Estimating Beta

The standard procedure for estimating betas is to regress stock returns (Rj) against market returns (Rm) -

Rj = a + b Rm

• where a is the intercept and b is the slope of the regression.

The slope of the regression corresponds to the beta of the stock, and measures the riskiness of the stock. This beta has three problems:

• It has high standard error

• It reflects the firm’s business mix over the period of the regression, not the current mix

• It reflects the firm’s average financial leverage over the period rather than the current leverage.

Solutions to the Regression Beta Problem

Modify the regression beta by

• changing the index used to estimate the beta

• adjusting the regression beta estimate, by bringing in information about the fundamentals of the company

Estimate the beta for the firm using

• the standard deviation in stock prices instead of a regression against an index

• accounting earnings or revenues, which are less noisy than market prices.

Estimate the beta for the firm from the bottom up without employing the regression technique. This will require

• understanding the business mix of the firm

• estimating the financial leverage of the firm

Use an alternative measure of market risk not based upon a regression

Within any business, firms with lower fixed costs (as a percentage of total costs) should have lower unlevered betas. If you can compute fixed and variable costs for each firm in a sector, you can break down the unlevered beta into business and operating leverage components.

                     Unlevered beta = Pure business beta * (1 + (Fixed costs/ Variable costs))

The biggest problem with doing this is informational. It is difficult to get information on fixed and variable costs for individual firms. In practice, we tend to assume that the operating leverage of firms within a business are similar and use the same unlevered beta for every firm.

Calculating Equity Betas and Leverage

Conventional approach- If we assume that debt carries no market risk (has a beta of zero), the beta of equity alone can be written as a function of the unlevered beta and the debt-equity ratio.

                                             βL = βu (1+ ((1-t)D/E))

In some versions, the tax effect is ignored and there is no (1-t) in the equation. Debt Adjusted Approach: If beta carries market risk and you can estimate the beta of debt, you can estimate the levered beta as follows
                                           βL = βu (1+ ((1-t)D/E)) - βdebt (1-t) (D/E)

While the latter is more realistic, estimating betas for debt can be difficult to do.