Price discovery in the presence of boundedly rational agents

Abstract

In this paper we propose a sequential model of security trading which, compared to existing models, is extended along the notions of (Simon, H.A., A behavioral model of rational choice. Quart. J. Econ., 1955, 64, 99–118; Rubinstein, A., Modeling Bounded Rationality, Zeuthen Lecture Book Series, 1998 (MIT Press: Cambridge, MA), and Odean, T., Do investors trade too much? Am. Econ. Rev., 1999, 89(5), 1279–1298) by adding boundedly rational traders. Our results indicate that both momentum and mean-reversion in asset prices can be attributed to the presence of agents who are subject to systematic errors in the process of forecasting the liquidation value of a risky security. The length of the momentum period is inversely related to both the amount of information-based trading in the market and the rate at which asset specific information is learned by boundedly rational agents. Furthermore, the model allows explicitly to establish a link between the component of the bid–ask spread that can be explained by bounded rationality and both momentum and reversal.

Keywords:

• Sequential model of security trading
• Bounded rationality
• Momentum
• Reversal

Acknowledgments

The comments by two anonymous referees as well as by the participants of the 8th Annual Meeting of the German Finance Association 2001, the 5th Conference of the Swiss Society for Financial Market Research 2002, and the 12th Annual Meeting of the European Financial Management Association 2003 are gratefully acknowledged. Comments are welcome. Any errors are my responsibility.

Notes

†See Conlisk (1996) and Rabin (1998) for a review of the evidence for bounded rationality of economic agents or Kahneman et al. (1982) for an overview of the psychological biases economic agents are subject to.

‡We will briefly work through the major recent approaches in section 2.

†For instance, the papers by Easley and O'Hara (1987, 1991, 1992) Diamond and Verr (1987), Easley et al. (1997, 1998) all feature sequential trade models.

‡According to the representativeness bias the agent thinks that the last observation is representative for the next observation. Therefore, the agent assigns an earnings shock to be followed by another earnings shock of the same sign a high probability. This in turn makes her producing a trend.

If the agent is subject to conservatism she judges the actual observation to be an outlier and thinks conservatively that the next earnings shock is more likely to have the opposite sign. This generates mean-reversion in earnings shocks. Consequently, according to conservatism she assigns the event that the next earnings shock has the same sign a low probability.

†In Caginalp and Balenovich (1994, 1999) it is discussed how this ordinary differential equation can be obtained from some higher-order system of ordinary differential equations. Furthermore, it is demonstrated how to obtain stochastic counterparts of the(se) ordinary differential equation(s) and how to accommodate cash injections and withdrawals.

‡As the market makers are assumed to be symmetric, it is not relevant which market maker is clearing the order.

§One can think of the information-based traders all being boundedly rational with error probability , alternatively. I am grateful to an anonymous referee for this interpretation of the setup.

¶Allowing for learning on the part of the information-based traders explicitly captures the idea that in the end economic agents act fully rationally–-an argument which is favoured by proponents of as–if rationality. However, as usual in market microstructure, this paper studies the intermediate effects of the presence of bounded rationality on the one hand and the ignorance of bounded rationality on the other hand.

†As prior to transaction n the market makers do not know which order will be submitted next, the upcoming order is denoted by the random variable .

†The market makers therefore behave as they have learned about economic agents from economics textbooks. Namely, that economic agents in the end get things right and act as if they were rational. For most economists this as–if rationality argument makes bothering with bounded rationality issues superfluous. This paper highlights the consequences if the market makers are not concerned about less than full rationality on the part of some traders.

‡Note that this behaviour of the market makers violates the zero expected profits condition, as long as there are at least some boundedly rational traders present in the market. But, it is the only way to prevent–-with probability one–-the market makers from running the risk of realizing negative expected profits. Obviously, there should be competition among the market makers concerning the actual fraction . However, that market makers are not always prone to quote competitively was reported, for example, by the Christie and Schultz (1994) study.

§The term super-rationality is borrowed from Aumann (1997, p. 8) who points out that ‘… You must be super-rational in order to deal with my irrationalities.’

¶Note that bounded rationality does not mean the complete absence of rationality as conditionally on the boundedly rational traders' forecast the submitted orders are rational. Thus, there is no inconsistent behaviour of the boundedly rational traders as concerns order submission and forecasting.

†Note that since all orders are cleared at the quoted prices, the transaction prices are biased too. The dynamics of the transaction prices are studied in section 4.

‡Of course, under super-rationality the bid–ask spread becomes negative for . However, the case of super-rationality simply serves as a benchmark. If the presence of boundedly rational traders is ignored–-which is the case we study–-the bid–ask spread is strictly non-negative.

†Restricting on the release of good news in Step 1 implies that the rational traders would submit a buy order and the boundedly rational traders would submit a sell order in Step 2. However, the liquidity traders' trading intentions are unaffected by Step 1.

†Table II in Hong et al. (2000) reports the systematic dependency of analyst coverage on size. Thus, the proxy for analyst coverage is not the raw number of analysts following a stock but the residual analyst coverage which is systematically corrected for size.

‡Cf. table V and panel A of figure 2 in Hong et al. (2000).

§The same is true for the papers by Barberis et al. (1998) and Hong and Stein (1999). Hence, the present paper truly contributes to the body of literature.