PRICING STOCKS BY USING FUZZY DIVIDEND DISCOUNT MODELS

Abstract

Although the classical discount model (DDM) is a well- known and widely used model in evaluating the intrinsic price of common stock, the practical pattern of dividends, required rate of return or growth rate of do not generally coincide with any of the model's assumptions. It is just the opportunity to develop a fuzzy logic system that takes these vague parameters into account. This paper extends the classical DDMs to more realistic fuzzy pricing models in which the inherent imprecise information will be fuzzified as triangular fuzzy numbers, and introduces a novel -signed distance method to defuzzify these fuzzy parameters without considering the membership functions. Through the conscientious mathematical derivation, the fuzzy discount models (FDDMs) proposed in this paper can be regarded as one more explicit extension of the classical (crisp) DDMs, so that stockholders can use it to make a specific analysis and insight into the intrinsic value of stock. Stock represents an ownership interest in a corporation, but for the typical stock- holders, the purpose of holding the stock can be simply characterized by two fea- tures: one is to expect to receive the continuous payments by holding the stock; another is to earn a capital gain by selling the stock at a certain higher price. Generally speaking, common stocks are evaluated on the basis of either a corpora- tion's expected profitability or its expected distributions to stockholders. Since the analysis of common stocks can be based on the analysis of its payments, if stockholders can estimate the future cash-flow streams of payments by matching up an appropriate discount rate, then the theoretical value of the stock can be easily determined. The evaluating method is commonly known as the dividend discount models (DDMs) (1, 6, 15). However, such the classical DDMs do not take the imprecision into account that may be inherent in these parameters used in it. These parameters include future cash-flow streams of distributions, required rate of return, and growth rate of which are always subjectively quantified and determined by the listed companies. Thus, previous study has applied such a model to derive the upper and lower bounds of fluctuation of stock price, but the empirical result showed that the real stock price obviously went beyond the scope (16). In addition, most