Fuzzy portfolio selection in the trade-off between different economy trends and security returns

Portfolio selection has been applied to the allocation of assets among the selected securities for obtaining the most profitable return. However, the theory of behavioural finance proposes that the investment proportions of securities are not only determined by the intrinsic value of the security but also largely affected by the behaviour of investors. Therefore, the behaviour analysis of an investor should play a major role in the portfolio selection. In this study, we apply a piecewise linear function to decompose the fuzzy expected return rates by judging the economy trend which transits from the current stage into the next stage and an upward or downward trend for each security return in the next stage. Analysis results indicated that we could obtain the investment proportions for the selected securities in different transitions to the economy stage with the judgement of upward or downward trend to each security. The portfolio selection in which the economy transits to the recovery stage derived a higher expected return rate than the other stages. Finally, in the illustration, any investor can use the selected portfolio by his investment behaviour after collecting the required information for the economy stage and return trends of securities.