Three Essays on Nonlinear Limits to Arbitrage

Arbitrage costs and funding constraints are two major frictions that limit arbitrage. Arbitrage costs, such as learning costs, transaction costs and holding costs, render arbitrageurs unwilling to take on positions, whilst funding constraints, including equity and leverage constraints, reduce their ability to obtain funding and thus correct mispricings. This thesis contains theoretical studies and empirical applications of these two frictions, both individually and jointly. First we investigate the combined impact of arbitrage costs and funding constraints on the arbitrage activity, where we reveal the nonlinearity of limits to arbitrage: when funding constraint is not binding, arbitrage costs serve as the dominating friction, and thus the arbitrage activity increases with mispricing; however, in extreme situations where funding constraints become binding and establish dominance over arbitrage costs, the arbitrage activity tends to decline with larger mispricing. Second we narrow our focus on the time-varying leverage constraint, and construct a funding liquidity measure via the efficacy of arbitrage. The measure ex ante identifies four periods of binding funding constraint: the collapse of dot-com bubble, the financial crisis in 2007-2008 and the two debt ceiling crises in 2011 and 2013, which supports the slow-moving capital hypothesis. The measure also predicts the market volatility and the volatility risk premia, and the predictive power is most prominent during the period of binding funding constraint, which confirms the presence of amplification. Third, we provide further investigation on the holding costs, i.e. fundamental and sentiment risk, and reveal their distinctive influences on the arbitrage activity. It offers an unified approach to examine the level of the respective risk exposure, which is then applied to investigate the value premium anomaly. We find supporting evidence for the behavioral explanation, such that higher sentiment risk exposure deters the arbitrage activity and earns a higher return.