We consider a model of external financing in which entrepreneurs are privately informed about the quality of their projects and seek funds from competitive financiers. The literature restricts attention to monotonic, or “manipulation proof,” securities and finds that straight debt is the uniquely optimal contract. Monotonicity is commonly justified by the argument that it would endogenously arise if the entrepreneur can window dress the realized earnings before contract maturity. We explicitly characterize the optimal contracts when entrepreneurs engage in window dressing and/or output diversion and derive necessary and sufficient conditions for straight debt to be optimal. Contrary to conventional wisdom, debt is often suboptimal, and it is never uniquely optimal. Optimal contracts are nonmonotonic and induce profit manipulation in equilibrium. They can be implemented as performance-sensitive debt. Received: March 24, 2018; Editorial decision September 22, 2018 Editor: Uday Rajan

This paper studies asymmetric profitability of the momentum trading strategy. When investors face Knightian uncertainty, they react differently to past winners and losers, which creates asymmetric patterns in price continuations. This asymmetry increases with the level of market and idiosyncratic uncertainty relating to the fundamental value of stocks. We provide a model explaining this phenomenon and empirical evidence supporting the hypothesis. Our results also imply that momentum is more likely to continue for downward trends in a highly uncertain market.

We develop a new method for measuring moment risk premiums. We find that the skew premium accounts for over 40% of the slope in the implied volatility curve in the S&P 500 market. Skew risk is tightly related to variance risk, in the sense that strategies designed to capture the one and hedge out exposure to the other earn an insignificant risk premium. This provides a new testable restriction for asset pricing models trying to capture, in particular, disaster risk premiums. We base our results on a general trading strategy by replicating contracts that swap implied for realized conditional asset moments.

We identify a global risk factor in the cross-section of implied volatility returns in currency markets. A zero-cost strategy that buys forward volatility agreements with downward sloping implied volatility curves and sells those with upward slopes–a volatility carry strategy–generates significant excess returns. The covariation with volatility carry returns fully explains the cross-sectional variation of our slope-sorted portfolios. The lower the slope, the more the forward volatility agreement is exposed to volatility carry risk.