Anand Bharadwaj

Why do stocks with high idiosyncratic volatility earn low returns? Greater fundamental volatility raises both uncertainty and disagreement, with disagreement increasing proportionately more. Under short sale constraints, these forces have opposing effects on prices. We establish a sharp common prior bound relating uncertainty and disagreement and characterize an exact nonlinear rational expectations equilibrium with risk-averse investors, continuously varying positions, and learning from prices. Greater fundamental volatility can raise prices when ownership is sufficiently narrow. Consistent with the theory, we find empirically that the negative relationship between idiosyncratic volatility and subsequent returns strengthens as borrowing costs rise and ownership breadth declines, and that disagreement accounts for much of the anomaly around earnings announcements, when firm-specific public information is revealed.

How complex must a characteristic model be to capture the cross-section of stock returns? The answer depends not only on how flexibly returns depend on characteristics, but also on how those characteristics are converted into traded portfolios. When characteristics overlap across firms, conventional managed portfolios mix the underlying payoff directions, and that mixing changes over time. We introduce a rotation that separates these directions and use it to compare linear, sorted, and nonlinear representations on common terms. Rich nonlinear functions can improve portfolio performance, but adding basis functions is not a substitute for accounting for overlap. Many characteristics remain useful even when the model can select among them, while only a few combinations of the resulting returns are needed to preserve most of their performance. Thus a rich relation between characteristics and returns can give rise to a comparatively simple set of traded payoffs.

A seller contracts with an intermediary who designs information to persuade consumers. The intermediary values both monetary incentives from the seller and reputational payoffs from improving consumer welfare. Using Lagrangian duality, we derive the sender-optimal information design in a general class of two-action Bayesian persuasion problems. The optimal contract is a commission scheme that is non-monotonic in the intermediary’s relative preference: the commission rises, then falls, as pecuniary motives strengthen. With endogenous pricing, persuasion and pricing act as substitutes. The seller induces maximal persuasion when the intermediary’s weight on monetary payoffs is sufficiently high, but refrains from using persuasion otherwise. Finally, we show that this setting is isomorphic to one where the influencer is a data broker with private knowledge of consumer valuations.

Bunching at tax kinks shows that reported income responds to incentives, but not whether total income changes or income is merely reallocated across taxpayers. We show that real responses constrain the distribution of total family income, whereas reallocation can generate individual bunching while leaving family income smooth. Using linked Australian tax records from 2001 to 2022 and a novel global bootstrap Kolmogorov–Smirnov test, we find sharp individual bunching in every year but no detectable bunching in family average income. The results suggest that individual bunching in Australia is driven primarily by intra-family income shifting rather than real responses.