Abstract
Yang and Qiu proposed and then recently improved an expected utility-entropy (EU-E) measure of risk and decision model. When segregation holds, Luce et al. derived an expected utility term, plus a constant multiplies the Shannon entropy as the representation of risky choices, further demonstrating the reasonability of the EU-E decision model. In this paper, we apply the EU-E decision model to selecting the set of stocks to be included in the portfolios. We first select 7 and 10 stocks from the 30 component stocks of Dow Jones Industrial Average index, and then derive and compare the efficient portfolios in the mean-variance framework. The conclusions imply that efficient portfolios composed of 7(10) stocks selected using the EU-E model with intermediate intervals of the tradeoff coefficients are more efficient than that composed of the sets of stocks selected using the expected utility model. Furthermore, the efficient portfolio of 7(10) stocks selected by the EU-E decision model have almost the same efficient frontier as that of the sample of all stocks. This suggests the necessity of incorporating both the expected utility and Shannon entropy together when taking risky decisions, further demonstrating the importance of Shannon entropy as the measure of uncertainty, as well as the applicability of the EU-E model as a decision-making model.
Highlights
The von Neumann and Morgenstern expected utility model [1] has been generally accepted as a normative decision-making model of rational choice under risk, and widely applied as a descriptive model of economic behavior [2]
Taking 30 component stocks of Dow Jones Industrial Average (DJIA) in December 2016 as an example, we select a set of stocks from 30 component stocks, and derive efficient portfolios using this set of stocks
We applied the expected utility-entropy (EU-E) decision model to stock selection for portfolios of 7(10) stocks from the 30 DJIA components stocks, and derived efficient portfolios using sets of stocks selected by the EU-E model for different values of λ
Summary
The von Neumann and Morgenstern expected utility model [1] has been generally accepted as a normative decision-making model of rational choice under risk, and widely applied as a descriptive model of economic behavior [2]. As a measure of uncertainty of returns, can be an important factor to select an appropriate set of stocks in which to invest This consideration suggests the use of the EU-E decision-making model to select stocks at first, after which various kinds of portfolios can be constructed to invest using these stocks. Differing from previous studies, in this paper, we apply the EU-E decision model to stock selection, i.e., selecting the set of stocks with the lowest EU-E measure of risk for tradeoff coefficients within certain intervals, and derive the efficient portfolios using these sets of stocks in the mean-variance framework proposed by Markowitz. Yang et al [23], the conclusions in this paper further demonstrate the necessity of incorporating both the expected utility and Shannon entropy together for risky choices, and shows the usefulness of Shannon entropy as the measure of uncertainty in a decision-making model. The results show that the EU-E decision model can be a useful method for stock selection
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