Beta and Sharpe ratio are two of the most fundamental expressions in investment economics, but so few seem to really
understand them, and even fewer can calculate them. In a statistical sense, beta, or beta coefficient, as it is technically, is found in regression analysis. Regression assumes three constructs, including normality, homoscedasticity, and the absence of multicollinearity, all three of which are beyond our scope here. However, recalling that algebraically, “simple regression” is expressed as Y=mX+b+e, with the beta coefficient, noted as m, being considered as the degree of change in the dependent variable for every unit change in the independent variable. So, the beta coefficient is merely the slope of the best fit line for a set of data. Y is the dependent variable,
X is the independent variable, b is the constant, and e is the error in the equation. Consider the scatterplot below.