Beta

Anyone who has ever dealt with valuation or modern corporate finance has probably encountered the use of beta. In modern finance beta is the key relative risk measure used in the Capital Asset Pricing Model (CAPM) to determine the risk premium demanded by equity investors. I’d like to take a minute to talk about what exactly beta is measuring along with methods by which to determine the beta used in CAPM.

Let’s begin with what exactly beta is meant to measure. Beta is a measure of systemic risk of a security versus the market as a whole. It is generally viewed as the covariance between the returns of the security and the returns of the aggregate market divided by the variance of returns of the aggregate market. Or rewritten as the correlation between the returns of the stock and the aggregate market multiplied by the standard deviation of the stock returns dividend by the standard deviation of aggregate market returns. 

Most commonly these calculations are done using a simple regression with the returns of the aggregate market being the independent variable and the returns of the stock being the dependent variable. The regression result will provide the coefficient of the x variable which will represent beta. In essence, if we apply the simple linear equation (Y = mX + B) the “m” is beta which show how much of a movement can be expected in the given stock based on the movement of the aggregate market. It is common to use the returns of the S&P 500 to represent the market and between a 3-5 year time horizons for return data.

While much more could be said regarding the technical side of regressing to find beta, I would like to look at one simple fact. In any regression the coefficient of determination (R²) indicates how much of the data can be explained by the regression model. Put simply, it is a measure of accuracy within the regression model. In almost any regression model to find beta, the R² will be very low (0.30 or less), this leads us to question the accuracy of using this method to calculate such an important variable when calculating the cost of equity capital.

Before I get into an alternative method for beta, I would like to shift our focus back to what beta measures for a moment. Beta is the measure of systemic risk of a firm, and part of this risk is both operating risk and financial risk. Operating risk can be defined as the risk inherent in a firm that is fully financed with equity, essentially the risk of the business if it had not required debt payments. The firm’s operating risk is impacted by the amount of fixed versus variable costs. The other part of this risk is financial risk, which is the risk as firm’s equity holder bear due to the use of leverage and thus required debt payments. Now in calculating a regression beta we will have a result of levered beta, which is the beta that includes both operating risk and financial risk. Let’s now jump to an alternative method for calculating beta. 

An alternative that is commonly used is to first identify the firm’s industry and collected data on a group of comparable companies. Then take these firms and run a simple regression to calculate beta. The betas collected, as described above, are levered betas. Since our firm, and each firm in the group of comparable companies will most likely have different uses of leverage, we must “unlever” these betas. The process of unlevering beta is essentially factoring in both the amount of debt capital used as compared to equity capital along with the benefits provided by the tax shield offered from interest payments. Levered beta can also be calculated from unlevered beta. The calculations for both are described below.

To continue with the alternative beta calculation, you first must take the levered betas found through regression and unlevered each of these based on each firms respective debt to equity capital structure and corporate marginal tax rate. Then a mean or median of these unlevered betas can be used to determine and estimate for the industry beta; the choice of mean of median will be a judgment based on variance of these betas. Once the industry’s unlevered beta is found, the beta can be relevered using our given firm’s debt to equity structure and marginal tax rate to determine the beta used within the CAPM.

Now you may ask “what is the benefit of completing this process versus using a simple regression?” Well as discussed above, simple regressions have very low predictability value and can lead to misleading betas. By using this alternative, you are collecting date on multiple firms within the industry which can eliminate some of the risk of having an outlier. Is it perfect? No, but I do believe that it can provide a better estimate of the true systemic risk of a firm. 

Hope you found this interesting.