Academic Journal of Business & Management, 2024, 6(3); doi: 10.25236/AJBM.2024.060307.
Jia Li
Guangzhou College of Commerce, Guangzhou, China
In the exploration of discrete-time behavioural portfolio choice under Cumulative Prospect Theory, this study, conducted within a single-period economy, establishes a portfolio optimization model with the objective of maximizing distorted expected utility. Analytic solutions for optimal allocation are derived under two key assumptions: prohibiting short-selling while allowing borrowing, and prohibiting both short-selling and borrowing. Under the assumption of forbidding short-selling and allowing borrowing, a unique optimal portfolio emerges when the risk aversion on gains dominates the risk propensity on losses. In contrast, in cases where the latter prevails, there may be multiple optimal portfolios or none. Transitioning to the scenario where both short-selling and borrowing are forbidden, dominance of risk aversion on gains results in two optimal portfolios. When risk aversion equals risk propensity on losses, multiple portfolios may arise; otherwise, a unique optimal portfolio emerges or none at all. If risk propensity on losses dominates, two optimal portfolios exist; otherwise, uniqueness or absence of an optimal portfolio may occur. Concluding the study, sensitivity analysis is presented, highlighting the impact of the CPT-ratio and the level of loss aversion on the optimal portfolio, provided it exists and is unique.
Behavioural Finance; CPT Model; Portfolio Choice; Utility Function; Weighting Distortions
Jia Li. Discrete-Time Behavioural Portfolio Choice in Frictionless Markets. Academic Journal of Business & Management (2024) Vol. 6, Issue 3: 59-65. https://doi.org/10.25236/AJBM.2024.060307.
[1] Allais, M. (1953). The behavior of rational individuals in the face of risk: a critique of the assumptions and axioms of the American school. Econometrics, 21, 503-546. http://dx.doi.org/ 10.2307/1907921
[2] Ellsberg, D. (1961) Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75, 643-669.
[3] Kahneman, D. and Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2):263–292. doi:10.2307/1914185.
[4] Kahneman, D. and Tversky, A. (1992). Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4):297–323. doi:10.1007/BF00122574.
[5] He, X. D., & Zhou, X. Y. (2010). Portfolio choice under cumulative prospect theory: an analytical treatment. Ssrn Electronic Journal.
[6] Bernard, C. and Ghossoub, M. (2010). Static portfolio choice under Cumulative Prospect Theory. Math. Financ. Econ., 2(4):277–306. doi:10.1007/s11579-009-0021-2.
[7] Chao Gong, Chunhui Xu, Masakazu Ando and Xiangming Xi (2018). A New Method of Portfolio Optimization under Cumulative Prospect Theory. Tsinghua Science and Technology, February 2018, 23(1): 75–86. doi: 10.26599/TST.2018.9010057.
[8] Giorgi, E. D, & Hens, T. . (2005). Making prospect theory fit for finance. Norwegian School of Economics, Department of Business and Management Science(3).
[9] ZENG, J.M. (2007). An experimental test on cumulative prospect theory. Journal of Jinan University, Natural Science. doi:10.3969/j.issn.1000- 9965.2007.01.011.