Illusion of Control as a Source of Poor Diversification: Experimental Evidence

Abstract

Abstract This paper investigates factors that influence individual portfolio allocations, with particular focus on illusion of control. Participants in the experiment form their portfolios of two risky lotteries and one risk-free alternative with the target to reach a predetermined income. Subjects show illusion of control as they excessively invest in a lottery when they are in charge of the chance move. This finding is amplified when self-selection is possible and mitigated when a well-diversified default portfolio is offered. Presenting sequences of chance moves prior to investment does not affect diversification. In line with excessive extrapolation, the higher the number of observed positive prior outcomes, the more likely is a positive prediction and in turn a higher investment. Keywords: Investment decisionsPortfolio selectionEgocentric biasesIllusion of controlExcessive extrapolationUnrealistic optimismExperimental economics ACKNOWLEDGMENTS I am indebted to Uwe Cantner and Werner Güth for valuable comments and Bettina Bartels and Håkan Fink for research assistance. Financial support by the Max Planck Institute of Economics, Jena, is gratefully acknowledged. Notes 1. In 2001, the balances in 401(k) accounts amounted to $ 1.76 trillion. That corresponds to 44% of all assets in private trusteed retirement plans (data from McDonnell [2002] and Holden and VanDerhei [2003]). 2. While nonexperts usually expect the continuation of a past trend in prices (DeBondt [1993] DeBondt, W. F. M. 1993. "Betting on Trends: Intuitive Forecasts of Financial Risk and Return.". International Journal of Forecasting, 9: 355–371. [Crossref], [Web of Science ®] , [Google Scholar]), economic experts too often predict contrarian developments, resembling a gambler's fallacy (DeBondt [1991] DeBondt, W. F. M. 1991. "What Do Economists Know About the Stock Market?". Journal of Portfolio Management, 18: 84–91. [Google Scholar]). 3. Instructions are available from the author upon request. 4. The exchange rate to [euro] was 20:1; that is, 100 ECU corresponded to [euro]5. 5. This procedure of reaching a target resembles aspiration levels as suggested by the bounded rationality concept (Simon [1955] Simon, H. 1955. "A Behavioral Model of Rational Choice.". Quarterly Journal of Economics, 69: 99–118. [Crossref], [Web of Science ®] , [Google Scholar]). Not only does it help to make the merits of diversification clear to subjects, but it also supports the saliency of payments: the endowment is only of value if subjects succeed in increasing it. 6. The assumption that individuals try to maximize the probability of reaching their profit target and therefore grant a positive income is weaker than the assumption of μ −σ-preferences that is required to calculate the optimal portfolio allocation according to standard portfolio theory (Markowitz [1952]). However, risk neutral individuals who decide only upon expected value of the portfolio should invest solely in B, the prospect with the higher expected return. Still, the results on the elicitation of individual risk attitudes justify the general assumption of risk aversion. 7. This objective closely resembles the safety-first criterion of portfolio selection proposed by Roy [1952] Roy, A. D. 1952. "Safety-first and the Holdings of Assets.". Econometrics, 20: 431–449. [Crossref], [Web of Science ®] , [Google Scholar], which avoids the complex expected utility calculus. Instead, the investor seeks the portfolio that minimizes the probability of producing a return below a specified level. 8. In any case subjects were compensated with the show-up fee and earned a small amount according to their lottery choice in stage one. 9. The fact that in the baseline treatment one die throw determines the return of the investment for all participants while in the illusion of control treatments, subjects individually throw the die for one of the two investments creates more heterogeneity in payments in the illusion of control treatments than in the baseline treatment. However, this has no immediate consequence for the individual investment task, since it should be anyhow irrelevant if the die for one investment is thrown by the subject or the experimenter. 10. It was duly explained that, for instance, a confidence level of 100 means being correct 100 times out of 100 predictions. Subjective confidence was, however, not monetarily rewarded. 11. Denoting p() = p = p(), lottery X is preferred to lottery Y if with the left hand-side being positive for the experimental parameter constellation. 12. Subjects who did not switch to the higher sure payoff in lottery 10 were also excluded from this analysis, since it can be assumed that they did not exhibit effort in making their choice. 13. The advantage of a regression analysis in comparison to non-parametric comparisons of distributions is that potentially influential personal characteristics, like risk attitude, or situational parameters, such as win or loss experiences, can be controlled for. However, all results can essentially be reproduced in nonparametric pairwise treatment comparisons. 14. Note, that the base period in this regression is in fact period 2, since period 1 is not considered because of lagged variables. Taking period 1 as baseline instead, risk-free investment decreases significantly over all periods.