Dynamic CAPM under ambiguity—An experimental approach

Accepted Manuscript Dynamic CAPM under ambiguity–An experimental approach Bogdan Negrea, Mihai Toma

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S2214-6350(17)30063-1 https://doi.org/10.1016/j.jbef.2017.09.001 JBEF 121

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Journal of Behavioral and Experimental Finance

Received date : 11 May 2017 Revised date : 26 August 2017 Accepted date : 14 September 2017 Please cite this article as: Negrea B., Toma M., Dynamic CAPM under ambiguity–An experimental approach. Journal of Behavioral and Experimental Finance (2017), https://doi.org/10.1016/j.jbef.2017.09.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Dynamic CAPM under ambiguity – an experimental approach Bogdan NEGREAa,*, Mihai TOMAb

a, b

Money and Banking Department, Faculty of Finance, Insurance, Banks and Capital

Markets, Bucharest University of Economic Studies, Bucharest, Romania *

Corresponding author

Address: Bucharest University of Economic Studies, Mihail Moxa Street, no. 5-7, Bucharest, Romania, Zip code 010961 E-mail: [email protected], [email protected] Tel.: +40-021-3191900 b

Address: Bucharest University of Economic Studies, Mihail Moxa Road, no. 11, Bucharest,

Romania, Zip code 010964

Abstract We develop an experimental financial market using real data in which subjects trade two assets for 30 periods in an ambiguous environment. The main goal is to verify if CAPM holds when subjects have homogenous knowledge about future payoffs given current ambiguous market conditions. We find that (i) CAPM holds in a dynamic market setting when exogenous information on the issuing companies’ states changes over time and when economic conditions are experiencing steady growth, (ii) subjects are mostly influenced by indebtedness and profitability fundamentals, (iii) the number of years of study in financial markets and stress positively influenced their final payoff, (iv) statistically, women obtained lower returns and (v) overconfidence negatively influenced individual payoffs. One novelty of the study consists in the use of real fundamental and macroeconomic variables as exogenous information for participants in generating the price processes, thus simulating an experimental financial market. Dynamic CAPM under ambiguity – an experimental approach 1

Abstract: We develop an experimental financial market using real data in which subjects trade two assets for 30 periods in an ambiguous environment. The main goal is to verify if CAPM holds when subjects have homogenous knowledge about future payoffs given current ambiguous market conditions. We find that (i) CAPM holds in a dynamic market setting when exogenous information on the issuing companies’ states changes over time and when economic conditions are experiencing steady growth, (ii) subjects are mostly influenced by indebtedness and profitability fundamentals, (iii) the number of years of study in financial markets and stress positively influenced their final payoff, (iv) statistically, women obtained lower returns and (v) overconfidence negatively influenced individual payoffs. One novelty of the study consists in the use of real fundamental and macroeconomic variables as exogenous information for participants in generating the price processes, thus simulating an experimental financial market. Keywords: experimental financial market; CAPM; fundamentals; Sharpe ratio; behavioral traits. JEL classification: G10, G11, G12

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1.

Introduction The capital asset pricing model has been a central topic of debate in financial studies

ever since its development in the early 1960s. There has been widespread debate on whether expected returns can be explained in terms of aggregate market risk. Even though simple and elegant, critiques have been brought to the model’s hypotheses, which are not in line with the reality of financial markets. Nonetheless, academic literature has produced experimental and non-experimental studies which have both validated and rejected CAPM’s validity. In this paper, an experimental approach is taken in order to see whether the model holds in a dynamic trading context, by controlling its hypotheses. The main contribution of the study is the validation of CAPM equilibrium by ambiguity-averse subjects when state probabilities of the assets’ payoffs are unknown. The pricing relation holds in tranquil times of steady growth, when uncertainty is low and subjects have homogenous knowledge and expectations of future payoffs. Divergence seems to appear when uncertainty increased. Experimental methods in financial markets studies have significantly contributed to insights on interactions between agents, their inter-temporal preferences, identifying cognitive biases or personality traits which lead to sub-optimal behavior. Unlike traditional econometric analysis of this sort, the experimenter is able to have control over the developed framework. Moreover, he is able to know exactly the number of subjects which form a market, the type and volume of orders and who generated the market activity. Experimentation is hence needed in reaching a deeper understanding of the theory behind the data and can provide researchers with a higher level of confidence in assessing its statistical validity. Research in asset valuation can be particularly difficult, where experimental methods have proven to bring valuable contributions (e.g. market equilibrium, bubble formation etc.). In elaborating experiments, asset pricing models typically break models in two broad categories: static and dynamic asset pricing models. The study of dynamic asset pricing under an experimental framework has focused most notably on analyzing the emergence of bubble formation. Subjects trade in a continuous double auction market setting for a number of n periods and usually receive liquidating dividends at the end of the experiment. Pioneer studies have employed such frameworks, such as those performed by Plott and Agha (1982) or Williams and Smith (1984). The seminal work of Smith et al. (1988) has opened the path for future research on dynamic asset pricing models. Among several important findings, they showed in a laboratory context that market prices differed considerably from their fundamental values and formed bubbles which 3

burst after some time period. The bubbles were formed by inexperienced traders, but tended to reduce in magnitude when traders gained experience. Experimental methods have been used in static asset pricing as well, to verify if markets reach equilibrium as defined by the CAPM or Arrow-Debreu framework. In an experiment, Levy (1997) finds that there is a positive relationship between mean excess return and covariance with the market return. Bossaerts and Plott (2004) have found that in simple static asset markets, prices reach both CAPM and Arrow-Debreu equilibrium, when the probabilities of payoffs of the securities are known. Bossaerts et al. (2007) extend the experiment and build a CAPM +

modelling framework, using novel econometric tests. For

a thorough review of asset pricing in experimental markets, we revert the readers towards Noussair and Tucker (2013) and Nuzzo and Morone (2017). Using field data, CAPM or variations of this asset pricing model have been thoroughly tested and developed in academic literature, of which we only mention a few. Some authors (Brown and Walter, 2013) state that CAPM holds ex-post only when the market is efficient ex-ante, however, it does not hold when the market is inefficient, as the model in itself relates to expectations of investors towards future returns. Guermat (2014) empirically tests the CAPM and build on a two-step procedure in order to assess the efficiency of the market index prior to estimating beta in order to mitigate the issue of inefficiency. For a review of static asset pricing and CAPM equilibrium, we revert the reader towards Bossaerts (2009). Market dynamics are affected by behavioral traits or biases as well. Odean (1998) and Barber and Odean (2001) have shown that overconfidence affects men more than women and that these investors earn lower returns. Chen et al. (2007) find that frequent trading leads to higher returns. Overconfidence differentiated by gender has been studied by Yang and Zhu (2016) as well. They perform an experiment consisting of an asset market with symmetric information and find that overconfident traders are on average better in terms of trading ability and that men are more overconfident than women. Almost all experiments simulating trading have used setups with controlled price patterns. The returns of the securities from the experimental markets either have a known uniform payoff distribution or subjects trade under risk (with known probabilities for assets' states) or uncertainty in making their trading choices. Usually, there is also a dividend payment involved for market participants either associated with a certain probability of occurrence or extracted from a uniform distribution.

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However, it should be worth studying how exogenous fundamental and macroeconomic information drive the behavior of market participants in a simulated experimental market. Even though there are studies which have both validated and rejected CAPM’s validity, an experimental financial market which (i) aims at simulating a real trading context as much as possible, given laboratory constraints, but (ii) at the same time controls the asset pricing’s hypotheses might prove valuable for future studies in this direction. This can be even more stressed out considering the relative importance of distinguishing between risk and uncertainty, with implications in other fields as well, not only financial asset pricing. Furthermore, the possibility of differentiating between times of steady economic growth and crises periods in a controlled setting can shed further insights on subjects’ behavior during such times in experiments. We motivate the relevance of the experiment as follows. Firstly, the experiment permits the simulation of a financial market where the hypotheses of the CAPM can be controlled. The framework we employed was specifically designed to simulate a market with no information asymmetry using real data as information for subjects. By controlling the hypotheses of the pricing model we can test whether and in which conditions CAPM holds. Secondly, departing from the above, we can test whether students used CAPM in their trading decisions by assessing its convergence throughout all periods. In verifying this, we follow the methodology of Bossaerts and Plott (2004) with two modifications: the subjects cannot trade notes (risk-free instruments) and they trade dynamically in ambiguity, as opposed to the experiment of the aforementioned study, in which state probabilities of asset payoffs are known. The model has been treated as if it holds inter-temporally, even though it is a static asset pricing model. Fama (1970) has shown that if preferences of investors are not state-dependent, then the model can be treated as if the investor(s) had a single period utility function. We advocate that even in a more complex setting, participants should track the market portfolio in their trading and CAPM convergence should emerge in times of steady growth, if there exists homogenous knowledge and expectations of market participants, even when the set of information changes from one period to another. Levy (2010) has shown that CAPM cannot be rejected as long as ex-ante experimental parameters are employed in CAPM tests. Thirdly, we are able to verify which behavioral traits of the subjects had an influence on their final payoffs. We posit that, if CAPM holds in a trading context with inexperienced subjects, then theoretical knowledge of portfolio management should positively influence their final payoff. 5

The design we provide can be easily modified in order to study further effects, such as: changing the indicators, the asset’s payoff, dividend payout, the incentive scheme, the number of subjects, the coloring of the information etc. As such, we aim at answering the following research question: can CAPM equilibrium occur under dynamic ambiguous conditions in a market generated by risk-averse inexperienced subjects, what are the fundamentals they took into account when trading and what are the behavioral characteristics that influenced their individual payoffs? The current study is divided as follows: the next section describes the experimental design we employed, the payoff structure and the information provided to the subjects. The third section presents the data analysis and the fourth section provides the obtained results and discusses their implication on the CAPM-type behavior. We provide concluding remarks in the last section.

2.

Experimental design

2.1

Description of the experimental process The experiment was developed and run with students from the Bucharest University

of Economic Studies, Faculty of Finance and Banking. The sample consisted of 19 subjects (10 women), with an average age of 21 years. Most of the students were in their third year of bachelor studies and had two years of studies in financial markets. Descriptive statistics for the whole subject sample are presented in Table 1. Table 1: Subjects descriptive statistics Indicator Payoff Min 2231.19 Mean 2404.38 Median 2351.02 Max 2793.28 Std. dev. 151.46

Age 19.00 20.83 21.00 23.00 0.99

Years of study 2.00 2.33 2.00 4.00 0.77

Experience 1.00 1.06 1.00 2.00 0.24

Note: Columns 3-5 are measured in number of years. Payoff is measured in experimental currency.

We used the Flexemarkets software in developing the experiment given its simplicity, speed and user-friendly interface which could enable subjects to quickly catch on with its characteristics. The experiment is implemented in a dynamic setting using a double auction continuous market framework for 30 periods, each period lasting for 270 seconds (4.5 minutes). The market consists of two securities (A and B), which subjects trade in ambiguity, as they receive real data about the fundamentals of the issuing companies as information. We 6

select several macro variables and fundamental indicators to provide as exogenous information for our subjects. More details are given in sub-section 2.3. Each subject received four units of security A and six units of security B at the beginning of the experiment, as well as 1.024 units of cash to use in trading. Subjects were told that they held bonds worth 100 monetary units, but that they could not modify the bond portfolio holdings or trade the bonds. This is done so they know that the portfolio is remunerated at each point in time with the risk-free rate. Even though this is not controllable, by offering this information, we reinforce the presence of the risk-free rate which needs to be taken into account in their trading. This will be used in section 4. The starting prices for the securities were 106 for A and 100 for B. They were selected to match the values of the real prices of companies A and B corresponding with the first period for which we gathered the fundamentals and macro variables. However, they were rescaled taking as a point of reference the 100 value for B. Any subject willing to buy (sell) the security at the lowest (highest) price may elicit his/her order. When both sides of the transaction “agree” to a certain price, a trade is performed and disappears from the market. All subjects can see all on-going and terminated orders in the market. At the end of each 4.5-minute period, markets are paused for about 5-10 seconds and subjects are asked to write down the holdings from their portfolio. After the 5-10 seconds pause, the next period begins where subjects receive updated information on (i) the fundamentals and (ii) the macroeconomic variables. Before running the actual experiment, we held (i) a training session for the subjects and (ii) a training trading round. The former consisted in providing participating students general information pertaining to the macro variables and fundamentals which were used as information in the experiment. Even though most subjects already had basic knowledge of financial markets and macroeconomics, we wanted to provide the same information before the experiment to all participants in order to create an as homogenous group of subjects as possible. By providing the same knowledge to participating students prior to running the experiment, we verify one of CAPM’s assumptions. After the training session, the subjects traded for seven periods of dummy rounds, in order for them to accommodate with the software. During these rounds, subjects could ask any question as it related to both the information they received and the experimental software. Several questions on the functionality of the software and trading activity were asked by the experimenters so as to verify students’ understanding of the software and of the provided information. 7

2.2 Payoff structure The payoff for each student is determined at the end of the whole 30-period trading experiment. At the beginning of each trading session, subjects can see the one-period ahead dividend which will be paid, but the value of which cannot be used in trading. The dividend structure is not determined stochastically, but it is provided exogenously. The dividend series (at each point in time) represents the actual dividend series from reality for securities A and B. Students need to keep track of dividends they receive at the end of each period and of their portfolio structure. The dividends they gain from holding certain amounts of securities cannot be used within periods, but are stored in order to compute the final payoff for each student at the end of the experiment. As such, the dividend is a martingale, as subjects know at time t its value from t+1. Furthermore, at the end of each period, securities do not expire worthless, but students continue to trade in the next period using the last price of the security from the previous period. Thus, subjects acknowledge each period separately and keep track of their earnings. The dividend which is given as information at time t is "paid" at time t+1. At the end of the experiment, we compute the final payoff for each subject

as

following: where

,

,

∙

∙

∑

(1)

represents the amount of money resulted (won or lost – the balance of the

account) from trading securities A and B throughout all 30 periods, prices of securities A and B at the end of period T, and B respectively at the end of period T and and B) at the end of each period

and

and

represent the

are the number of securities A

represents the total dividend value (from A

2, 30.

Even though CAPM has been developed as static model in which investors only live for two periods, it can be extended to a multi-period context, as per Fama (1970). If we assume a two-period quadratic utility function for investors, we need only replace the utility function with a quadratic value function. This requires an additional assumption in the sense that there are no shifts in the investment opportunity set – which in our case is verified. Therefore, the acquisition of stocks by investors simply implies their taking bets over wealth. The fundamental assumption which actually determines CAPM-type behavior is that marginal utility of wealth is linear in wealth and no other variables. (Cochrane, 2005).

8

As incentive for participating in the experiment, we offered the equivalent of 7 euros (at the then prevailing EUR/RON exchange rate) for subjects as the show-up fee. We considered it to be appropriate, considering the minimum hour pay in Romania of about 2 euros. As per Camerer and Hogarth (1999), higher financial incentives do not affect mean performance, but they do reduce variance of outcomes. In order to induce risk aversion directly related to the tasks at hand, the top 3 students who achieved the highest payoffs were incentivized with the chance of performing a three month internship at Tradeville, one of the top financial companies activating in the financial in Romania. Given that they were bachelor students seeking future employment, we believe to have provided an adequate incentive, considering that it was contingent and directly related to their decisions from the experiment itself and consistent with the activity at hand (Croson, 2005). A similar scheme in a risk measurement experiment has been performed by Ferecatu and Onculer (2016).

2.3 The information provided to subjects We gathered real-market data on twenty of the most liquid issuing companies from the New York Stock Exchange. Data was collected from December 2003 to March 2011 and this was the source of exogenous information for market participants in the experiment. For all companies, we took end of quarter fundamentals and adjusted closing prices. We looked at issue data, profitability, growth potential, cash-flow analysis indicators and per-share data. We selected: the book value, sales value, ROA, Debt-to-Assets and the dividend-per-share. Out of all companies, we chose two for which a common set of fundamentals had significant statistical effects: two of the largest conglomerates from the financial and IT industry, respectively. We will refer to them from now on as securities A and B. Next, we selected six macroeconomic variables: the monetary policy reference interest rate, the consumer confidence index, the PMI index, the surprise index, the 10-year government bond yield and the unemployment rate. The variables were chosen based on several considerations. First, the interest rate, unemployment rate and the 10-year government bond yield are indicators which can act as proxies towards the state of the economy. The consumer confidence index acts as an indicator towards the general consumer sentiment from certain periods, the PMI index acts as a proxy for the production activity of an economy and the surprise index can provide indications towards deviations of the actual and forecasted economic activity. We acknowledge that there are other macroeconomic variables which can influence the price process. However, in order to incorporate macro information within the experiment, 9

we hadd to reducee our choice to a lim mited num mber of varriables andd to includee an as heteroggeneous group of indiccators as poossible as prroxies for various v meaasures of ecconomic conditioons, in ordder to offerr a broad vview of thee economy, while beaaring in mind m two constraiints: limitedd technolog gical resourcces and the fact that stu udents needded to actuaally take into acccount said variables, v th herefore vallidating thee need to minimize theeir number. The list of all fuundamentals and macro oeconomic variables we w chose for the experiiment can be b found in Tablee A.1 in thee appendix. Except for the dividen nd per share, the fundam mental facto ors were given as changes over o the previous perio d, in order for them to relatively eevaluate wh hether or not funndamentals changed upwards u or downward ds. This way, subjectts could deetermine whetherr or not thee issuing co ompany perrformed better (or worse) than thhe previouss period. Based oon this, theey could up pdate their beliefs tow wards futuree companyy performan nce. The macroeconomic vaariables werre given in llevel. Each slide provid ded informaation for thee current period sstate of the economy and a the issuuing compan nies. Studen nts were tolld to think of o slides as end-of-quarter information i n from issuinng companies. All of the t informaation was diisplayed on proggrammed sllides and th heir sequenccing was co ontrolled by y the experiimenters so o that all subjectss could seee the samee informatiion at the same timee. A slide as an exam mple of informaation whichh was given to the subjeects, along with further informatioon on each variable can be ffound in thee appendix in Figure A A.2. The exp periment tim meline at sevveral pointss in time can be ffound in Diagram 1.

Diagram 1. Timeline of the ex xperiment. A All upward changes c of the given inndicators were w presentted in greenn and all do ownward changess in red. Innsignificant variation, w while rare, was given in orange. However, students were exxplicitly infformed thatt colors didd not bear any a financial significaance and they were only used to indicaate mathemaatical variattion over prrevious periiods. Even tthough usin ng colors might bbe thought of o as influen ncing the suubjects in th heir decision ns, we chosee this speciffic setup as we cconsidered it difficult for subjectts to memo orize all numbers from m previous periods, 10

while uunder the strress of tradiing and tryiing to makee profit. This is also duue to ratherr limited technological resouurces on peerforming m market experiments. Fu urthermore, as we are trying t to replicatte a real maarket, colorss aid towardds this end, as such ind dicators aree presented in green or red inn real-life trrading softw ware as welll.

3.

D Data analysiis C Considering that each period lastted for 270 0 seconds in which sstudents co ould see

informaation on issuuing compaanies, we toook the averrage price from f each pperiod to ob btain the numberr of observaations correesponding too the 30 qu uarters whicch representted the info ormation given too subjects. By analyzinng Figure 1, we note thhat the dynaamics of thee real stock prices and the t ones generated by the suubjects in th he experimeent bears lim mited resem mblance in tthe case of security A. The price maniifested an upward u trennd in the firrst part of the t experim ment, follow wed by a slight ccorrection downwards, d , several tim me periodss before thee plummet of 2008. There T is howeveer a slight and interessting effectt - several periods before the crrash of the formed bubble, the price started s to stabilize and to switch trends. t On the t other haand, for seccurity B, the expeerimental prices resem mble the timee dynamics of the real series relatiively well.

D of securities A (left) and d B (right) – real and exxperimentaal Figure 1: Dynamics In this casee, the trend of the real series did not n exhibit such a volaatile boom and a bust type behhavior in tim me and eveen if the pricce of the sto ock manifessted a drop in 2008, it was not as errattic as that of o security A, A which m manifested a much steeeper fall duuring the sam me time period. The correlaation matricces for bothh securities are a found in n Tables A. 2 and A.3 from f the appendiix. We leavve the analy ysis of the ddynamic priice behavio or and of buubble formaation for future rresearch. We plot thhe dynamics of the prrice-to-book k and price-to-sales raatios using the real price seeries and the t experim mental seriees. In the case of security B, tthe resemblance is 11

remarkaable, as cann be seen from Figurre 2. The dynamics d denote d a higgh chance that the subjectss based theiir trading deecisions on the fundam mental inform mation, the correlation of these being vvery high. The T corresponding dynnamics for security s A can c be founnd in Figuree A.1 in the appeendix.

Figure 2: Price-to-Bo ook (left) annd Price-to--Sales (rightt) ratios for security B We furtherr test the impact off the fundaamentals on generateed returns using a multivaariate regression framework, thee results off which aree presentedd in Table 2. The dependeent variablee is given by b the returrns of the experimenta e al price seriies for both h stocks. The inddependent variables v aree the fundam mentals of th he issuing companies. c Table 22: Impact off fundamenttal variabless for securitties A and B Variablle Security A Security S B Constannt 0.0250*** 0.0046** 0 (0.0022) (0.0068) Δ% Boook price (-11) / (0) -0.0585 0.0273* 0 (0.0368) (0.0149) Δ% Salles (-2) / (-1) -0.1011 -0.0221* (0.0756) (0.0109) Δ% RO OA (-2) / (-1) 0.1199*** 0 0.0134*** (0.0029) (0.0411) Δ% Tottal debt to tootal assets (-2) ( / (0) -0.0488*** * 0.0115 0 (0.0167) (0.0244) Dividennd (0) / N.A A. -0.0609*** * N.A N (0.0209) N.A N 60.93% R-squarred 38.48% 3 Adj. R--squared 51.63% 28.23% 2 Prob. F-stat 0.00 0.00 0 Note: Thhe table displaays the resultss of the multivvariate regresssions between n the returns of securities A and B (dependeent variables) and the fund damentals useed in the exp periment (indeependent variiables). The values v in parenthesses after the coefficients denote the llag number (0 signifying g no lags). SSerial correlattion and heteroskeedasticity werre not present in the series oof residuals. Statistical S sign nificance is deenoted by *** *, ** and * at the 11%, 5% and 100% values resspectively. t-sttats are given below estimatted coefficiennts in parentheeses.

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When running the regressions, we specifically chose relative changes of the variables, as subjects were told that the modifications of the fundamentals were the drivers of the companies’ performances. Most of the variables are statistically significant, showing that subjects indeed tracked the dynamics of these variables in making their trading decisions. For both securities, the return on assets indicator exhibits a positive relationship with the returns, as expected. On the other hand, the level of indebtedness negatively affected only security A. The results are interesting considering the small number of inexperienced students which formed the market. Furthermore, we see that profitability one or two periods prior to the current returns affected their dynamics, suggesting that students planned ahead for one or two periods. The obtained causal relationships between fundamentals and returns are in line with financial intuition. This is especially important, considering that the relatively small sample of students only had theoretic knowledge of investing on financial markets and virtually no trading experience. Furthermore, the results denote that students did not trade erratically, but indeed took into account the provided information, albeit only partially. Future replicating experiments can be easily modified in order to reduce the number of variables provided and obtain more robust results.

4.

CAPM-type behavior We continue to verify whether CAPM equilibrium occurred in the experimental

setting we proposed. We review the basics of the capital asset pricing model framework. The model was developed independently by Sharpe (1964), Lintner (1965) and Mossin (1966). In the CAPM world, investors are compensated for the non-diversifiable risk of an aggregate market index. In this sense, investors are rational expected utility maximizers who build portfolios which are mean-variance efficient in the sense of Markowitz (1952). At the same time, the theory behind CAPM states that investors should be risk-averse. Earlier experimental work has shown that this is the case (Bossaerts and Plott, 2004) and furthermore, that market participants are averse to ambiguity even more so than when faced with known probability distributions of asset returns (Bossaerts et al., 2007). Nonetheless, we will see that even though most of these assumptions do not verify in practice and the information provided to subjects is taken from the real-world, the CAPM does hold in our experimental setting. For a review of theoretical and empirical evidence of the capital asset pricing model, please see Fama and French (2004). Formally stated, we write: 13

∙ where

is the retturn on secu urity ,

rate andd

(2)

is the returrn of the market m indexx,

is the risk-free r

is definned as the measure m of ccovariance between thee return of tthe market and that

of securrity , as succh: ,

(3)

The system matic risk is given by thhe covarian nce of the security's exxcess return ns over a risk-free rate with the t excess returns r of a market index over the same risk-ffree rate. Most of thee CAPM asssumptions are verified d: subjects aim to maxximize theirr wealth and plaan for the same identtical periodd, have hom mogenous knowledge k and the market m is frictionless. The market m we have h designned does no ot verify on ne hypothesiis from thee CAPM kets are world, namely thaat markets should be complete. Indeed, in our frameework, mark overly iincomplete,, as there arre

possibble payoff states for eaach securityy and there are only

two seccurities to trrade. However, this is part of the main objecctive: by noot knowing payoffs’ p distribuutions, subjeects trade in n an uncertai ain environm ment. An importaant remark needs to bbe made: subjects s weere not toldd what the market portfoliio was. Eveen though th hey do not have this information i explicitly aand so they y cannot use thee CAPM inn making th heir tradingg decisionss, they do however trrade in the CAPM directioon without knowledg ge of the securities’ market shares. We calculate market capitalization at the end of eacch period, kknowing thaat there are a fixed num mber of secu urities in t the marrket. Figure 3 displays the

coeffi ficients for all a 30 period ds for securiities A and B.

Figuree 3: Beta dy ynamics We note thhat after several periodss, security A bears extrra risk throuughout periiods 4 to 13. Inteerestingly, there t is a raather erraticc behavior in the beta coefficientts right at th he onset and afteer the periodd correspon nding to the financial crisis. Subjects seemed to have maanifested volatilee behaviors towards thee holding o f the securiities during the time-frrame corresponding to perioods 13 to 200. Considerring the chaanges in com mpanies’ fu undamentalss and the do ownturn

14

of the macroeconomic environment, we can interpret that subjects were uncertain towards which asset bears more risk in terms of the aggregate market risk. Subjects did not have any information, other than that of fundamentals and macro variables and even though an advanced finance student should have realized there was a crisis during that period because of deteriorating macro-financial conditions, it is still interesting that their behavior was, on aggregate, altered by the period in question, considering their lack of experience. The time-varying characteristic of

is also consistent

with some empirical papers on CAPM validity. For instance, Abdymomunov and Morley (2011) find that betas vary significantly across changing volatility regimes. The time-varying character of the beta coefficient when financial market volatility is high (i.e. in times of crises) is also in line with Choudhry (2005, 2010) who has shown that during the Asian financial crisis in 1997-1998, beta coefficients varied consistently. This is also in line with Bollerslev et al. (1988), who show using a multivariate GARCH model that implied betas are time-varying. Asset pricing theory suggests that in times of steady growth, where uncertainty is at a minimum and where all investors should have the same expectations towards the oneperiod ahead stock dynamics, CAPM should hold. However, when uncertainty increases and expectations change, CAPM diverges from equilibrium. We will shortly see that the Sharpe ratio approach confirms our statements. As opposed to a real life situation, our subjects were not able to trade the bonds. This is the reason why we introduced the 10-year government yield as exogenous information for subjects. We wanted to see how the implied risk-free rate from the estimated CAPM compares with the actual risk-free rate the students were given as exogenous information. Ideally, the difference between the two rates should tend towards zero. Black (1972) has shown that even if there is no riskless asset and that no riskless borrowing or lending is permitted, the expected return on any risky asset is a linear function of its . Beta is usually estimated using least squares or is determined as per equation 4. It can be seen that: ∙ where By denoting 1

0 and

, ∙

∙

(4)

0.

with , we can estimate: ∙

In this case, we can determine the risk-free rate as being equal to:

15

(5)

(6) In our ccase, we com mpute

fo or both secuurity A and B. Upon esstimating beeta for each h period,

we com mpute the riisk-free ratee in order tto study its dynamics. We hypothhesize that students were abble to track the dynamiics of the 1 0-year goveernment bond yield, ass provided by b us, if the diffference betw ween the riisk-free ratees calculateed using the above foormula and the real bond yiield approacches zero. Apart A from certain dev viations (perriods 4, 21 aand 27), wee indeed see thatt the differeence approaaches zero, the series having h a mean of -0.00031 and a standard s deviatioon of 0.0088. In order to further sstatistically y confirm th hat the twoo risk-free rates r are approxiimately equual, we perfform a boottstrap proceedure and create 1000 samples off and

. We then re-estimate r

,

and

,

, as welll as the risk k-free rate foor each sam mple. We

finally ccompute thhe differencee between tthe implied--CAPM risk k-free rate aand the actu ual riskfree ratee offered ass informatio on to the stuudents. We perform a simple -tesst on the difference time seeries to see if the meaan of the seeries comess from a no ormally dist stributed zerro-mean populattion. After performing p 30 tests of tthis bootstraap procedurre, we note that for all periods, the p-vvalues are above the 5% confiddence limitt and hence, we cannnot reject that the differennce comes from a norrmally distrributed sam mple with zeero mean. T The differeence and results aare displayeed in Figuree 4. This is tthe second finding f supp porting CAPPM converg gence.

Figgure 4: Diffference between real aand implied risk-free raates (upper hhalf) and corrrespondingg 30 time- av verage p-Vaalue from bootstrap b pro ocedure (low wer half) Following Bossaerts B and a Plott (20004), we tak ke our analy ysis a step ffurther in assessing whetherr CAPM coonverges tow wards equillibrium. In CAPM equ uilibrium, thhe market portfolio p Sharpe ratio (Sharrpe, 1964) should tennd towards the maxim mal possiblee Sharpe rattio. The market portfolio is mean-variaance optimaal if and onlly if the marrket’s Sharppe ratio is maximal. m The Sharpee ratio is giv ven by:

16

(7) Taking intoo account th he short-salle constrain nt for securities A and B, we com mpute the maximaal Sharpe ratio r for eacch period aand for eacch correspon nding tradee from with hin each period. Figure 5 diisplays the distance d froom the maxiimal Sharpee ratio and tthe market'ss Sharpe Y-axis) for each e trade th hat occurredd (X-axis). ratio (Y There is a tendency t fo or this differrence to red duce and ten nd towards zero in thee first 12 periods. This is seeen in perio ods 14, 15, 17, 18 as well, w even though t periiod 14 is distanced from thhe others. One O can also o note that during periiods 18-22 (correspondding to yeaar 2008), there is shortage off liquidity: students s weere reluctantt to trade. Upon U the ons nset of the crrisis, the i in line differennce becomes completelly volatile aand the diffference diveerged from zzero. This is with thee estimated beta coefficcients, as w we previously saw.

Figure 5: S Sharpe ratio o differencee In order to statistically y verify thee accuracy of the CAP PM equilibrrium, we peerform a statisticcal test, sim milar to the one o perform med by Bosssaerts and Plott P (20044). We deno ote Δ as the disttance betw ween the market Sharppe ratio an nd the max ximum Shaarpe ratio for f each transacttion at time . We writee: (8) The null hyypothesis iss given by th the existencce of a random walk: C CAPM is veerified if the nulll is rejected. We perforrm three setts of tests: (ii) for the wh hole samplee of differen nces, (ii) for bothh the first and second d halves of the samplee and (iii) given the ddynamic co ontext in which ttrading tookk place, wee perform tthe test for each perio od as well. Even if visually it would sseem that CAPM C did not n hold duuring the fin nancial crisis, for bothh halves, thee null is rejectedd at the 1% confidence level and w we find conv vergence to owards CAPPM. Table 3 reports the resuults. We seee that

has a negative value, mean ning that the differencee tends to reeduce as 17

time paasses. As thee visual rep presentationn of this diffference in tiime seems tto pinpoint towards CAPM deviation in the secon nd half of thhe sample (after the on nset of the ffinancial criisis), we proceedded in perfoorming the same s two sttatistical tests for the seecond sampple as well. We W note similar results - wee find a smaaller value inn the first half h compareed with the second halff. Table 33: Statisticall test resultss Differeence test Paarameter vaalue Wholee sample 0.071 16 First hhalf 0.086 69 Secondd half 0.061 19

p-Valuee 0.00 0.00 0.00

Note: Thhe table reportss the coefficieents and p-Vallues of the diffference regresssion.

Figure 6 plots p the atttraction coeefficient of the differeence for eacch period with w the corresponding probbability of it i being signnificant. We W see that prior p to the financial crrisis, the mediately iincreases – CAPM co onvergence seems to be b faster coefficiient decreasses and imm right beefore the crrisis. The tendency t foor the coeffficient to reeduce after period 17 and the smaller negative values v seen up to periood 25 corresspond to thee crisis periiod. Hence,, CAPM equilibrrium occurrs slower during d thatt time periiod and for half of these perio ods, the coefficiient was nott statistically significannt.

Figure 6: Estimateed coefficien nts (lower hhalf) and staatistical sign nificance (uupper half) This suggeests that CA APM diverrgence seem ms to have manifestedd at the on nset and during the crisis. This relatees directly to the fun ndamentals as well – before the crisis, dynamiics of profittability for both b compaanies were steady, s but started to go a downward path several periods ahhead of the drop in proofits, in parrticular for security A (Figure A.3 in the appendiix). Given the increase in volattility severaal periods before andd during the crisis, predictaable portfolio managem ment was moore difficult. This is the third suppo orting evideence of CAP PM equilibrrium, in linne with the findings of Bosssaerts and Plott (2004 4). We maanage to ob btain similaar results eeven in a different d

18

experimental framework where subjects trade in ambiguity and in which the risk-free instrument cannot be traded. We hence establish that prices converge towards CAPM equilibrium in times of steady growth when uncertainty is at a minimum. This is quite remarkable given our experimental context of ambiguity and dynamic trading. The information we provide is taken from the real-world and we perform no intervention in any of the provided variables. Even though in reality the CAPM assumptions do not hold, most of them hold in our experimental setting and CAPM verifies. CAPM equilibrium occurred because of financial market equilibration made by ambiguity-averse subjects, not because of their explicit trading towards CAPM, as they did not know what the market portfolio was. The findings raise a natural question – what are the characteristics of the sample of subjects who formed the market and who generated the prices and hence how the CAPM equilibrium occurs? The experimental market permits us to collect such data. Table 4 denotes statistics of the subjects according to age, years of study and gender in terms of average payoff. Table 4: Statistics pertaining to subjects’ winnings Category Sub-category Average payoff Age 19 2573.89 20 2359.63 21 2379.57 22 2459.10 23 2338.28 Gender Men 2486.71 Women 2338.51 Years of studies Bachelor’s 2382.32 Master’s 2514.67 Note: Approximately 15.75% percent of participating subjects were educated to a master’s degree.

It appears that men earned more money on average, while the subjects with the most years of schooling were the highest earners. There are no significant effects when it comes to overall age, but it seems that the highest earner was also a first-year subject (the 19 age category). Apart from this outlier, larger earnings seem to be positively correlated with age. We next determine whether or not there are any effects between certain characteristics of the participating subjects and their individual payoffs. At the end of the experiment, we administered questionnaires which lasted for around 45 minutes regarding: demographics, perceived stress and risk stress and the HEXACO personality test. The subjects filled in the questionnaires through Google forms which were automatically sent to the experimenters upon completion. 19

The demographics questionnaire contained basic questions regarding their age, sex, experience in trading and the field of study etc. The subjects also filled in a questionnaire related to risk and stress perception. The questionnaire comprised of: a self-reported risk preference questionnaire as per Dohmen et. al (2005), a perceived stress reactivity scale questionnaire, which measures the perceived stress in everyday life (Engelbrecht et al., 2011), a perceived stress scale (in the past month) questionnaire (Levenstein et al., 1993; Cohen et al., 1983) and they answered the dictator game question. The last section covered the personality traits of market participants, in which they had to answer the questions from the HEXACO personality questionnaire, as per Lee and Ashton, (1992). We also collected an indirect stated measure of overconfidence, by asking subjects to state the number of years they had as trading experience. As such, conditional on the task at hand, we wanted to see how good students thought they were at trading ex-ante. We consider it a viable measure, taking into account their age – at which no valid trading experience could have been gained. Table 5: Impact of behavioral traits on individual payoffs Independent variables Coefficient Constant 8.1158*** (118.56) Gender -0.0869*** (-4.6619) PSRS Score 0.0189*** (3.4038) Overconfidence -0.1385*** (-3.2720) (self-stated) Years of study 0.0238*** (3.3747) Frequent trading -0.3542*** (-5.6189) Age -0.1326*** (-4.1769) Risk attitude 0.0037* (1.8707) R-Squared 77.44% Adj. R-Squared 61.65% Prob. F-Stat 0.00% Note: The table reports an estimated multivariate linear regression between the dependent variable (the natural log of the total payoff of each subject) and the independent variables from the first column. Gender takes the value 1 if the subject is a woman. Statistical significance is denoted by ***, ** and * at the 1%, 5% and 10% values respectively. t-stats are given below estimated coefficients in parentheses. The regression was run with data which correspond to only 18 participants as one subject did not manage to successfully fill the questionnaire at the end of the experiment.

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From all the questionnaires, we report several statistically significant results, which can be found in Table 5. We find that female subjects obtained lower payoffs and that overconfidence (as self-reported) negatively influenced the result at the end of the trading experiment. However, it is the number of years of education in financial markets and the perceived amount of stress in everyday life that positively influenced the final payoff for the subjects. We also calculate another measure of overconfidence – frequent trading. We compute the number of trades a subject executes for each security and divide it over the total number of trades executed by all subjects. We then take the average for both securities in order to calculate the frequent trading variable. As reported by Barber and Odean (2001) and Glaser and Weber (2007) overconfident men tend to earn less in trading, the frequency in trading being regarded as a measure for overconfidence, an empirical financial market fact. It appears that in our experimental context, overconfident traders (measured both directly and indirectly) have been prone to more losses, in line with such empirical evidences, even though women gained less than men. At the same time, it appears that subjects who had a more acute sense for financial risk taking have been positively influenced by such behavior. On the other hand, subjects did not trade as much before and during the financial crisis, as can be seen in Figure A.4 from the Appendix. Therefore, overconfidence did not seem to manifest during the period corresponding with the financial crisis, when CAPM diverged from equilibrium. Daniel et al. (2001) develop a model of equilibrium asset pricing and show that fundamental/price ratios are found to predict high future returns if investors are overconfident. The results we obtain seem to support the analysis we performed throughout the study and our initial prediction – CAPM seems to emerge while subjects who earned more relied on their theoretical knowledge in financial markets. It can be stated that the behavior generated in the experimental market is in line with empirical evidences observed in real life.

5. Conclusions Our experimental setup aimed at verifying whether CAPM equilibrium attains under ambiguity, what are the fundamentals which influenced inexperienced subjects in forming portfolios and what are the behavioral characteristics which influence their payoffs. We first report that subjects tracked profitability and indebtedness indicators in making trading decisions. Second, we show that subjects trade in the CAPM direction and that convergence towards this asset pricing model is reached. Using the Sharpe ratio difference, we statistically 21

find that throughout the whole period, CAPM convergence emerges. The trading period corresponding with the financial crisis determined CAPM to diverge from equilibrium, albeit temporary. This is also seen in the volatile levels of betas for A and B during that timeframe. Third, we find that financial education, as measured in the number of years of studies and the perceived stress scale from day to day life positively influenced individual payoffs, further supporting the CAPM equilibrium findings. Women and overconfident subjects seemed to have been more prone to obtaining lower payoffs, while self-reported risk seeking attitude seem to be an indicator of higher returns. We conclude that, in a dynamic context of ambiguity using fundamentals and macroeconomic variables as information for subjects with no trading experience, when market participants have homogenous knowledge and the same expectations, even if the set of information changes from one period to the other, CAPM holds in tranquil times of steady growth and that temporary divergence exists when the financial crisis emerged, when uncertainty increased and expectations changed.

Acknowledgements: The authors would like to thank Dr. Peter Bossaerts and the team from Flexemarkets for providing the license for the software in carrying out the experiment. More information can be found at www.flexemarkets.com. The authors wish to express their gratitude towards Tradeville Romania (most notably Ovidiu Dumitrescu) for their support in providing the 3 internships for the students. The authors would also like to thank Virgil Damian, Victor Dragotă, Matei Kubinschi and Alexie Alupoaiei for insightful comments. Mihai Toma also wishes to thank Smarandita Ceccato from the Heidelberg Summer School in Neuroeconomics for the insightful knowledge transfer on psychological and stress related topics. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Appendix Table A.1: List of fundamentals and macroeconomic variables provided to subjects Reference interest rate (monetary policy) Book value of asset (Δ%) PMI index Sales of issuing company (Δ%) Unemployment rate ROA (Δ%) Surprise index Debt-to-Assets (Δ%) Dividend per share 10-year government bond yield Table A.2: Correlations of Price-to-Book and Price-to-Sales ratios and price series for A Price A Price A P/B P/B P/S P/S reality experiment reality experiment reality experiment Price A 1.0000 reality Price A 0.4929 1.0000 experiment P/B 0.3787 -0.3600 1.0000 Reality P/B -0.5102 -0.7760 0.5882 1.0000 Experiment P/S -0.1869 -0.1719 -0.0126 0.2553 1.000 reality P/S -0.7488 -0.6173 -0.0172 0.7008 0.7174 1.0000 experiment Table A.3: Correlations of Price-to-Book and Price-to-Sales ratios and price series for B Price B Price B P/B P/B P/S P/S reality experiment reality experiment reality experiment Price B 1.0000 reality Price B 0.8580 1.0000 experiment P/B 0.6545 0.7174 1.0000 reality P/B 0.2140 0.4489 0.8664 1.0000 experiment P/S 0.7515 0.4124 0.3123 -0.1504 1.000 reality P/S 0.6398 0.7946 0.4792 0.2397 0.4903 1.0000 experiment

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Figure A.1: Price-to-B Book (left) aand Price-to o-Sales (righ ht) ratios forr security A

Figuree A.2: Relaative changees of ROA aand Debt-to-Assets for securities A (up) and B (low)

Figure A.3: Numb ber of tradess for securitties A and B for all periiods (x-Axiis)

27