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July  2019, 15(3): 1473-1492. doi: 10.3934/jimo.2018105

## Risk measure optimization: Perceived risk and overconfidence of structured product investors

 1 School of Business, Central South University, Changsha, China 2 School of Mathematics and Statistics, Central South University, Changsha, China 3 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

* Corresponding author: Zongrun Wang

Received  January 2018 Revised  March 2018 Published  July 2018

In financial optimization, it is important to quantify the risk of structured financial products. This paper quantifies the risk of structured financial products by perceived risk measures based on a standard measure of risk, and then we construct the risk perception and decision-making models of individual investors considering structured products. Moreover, based on bullish and bearish binary structured products, we introduce the psychological bias of overconfidence to explore how this bias affects investors' perceived risk. This study finds that overconfident investors believe in private signals and underestimate the variance of noise in private signals, which affects their expectation of the underlying asset price of structured financial products. Furthermore, overconfidence bias leads investors to overestimate the probability of obtaining a better return. With the increase in overconfidence, the overestimation of the probability is intensified, which eventually leads to lower perceived risk.

Citation: Xi Chen, Zongrun Wang, Songhai Deng, Yong Fang. Risk measure optimization: Perceived risk and overconfidence of structured product investors. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1473-1492. doi: 10.3934/jimo.2018105
##### References:
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Bregu, Overconfidence and (Over) Trading: The Effect of Feedback on Trading Behavior, Technical report, University of Arkansas, 2016. Google Scholar [7] J. C. Butler, J. S. Dyer and J. Jia, An empirical investigation of the assumptions of risk-value models, Journal of Risk and Uncertainty, 30 (2005), 133-156.  doi: 10.1007/s11166-005-6562-8.  Google Scholar [8] C. Celerier and B. Vallee, Catering to investors through security design: Headline rate and complexity, Quarterly Journal of Economics, 132 (2017), 1469-1508.   Google Scholar [9] A. Cillo and P. Delquié, Mean-risk analysis with enhanced behavioral content, European Journal of Operational Research, 239 (2014), 764-775.  doi: 10.1016/j.ejor.2014.06.001.  Google Scholar [10] C. H. Coombs and J. N. Bowen, A test of ve-theories of risk and the effect of the central limit theorem, Acta Psychologica, 35 (1971), 15-28.  doi: 10.1016/0001-6918(71)90028-X.  Google Scholar [11] C. H. Coombs and L. C. Huang, Polynomial psychophysics of risk, Journal of Mathematical Psychology, 7 (1970), 317-338.  doi: 10.1016/0022-2496(70)90051-9.  Google Scholar [12] A. H. Crespo, I. R. del Bosque and M. G. de los Salmones Sanchez, The influence of perceived risk on internet shopping behavior: a multidimensional perspective, Journal of Risk Research, 12 (2009), 259-277.  doi: 10.1080/13669870802497744.  Google Scholar [13] K. Daniel, D. Hirshleifer and A. Subrahmanyam, Investor psychology and security market under- and overreactions, the Journal of Finance, 53 (1998), 1839-1885.  doi: 10.1111/0022-1082.00077.  Google Scholar [14] S. Das, Structured products & hybrid securities, J. Wiley, 2001. Google Scholar [15] J. S. Dyer and J. Jia, Relative risk-value models, European Journal of Operational Research, 103 (1997), 170-185.  doi: 10.1016/S0377-2217(96)00254-8.  Google Scholar [16] M. S. Featherman and P. A. Pavlou, Predicting e-services adoption: a perceived risk facets perspective, International Journal of Human-Computer Studies, 59 (2003), 451-474.  doi: 10.1016/S1071-5819(03)00111-3.  Google Scholar [17] M. Glaser, T. Langer and M. Weber, True overconfidence in interval estimates: Evidence based on a new measure of miscalibration, Journal of Behavioral Decision Making, 26 (2013), 405-417.  doi: 10.2139/ssrn.712583.  Google Scholar [18] M. Grinblatt and M. Keloharju, Sensation seeking, overconfidence, and trading activity, The Journal of Finance, 64 (2009), 549-578.  doi: 10.3386/w12223.  Google Scholar [19] T. Hens and M. O. Rieger, Can utility optimization explain the demand for structured investment products?, Quantitative Finance, 14 (2014), 673-681.  doi: 10.1080/14697688.2013.823512.  Google Scholar [20] D. Hirshleifer and G. Y. Luo, On the survival of overconfident traders in a competitive securities market, Journal of Financial Markets, 4 (2001), 73-84.  doi: 10.1016/S1386-4181(00)00014-8.  Google Scholar [21] P.-H. Ho, C.-W. Huang, C.-Y. Lin and J.-F. Yen, Ceo overconfidence and financial crisis: Evidence from bank lending and leverage, Journal of Financial Economics, 120 (2016), 194-209.   Google Scholar [22] J. Jia and J. S. Dyer, A standard measure of risk and risk-value models, Management Science, 42 (1996), 1691-1705.   Google Scholar [23] J. Jia, J. S. Dyer and J. C. Butler, Measures of perceived risk, Management Science, 45 (1999), 519-532.  doi: 10.1287/mnsc.45.4.519.  Google Scholar [24] J. Jia, J. S. Dyer and J. C. Butler, Generalized disappointment models, Journal of Risk and Uncertainty, 22 (2001), 59-78.   Google Scholar [25] L. R. Keller, R. K. Sarin and M. Weber, Empirical investigation of some properties of the perceived riskiness of gambles, Organizational Behavior and Human Decision Processes, 38 (1986), 114-130.  doi: 10.1016/0749-5978(86)90029-4.  Google Scholar [26] C. Liao, H.-N. Lin and Y.-P. Liu, Predicting the use of pirated software: A contingency model integrating perceived risk with the theory of planned behavior, Journal of Business Ethics, 91 (2010), 237-252.  doi: 10.1007/s10551-009-0081-5.  Google Scholar [27] R. D. Luce, Several possible measures of risk, Theory and Decision, 12 (1980), 217-228.  doi: 10.1007/BF00135033.  Google Scholar [28] R. D. Luce, Correction to "several possible measures of risk", Theory and Decision, 13 (1981), 381-381.  doi: 10.1007/BF00126971.  Google Scholar [29] R. D. Luce and E. U. Weber, An axiomatic theory of conjoint, expected risk, Journal of Mathematical Psychology, 30 (1986), 188-205.  doi: 10.1016/0022-2496(86)90013-1.  Google Scholar [30] C. Martins, T. Oliveira and A. Popovi, Understanding the internet banking adoption: A unified theory of acceptance and use of technology and perceived risk application, International Journal of Information Management, 34 (2014), 1-13.  doi: 10.1016/j.ijinfomgt.2013.06.002.  Google Scholar [31] T. Odean, Volume, volatility, price, and profit when all traders are above average, The Journal of Finance, 53 (1998), 1887-1934.   Google Scholar [32] M. Ofir and Z. Wiener, Investment in Financial Structured Products from a Rational Choice Perspective, Technical report, Hebrew University of Jerusalem, 2009. Google Scholar [33] A. M. Olazábal and H. Marmostein, Structured products for the retail market: The regulatory implications of investor innumeracy and consumer information processing, Ariz. L. Rev., 52-623 (2010), 623-673.   Google Scholar [34] C. Park, S. Ahn and S. Lee, A bayesian decision model based on expected utility and uncertainty risk, Applied Mathematics & Computation, 242 (2014), 643-648.  doi: 10.1016/j.amc.2014.06.005.  Google Scholar [35] A. Pollatsek and A. Tversky, A theory of risk, Journal of Mathematical Psychology, 7 (1970), 540-553.  doi: 10.1016/0022-2496(70)90039-8.  Google Scholar [36] M. O. Rieger and T. Hens, Explaining the demand for structured financial products: survey and field experiment evidence, Zeitschrift für Betriebswirtschaft, 82 (2012), 491-508.   Google Scholar [37] A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Readings in Formal Epistemology, 1 (1992), 493-519.  doi: 10.1007/978-3-319-20451-2_24.  Google Scholar [38] X. T. Wang and J. G. Johnson, A tri-reference point theory of decision making under risk, Journal of Experimental Psychology General, 141 (2012), 743-756.  doi: 10.1037/a0027415.  Google Scholar [39] E. U. Weber, Combine and conquer: A joint application of conjoint and functional approaches to the problem of risk measurement, Journal of Experimental Psychology: Human Perception and Performance, 10 (1984), 179-194.   Google Scholar [40] E. U. Weber, Risk as an Independent Variable in Risky Choic, PhD thesis, Harvard University, 1984. Google Scholar [41] E. U. Weber and W. P. Bottom, An empirical evaluation of the transitivity, monotonicity, accounting, and conjoint axioms for perceived risk, Organizational Behavior and Human Decision Processes, 45 (1990), 253-275.  doi: 10.1016/0749-5978(90)90014-Z.  Google Scholar

show all references

##### References:
 [1] B. N. Adebambo and X. S. Yan, Momentum, reversals, and fund manager overconfidence, Financial Management, 45 (2016), 609-639.  doi: 10.1111/fima.12128.  Google Scholar [2] A. A. Alalwan, Y. K. Dwivedi, N. P. Rana and M. D. Williams, Consumer adoption of mobile banking in jordan: Examining the role of usefulness, ease of use, perceived risk and self-efficacy, Journal of Enterprise Information Management, 29 (2016), 118-139.  doi: 10.1108/JEIM-04-2015-0035.  Google Scholar [3] F. H. Barron, Polynomial psychophysics of risk for selected business faculty, Acta Psychologica, 40 (1976), 127-137.  doi: 10.1016/0001-6918(76)90004-4.  Google Scholar [4] D. E. Bell, Disappointment in decision making under uncertainty, Operations Research, 33 (1985), 1-27.  doi: 10.1287/opre.33.1.1.  Google Scholar [5] M. Bennet, Complexity and its discontents: recurring legal concerns with structured products, New York University Journal of Law & Business, 7 (2010), 811-843.   Google Scholar [6] K. Bregu, Overconfidence and (Over) Trading: The Effect of Feedback on Trading Behavior, Technical report, University of Arkansas, 2016. Google Scholar [7] J. C. Butler, J. S. Dyer and J. Jia, An empirical investigation of the assumptions of risk-value models, Journal of Risk and Uncertainty, 30 (2005), 133-156.  doi: 10.1007/s11166-005-6562-8.  Google Scholar [8] C. Celerier and B. Vallee, Catering to investors through security design: Headline rate and complexity, Quarterly Journal of Economics, 132 (2017), 1469-1508.   Google Scholar [9] A. Cillo and P. Delquié, Mean-risk analysis with enhanced behavioral content, European Journal of Operational Research, 239 (2014), 764-775.  doi: 10.1016/j.ejor.2014.06.001.  Google Scholar [10] C. H. Coombs and J. N. Bowen, A test of ve-theories of risk and the effect of the central limit theorem, Acta Psychologica, 35 (1971), 15-28.  doi: 10.1016/0001-6918(71)90028-X.  Google Scholar [11] C. H. Coombs and L. C. Huang, Polynomial psychophysics of risk, Journal of Mathematical Psychology, 7 (1970), 317-338.  doi: 10.1016/0022-2496(70)90051-9.  Google Scholar [12] A. H. Crespo, I. R. del Bosque and M. G. de los Salmones Sanchez, The influence of perceived risk on internet shopping behavior: a multidimensional perspective, Journal of Risk Research, 12 (2009), 259-277.  doi: 10.1080/13669870802497744.  Google Scholar [13] K. Daniel, D. Hirshleifer and A. Subrahmanyam, Investor psychology and security market under- and overreactions, the Journal of Finance, 53 (1998), 1839-1885.  doi: 10.1111/0022-1082.00077.  Google Scholar [14] S. Das, Structured products & hybrid securities, J. Wiley, 2001. Google Scholar [15] J. S. Dyer and J. Jia, Relative risk-value models, European Journal of Operational Research, 103 (1997), 170-185.  doi: 10.1016/S0377-2217(96)00254-8.  Google Scholar [16] M. S. Featherman and P. A. Pavlou, Predicting e-services adoption: a perceived risk facets perspective, International Journal of Human-Computer Studies, 59 (2003), 451-474.  doi: 10.1016/S1071-5819(03)00111-3.  Google Scholar [17] M. Glaser, T. Langer and M. Weber, True overconfidence in interval estimates: Evidence based on a new measure of miscalibration, Journal of Behavioral Decision Making, 26 (2013), 405-417.  doi: 10.2139/ssrn.712583.  Google Scholar [18] M. Grinblatt and M. Keloharju, Sensation seeking, overconfidence, and trading activity, The Journal of Finance, 64 (2009), 549-578.  doi: 10.3386/w12223.  Google Scholar [19] T. Hens and M. O. Rieger, Can utility optimization explain the demand for structured investment products?, Quantitative Finance, 14 (2014), 673-681.  doi: 10.1080/14697688.2013.823512.  Google Scholar [20] D. Hirshleifer and G. Y. Luo, On the survival of overconfident traders in a competitive securities market, Journal of Financial Markets, 4 (2001), 73-84.  doi: 10.1016/S1386-4181(00)00014-8.  Google Scholar [21] P.-H. Ho, C.-W. Huang, C.-Y. Lin and J.-F. Yen, Ceo overconfidence and financial crisis: Evidence from bank lending and leverage, Journal of Financial Economics, 120 (2016), 194-209.   Google Scholar [22] J. Jia and J. S. Dyer, A standard measure of risk and risk-value models, Management Science, 42 (1996), 1691-1705.   Google Scholar [23] J. Jia, J. S. Dyer and J. C. Butler, Measures of perceived risk, Management Science, 45 (1999), 519-532.  doi: 10.1287/mnsc.45.4.519.  Google Scholar [24] J. Jia, J. S. Dyer and J. C. Butler, Generalized disappointment models, Journal of Risk and Uncertainty, 22 (2001), 59-78.   Google Scholar [25] L. R. Keller, R. K. Sarin and M. Weber, Empirical investigation of some properties of the perceived riskiness of gambles, Organizational Behavior and Human Decision Processes, 38 (1986), 114-130.  doi: 10.1016/0749-5978(86)90029-4.  Google Scholar [26] C. Liao, H.-N. Lin and Y.-P. Liu, Predicting the use of pirated software: A contingency model integrating perceived risk with the theory of planned behavior, Journal of Business Ethics, 91 (2010), 237-252.  doi: 10.1007/s10551-009-0081-5.  Google Scholar [27] R. D. Luce, Several possible measures of risk, Theory and Decision, 12 (1980), 217-228.  doi: 10.1007/BF00135033.  Google Scholar [28] R. D. Luce, Correction to "several possible measures of risk", Theory and Decision, 13 (1981), 381-381.  doi: 10.1007/BF00126971.  Google Scholar [29] R. D. Luce and E. U. Weber, An axiomatic theory of conjoint, expected risk, Journal of Mathematical Psychology, 30 (1986), 188-205.  doi: 10.1016/0022-2496(86)90013-1.  Google Scholar [30] C. Martins, T. Oliveira and A. Popovi, Understanding the internet banking adoption: A unified theory of acceptance and use of technology and perceived risk application, International Journal of Information Management, 34 (2014), 1-13.  doi: 10.1016/j.ijinfomgt.2013.06.002.  Google Scholar [31] T. Odean, Volume, volatility, price, and profit when all traders are above average, The Journal of Finance, 53 (1998), 1887-1934.   Google Scholar [32] M. Ofir and Z. Wiener, Investment in Financial Structured Products from a Rational Choice Perspective, Technical report, Hebrew University of Jerusalem, 2009. Google Scholar [33] A. M. Olazábal and H. Marmostein, Structured products for the retail market: The regulatory implications of investor innumeracy and consumer information processing, Ariz. L. Rev., 52-623 (2010), 623-673.   Google Scholar [34] C. Park, S. Ahn and S. Lee, A bayesian decision model based on expected utility and uncertainty risk, Applied Mathematics & Computation, 242 (2014), 643-648.  doi: 10.1016/j.amc.2014.06.005.  Google Scholar [35] A. Pollatsek and A. Tversky, A theory of risk, Journal of Mathematical Psychology, 7 (1970), 540-553.  doi: 10.1016/0022-2496(70)90039-8.  Google Scholar [36] M. O. Rieger and T. Hens, Explaining the demand for structured financial products: survey and field experiment evidence, Zeitschrift für Betriebswirtschaft, 82 (2012), 491-508.   Google Scholar [37] A. Tversky and D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Readings in Formal Epistemology, 1 (1992), 493-519.  doi: 10.1007/978-3-319-20451-2_24.  Google Scholar [38] X. T. Wang and J. G. Johnson, A tri-reference point theory of decision making under risk, Journal of Experimental Psychology General, 141 (2012), 743-756.  doi: 10.1037/a0027415.  Google Scholar [39] E. U. Weber, Combine and conquer: A joint application of conjoint and functional approaches to the problem of risk measurement, Journal of Experimental Psychology: Human Perception and Performance, 10 (1984), 179-194.   Google Scholar [40] E. U. Weber, Risk as an Independent Variable in Risky Choic, PhD thesis, Harvard University, 1984. Google Scholar [41] E. U. Weber and W. P. Bottom, An empirical evaluation of the transitivity, monotonicity, accounting, and conjoint axioms for perceived risk, Organizational Behavior and Human Decision Processes, 45 (1990), 253-275.  doi: 10.1016/0749-5978(90)90014-Z.  Google Scholar
The lottery form of binary structured financial products
Expected price distribution of overconfident investors when $\theta+\varepsilon>\mu$
Expected price distribution of overconfident bullish investors of type Ⅰ
Expected price distribution of overconfident bullish investors of type Ⅱ
Expected price distribution of overconfident bullish investors of type Ⅲ
Perceived risk of overconfident bullish investors of type Ⅰ
Perceived risk of overconfident bullish investors of type Ⅱ or type Ⅲ(2)(4)
Perceived risk of overconfident bullish investors of type Ⅲ(3)
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