Abstract
While the international lockdown for the COVID-19 pandemic has greatly influenced the global economy, we are still confronted with the dilemma about the economy recession when the stock market hits record highs repeatedly. As we know, since portfolio selection is often affected by many non-probabilistic factors, it is of not easiness to obtain the precise probability distributions of the return rates. Therefore, fuzzy portfolio model is proposed for solving the efficient portfolio when the economy environment remains in vagueness for the future. To manage such an investment, we revise the Chen and Tsaur’s fuzzy portfolio model by using fuzzy goal programming model. Then, two numerical examples are illustrated by the proposed model which shows that the portfolio selection can be solved by the linguistic imprecise goal of the expected return. With different linguistic descriptions for the imprecise goal of expected return for the future stock market, the optimal portfolio selection that can be solved under different investment risks which is considered better than Chen and Tsaur’s model in real world situations. The sensitivity analysis with some parameter groups can be provided for more invested risk selection in the portfolio analysis.
Highlights
Portfolio selection is first proposed by Markowitz [1] to deal with the fact that asset future returns are represented by random variables where the mean-variance model has been developed by some famous researchers, including Sharpe [2], Pang [3], Best and Grauer [4], Best and Hlouskova [5], and Mari [6]
The second example is a real case study from Taiwan Stock Exchange (TWSE) covering the COVID-19 spreading period, and we show that our proposed model can applied to the portfolio selection under different investment risks with the given imprecise goal of expected return
In order to obtain the portfolio selection to be as near as the imprecise goal of expected return b from the collected data, we suggest that if the decision maker is optimistic about the stock market, we choose the larger values of p1, p2, and p3
Summary
Portfolio selection is first proposed by Markowitz [1] to deal with the fact that asset future returns are represented by random variables where the mean-variance model has been developed by some famous researchers, including Sharpe [2], Pang [3], Best and Grauer [4], Best and Hlouskova [5], and Mari [6]. Wang et al [14] propose a new portfolio-selection model based on fuzzy value-at-risk and directly reflect the greatest loss of a selected case at a given confidence level by an improved particle swarm optimization algorithm. Chen and Tsaur [17] use a weighted function to propose a weighted fuzzy portfolio model to approach portfolio selection differently in response to the varying investment return for each stage of the business cycle. In order to cope with the above two issues, we try to revise Chen and Tsaur’s model [17] to analyze the fuzzy portfolio selection in the recession stage of business cycle to imitate the vague stock market information in the COVID-19 spreading period.
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