A Test of the Modigliani‐Miller Invariance Theorem and Arbitrage in Experimental Asset Markets

• DOI: http://doi.org/10.1111/jofi.12736
• Author: TIBOR NEUGEBAUER,GARY CHARNESS
• Published date: 01 February 2019
• Date: 01 February 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 1 •FEBRUARY 2019

A Test of the Modigliani-Miller Invariance

Theorem and Arbitrage in Experimental Asset

Markets

GARY CHARNESS and TIBOR NEUGEBAUER

ABSTRACT

Modigliani and Miller show that the total market value of a firm is unaffected by a

repackaging of asset return streams to equity and debt if pricing is arbitrage-free.

We investigate this invariance theorem in experimental asset markets, finding value-

invariance for assets of identical risks when returns are perfectly correlated. However,

exploiting price discrepancies has risk when returns have the same expected value

but are uncorrelated, in which case the law of one price is violated. Discrepancies

shrink in consecutive markets, but persist even with experienced traders. In markets

where overall trader acuity is high, assets trade closer to parity.

IN THEIR SEMINAL PAPER, Modigliani and Miller (1958,1963) show mathemat-

ically that the market value of a firm is invariant to the firm’s leverage—

different packaging of contractual claims on the firm’s assets does not im-

pact the total market value of the firm’s debt and equity. The Modigliani and

Miller—henceforth MM—value-invariance theorem suggests that the law of

one price prevails for assets of the same “risk class.” The core of the theorem is

an arbitrage proof, whereby if two assets, one leveraged and one unleveraged,

represent claims on the same cash flow,any market discrepancies that arise are

arbitraged away. But due to its assumptions of perfect capital markets and the

no-limits-to-arbitrage condition (which requires the perfect positive correlation

*Tibor Neugebauer is at the University of Luxembourg and is the corresponding author. Gary

Charness is at University of California, Santa Barbara. The authors have no conflicts of interest to

disclose. The authors obtained Institutional Review Board approval for data collection. We grate-

fully acknowledge the helpful comments of Bruno Biais (the Editor), the anonymous Associate

Editor, two anonymous reviewers, Peter Bossaerts, Martin Duwfenberg, Darren Duxbury, Cather-

ine Eckel, Ernan Haruvy,Chad Kendall, Roman Kr ¨

aussl, Ulf von Lilienfeld-Toal,Raj Mehra, Luba

Petersen, Jianying Qiu, Kalle Rinne, Jean-Charles Rochet, Jason Shachat, and Julian Williams

for helpful comments. We also thank seminar participants at Durham Business School, University

of Luxembourg, and Radboud University of Nijmegen, and at the conferences Experimental Fi-

nance in Nijmegen, the Netherlands, Experimental Finance in Tucson, Arizona, the International

Meeting on Experimental and Behavioral Sciences in Toulouse,France, Conference on Behavioural

Aspects of Macroeconomics & Finance at House of Finance, Frankfurt, Germany, Barcelona GSE

Summer Forum, Spain, and CESifo in Munich, Germany. The scientific research presented in

this publication received financial support from the National Research Fund of Luxembourg (IN-

TER/MOBILITY/12/5685107), and University of Luxembourg provided funding of the experiments

through an internal research project (F2R-LSF-PUL-10IDIA).

DOI: 10.1111/jofi.12736

493

494 The Journal of Finance R

of asset returns, no fees on the use of leverage, etc.), the MM theorem has not

been satisfactorily tested on real-world market data. Its empirical significance

has thus been unclear.1

Such a test is feasible in the laboratory, however. Providing an empirical test

of the MM theorem is a primary purpose of this study. Since perfect return

correlation is rare in naturally occurring equities, we also check how limits to

arbitrage affect the empirical validity of the MM theorem with regards to cross-

asset pricing. In particular, we examine whether a perfect positive correlation

between asset returns is necessary for the empirical validity of value-invariance

or whether the same expected (rather than identical) future return is sufficient,

as suggested by the capital asset pricing model for our setting. Our data indeed

suggest that perfect correlation is indeed necessary for the law of one price to

prevail.

Our main design adapts the experimental asset market research of Smith,

Suchanek, and Williams (1988), which features multiperiod cash flows, zero

interest rates, and a repetition of markets with experienced subjects.2However,

in contrast to the standard, single-asset market approach of Smith, Suchanek,

and Williams (1988), and in line with MM, we allow for simultaneous trading in

two shares of the same “equivalence class.” These “twin shares,” which we refer

to as the L-shares and U-shares, are claims on the same underlying uncertain

future cash flows. In one treatment, the returns of the L-share and the U-

share are perfectly correlated and thus any price discrepancies that arise can

be arbitraged away at no risk. In a second treatment, where the returns of

the L-share and the U-share are uncorrelated, we study the impact of limits to

arbitrage. In both cases, the expected stream to shareholders of L-shares and U-

shares differs by a constant amount, which we refer to as the “synthetic” value

of debt, as we discuss below, so the L-share and U-share represent “leveraged”

and “unleveraged” equity streams.

1The assumption of perfect capital markets requires, among other things, that no taxes and

transaction fees be levied and that the same interest rate applies to everyone. Lamont and Thaler

(2003) present several real-world examples where the law of one price is violated. They argue

that these violations result from limits to arbitrage. An early objection concerned the applicability

of value-invariance in relation to the variation of payout policy. Modigliani and Miller (1959)

replied to this objection by stating that a firm’s dividend policy is irrelevant for the value of the

company. However, it is now widely accepted that dividends impact empirical valuations (for a

recent discussion of the dividend puzzle, see DeAngelo and DeAngelo (2006)). With the dividend-

irrelevance theorem thus empirically rejected, it is considered as of theoretical interest only. The

value-invariance theorem and its proof, however, have remained widely accepted in the profession

even without empirical evidence to support it.

2See Palan (2013) for a recent literature survey. The literature is mainly concerned with mea-

suring mispricing in the single-asset market. The conclusion is that confusion of subjects and spec-

ulation are the main sources of price deviations from fundamentals in the laboratory (e.g., Smith,

Suchanek, and Williams (1988), Lei, Noussair and Plott (2001), Kirchler, Huber, and Stoeckl

(2012)). Mispricing occurs in the single-asset market, and also when assets are simultaneously

traded in two markets (Ackert et al. 2009, Chan, Lei and Vesely 2013). Smith and Porter (1995),

Noussair and Tucker (2006), and Noussair,Tucker, and Yu(2016) report reduced mispricing when

a futures market enables subjects to arbitrage price discrepancies of underlying asset and futures

contracts.

MM Experimental Asset Markets 495

By comparing the market prices of shares, we present a very simple test of

the MM theorem.3If at any point in time the price deviates from parity, in

other words if the difference between the L-share and the U-share is not the

same as the synthetic debt value for the investor, then a market participant

can exploit the price discrepancy. Since short-selling and borrowing is costless,

a trader can make a riskless arbitrage gain by going short the expensive share

and long the inexpensive share. Exploited pricing discrepancies thereby undo

the divergence of market values.

Our data provide support for the MM theorem since average prices are close

to parity, even though some price discrepancies and deviations from the risk-

neutral value persist throughout the experiment. In our perfect-correlation

treatment, we observe that perfect correlation is essential for value indiffer-

ence as we control for variations in correlation. In our control no-correlation

treatment, we consider independent draws of dividends of the two simulta-

neously traded shares. Here, L-shares and U-shares have the same expected

dividend and idiosyncratic risk as in the perfect-correlation treatment, but an

asset swap has risk.

We find a clear treatment effect: we observe a higher level of price discrepan-

cies in the no-correlation treatment. With perfect correlation our measures of

cross-asset price discrepancy, relativef requency of discrepant limitorders, and

deviation from fundamental dividend value indicate smaller deviations from

the theoretical benchmarks than in the no-correlation treatment.4The market

corrects relative mispricing with perfectly correlated returns but not as well

with independent asset returns.

Thus, although potential price discrepancies never disappear in absolute

quantitative terms for the perfect-correlation treatment, our data provide

strong qualitative support for the equilibrium through the comparison of our

treatments. That said, as with evidence observed with experienced subjects in

single-asset market studies (e.g., Haruvy,Lahav, and Noussair (2007), Dufwen-

berg, Lindqvist, and Moore (2005)), the price deviation from fundamental div-

idend values declines in consecutive markets in both treatments. The move-

ment towards the theoretical benchmarks, however, seems to be more rapid in

the perfect-correlation treatment than in the no-correlation treatment, both in

terms of the decrease in price discrepancies and the deviation from fundamen-

tal dividend value. Nevertheless, some potential price discrepancies persist in

both treatments, even with experienced subjects.

We next consider the impact of traders’ acuity, as measured by the cognitive

reflection task (CRT; Frederick (2005)), on the level of price discrepancy. The

literature suggests that smart traders search for and eliminate price discrep-

ancies.5Our measure correlates with the reduction in price discrepancy on the

3In Section II, we show how our design maps into the MM theorem.

4In line with studies that apply a zero discount rate in the Smith, Suchanek, and Williams(1988)

experimental framework, we define the fundamental dividend value as the sum of discounted

expected future dividends.

5See the discussions in Shleifer (2000) and Lamont and Thaler (2003).