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Decision Theory Matters for Financial Advice

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Abstract

We show that the optimal asset allocation for an investor depends crucially on the decision theory with which the investor is modeled. For the same market data and the same client data different theories lead to different portfolios. The market data we consider is standard asset allocation data. The client data is determined by a standard risk profiling question and the theories we apply are mean–variance analysis, expected utility analysis and cumulative prospect theory. For testing the robustness of our results, we carry out the comparisons for alternative data sets and also for variants of the risk profiling question.

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Notes

  1. Comparing also with expected utility, which is consistent with second-order stochastic dominance, implies that we also touch on portfolio optimization based on stochastic dominance that was recently proposed by Kopa and Post (2015) for second-order stochastic dominance and in a subsequent paper by Post and Kopa (2016) for third-order stochastic dominance.

  2. BhFS stands for Behavioral Finance Solutions, which is a spin-off company of the universities of St. Gallen and Zurich; for more information, see www.bhfs.ch.

  3. The classical definition is the ratio of gains to losses which an investor with piecewise linear utility finds indifferent to an outside option of zero on a binary lottery with equal probabilities.

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Acknowledgements

This research was supported by the Swiss National Science Foundation, Grant No. 100018-149934.

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Correspondence to Thorsten Hens.

Appendix

Appendix

See Tables 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13 and Figs. 7, 8, 9, 10, 11 and 12.

Table 3 Summary statistics for the monthly-returns data set; the statistics is for annualized data
Table 4 The empirical distribution, constructed via k-means clustering (\(k=15\)) from the monthly returns data set with the last column corresponding to the appended European call-option on MXWO
Table 5 The CPT parameter values from Abdellaoui et al. (2007), the computed \(\gamma \) and \(\delta \) values, the computed losses \(-x\) in the lottery as well as the corresponding \(\kappa \), \(\alpha \) and \(\theta \) parameters in the alternative objective functions
Table 6 Original data set: distances between the portfolios measured in terms of CE, expressed in percents and showing annualized values
Table 7 Call option added: distances between the portfolios measured in terms of CE, expressed in percents and showing annualized values
Table 8 Associated normal distribution: distances between the portfolios measured in terms of CE, expressed in percents and showing annualized values
Table 9 Fama–French industrial data set: distances between the portfolios measured in terms of CE, expressed in percents and showing annualized values
Table 10 Fama–French factors data set: distances between the portfolios measured in terms of CE, expressed in percents and showing annualized values
Table 11 Second lottery type with \(p=0.5\), original data set: distances between the portfolios measured in terms of CE, expressed in percents and showing annualized values
Table 12 CPT–EUQ: distances between the portfolios measured in terms of CE, expressed in percents and showing annualized values
Table 13 EUQ–CPT: distances between the portfolios measured in terms of CE, expressed in percents and showing annualized values
Fig. 7
figure 7

Original data set; portfolios selected according to the four different portfolio selection approaches

Fig. 8
figure 8

Call option added; portfolios selected according to the four different portfolio selection approaches

Fig. 9
figure 9

Associated normal distribution; portfolios selected according to the four different portfolio selection approaches

Fig. 10
figure 10

Fama–French industry portfolios; average value-weighted monthly returns; portfolios selected according to the four different portfolio selection approaches

Fig. 11
figure 11

Fama–French benchmark factors; monthly returns; portfolios selected according to the four different portfolio selection approaches

Fig. 12
figure 12

Original data set; second type of lottery with \(p=0.5\); portfolios selected according to the four different portfolio selection approaches

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Hens, T., Mayer, J. Decision Theory Matters for Financial Advice. Comput Econ 52, 195–226 (2018). https://doi.org/10.1007/s10614-017-9668-6

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