We model how investors allocate between asset managers, managers choose their portfolios of multiple securities, fees are set, and security prices are determined. The optimal passive portfolio is linked to the “expected market portfolio,” while the optimal active portfolio has elements of...

Using a lifecycle framework with Epstein-Zin (1989) utility and a mixed-integer optimization approach, we compute the optimal age to claim Social Security benefits. Taking advantage of homogeneity, a sufficient statistic is the ratio of wealth to the primary insurance amount (PIA). If the...

Economists have long recognized that investors care differently about downside losses versus upside gains. Agents who place greater weight on downside risk demand additional compensation for holding stocks with high sensitivities to downside market movements. We show that the cross-section of...

Stocks with greater downside risk, which is measured by higher correlations conditional on downside moves of the market, have higher returns. After controlling for the market beta, the size effect and the book-to-market effect, the average rate of return on stocks with the greatest downside risk...

"We present a model in which some investors are prohibited from using leverage and other investors' leverage is limited by margin requirements. The former investors bid up high-beta assets while the latter agents trade to profit from this, but must de-lever when they hit their margin...