FuzzyTree crossover for multi-valued stock valuation

Stock valuation is very important for fundamental investors in order to select undervalued stocks so as to earn excess profits. However, it may be difficult to use stock valuation results, because different models generate different estimates for the same stock. This suggests that the value of a stock should be multi-valued rather than single-valued. We therefore develop a multi-valued stock valuation model based on fuzzy genetic programming (GP). In our fuzzy GP model the value of a stock is represented as a fuzzy expression tree whose terminal nodes are allowed to be fuzzy numbers. There is scant literature available on the crossover operator for our fuzzy trees, except for the vanilla subtree crossover. This study generalizes the subtree crossover in order to design a new crossover operator for the fuzzy trees. Since the stock value is estimated by a fuzzy expression tree which calculates to a fuzzy number, the stock value becomes multi-valued. In addition, the resulting fuzzy stock value induces a natural trading strategy which can readily be executed and evaluated. These experimental results indicate that the fuzzy tree (FuzzyTree) crossover is more effective than a subtree (SubTree) crossover in terms of expression tree complexity and run time. Secondly, shorter training periods produce a better return of investment (ROI), indicating that long-term financial statements may distort the intrinsic value of a stock. Finally, the return of a multi-valued fuzzy trading strategy is better than that of single-valued and buy-and-hold strategies.