The state of the art of study of the relation between the volatility of the price of an asset and the return on it

This paper presents the state of the art of the most important results in the relation between the volatility of the price of an asset, β, and the return of the class of stocks. The majority of the empirical studies on the relation of the values of the volatility and the mean return have used arithmetic means of the percentages of discrete returns. In this paper we characterize these relationships, they are not present in text books and are not treated in theoretical papers. This will allow to establish a basis for a theoretical study of the mathematical models that appear in financial problems.