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.

ABSTRACT 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.