All Title Author
Keywords Abstract


Segregation and Integration: A Study of the Behaviors of Investors with Extended Value Functions

DOI: 10.1155/2010/302895

Full-Text   Cite this paper   Add to My Lib

Abstract:

This paper extends prospect theory, mental accounting, and the hedonic editing model by developing an analytical theory to explain the behavior of investors with extended value functions in segregating or integrating multiple outcomes when evaluating mental accounting. 1. Introduction and Literature Review 1.1. Prospect Theory and Mental Accounting A central tenet within economics is that individuals maximize their expected utilities [1] in which all outcomes are assumed to be integrated with current wealth. Kahneman and Tversky [2] propose prospect theory to reflect the subjective desirability of different decision outcomes and to provide possible explanations for behavior of investors who maximize over value functions instead of utility functions. Let be the set of extended real numbers and in which and . Rather than defining over levels of wealth, the value function is defined over gains and losses relative to a reference point (status quo) with , satisfying where is the derivative of . The value function is a psychophysical function to reflect the anticipated happiness or sadness associated with each potential decision outcome. Without loss of generality, we assume the status quo to be zero. Thus, we refer to positive outcomes as gains and negative outcomes as losses. In this situation, investors with the value functions are risk averse for gains but risk seeking for losses. Since the value function is concave in the positive domain and convex for the negative domain, it shows declining sensitivity in both gains and losses. Kahneman [3] comments that evaluating an object from a reference point of “having” (“not having”) implies a negative (positive) change of “giving something up” (“getting something”) upon relinquishing (receiving) the object. Many functions have been proposed as value functions; see, for example, Stott [4]. Kahneman and Tversky [2] first propose the following value function: Al-Nowaihi et al. [5] show that under preference for homogeneity and loss aversion, the value function will have a power form with identical powers for gains and losses. Tversky and Kahneman [6] estimate the parameters and identify and as median values whereas Abdellaoui [7] estimates a power value function varying in the range . The parameter in (1.2) describes the degree of loss aversion and and measure the degree of diminishing sensitivity. Nonetheless, Levy and Wiener [8], M. Levy and H. Levy [9, 10], Wong, and Chan [11] and others suggest extending the value function in (1.2) without restricting to be greater than one. In this paper, we first study the

References

[1]  J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, NJ, USA, 1944.
[2]  D. Kahneman and A. Tversky, “Prospect theory: an analysis of decisions under risk,” Econometrica, vol. 47, pp. 263–291, 1979.
[3]  D. Kahneman, “Objective happiness,” in Well Being: The Foundations of Hedonic Psychology, D. Kahneman, E. Diener, and N. Schwartz, Eds., pp. 3–25, Russell Sage Foundation, New York, NY, USA, 1999.
[4]  H. P. Stott, “Cumulative prospect theory's functional menagerie,” Journal of Risk and Uncertainty, vol. 32, no. 2, pp. 101–130, 2006.
[5]  A. Al-Nowaihi, I. Bradley, and S. Dhami, “A note on the utility function under prospect theory,” Economics Letters, vol. 99, no. 2, pp. 337–339, 2008.
[6]  A. Tversky and D. Kahneman, “Advances in prospect theory: cumulative representation of uncertainty,” Journal of Risk and Uncertainty, vol. 5, no. 4, pp. 297–323, 1992.
[7]  M. Abdellaoui, “Parameter-free elicitation of utility and probability weighting functions,” Management Science, vol. 46, no. 11, pp. 1497–1512, 2000.
[8]  H. Levy and Z. Wiener, “Stochastic dominance and prospect dominance with subjective weighting functions,” Journal of Risk and Uncertainty, vol. 16, no. 2, pp. 147–163, 1998.
[9]  M. Levy and H. Levy, “Prospect theory: much ado about nothing?” Management Science, vol. 48, no. 10, pp. 1334–1349, 2002.
[10]  H. Levy and M. Levy, “Prospect theory and mean-variance analysis,” Review of Financial Studies, vol. 17, no. 4, pp. 1015–1041, 2004.
[11]  W.-K. Wong and R. H. Chan, “Prospect and Markowitz stochastic dominance,” Annals of Finance, vol. 4, no. 1, pp. 105–129, 2008.
[12]  R. H. Thaler, “Mental accounting and consumer choice,” Marketing Science, vol. 4, pp. 199–214, 1985.
[13]  E. Shafir and R. H. Thaler, “Invest now, drink later, spend never: on the mental accounting of delayed consumption,” Journal of Economic Psychology, vol. 27, no. 5, pp. 694–712, 2006.
[14]  R. H. Thaler, “Mental accounting and consumer choice,” Marketing Science, vol. 27, no. 1, pp. 15–25, 2008.
[15]  A. Tversky and D. Kahneman, “The framing of decisions and the psychology of choice,” Science, vol. 211, no. 4481, pp. 453–458, 1981.
[16]  R. H. Thaler and E. J. Johnson, “Gambling with the house money and trying to break even: the effects of prior outcomes on risky choice,” Management Science, vol. 36, no. 6, pp. 643–660, 1990.
[17]  S. Benartzi and R. Thaler, “Myopic loss aversion and the equity premium puzzle,” Quarterly Journal of Economics, vol. 110, pp. 73–92, 1995.
[18]  U. Gneezy and J. Potters, “An experiment on risk taking and evaluation periods,” Quarterly Journal of Economics, vol. 112, no. 2, pp. 631–645, 1997.
[19]  R. H. Thaler, A. Tversky, D. Kahneman, and A. Schwartz, “The effect of myopia and loss aversion on risk taking: an experimental test,” Quarterly Journal of Economics, vol. 112, no. 2, pp. 646–661, 1997.
[20]  S. S. Lim, “Do investors integrate losses and segregate gains? Mental accounting and investor trading decisions,” Journal of Business, vol. 79, no. 5, pp. 2539–2573, 2006.
[21]  M. Petrovic, “Sur une equation fonctionnelle,” Publications Mathematiques de l'Universite da Belgrade, vol. 1, pp. 149–156, 1932.
[22]  P. W. Linville and G. W. Fischer, “Preferences for separating or combining events,” Journal of Personality and Social Psychology, vol. 60, no. 1, pp. 5–23, 1991.
[23]  T. Odean, “Are investors reluctant to realize their losses?” Journal of Finance, vol. 53, no. 5, pp. 1775–1798, 1998.
[24]  T. Langer and M. Weber, “Prospect theory, mental accounting, and differences in aggregated and segregated evaluation of lottery portfolios,” Management Science, vol. 47, no. 5, pp. 716–733, 2001.
[25]  T. Loughran and J. R. Ritter, “Why don't issuers get upset about leaving money on the table in IPOs?” Review of Financial Studies, vol. 15, no. 2, pp. 413–443, 2002.
[26]  A. Ljungqvist and W. J. Wilhelm Jr., “Does prospect theory explain IPO market behavior?” Journal of Finance, vol. 60, no. 4, pp. 1759–1790, 2005.
[27]  G. Loewenstein, T. O'Donoghue, and M. Rabin, “Projection bias in predicting future utility,” Quarterly Journal of Economics, vol. 118, no. 4, pp. 1209–1248, 2003.
[28]  L. Van Boven, G. Loewenstein, and D. Dunning, “Mispredicting the endowment effect: underestimation of owners' selling prices by buyer's agents,” Journal of Economic Behavior and Organization, vol. 51, no. 3, pp. 351–365, 2003.
[29]  H. M. Markowitz, “The utility of wealth,” Journal of Political Economy, vol. 60, pp. 151–156, 1952.
[30]  Z. Bai, H. Liu, and W.-K. Wong, “Enhancement of the applicability of Markowitz's portfolio optimization by utilizing random matrix theory,” Mathematical Finance, vol. 19, no. 4, pp. 639–667, 2009.
[31]  M. Egozcue and W.-K. Wong, “Gains from diversification on convex combinations: a majorization and stochastic dominance approach,” European Journal of Operational Research, vol. 200, no. 3, pp. 893–900, 2010.
[32]  W.-K. Wong, B. K. Chew, and D. Sikorski, “Can P/E ratio and bond yield be used to beat stock markets?” Multinational Finance Journal, vol. 5, no. 1, pp. 59–86, 2001.
[33]  K. Lam, T. Liu, and W.-K. Wong, “A pseudo-Bayesian model in financial decision making with implications to market volatility, under- and overreaction,” European Journal of Operational Research, vol. 203, no. 1, pp. 166–175, 2010.
[34]  T. Post and H. Levy, “Does risk seeking drive stock prices? A stochastic dominance analysis of aggregate investor preferences and beliefs,” Review of Financial Studies, vol. 18, no. 3, pp. 925–953, 2005.
[35]  W. M. Fong, W.-K. Wong, and H. H. Lean, “International momentum strategies: a stochastic dominance approach,” Journal of Financial Markets, vol. 8, no. 1, pp. 89–109, 2005.
[36]  W. M. Fong, H. H. Lean, and W.-K. Wong, “Stochastic dominance and behavior towards risk: the market for Internet stocks,” Journal of Economic Behavior and Organization, vol. 68, no. 1, pp. 194–208, 2008.
[37]  E. M. Matsumura, K. W. Tsui, and W.-K. Wong, “An extended multinomial-Dirichlet model for error bounds for dollar-unit sampling,” Contemporary Accounting Research, vol. 6, pp. 485–500, 1990.
[38]  W.-K. Wong and R. H. Chan, “On the estimation of cost of capital and its reliability,” Quantitative Finance, vol. 4, no. 3, pp. 365–372, 2004.
[39]  C. Ma and W.-K. Wong, “Stochastic dominance and risk measure: a decision-theoretic foundation for VaR and C-VaR,” European Journal of Operational Research. In press.
[40]  J. Tobin, “Liquidity preference and behavior towards risk,” Review of Economic Studies, vol. 25, pp. 65–86, 1958.
[41]  W.-K. Wong, “Stochastic dominance theory for location-scale family,” Journal of Applied Mathematics and Decision Sciences, vol. 2006, Article ID 82049, 10 pages, 2006.
[42]  W.-K. Wong, “Stochastic dominance and mean-variance measures of profit and loss for business planning and investment,” European Journal of Operational Research, vol. 182, no. 2, pp. 829–843, 2007.
[43]  W.-K. Wong and C. Ma, “Preferences over location-scale family,” Economic Theory, vol. 37, no. 1, pp. 119–146, 2008.
[44]  S. Sriboonchita, W.-K. Wong, S. Dhompongsa, and H. T. Nguyen, Stochastic Dominance and Applications to Finance, Risk and Economics, Chapman and Hall/CRC, Taylor and Francis, Boca Raton, Fla, USA, 2009.
[45]  A. E. Bargagliotti, “Aggregation and decision making using ranked data,” Mathematical Social Sciences, vol. 58, no. 3, pp. 354–366, 2009.
[46]  L. Eeckhoudt, J. Etner, and F. Schroyen, “The values of relative risk aversion and prudence: a context-free interpretation,” Mathematical Social Sciences, vol. 58, no. 1, pp. 1–7, 2009.
[47]  W.-K. Wong and R. B. Miller, “Analysis of ARIMA-noise models with repeated time series,” Journal of Business and Economic Statistics, vol. 8, no. 2, pp. 243–250, 1990.
[48]  P. L. Leung and W.-K. Wong, “On testing the equality of the multiple Sharpe Ratios, with application on the evaluation of iShares,” Journal of Risk, vol. 10, no. 3, pp. 1–16, 2008.

Full-Text

comments powered by Disqus