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##### Subject 3. The Required Return on Equity - The CAPM Approach
This is a Level I concept. To recap:

Required return on share i = rf + βf (equity risk premium)

For example, firm A has a βi of 0.6 for its stock. The risk-free rate, Rf, is 5%. The expected rate of return on the market, E(RM), is 10%. The firm's cost of common equity is therefore calculated as 5% + (10% - 5%) x 0.6 = 8%.

Both the βi and the equity risk premium need to be estimated.

To estimate βi an analyst needs to make several choices:

• Which index should be used to represent the market portfolio? The S&P 500 is a traditional choice to represent U.S. equities.
• What should be the length of data period and the frequency of observations?

Adjusted beta is a historical beta adjusted to reflect the tendency of beta to be mean-reverting. The motivation for adjusting beta estimates is that, on average, the beta coefficients of stocks seem to move toward 1 over time.

The Blume method adjusts beta estimates in a simple way. It takes the sample estimate of beta and averages with 1, using weights of two-thirds and one-third:

Adjusted β = 2/3 Sample β + 1/3 (1)

An adjusted beta tends to predict future beta better than historical beta.

Estimate Beta for a Private Firm

Most models of risk and return use past prices of an asset to estimate its risk parameters (beta(s)). Private firms, however, are not traded and thus do not have past prices. The beta for a private firm can be estimated by looking at the average betas for publicly traded companies in the same industry. Any differences in financial leverage can be adjusted for in the final estimate.

• Estimate the average beta for the public traded comparable firms. This is the benchmark beta (levered): βe.
• Estimate the average market value debt-equity ratio of these firms, and calculate the unlevered beta for the business: βu = βe/ (1 + D/E).
• Estimate the debt-equity ratio for the private firm: D'/E'.
• βprivate firm = βu (1 + D'/E'/)

This method is called pure-play which is covered in Level I.

Learning Outcome Statements

c. determine the required return on an equity investment using the capital asset pricing model, the Fama-French model, the Pastor-Stambaugh model, macroeconomic multifactor models, and the build-up method (e.g., bond yield plus risk premium);

d. explain beta estimation for public companies, thinly traded public companies, and non-public companies;

e. describe strengths and weaknesses of methods used to estimate the required return on an equity investment;

f. explain international considerations in required return estimation;

CFA® 2023 Level I Curriculum, Volume 3, Module 21

User Comment
actiger What does D/E tell about Beta? Is beta for private firm usually high or low?
JBryce The greater a firms reliance on debt finance, the greater its equity beta.

Beta estimates from private (or smaller cap) companies are usually adjusted upward to reflect the risk inherent in small firms.
soorajiyer Thanks JBryce, nice points to note!