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Asymmetric reaction is rational behavior

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Abstract

De Bondt and Thaler (Int J Fore 9(3):355–371, 1995) point out that while von Neumann-Morgenstern (1947) utility functions, the axioms of cardinal utility (Copeland and Weston 1988), risk aversion, rational expectations, etc., have formed the basis for theories of choice under uncertainty, research in behavioral science, has either challenged these foundations or outright rejected them. Requiring investors to be utility maximizers, and using an approach similar to Scott-Horvath (J Financ 35(4):915–9¸1980), and arguing investors’ to have different utility for partial upper and partial lower moments, this paper proves that loss, regret, and myopic loss aversion and sign effects, is in fact central to understanding of rational behavior.

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Notes

  1. Page 79–80 of 3rd edition of Financial Theory and Corporate Policy by Copeland and Weston (Copeland and Weston 1988). The five axioms are comparability, transitivity, strong independence, measurability, and ranking.

  2. For a comprehensive review see Shefrin (2010).

  3. Bias arising out of reliance based on one piece of information. For example, as observed by De Bondt (1993) and Muradoglu and Onkal (1994) investors base forecasts on the purchase price of securities.

  4. Biases arising from dependence on trend extrapolations.

  5. Biases arising from investors’ tendency to overweigh easily available or accessible information.

  6. Bias arising from the tendency of individuals to over-value their own knowledge and skill, which may result in their overestimating their own ability to beat the market and underestimating risk.

  7. Loss aversion, refers to investors weighing loses twice as much as gains of similar magnitude, and thereby exhibit their aversion to realize losses.

  8. The tendency of individuals to categories wealth and financial outcomes.

  9. Myopic loss aversion is a consequence of investors combining horizon-based framing and loss-aversion. Investors are more risk averse if investor horizon is shorter than longer.

  10. The ability, or lack thereof, of individuals to control impulses resulting in undesired ramifications for financial decisions.

  11. The tendency to avoid taking decisions that result in regret.

  12. Sign effect refers to Thaler’s (1981) observation that gains are discounted more than losses. Sign effect also includes the propensity of individuals to incur losses immediately rather than delay it (Frederick et al. 2002; Benzion et al. 1989; Loewenstein 1987; MacKeigan et al. 1993; Mischel et al. 1969; Redelmeier and Heller 1993; Yates and Watts 1975).

  13. The magnitude effect refers to the tendency of investors to discount small outcomes more than large ones.

  14. The dramatic effect on discount rates depended on the outcome being framed as an acceleration sequence or a delay sequence.

  15. This refers to the tendency of individuals to prefer an increasing sequence of outcomes to declining sequences (Loewenstein and Prelec 1993), even if say a decreasing wage sequence (Hsee et al. 1991) were to confer more money.

  16. As discussed exhaustedly in Frederick, Loewenstein and O’Donoghue (2002), the discounted utility model assumes the marginal rate of substitution between consumption in two periods to be independent of consumption in some other period. Loewenstein and Prelec (1993), however, found evidence that respondents violated this assumption. Furthermore, they also found preference for spread while making consumption decisions.

  17. Hyperbolic discounting refers to the preference of high short-run rates of return and low long-run rates to return. Horvath and Sinha (2013), however, argue that hyperbolic discounting rather than being evidence of investor irrationality may actually be evidence of rational behavior.

  18. Cheremushkin (2009) actually challenges some of the empirical assumptions used in a number of Estrada’s papers.

  19. Since these figures are for illustrative purposes only, we develop plots for the second and third moments.

  20. The four distinctive features of Prospect Theory (Tversky and Kahneman 1992) as summarized in Shefrin (2010) are: (1) utility is relative to a reference point than the final position; (2) the utility function, concave in losses and gains with an indifference point at the origin, and is steeper for losses than for gains. Accordingly, the utility function of an investor would take an S-shape, with a kink at the indifference point; (3) while evaluating prospects, investors may weigh or distort probabilities. Weighting function for losses may be different from that of gains; and (4) investors are subject to framing issues while evaluating risky prospects. Prima fascia, these salient features of Prospect Theory appear to be contrary to the neoclassical concept of complete rational decisions based on the axioms of cardinal utility (Copeland and Weston 1988).

  21. See Bawa (1975) and Fishburn (1977) for development of the lower partial moment concept as a powerful generalization of semivariance. Here the mean is used as the Fishburn’s target.

  22. This treatment of the axioms of choice under uncertainty largely follows the development found in Copeland and Weston (3rd ed., 1988).

  23. Refer to Adam Smith’s statement - “we suffer more when we fall from a better to a worse situation than we ever enjoy when we rise from a worse to a better” in The Theory of Moral Sentiments. Reference obtained from De Bondt et al., 2008.

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Acknowledgments

The paper benefited from comments, feedback and help from Dr. Rick Gretz, Mr. Brady Olzewsky, Mr. Samuel Harger and Ms Teri Foster. The authors also acknowledge the blind reviewer(s). Addressing the comments and suggestions raised by reviewer(s) improved the quality of this manuscript. All errors are the authors.

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  1. Department of Finance and Quantitative Methods, Foster College of Business, Bradley University, Peoria, IL, 61625, USA

    Philip A. Horvath & Amit K. Sinha

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Correspondence to Amit K. Sinha.

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Horvath, P.A., Sinha, A.K. Asymmetric reaction is rational behavior. J Econ Finan 41, 160–179 (2017). https://doi.org/10.1007/s12197-015-9344-4

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