investigates the information content of signals about the identity of investors and their role in price formation. Whereas we document that investors use multiple brokers, broker identity is nevertheless a powerful signal about the identity of investors who initiate trades. The market also correctly processes this signal: the permanent price impact of orders coming from different brokers fits the information profile of the investors associated with these brokers. Our results suggest that an increase in the degree of anonymity may render order flow less informative, which could explain why the literature has documented liquidity improvements in exchanges that reduce transparency.

Using data spanning the twentieth century, we show that the majority of accounting-based return anomalies, including investment, are most likely an artifact of data snooping. When examined out-of-sample by moving either backward or forward in time, the average returns and Sharpe ratios of most anomalies decrease, whereas their volatilities and correlations with other anomalies increase. The few anomalies that do persist out-of-sample correlate with the shift from investment in physical capital to intangible capital and the increasing reliance on debt financing over the twentieth century. Received November 25, 2016; editorial decision September 23, 2017 by Editor Andrew Karolyi.