![]() This function calculates the gradient of the best-fitted line when we plot Y against X. Method 1: Using Slope() and Intercept()įor 2-dimensional fitting problems like finding the Alpha and Beta of a portfolio, you can use the SLOPE() and INTERCEPT() function in Excel. To simplify matters, lets set the risk-free rate, Rf, to zero. Let’s say we have the monthly returns of a US portfolio and we want to know its Alpha and Beta against the S&P 500 index. Rp is the portfolio return, Rm is the market return and Rf is the risk-free rate. The equation below is what we want to fit. If you want a recap on what Alpha and Beta is, please read this article. Regression Example (Alpha and Beta) Finding the Alpha and Beta of a Portfolio ![]() Else, let’s see how we can use Excel to find the Alpha and Beta of a portfolio. In case you want a more rigorous treatment of the topic, you can look up Wikipedia. If you took high school math, this should not be something unfamiliar. I am not going into the academic details. Given the Ys and Xs, linear regression tells you what are the ms (gradients) and c (constant). X1, …, Xn are the independent variables.m1, …, mn are the exposure (gradients) to the respective independent variables Xs.The central idea is to determine the best fitted straight line, plane or hyperplane through the data points depending on how many input variables (dimensions) there are. As we vary the inputs, we want to observe its impact on the outcome. In mathematical terms, we call this outcome the dependent variable and the inputs the independent variables. ![]() Linear regression is, as the name suggests, about investigating linear relations between an outcome and one or more inputs. But it is, in fact, simple and fairly easy to implement in Excel. If you are new to this, it may sound complex. For instance, within the investment community, we use it to find the Alpha and Beta of a portfolio or stock. Linear regression is a widely used data analysis method.
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