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Prospect Theory in the Heterogeneous Agent Model

Abstract

Using the Heterogeneous Agent Model framework, we incorporate an extension based on Prospect Theory into a popular agent-based asset pricing model. This extension covers the phenomenon of loss aversion manifested in risk aversion and asymmetric treatment of gains and losses. Using Monte Carlo methods, we investigate behavior and statistical properties of the extended model and assess how our extension is manifested in different strategies. We show that, on the one hand, the Prospect Theory extension keeps the essential underlying mechanics of the model intact, but on the other hand it considerably changes the model dynamics. Stability of the model is increased and fundamentalists may be able to survive in the market more easily. When only the fundamentalists are loss-averse, other strategies profit more.

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Notes

  1. According to Ehrentreich (2007, p. 56), at the time when the foundations of the EMH were laid, logarithmic asset returns were assumed to be distributed normally and the prices therefore followed the log-normal distribution.

  2. The ‘irrationality’ is meant within the expected utility theory.

  3. PT is descriptive in the sense that it tries to capture the real-world decision-making whereas the expected utility theory is de facto normative—it models how people are supposed to decide.

  4. Regular prospect is a prospect such that either \(p + q < 1\), \(x \geqslant 0 \geqslant y\), or \(x \leqslant 0 \leqslant y\). Evaluation of prospects which are not regular follows a different rule—details are provided in Kahneman and Tversky (1979, p. 276).

  5. The equity premium puzzle is a phenomenon that the average return on equity is far greater than return on a risk-free asset. Such a characteristic has been observed in many markets. The term was first coined by Mehra and Prescott (1985).

  6. Hommes (2013, p. 162) remarks that Eq. 9 is also satisfied by the so-called rational bubble solution of the form \({p_t} = p_t^ * + {\big ( {1 + r} \big )^t} \cdot \big ( {{p_0} - p_0^ * } \big )\). However, this solution does not satisfy the transversality (or ‘no-bubbles’) condition.

  7. The notation difference consists of ‘shifting’ time subscripts of realized excess return by one period—for this reason, Eq. 16 is reduced to Eq. 17 only after this shift.

  8. We run another ‘benchmark’ simulation of the model without the proposed extensions, that is, for the K–W test, we use a different benchmark than that examined in Sect. 5.3.1.

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Correspondence to Jan Polach or Jiri Kukacka.

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The views expressed in this article are those of the authors and do not necessarily reflect the position of Moody’s Analytics, Moody’s Investors Service, or Moody’s Corporation. J. Kukacka gratefully acknowledges financial support from the Czech Science Foundation under the P402/12/G097 DYME—‘Dynamic Models in Economics’ project.

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Polach, J., Kukacka, J. Prospect Theory in the Heterogeneous Agent Model. J Econ Interact Coord 14, 147–174 (2019). https://doi.org/10.1007/s11403-018-0219-6

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Keywords

  • Heterogeneous Agent Model
  • Prospect Theory
  • Behavioral finance
  • Stylized facts