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A test of the Modigliani-Miller invariance

theorem and arbitrage in experimental asset


Gary Charness and Tibor Neugebauer

A test of the Modigliani-Miller invariance theorem

and arbitrage in experimental asset markets

Gary Charnessa & Tibor Neugebauerb


b. University of Luxembourg

July 4, 2015

Abstract: Modigliani and Miller (1958) show that a repackaging of asset return streams to equity

and debt has no impact on the total market value of the firm if pricing is arbitrage-free. We test the empirical validity of this invariance theorem in experimental asset markets with simultaneous trading in two shares of perfectly correlated returns. Our data support 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, and we find that the law of one price is violated in this case. Discrepancies shrink in consecutive markets, but seem to persist even with experienced traders. In markets where overall trader acuity is high, assets trade closer to parity.

Keywords: Modigliani-Miller theorem, asset market, twin shares, experiment, limits of arbitrage, perfect correlation, experience, cognitive reflection test, risk aversion JEL Codes: C92, G12

1. Introduction In their seminal paper, Modigliani and Miller (1958, 1963) showed mathematically that the market value of the firm is invariant to the firm’s leverage; different packaging of contractual claims on the firm’s asset returns does not impact 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; if two assets, one leveraged and one unleveraged, represent claims on the same cash flow, any arising market discrepancies are arbitraged away by homemade (un-)leveraging.

But due to its assumption of perfect capital markets and the no-limits-to-arbitrage condition (requiring perfect positive correlation of asset returns), the MM theorem has not been tested in a satisfactory manner on real-world market data. Thus, its empirical significance has been unclear. 1 Nevertheless, such a test is feasible in the laboratory, and providing an empirical test of the MM theorem is a particular purpose of this laboratory study. Since perfect return correlation is rare in naturally-occurring equities, we also check how limits of arbitrage affect the empirical validity of the MM theorem with regards to cross-asset pricing. In particular, we address the question of whether a perfect positive correlation between asset returns is necessary for the empirical validity of value invariance or if the same expected (rather than identical) future return 1 The perfect-capital-markets assumption requires among other things that no taxes and transaction fees are levied, and that the same interest rate applies for everyone. Lamont and Thaler (2003a) present several real-world examples where the law of one price is violated. They argue that these violations result from limits of arbitrage. There was an early objection concerning the applicability of value invariance in relation to the variation of payout policy.

Modigliani and Miller (1959) replied to this objection by stating that the dividend policy is irrelevant for the value of the company. However, it is now well-accepted that dividends impact empirical valuations (for a recent discussion of the dividend puzzle, see DeAngelo and DeAngelo 2006). The dividend-irrelevance theorem was thus empirically rejected and is considered as being of theoretical interest only. Still, the value-invariance theorem and its proof remain well-accepted in the profession even without an empirical test. It is noteworthy that the put-call-parity theorem (which is conceptually similar to value invariance, as it makes use of the idea of a self-financing replicating portfolio) finds some support with real-world data (Stoll 1969).

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price to prevail.

Our design follows the standard line of experimental asset markets research of Smith, Suchanek and Williams (1988), featuring multi-period cash flows, zero interest rates, and a repetition of markets with experienced subjects. 2 However, in contrast to the standard, singleasset market approach of Smith et al. and in line with MM, we have simultaneous trading taking place in two shares of the same “risk class”. These twin shares, which we call the A-share and the B-share, are claims on the same underlying uncertain future cash flows. So, returns of the Ashare and the B-share are perfectly correlated and any price discrepancies that might arise can be arbitraged away at no risk. (In a second treatment where returns of the A-share and the B-share are uncorrelated, we study the impact of limits to arbitrage). However, the stream to shareholders of A-shares and B-shares differs by a constant amount, i.e., the synthetic value of debt as we discuss below. Owed to our implementation with zero interest rates, the A-share and B-share can represent accounting “leveraged” and “unleveraged “equity streams. By comparing the market prices of shares, we thus present a very simple test of the MM theorem. 3 At any point in time when the price deviates from parity, in other words if the difference between the A-share and the B-share is not the same as the synthetic debt value, each market participant can exploit the price discrepancy. Since short-selling and borrowing is costless a trader can make a riskless arbitrage gain by homemade leveraging or unleveraging. Exploited pricing discrepancies thereby undo the divergence of market values.

2 See Palan (2013) for a recent literature survey. The literature is mainly concerned with the measuring of mispricing in the single asset market. The conclusion is that confusion of subjects is a main source of the price deviations from fundamentals in the laboratory (e.g., Kirchler et al. 2012). When assets are simultaneously traded in two markets, mispricing seems to be lower than in the single asset market (Ackert et al 2009, Chan, Lei and Veseley 2013).

3 We show in Section 3 how our design matches the MM theorem.

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though some price discrepancies and deviations from the risk-neutral value seem to persist throughout the experiment. We notice that perfect correlation is essential for value indifference as we control for variations in correlation. Besides the perfect-correlation treatment with twin shares we consider independent draws of dividends of the two simultaneously traded shares in our control no-correlation treatment. Here, A-share and B-share have the same expected dividend and idiosyncratic risk as in the perfect-correlation treatment, but there are limits to arbitrage since an asset swap has risk. We find a clear treatment effect: comparing pricing across treatments, the (leveraged) A-share is less highly priced than the (all-equity) B-share in most of the markets of our no-correlation treatment, suggesting a risk premium.

We also observe a higher level of price discrepancies in the no-correlation treatment.

With perfect correlation our measures of cross-asset price discrepancy and deviation from fundamental value indicate smaller deviations from the theoretical benchmarks than in the nocorrelation treatment. Hence, although an arbitrage-free equilibrium cannot be supported in absolute quantitative terms for the perfect-correlation treatment, our data provide rather 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; Dufwenberg, Lindqvist, and Moore 2005), the price deviation from fundamental values declines in consecutive markets in both treatments. The movement towards the theoretical benchmarks, nonetheless, seems to be more rapid in the perfect-correlation treatment than in the no-correlation treatment, both in decline of price discrepancies and in deviation from fundamental value. Nevertheless, some potential price discrepancies persist in

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We investigate 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 and eliminate price discrepancies. 4 Our measure correlates with the reduction in price discrepancy on the overall sample. While there are some price discrepancies in markets with overall high trader aptitude, these are substantially less common and smaller.

More generally our study contributes to the modest experimental literature that tries to evaluate the market’s ability to reduce or eliminate arbitrage opportunities. 5 The observation of persistence in price discrepancies confirms earlier empirical results. O’Brien and Srivastava (1993) replicate portfolios of options, stocks and cash in a multiple-asset experimental market with two stages and information asymmetries. The authors report that if the information asymmetry cannot be resolved, price discrepancies frequently persist. Froot and Daborah (1999) study cases with frictions of twin shares that are traded in different real world exchanges; they report persistent deviations from parity in pricing, creating limited potential for arbitrage since significant risks remain. 6 Lamont and Thaler (2003b) report a related result with limits to arbitrage, finding that the market value of the sum of the parts in corporate carve-outs deviates significantly from the market value of the entire company (see also Gromb and Vayanos 2010).

Oliven and Rietz (2004) investigate the data of the 1992 IOWA presidential election market (IEM), a large-scale experiment conducted for several months on the Internet. Arbitrage opportunities in this market were quite easy to spot; if the value of the market portfolio deviated 4 See the discussions in Shleifer (2000) and Lamont and Thaler (2003a).

5 See the surveys in Cadsby and Maynes (1998), and Sunder (1995).

6 For instance, mineral oil companies Royal Dutch and Shell share their joint future cash flows at a ratio 3:2. Price discrepancies arise as their shares usually do not trade at this 3:2 parity. Limits to arbitrage arise from exchange rate risks as shares trade on different exchanges and from margin risks due to the exposure to market volatility.

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issue price. Oliven and Rietz report a substantial number of price discrepancies, but find that these were quickly driven out. Rietz (2005) reports on a laboratory prediction market experiment with state-contingent claims. Similarly to the IEM, arbitrage opportunities were easily spotted, but trading was over 100 minutes rather than 100 days. Rietz concludes that this market is prone to violate the no-arbitrage requirement. However, if (as in one treatment) the experimenter automatically eliminates each price discrepancy, this automatic arbitrager was involved in most trades in the experiment. Rockenbach and Abbink (2006) report that, even after hours of experience, both students and professional traders left arbitrage opportunities unexploited in an individual investment-allocation task of cash to options, bonds and stock.

To the best of our knowledge, Levati, Qiu, and Mahagaonkar (2012) propose the only other available experimental study to test the MM theorem. Their design forecloses any arbitrage possibility or homemade leveraging and unleveraging. 7 Levati et al. examine evaluations for eight independent lotteries with varying degree of risks in a sequence of experimental single-asset call auction markets, where the risks represent different levels of company leverage. In line with our results obtained in the no-correlation treatment, their results indicate a risk premium on leveraged equity capital. In contrast to our perfect-correlation treatment, the market data in Levati et al. show no support for value invariance. The authors acknowledge the foreclosure of any arbitrage possibility as a potential reason for this result.

We provide evidence regarding how limits to arbitrage impact value invariance. Our main contribution is that we are able to empirically validate value invariance under perfect correlation. The observation of a treatment effect is also an important contribution of our paper, 7 Stiglitz (1969) proves MM value invariance within a general equilibrium approach, without explicit arbitrage assumptions.

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correlation to no correlation. Finally, we observe that high trader acuity significantly reduces the price discrepancy in the market and shares trade closer to fundamentals.

The remainder of the paper is organized as follows. In Section 2 we explain the experimental design. In section 3 we discuss the MM theorem in light of our design, and in Section 4 we present our measures of price discrepancies and hypotheses. Our experimental results are presented in Section 5 and we conclude the paper in Section 6.

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Following Smith et al (1988), subjects can buy and sell multi-period lived assets in continuous double auction markets. The assets involve claims to a stochastic dividend stream over a lifespan of ten periods, = 10, after which these assets have no further value. The instructions can be found in the Appendix.

Trading occurs in two asset classes named A-shares and B-shares. We follow the Smith et al. (1988) design, where the dividend paid on an A-share is independently drawn {0, 8, 28 or 60 cents} with equal probability at the end of every period. The possible dividends paid on the B-share are 24 cents higher, so that the expected dividends per period are 24 cents on A-shares and 48 cents on B-shares. The interest rate is zero and thus the discounted sum of expected dividends or fundamental equity value of A-shares and B-shares are initially 240 and 480 cents and decrease by 24 and 48 cents per period, respectively.

Our treatment variation between subjects is the correlation between the dividends on Ashares and B-shares. In the perfect-correlation treatment, the B-share pays exactly 24 cents more in each period than does the A-share. In the no-correlation treatment the dividend on the B-share is independently drawn {24, 32, 52, 84 cents} with equal probability. Our treatment variation

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