The Pricing of Risky Securities in a Fuzzy Least Square Regression Model

This work aims to estimate the relationship between the expected return of a financial investment and its risk by means of a fuzzy version of the Capital Asset Pricing Model (CAPM). The expected return is usually computed as a function both of the rate of a risk-free security, that represents the time value of money, and of a premium that compensates investors for taking on an additional risk in the market. Actually we estimate the parameters of a simple regression model, where the dependent variable consists in the percentage change in prices of a surveyed (stable or volatile) stock and the independent variable consists in the percentage change in market indexes. As both changes in closure prices only partially represent the actual trend in returns, we use a range of observed values for each price; this allows us to estimate the sensitiveness of the stock to risk by means of the so called Fuzzy Least Square Regression. The corresponding estimates are compared with the ones obtained by means of the Ordinary Least Square Regression.