Collateral Constraints and the Law of One Price: An Experiment

• DOI: http://doi.org/10.1111/jofi.12722
• Published date: 01 December 2018
• Author: MARCO CIPRIANI,DANIEL HOUSER,ANA FOSTEL
• Date: 01 December 2018

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 6 •DECEMBER 2018

Collateral Constraints and the Law of One Price:

An Experiment

MARCO CIPRIANI, ANA FOSTEL, and DANIEL HOUSER∗

ABSTRACT

We test the asset pricing implications of collateralized borrowing (that is, of using

assets as collateral to borrow money) in the laboratory. To this purpose, we develop

a general equilibrium model with collateral constraints amenable to laboratory im-

plementation and gather experimental data. In the laboratory, assets that can be

leveraged fetch higher prices than assets that cannot, even though assets’ payoffs are

identical in all states of the world. Collateral value, therefore, creates deviations from

the Law of One Price. The spread between collateralizeable and noncollateralizeable

assets is significant and quantitatively close to theoretical predictions.

THE 2008 FINANCIAL CRISIS HIGHLIGHTED THE limited understanding of the role

of leverage in financial markets among both academics and practitioners.1As

a result, in the years following the crisis, a strand of the theoretical finan-

cial literature focused on the impact of leverage on asset prices.2During the

crisis, it also became apparent that cross-sectional differences in asset prices

were related to heterogeneity in asset collateral capacities. Several theoret-

ical papers study the cross-sectional implications of collateralized borrowing

in a world where agents are heterogeneous and markets are incomplete: for

instance, Fostel and Geanakoplos (2008) in a collateral general equilibrium

model, Garleanu and Pedersen (2011) in a CAPM model, and Brumm et al.

∗Marco Cipriani is at Federal Reserve Bank of New York, Ana Fostel is at the University

of Virginia and NBER, and Daniel Houser is at George Mason University. We thank Olivier

Armantier, Douglas Gale, John Geanakoplos, Antonio Guarino, Charles Holt, Gabriele La Spada,

Rosemary Nagel, Andrew Schotter, and seminar participants for very helpful comments. We also

thank Bruno Biais (the Editor), two Associate Editors, and two referees for their valuable feedback.

We thank Jingnan Chen, Lina Diaz, Jeff Gortmaker,David Hou, Philip Mulder, Sean Myers, Adam

Spiegel, and Joe Step for outstanding research assistance during this project. The views in this

paper should not be interpreted as reflecting the views of the Federal Reserve Bank of New Yorkor

the Federal Reserve System. We declare that we have no relevant or material financial interests

that relate to the research described in this paper. All errors are ours.

1See, for example, Brunnermeier (2009), Geanakoplos (2010b), and Gorton (2009).

2See, for instance, Acharya and Viswanathan (2011), Adrian and Shin (2010), Brunnermeier

and Pedersen (2009), Fostel and Geanakoplos (2008,2012a,2012b,2014,2015), Garleanu and

Pedersen (2011), Geanakoplos (2010a), and Simsek (2013). Early studies on the effect of leverage

constraints on asset prices were published before the crisis, see, for instance, Hindy (1995)fora

partial equilibrium model, and Geanakoplos (1997,2003) for a general equilibrium model with

incomplete markets.

DOI: 10.1111/jofi.12722

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2758 The Journal of Finance R

(2015) in an infinite-horizon exchange economy. These papers show that col-

lateral value increases asset prices, creating deviations from the Law of One

Price.3

Fostel and Geanakoplos (2008) show that when an asset can be used as col-

lateral, its price can be decomposed into two parts, its payoff value and its

collateral value. The payoff value reflects the owner’s valuation of the asset’s

future cash flow. The collateral value reflects the owner’s valuation of being

able to leverage the asset, that is, of being able to use it as collateral to borrow.

The asset collateral role is priced in equilibrium and as a result creates devi-

ations from the Law of One Price: two assets with identical payoffs are priced

differently if their collateral capacities are different.4A well-documented ex-

ample of such deviations is the so-called “CDS-bond basis,” the price difference

between Treasuries and covered CDS positions.5

In this paper, we study the impact of collateral constraints on asset prices

in a controlled experiment. In the laboratory, we can study assets with iden-

tical payoffs that differ only in their collateral capacities; this cannot be done

with field data (for instance, even when comparing Treasuries to covered CDS

positions, counterparty risk muddies the water).6

To this purpose, we build a model of a financial economy, amenable to lab-

oratory implementation, with incomplete markets, heterogeneous agents, and

collateralized borrowing. Agents trade two risky assets with identical payoffs

in all states of the world. Agents can borrow only by posting collateral, and

only one of the two assets can be used as collateral. In equilibrium, collateral is

valuable because agents who value the risky assets the most are constrained,

and collateral allows them to borrow and purchase more risky assets. For this

reason, the price of the collateralizeable asset is higher than the price of the

asset that cannot be used as collateral. Since the two assets have identical

payoffs, this spread represents a deviation from the Law of One Price due to

the presence of collateral value. Finally, since agents need to post collateral to

borrow and collateral is scarce, the equilibrium fails to implement the Pareto-

efficient allocation, in which the agents with the highest asset valuation own

all of the risky-asset supply.

We bring the model to the laboratory by having students play in a two-

asset double auction experiment with collateralized borrowing, and we gather

3Other drivers of deviations from the Law of One Price, similar to collateral, are the “divert-

ibility premium” under incentive problems in Biais, Hombert, and Weill (2017) and the “liquidity

premium” in new monetarist papers such as Lagos (2010), Li, Rocheteau, and Weill (2012), and

Lester, Postlewaite, and Wright(2012).

4An early example of collateral value generating deviations from the Law of One Price can be

found in Geanakoplos (2003).

5A covered CDS consists of simultaneously holding a CDS and its underlying bond. Since the

CDS insures against the default of the bond (e.g., a corporate bond), the payoff of the covered CDS

position equals that of a riskless bond (e.g., a Treasury). However, since agents can borrow more

using a riskless bond than using the covered CDS as collateral, riskless bonds generally trade at

a positive spread over covered bond positions.

6Moreover, data on loan terms for securities used as collateral are only now beginning to be

collected in the United States on a limited basis. See, for instance, Baklanova et al. (2017).