Funding Liquidity and Limits to Arbitrage

Arbitrageurs play an important role in keeping market prices close to their fundamental values by providing market liquidity. Most arbitrageurs however use leverage. When funding conditions worsen they are forced to reduce their positions. The resulting selling pressure depresses market prices, and in certain situations, pushes arbitrage spreads to levels exceeding many standard deviations. This phenomenon drove many century old financial institutions into bankruptcy during the 2007−2009 financial crisis. In this thesis, we provide empirical evidence and demonstrate analytically the effects of funding liquidity on arbitrage. We further discuss the implications for risk management. To conduct our empirical studies, we construct a novel Funding Liquidity Stress Index (FLSI) using principal components analysis. Its constituents are measures representing various funding channels. We study the relationship between the FLSI index and three di↵erent arbitrage strategies that we reproduce with real and daily transactional data. We show that the FLSI index has a strong explanatory power for changes in arbitrage spreads, and is an important source of contagion between various arbitrage strategies. In addition, we perform “event studies” surrounding events of changing margin requirements on futures contracts. The “event studies” provide empirical evidence supporting important assumptions and predictions of various theoretical work on market micro-structure. Next, we explain the mechanism through which funding liquidity affects arbitrage spreads. To do so, we study the liquidity risk premium in a market micro-structure framework where market prices are determined by the supply and demand of securities. We extend the model developed by Brunnermeier and Pedersen [BP09] to multiple periods and generalize their work by considering all market participants to be risk-averse. We further decompose the liquidity risk premium into two components: 1) a fundamental risk premium and 2) a systemic risk premium. The fundamental risk premium compensates market participants for providing liquidity in a security whose fundamental value is volatile, while the systemic risk premium compensates them for taking positions in a market that is vulnerable to funding liquidity. The first component is therefore related to the nature of the security while the second component is related to the fragility of the market micro-structure (such as leverage of market participants and margin setting mechanisms)