We show that firms' idiosyncratic volatility obeys a strong factor structure and that shocks to the common factor in idiosyncratic volatility (CIV) are priced. Stocks in the lowest CIV-beta quintile earn average returns 5.4% per year higher than those in the highest quintile. The CIV factor...

We study the pricing of uncertainty shocks using a wide-ranging set of options that reveal premia for macroeconomic risks. Portfolios hedging macro uncertainty have historically earned zero or even significantly positive returns, while those exposed to the realization of large shocks have earned...

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 constraints....

Many financial instruments are designed with embedded leverage such as options and leveraged exchange traded funds (ETFs). Embedded leverage alleviates investors' leverage constraints and, therefore, we hypothesize that embedded leverage lowers required returns. Consistent with this hypothesis,...

Berkshire Hathaway has realized a Sharpe ratio of 0.76, higher than any other stock or mutual fund with a history of more than 30 years, and Berkshire has a significant alpha to traditional risk factors. However, we find that the alpha becomes insignificant when controlling for exposures to...

We derive a closed-form optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean-reversion speeds. The optimal strategy is characterized by two principles: 1) aim in front of the target and 2) trade partially towards the current...