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 fi-nancial investment and its risk by means of a fuzzy version of the Capital Asset Pricing Model. The expected return is usually computed depending both on the rate of a risk-free security, that representing the time value of money, and on a premium that compensates investors for taking on an additional risk in the market. In this case we estimated the parameters of a simple regression model, where the dependent variable consists in the percentage change in prices of the surveyed investment and the independent variable consists in the percentage change in market rates. As both changes are characterized by an uncertain nature and can be treated as tri-angular fuzzy numbers, we estimated the sensitiveness of the investment to risk by means of the so called Fuzzy Least Square Regression. The corresponding results are compared with the ones obtained by means of the Ordinary Least Square Regression.