Behavioural Finance

The presumption of efficient markets, rational expectations and symmetric information, constitutes a neat set of premises. On these grounds is derived a framework on the formation of security prices in financial markets. The appealing rationale of efficient markets is that there are no free lunches. There is however a collection of real life phenomena that cannot be satisfactory supported within this theoretical space. Behavioral finance departs from the assumption of market efficiency and the rational expectations equilibrium. Models of

behavioral finance accept the existence of traders that have expectations which depend on the past. Behavioural finance demonstrates the feasibility of co-existence of irrational with rational traders. Noise traders can have a lasting impact on asset prices. The appeal of

behavioural finance is allowing for psychological bias and looking squarely into the eyes the issue of cognitive bias. Market psychology, mood and sentiment are invaluable instruments in explaining bubbles, panics, and crashes. The existence of fat tails in the probability

distribution of stock prices is explained through the introduction of noise risk. The conditions for the survival of noise traders can be justified in a complex chaotic world with bounded rationality. The cornerstones behavioral finance is building on are limits to arbitrage (see appendix A - xv) and psychology (Barberis and Thaler, 2003, pp.1051-1121).

Beliefs and psychological bias 4.4.7.1.1

People are not inclined to find evidence that contradict their established conceptions. Even when such evidence arises they might choose to ignore it. This is called selective attention. It lends itself to a tendency of awareness to some constituencies of the environment excluding others.

Keynes (1936, cited in Shiller 2011) asserted that picking stocks is much the same as the majority’s voting for the most beautiful women in a beauty contest. Sherif's experiment on the autokinetic effect the same year (1936, cited in Sherif 2009, p.138) showed that people’s perception of the movement of a fixed light beam in a dark room is influenced by the group norms.

Cognitive psychology research has resulted in a pile up of evidence on systematic biases in people's formation of beliefs.

63 The following biases imply a departure from the assumptions of rational expectations (Berk and De Marzo 2010, pp. 417-423):

- The familiarity bias. Investors prefer to invest on companies that they are familiar with.

- The overconfidence bias. Investors tend to overestimate their knowledge like football fans second guessing coaching decisions.

- The sensation seeking bias. Investors like the excitement of handling investments as lottery tickets.

- The disposition bias. Investors tend to sell out shares that have risen in value and hold on to shares that have lost value.

- Ambiguity aversion: Because probabilities are not objectively known, individuals built their beliefs on subjective probabilities. In ambiguous circumstances will individuals make choices that render subjective probabilities that are inconsistent with each other, see Ellsberg 1961.

- The sentiment bias. Investors are influenced in their decisions by mood and the market psychology.

Barberis and Thaler (2003, pp.1051-1121) describe beliefs as the process of forming expectations. Forming of beliefs is influenced by a number of psychological traits.

Experiments show that people assign too high probabilities to events that occur more often and too low probabilities to events that occur more rarely. This is pinned down to

overconfidence.

When an initial estimate on an unknown subject is asked for, people pick an arbitrary value.

The provision of new information leads to adjustments but not far off the initial values.

People tend to cling on too much to their initial guess. This is attributed to the anchoring effect.

According to Bayes'' rule is the probability of an event B given an event A as following:

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Kahneman and Tversky (1974) provide experimental evidence that the prior probability doesn't have an effect on the probability belief outcome which is Bayes' rule prediction.

64 4.4.7.2 Heterogeneity

Fama (1970) contains concordant beliefs as one of three sufficient conditions for capital market efficiency, the other two being no transaction costs and the availability of information to all market participants. Rubinstein (1975) puts forward a set of increasingly stronger conditions on informational capital market efficiency: 1) non speculative beliefs 2) consensus beliefs and 3) homogeneous beliefs. Non-speculative beliefs are beliefs for which portfolio revision is not an optimal strategy. Consensus beliefs are beliefs which generate the same equilibrium prices as an heterogeneous economy. He ascertains that the existence of

homogeneous beliefs is a sufficient but not necessary condition for consensus beliefs and non-speculative beliefs. Heterogeneity in Rubinstein’s terms mean individuals assigning different probabilities to the occurrence of a certain state of nature. It can also mean different tastes expressed as diverse utility functions.

Heterogeneity can be related to beliefs, risk aversion and time preferences. Heterogeneity in beliefs is expressed as the assignment of different probabilities by different investors to the same event. Shefrin (2000, pp.107-109) presents a model of two investors, one optimist and the other pessimist with logarithmic utility functions with binomial beliefs, i.e. at each time t the state of the economy evolves only in two states. Then he derives in this setting an

equilibrium price density function with fat tails.

Varian (1985) sets up a model with diversity of opinions but common time and state separable utility functions. In Varian’s terminology is diversity of opinions equivalent to Rubinstein’s heterogeneity in beliefs, that is assigning different probabilities to the same state. One of his model predictions is that given a utility function with constant relative risk aversion, the diversity of opinions is inversely proportional to asset prices if the absolute risk aversion is greater than 1.

Bhamra and Uppal (2010) assert that heterogeneous preferences and beliefs boost the ability of their model to match characteristics of asset returns. Their setting is an endowment economy with two types of agents who have different power utilities, i.e. different relative risk aversions, different subjective discount factors, i.e. different time preferences and

different beliefs, i. e. different stochastic discount factors. They conclude that heterogeneity in beliefs, time preferences and risk aversion increases the market price of risk and the volatility of asset prices. The consequence is a considerably higher equity premium.

65 In a classical financial theory framework in the sense of Fama it is assumed that agents

interpret information in the same way. So if information is publicly know they form

homogenous beliefs about the future. Relaxing the assumption of homogenous interpretation of information gives rise to heterogeneity in beliefs in a rational expectations setting. Xiouros (2009) assumes that agents don’t know the true data generating process. As a consequence they use a range of models that are statistically indistinguishable in order to form their beliefs.

Information costs make agents to choose randomly among these models. By this chain of arguments he arrives to dispersion of belies due to disparate interpretation of information without resorting to behavioral factors.

Xiouros and Zapatero (2010) put forward a discrete time model of heterogeneous agents with different degrees of risk aversion but with the same time preferences and beliefs. Agents have a power utility function with different degrees of risk aversion. The financial market they operate in is assumed to be complete, i.e. there is a unique security asset for every state of nature (Copeland et al. 2005, pp. 77, 78).The model includes an external consumption habit which depends on individual's previous consumption and on the aggregate consumption level in a "keep up with the Joneses" fashion. Xiouros and Zapatero derive a closed form solution for the equilibrium state price density. After a careful calibration of the distribution of agent types they conclude that it is unlikely that the heterogeneity in risk aversion alone can explain the volatility in stock prices. This is ascribed by the authors of the paper to the cross sectional redistribution of wealth in this setting being too low.

Cvitanic, Jouini, Malamud and Napp (2011) present a model in a complete financial market populated with agents of constant absolute risk aversion and heterogeneity in beliefs, risk aversion or liquidity preferences. They find that heterogeneity is constant at individual level but fluctuates at the aggregate level. In their setting, heterogeneity leads to excess volatility of asset prices and an additional risk premium in the long run.