Calculating Beta Using Market Model Regression (Slope)

This lesson is part 8 of 12 in the course Cost of Capital

While calculating the cost of equity, it is important for an analyst to calculate the beta of the company’s stock.

Beta of a publicly traded company can be calculated using the Market Model Regression (Slope).

In this method, we regress the company’s stock returns (r_i) against the market’s returns (r_m). The beta (β) is represented by the slope of the regression line.

$r_{i}=\alpha +\beta r_{m}$

Where,

r_i is the stock’s return

α represents the intercept

β is the stock’s beta

r_m is the market returns

See this article – How to Calculate Stock Beta Using Excel

Some of the issues while calculating beta are discussed below:

Estimation period: Beta is usually estimated using the historical data for 2-9 years. The choice of estimation period affects the calculation of Beta. If the estimation period is short, it does reflect the current dynamics of the company. For example, for a company that has recently undergone structural changes, it’s better to use short estimation period for calculating beta. However, for a company that has a stable operating history, a long estimation period will be suitable.
Return interval: An analyst may take daily, weekly, or monthly returns of the stock and market while performing regression. Generally a shorter observation period such as daily returns leads to lower standard error.
Choice of the market index: The analyst also needs to carefully choose a market index to regress the returns against.
Smoothing techniques: Betas also have a tendency to revert to 1. Analysts may have to use some smoothing techniques to adjust the beta.
Small-cap stocks: The small cap stocks tend to be more risk with a higher return potential. Therefore, analysts may want to adjust the beta pf small cap stock upwards.

Using the above methods, we can easily estimate the beta of a publicly traded company, as all the information such as historical returns is publicly available. The problem arises when an analyst is required to estimate the beta of a non-public company or a project, for which there is no historical stock return data. The analyst may have to use a proxy of the beta by using some combination of the information available about the company/project and a comparable public limited company. A commonly used method is the pure-play method, in which an analyst observes the beta of a comparable public company, and adjusts it for the difference in financial leverage.