Margin-based Asset Pricing and Deviations from the Law of One Price

Abstract

In a model with heterogeneous-risk-aversion agents facing margin constraints, we show how securities' required returns increase in both their betas and their margin requirements. Negative shocks to fundamentals make margin constraints bind, lowering risk-free rates and raising Sharpe ratios of risky securities, especially for high-margin securities. Such a funding-liquidity crisis gives rise to "bases," that is, price gaps between securities with identical cash-flows but different margins. In the time series, bases depend on the shadow cost of capital, which can be captured through the interest-rate spread between collateralized and uncollateralized loans and, in the cross-section, they depend on relative margins. We test the model empirically using the credit default swap-bond bases and other deviations from the Law of One Price, and use it to evaluate central banks' lending facilities. (JEL G01, G12, G13, E44, E50)The paramount role of funding constraints becomes particularly salient during liquidity crises, with the one that started in 2007 being an excellent case in point. Banks unable to fund their operations closed down, and the funding problems spread to other investors, such as hedge funds, that relied on bank funding. Therefore, traditional liquidity providers became forced sellers, interest-rate spreads increased dramatically, Treasury rates dropped sharply, and central banks stretched their balance sheets to facilitate funding. These funding problems had significant asset-pricing effects, the most extreme example being the failure of the Law of One Price (LoOP): Securities with (nearly)We are grateful for helpful comments from Markus Brunnermeier, Xavier Gabaix, Andrei Shleifer, and Wei Xiong, as well as from seminar participants at the Bank of Canada,

Bubbles, Crises, and Heterogeneous Beliefs

“…In other words, deterioration in market liquidity tightens traders' margin constraints and thus funding liquidity, which in turn further reduces market liquidity. Garleanu and Pedersen (2011) developed a dynamic equilibrium model to show that margin constraints can lead to deviations from the law of one price.…”

The TED spread as a risk factor in the cross section of stock returns

“…Studies relating margin requirements and the shadow cost of funding to asset prices (hence, the presence of TED Spread risk) in a credit constrained environment are found in Luttmer (1996), Bernardo and Welch (2003) and more recently in Brunnermeier and Pedersen (2009), Ashcraft et al (2010) and Gârleanu and Pedersen (2011). Those articles assume that agents are heterogeneous in a sense that they differ in their relative risk aversion and may face different margin constraints for taking leverage positions.…”

“…During times of crisis, as capital is constrained, expected returns are positively related to margins because agents face additional costs of funding. Credit constraints can also cause adverse impacts on asset prices, and the worst of all, according to Gârleanu and Pedersen (2011) is the failure of the "Law of One Price" (LoOP), by which two different assets with similar cash flows are negotiated under different prices, as margin requirements may differ. Also, Hedegaard (2011) studied margin impacts on commodity future returns, and found that an increase in futures margins, in which speculators hold long positions, reduces the futures price of long-term contracts.…”

“…In order to provide a theoretical reason why agents may consider TED spread as a risk factor, we use the Margin-based Asset Pricing Model of Gârleanu and Pedersen (2011), one that relates margin requirements 3 with asset prices 4 . During "good times", credit is unconstrained and leverage operations face no additional costs that would make them more expensive or even prohibitive (margin requirements are easily covered).…”

“…The rest of the paper is organized as follows: section 2 presents related literature to margin-based models and evidence of the TED Spread premium so far; section 3 presents the margin-based asset pricing model of Gârleanu and Pedersen (2011); section 4 gives a brief discussion of the TED spread and empirical results of the cross section of expected stock returns, as well as evidence supporting the relationship between the margins and asset's exposure on the TED spread; section 5 concludes the paper.…”