RMSc: Credit markets, an experimental game

The article “Overconfidence and risk seeking in credit markets: An experimental game” is now available online at Review of Managerial Science (JCR, impact factor 0.345).

This is the first article to be published of a series of three articles, all of them being a result of my doctoral research, which have been recently accepted for publication:

Peón, D., M. Antelo and A. Calvo (2015), A dynamic behavioral model of the credit boom, Journal of Economic Issues 49(4), forthcoming. DOI: 10.2753/JEI0021-362449040X

Peón, D., M. Antelo and A. Calvo (2015), Overconfidence and risk seeking in credit markets: An experimental game, Review of Managerial Science, forthcoming, DOI: 10.1007/s11846-015-0166-8

Peón, D., A. Calvo and M. Antelo (2015), On informational efficiency of the banking sector: A behavioral model of the credit boom, Studies in Economics and Finance 32(2), forthcoming. DOI: 10.1108/SEF-04-2013-0050

Dr. Peón

Alá van catro anos da miña vida…

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photo by pernasfrouxas (obrigado!)

Tentar agradecer nunhas breves liñas a todas as persoas e institucións que, durante os máis de catro anos de desenvolvemento e elaboración desta tese doutoral, prestaron a súa colaboración desinteresada ou influíron nos meus pensamentos e coñecementos sintetizados na mesma, sería de todo inacadable. Vaia o meu recoñecemento e agradecemento por tanto a todos vós, profesores, persoal e alumnos da FEE pola vosa axuda, e en particular a todos os compañeiros do Departamento de Economía Financeira e Contabilidade.

Quixera agradecer persoalmente a aqueles que realizaron achegas de moita valía na elaboración dos artigos e publicacións que resultaron desta tese: os compañeiros Ángel Fernández, Cristina Anido, Emma Iglesias, Fernando de Llano, Flora Muíño, José A. Novo, José M. Seijas, Manuel Gómez, Marcos Vizcaíno, Paolo Rungo e Rafael Gómez, así como a Andrea Ceschi, Javier Iglesias, Juan Vilar, Jose A. Vilar, Manuel F. Grela, Tomasz Michalski, revisores anónimos e editores dos diversos journals. O meu agradecemento especial a Enrico Cervellati e Jorge Rodriguez pola súa orientación. Colaboraron moi especialmente na elaboración dalgunhas partes da tese os compañeiros Paulino Martínez no deseño da aplicación informática e Xosé M. Filgueira en axuda técnica. Por último, agracecer a todos e cada un dos 126 alumnos participantes no experimento a súa participación.

Expreso finalmente a miña gratitude a todos aqueles os que, sen a súa colaboración, esta tese nunca tería sido unha realidade. Ao Grupo BBVA por facilitarme a miña dedicación á tese durante catro anos. Ao Departamento de Economía Financeira e Contabilidade da UDC por todas as facilidades para o desempeño das miñas actividades docentes e de investigación. A miña enorme gratitude e recoñecemento aos meus directores de tese, Dr. Manel Antelo e Dr. Anxo Calvo, pola súa sabedoría, orientación, e apoio en todo momento. Tivestes moita paciencia…

E moi especialmente a meus pais e irmans, e a María, a quen lle debo todo o seu apoio estes anos, a paciencia e o ánimo nas interminables horas e preocupacións que deu de si este traballo, e por sacar adiante ás nosas xoias, Anxo e Pablo. Quérovos.

Defensa Tese Doutoramento

E chegou o día.

O vindeiro 16 de xaneiro de 2015 terá lugar o meu acto de Defensa da Tese de Doutoramento Behavioral Microfoundations of Retail Credit Markets: A Theoretical and Experimental Approximation, depositada públicamente o pasado mes de novembro.

O Tribunal que avaliará a miña Tese está composto polos seguintes Profesores Doutores:

PRESIDENTE: ANDRÉS ARAÚJO DE LA MATA, Universidad del País Vasco – EHU

VOGAL 1ª: IRENE COMEIG RAMÍREZ, Universitat de Valencia

VOGAL 2º: IVÁN BARREDA TARRAZONA, Universitat Jaume I

VOGAL 3º: LUIS ALBERTO OTERO GONZÁLEZ, Universidade de Santiago de Compostela

SECRETARIA: SUSANA IGLESIAS ANTELO, Universidade da Coruña

A hora e lugar do evento será 16 de xaneiro ás 12:00 horas no Salón de Graos da Facultade de Economía e Empresa da UDC.

Estades tod@s convidad@s.

Experimental research (4) – PT (theory & results)

Prospect theory, PT, is the best known descriptive decision theory. Kahneman and Tversky (1979) proved that, when making decisions in a context of risk or uncertainty, most individuals (i) show preferences that depend on gains and losses with respect to a certain reference point, and (ii) form beliefs that do not correspond to the statistical probabilities (their perception of the risks associated with a decision may be biased). The combination of these properties implies a fourfold pattern of risk attitudes that is confirmed by experimental evidence: risk aversion for gains and risk seeking for losses of moderate to high probability; risk seeking for gains and risk aversion for losses of low probability.

We devised our tests to elicit the parameters of two classic specifications for PT. First, the (piecewise) power function by Tversky and Kahneman (1992), were α+ measures risk profile for gains, α measures risk profile for losses (aversion to a sure loss) and β measures loss aversion. Second, the Prelec-I (Prelec, 1998) weighting function, where γ+ measures the distortion of probabilities in the positive domain and γ does the same for losses.

The methodology we use for parameter estimation is based on the elicitation of certainty equivalents of prospects with just two outcomes. Following Abdellaoui et al. (2008), the elicitation method consists of three stages, with fifteen questions in total: six questions involving only positive prospects (i.e., a chance to win some positive quantity or zero) to calibrate α+ and γ+, six questions for negative prospects to calibrate α and γ, and three questions regarding the acceptability of mixed prospects, in order to estimate β. Figure 1 shows one of the six iterations participants had to answer involving positive domain.

FIGURE 1 – A sample question with positive prospects

In every iteration participants had to choose between a positive prospect (left) and a series of sure positive outcomes (right). To control for response errors we repeated the one outcome at the end of each trial. The certainty equivalent of a prospect was then estimated by the midpoint between the lowest accepted value and the highest rejected value. This procedure allows for the cash equivalent to be derived from observed choices, rather than assessed by the subject.

Participants in the experiment completed the fifteen questions in about 20 minutes and there were no relevant incidents in any of the five sessions. Results evidence our tests resulted largely satisfactory to replicate the main findings of prospect theory. They reiterate the classic evidence of concavity for gains, while risk seeking in the negative domain seems to be more acute. The percentage of individuals with alpha measures below one are 59.5% and 93.7%. We also observe a significant degree of probability weighting in both domains, with distortion being higher in the negative side. Finally, beta estimations are in consonance with classic results in the literature. The percentage of individuals with beta measures above two are 73.0%.

Figure 2 plots the risk attitudes of the average (idealized) participant.

FIGURE 2 – Risk attitudes of the average participant

The fourfold pattern of risk attitudes predicts people tend to be risk seeking for gains of low probability (1% and 5% in our test) and losses of medium and high probability, while we tend to be risk averse for gains of medium and high probability and losses of low probability. The pattern is clearly observable for the average respondent, with the nuance of an about risk neutrality for gains of medium probability.

Finally, we determine the validity of participants’ responses based on two kinds of errors: iteration errors (the reliability of the iterative questions we asked to control for response errors) and fitting errors (the errors obtained in the non-linear regressions for parameter estimation). Results were highly satisfactory in both instances: only 5.6% of responses were contradictory (94.4% reliability), while 80% and 65% of the individual regressions had a coefficient R2 > 90% in the positive and negative domain, respectively.

Hypothesis testing

Results on overconfidence and prospect theory were tested against several priors (gender, age, education, working experience and skills in finance) using several methodological techniques (correlation, regression, anova and factorial analyses). We found these significant (p < 0.05) results:

· Education increases loss aversion

· Women are more overconfident than men in terms of overprecision

· Women are more risk seeking in the positive and negative domains

· Experience reduces objectivity in terms of estimation of self-performance

· Skills in finance increases objectivity reducing probability distortion

· Skills in finance reduces risk aversion

· Overestimation and overplacement come together (E and P correlated)

· Risk seeking comes together in both domains (alpha+ and alpha-)

· Distortion of probabilities come together in both domains (gamma+ and gamma-)

· Loss aversion and risk aversion in the negative domain come together as well

· Regarding the relationship between overconfidence and PT parameters, we find only low statistical evidence (p < 0.1) that more aggressive profiles for losses (alpha and γ) are correlated with lower levels of overconfidence (E and P).

Experimental research (3) – Overconfidence (results)

This post is devoted to summarize some results obtained in the two tests of overconfidence explained in the previous post: a set of trivia tests devised to estimate individual measures of overestimation (E) and overplacement (P), and a series of questions on interval estimates to obtain an indicator of overprecision (M).

Trivia tests on overestimation and overplacement

Participants completed the four trivia in about 15 minutes, instructions included, and there were no incidents in any of the five sessions. The average respondent overestimated her performance in the trivia by 2.9 right answers (out of 40 questions in total) and the bias was persistent in both easy and hard tests. Whereas, the average respondent considered herself below average by -2.7 correct answers, with the bias being mostly attributable to an underplacement in hard tasks. Table 1 summarizes average data in the experiment.

TABLE 1 – Overestimation and overplacement

We also observe a strong correlation between both variables E and P. That is, participants that exhibited the highest overestimation tend to consider themselves above average (or, at least, featured a lower underplacement) and vice versa.

Finally, the trivia tests were devised to control for the hard – easy effect. Results were the expected for hard tests (overplacement reduces from -2.4 in hard tests to about zero in easy ones) and suffice for overestimation, which does not increase (suggesting a general bias towards overestimation in our sample). Figure 1 helps to appreciate the effect more clearly.

FIGURE 1 – The hard – easy effect

 

However, things would have been more evident if we did not fail to propose a pair of easy tests that were as easy as we expected. As we may see in Table 1 above, trivia tests T2 and T3 had average (median) correct answers of 2.29 (2.0) and 2.75 (3.0) out of 10 questions (with correct answers attributable only to good luck implying a coefficient of 2.0). In trivia tests T1 and T4, expected to yield correct answers of 7.0 to 8.0 on average, respondents only hit the right answer 5.4 (5.0) and 5.58 (6.0) out of 10 questions on average (median). This would represent a couple of tests of a medium –rather than easy- difficulty for respondents.

Test on confidence intervals

Participants completed the six questions on confidence intervals in about 6 to 8 minutes, instructions included. Results show a vast tendency towards overprecision, but we are concerned about the reliability of the estimations obtained at the individual level.

First, judges were significantly overconfident. Aggregate results show a strong tendency to overprecision: the 80% confidence intervals contained the correct answer only 38.3% of the time. As expected, the lowest degree of overprecision corresponds to the domain where participants could draw on personal experience (time to walk). However, they were still overconfident: 80% intervals hit the right answer 62.0% of the time. Using M ratios overprecision becomes even more prevalent: more than 90% of the respondents exhibit this bias. Table 2 summarizes the results.

TABLE 2 – Overprecision

Although results on aggregate are consistent with empirical literature, we are concerned about the reliability of the estimations obtained at the individual level. First, there is evidence that many participants did not fully understand the instructions. We had several incidents: a respondent that did not complete all three answers per question, responses where minimum and maximum boundaries were swapped, where answers were provided in a different order than required, or where the median estimation was identical to any of the boundaries.

Second, individual estimations of ratio M are highly variable depending on the refinement method to estimate M and whether indicators are estimated as the median or the average of the ratios across domains. In particular, following Soll and Klayman (2004) we compared three alternative refinement methods (the option-by-default M, estimator M2 where MAD assumes a symmetric distribution, and a third one that assumes normal distribution), and for each of them we computed mean and median ratios. Results evidence indicators are sensible to the estimation method.

Why this happened? Basically, tests were too simple. When only having two questions per domain, providing an answer to a single question that is close to the true response strongly affects the eventual estimation of M. In future research, having more questions per domain will be essential, but with the restriction of devising a test that is not highly time-consuming for a single indicator.

Experimental research (2) – Overconfidence (theory)

The prevalence of overconfidence, i.e., the human tendency to overestimate our own skills and predictions for success, is a classic in the behavioral literature. Experimental evidence confirmed the role of overconfidence in areas as diverse as financial markets, health, driving, insurance markets, job search or consumer behavior. Many anomalies in financial markets have also been suggested to be a consequence of investor overconfidence, like excessive volatility, return predictability, excessive trading, under-diversification, etc. Finally, research is also vast regarding managerial overconfidence. Executives appear to be particularly prone to display overconfidence, and its effects include literature on mergers and acquisitions and high rates of business failure, among others.

However, when we delve into the concept of overconfidence, things are more complex. Moore and Healy (2008) claim this bias had been studied in inconsistent ways. They identify three different measures of overconfidence that have been confounded in the literature before. In particular, people may exhibit overconfidence: (1) in estimating their own performance (‘overestimation’ E); (2) in estimating their own performance relative to others (‘overplacement’ P); and (3) having an excessive precision to estimate future uncertainty (‘overprecision’ M). Moore and Healy’s model predicts overprecision is systematic, overestimation increases with task difficulty and overplacement decreases with it. The latter findings explain the previously observed hard-easy effect: on easy tasks, people underestimate their performance but overplace themselves compared to others; hard tasks, instead, produce overestimation and underplacement.

In order to avoid confusing overestimation and overprecision, we study overestimation by measuring perceptions across a set of items, whereas overprecision is analyzed through a series of questions on interval estimates. In order to elicit parameters E and P, participants were required to complete a set of 4 trivia with 10 questions each one. In order to account for the hard-easy effect, two quizzes should be easy and two of hard difficulty. In each quiz, for each item participants have to mark the correct answer. Then, when they finish a quiz, they are required to estimate their own scores, as well as the score of a randomly selected previous participant, (RSPP).[1] They repeat the same process for all the 4 rounds.

Overestimation (E) is calculated substracting a participant’s actual score in each of the 4 trivia from his or her reported expected score and summing all 4 results. A measure E > 0 means the respondent exhibits overestimation, while E < 0 means underestimation. The hard-easy effect may be tested if similar estimations are calculated separately for the hard and easy tasks.

Overplacement (P) is calculated taking into account whether a participant is really better than others. For each quiz we compute (E[Xi] – E[Xj]) – (xi – xj) –where E[Xi] is her belief about her expected performance in a particular trivia, E[Xj] is her belief about the expected performance of the RSPP, and xi and xj measure the actual scores of the individual and the RSPP- and then sum all 4 results. A measure P > 0 means the judge exhibits overplacement and P < 0 means underplacement. Again, the hard-easy effect may be tested computing similar estimations separately for the hard and easy tasks.

In order to elicit parameter M, participants were presented a series of 6 questions on 3 domains (device inventions, mortality rates and time walking between two places). For each question they were asked to specify a 3-point estimate (median, 10% fractile and 90% fractile), so we have low and high boundaries for an 80% confidence interval. Soll and Klayman (2004) show overconfidence in interval estimates may result from variability of interval widths. Hence, in order to disentangle variability and true overprecision, they define the ratio M = MEAD/MAD, being MEAD the mean of the expected absolute deviations implied by each pair of fractiles a subject gives, and MAD the observed mean absolute deviation. Overprecision (M) is calculated by having an Mi estimation per domain, and then computing M either as a median (Mmed) or average (Mavg) across the 3 domains. Here M = 1 implies perfect calibration and M < 1 overprecision, with the higher overprecision the lower M is.

In a subsequent post we will provide the results of the experiment.

[1] In our experiment participants were required to estimate “the average score of other students here today and in similar sessions with students of this University”.

References

Moore, D. A. and P. J. Healy (2008), The trouble with overconfidence, Psychological Review 115(2), 502–517.

Soll, J.B. and J. Klayman (2004), Overconfidence in interval estimates, Journal of Experimental Psychology: Learning, Memory and Cognition 30(2), 299-314.

Experimental research (1) – Behavioral microfoundations of RCM

Behavioral economics and its related field, behavioral finance (BF), has been able to explain a wide array of anomalies, observed phenomena that mainstream economics is not able to explain. This field, based in insights of other social areas like psychology or sociology, has succeeded so much to improve our understanding of empirical data and real behavior of market participants (particularly in financial markets), that BF itself is becoming mainstream today. An evidence for that are the recent Nobel prizes by Kahneman (prospect theory) and Smith (experimental economics) in 2002, and Robert Shiller (asset pricing and behavioral finance) in 2013.

The main objective of my PhD investigation is to analyze the behavioral microfoundations of retail credit markets. Most behaviorist researchers come from the US where market-based financial systems move the economy. However, in Europe (and Eurozone in particular) most financial operations come through the banking system. The financial crisis of 2008-9 was, at least in Europe, mostly a result of a credit boom fostered by the banking industry. The classic explanations for this misbehavior (with which I agree) are moral hazard, the effect of incentives and a deficient regulation. In my PhD investigation I want to go further: analyzing the effects that behavioral biases of participants in the industry (CEOs, employees, authorities…) could have over credit policies implemented. In particular, whether just behavioral biases could be able to explain a credit boom -though we agree the alternative explanations would be still relevant.

For that purpose, I have already developed a model of banking competition (here a brief description) where the only presence of a biased bank (biased in terms of excessive optimism and/or overconfidence) is a sufficient condition for a bubble to be generated. The dynamic extension of this model predicts pessimism is not as pervasive as excessive optimism (i.e., financial crises are seeded during good times, when overconfident agents make too risky decisions, rather than during recessions) and that low-quality niche markets are more exposed to potential pervasive effects of bounded rationality. Both results of the model are validated by empiric observation.

The second section of the thesis is devoted to an experimental research. In particular, the purpose is to analyze the behavioral profile of participants in the experiment according to two fields: Prospect theory (theory and tests by Tversky and Kahneman, 1992; tests by Abdellaoui et al., 2008) and Overconfidence (theory and tests by Moore and Healy, 2008; tests by Soll and Klayman, 2004). Then, once participants have been described in terms of their risk profile (prospect theory) and different measures of overconfidence, we test the effects that different PT and OC profiles might have had over the policies implemented by the same participants in a strategy game.

The strategy game they played consists of an experimental simulation of a retail credit market. The basics of the game are as follows. Each participant runs a bank that grants credit to costumers. They play an individual, multiperiod game (same information but no interaction) with the purpose of setting a strategy defined as “price and volume of credit granted” to several costumers, given information available. Information about economic perspectives and quality of the new customer is updated every period.

The goal for participants in the experiment was to implement the best strategy (in terms of profit maximization). The winner of each experimental session (5 in total) was granted a prize of 60 eur. The goal of the experimenter, instead, was to analyze their decisions in a context of uncertainty and risk, and determine whether their profiles (in terms of PT and OC) are able to explain some decisions they made in terms of three types of indicators (seven indicators in total, which measure different aspects of prize, volume and quality of credit).

In subsequent and separate posts we will describe some of the basic results we obtained in terms of priors, risk profile and overconfidence of respondents, as well as in terms of the credit policies they implemented in the game.