David PeónWeb Personal


The EMH struggle



While I was working on the conference we gave yesterday about the Nobel Prize in Economics 2013 awarded to Fama, Shiller and Hansen, I came up with an idea that, to the best of my knowledge, has not been highlighted before. In short, the EMH as it is interpreted today faces a conflict to refute simultaneously two of the most relevant concepts in the behaviorist literature: the excess volatility (Shiller 1981) and the limits of arbitrage (Shleifer and Vishny 1997).


The original EMH interpretation (Fama 1970) did not account for investors' risk appetite. Prices would reflect fundamentals, and a 'sufficient number' of rational arbitrageus that correctly interpret those fundamentals ensure that possible price deviations from rationality are removed. Two challenges to the opposite view, one by behaviorists, other by rationalists, would follow. First, Shiller (1981) went to highlight markets are too volatile to be justified only by fundamentals. After some debate, rationalists responded (e.g., Fama-French 1989) arguing that volatility and some evidence of return predictability would be a consequence of changes in the discount factor due to (rational) changes in the appetite for risk of investors.


Second, a classic argument that rationalists used against the ‘anomalies’ reported by behaviorists was “how would price inefficiencies survive to the presence of rational arbitrageurs?” Shleifer and Vishny (1997) responded arguing that real world arbitrage is risky, and limited, because arbitrageurs are risk averse and their ability to bear losses due to mispricing is limited.


To defend itself against excess volatility, the EMH needs, on one hand, that changes in prices are justified by changes in investors' risk appetite. But this, on the other, is the same as accepting arbitrage is risky. The original interpretation of a 'rational arbitrageur' now does not make sense: now, arbitrageurs should be able to (i) correctly interpret fundamentals and (ii) correctly anticipate investors changes in risk appetit -otherwise their efforts to correct mispricings might be offset by changes in risk appetite in the contrary direction.


The EMH struggles between two choices: refuting excess volatility, or refuting limits to arbitrage. Refuting both, simultaneously, is not possible.


What may be their choice? Well, in my opinion, their choice has already been made. The rationalist choice has been to substitute an old artifact by a new artifact. The old artifact was the idea of a sufficient number of rational arbitrageurs. Honestly, if that idea is correct, if there are some clever guys that know at any moment what the correct price should be... why do we need markets? We need to know who those guys are and choose them as our leaders, our Presidents, our Kings for life!! Bye bye democracy!!


The new artifact follows. Under the current EMH interpretation, for a given fundamental asset value, many different prices may be correct: it depends on the risk appetite of the investors. In consequence, the new EMH does not need the figure of an arbitrageur anymore, because EMH does not say today what we believed the thing was about: EMH does not say “prices are unbiased estimations of the fundamental value, given information available” any more. Rationalists and the EMH are actually saying: “whatever the market prices, that’s the fundamental value”. Pleased to meet you, market fundamentalists.



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Spanish banking consolidation 2009 - 2013

I'm currently working on the final draft on my PhD dissertation, and this means among other things that graphs must be updated!! I follow IMF (2012) Country Report No. 12/137 on Spain to update it until today to show the restructuring process of the Spanish banking industry from 2009 to 2013. This is it.




I see this graph in Twitter, shared by @StephanieKelton , comparing savings rate and unemployment rate in the US:



I interpret this correlation between both variables as people increasing their efforts to save when they observe things are going bad in the economy (and a rising unemployment is indeed an evidence for that). In Spain there is a saying that goes "si las barbas de tu vecino ves cortar, pon las tuyas a remojar" ("if you see your neighbor's beard cut, put yours to soak") which not literally, it would be similar to "if you want peace, prepare for war". This correlation would be a good evidence for that behavior.


However, when I search for similar data in Spain I get this:



I found data only until year 2001, but there is clear evidence that savings and unemployment rate were correlated between 2001 and 2010. In particular, Spaniards were able to increase their savings rate between 2008 and 2010 in evidence of the worst economic depression in Spain in terms of unemployment. Additionally, there is a clear decoupling since 2010 onwards, too. The economic policy implemented, based on public spending cuts, tax increases, wage cuts and other austerity measures made households' savings rate fall back to a minimum level of 10%. However, the economic policy was not successful in terms of solving economic stagnation. Rather than that, unemployment rate continued to increase, making the pair 'low savings - high unemployment' a dire one for middle and lower classes.

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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).

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