The Fuzzy Portfolio Selection Based On Enhanced Tracking Index Model Under The Frictional Market

In modern finance, portfolio selection theory based on stochastic uncertainty has been well developed, however, the uncertainty in the stock market mostly demonstrated fuzzy uncertainty. The ambiguity of the securities market in previous theoretical studies has been ignored, so the portfolio selection problem based on fuzzy uncertainty has a very important and far-reaching significance in theory and practice.By combining the fuzzy function with index investment theory, this article builds up three fuzzy portfolio selection models based on enhanced index tracking model in the friction market. When it comes to the friction factors in the financial markets, all the three models only take the transaction cost into account, which is proportional to the number of transaction. This article uses minimax semi-absolute deviation index tracking error to measure risk, and then obtains the index tracking portfolio model by minimizing the error. Furthermore, given the constraints such as short selling restriction, the transaction cost in the real market and the portfolio’s expected return, the investors will have a minimum requirement about expected return, therefore we have offered the enhanced index tracking model. The three models are as follows:Firstly, introduce the liquidity, and see the portfolio’s liquidity as a fuzzy number, then we construct the first model which is the enhanced index tracking portfolio selection model with fuzzy liquidity constraint. Secondly, since investors’ satisfactory level of Portfolio’s expected return and tolerance level of tracking error is uncertain and vague, in order to measure investors’ satisfaction, we see those two targets as half trapezoidal fuzzy membership functions, then we get the second model which is enhanced index tracking portfolio selection model based on fuzzy decisions. Finally, considering tracking error, investors’ expected return and liquidity, we see the three objectives as non-linear membership function to describe investors’ satisfaction, which in turn construct a multi-objective fuzzy enhanced index tracking model. In the end, this article chooses the CSI300Index to be the underlying index, and randomly selects15constituent stocks of CSI300Index as the investment objective, and then does an empirical analysis by changing the models’ parameters to describe investors’ satisfaction level as accurately as possible, and finally gets all different portfolios under different parameters.