Betas

Types and Calculation

Beta is a measure of a stock's systematic risk, or its sensitivity to movements in the overall market. Understanding different types of betas and how they are calculated is crucial for estimating the cost of equity and performing valuation analysis.

1. Historical Market Beta:

• Definition: Beta is estimated by regressing a stock's historical returns against the historical returns of a market index (e.g., S&P 500).
• Calculation:
  • Collect historical stock returns and market index returns (e.g., daily, weekly, or monthly).
  • Run a regression analysis with the stock's returns as the dependent variable and the market index returns as the independent variable.
  • The slope coefficient from the regression is the historical market beta.
• Sources: Financial data providers (e.g., Bloomberg, Reuters, Yahoo Finance) often provide historical betas.
• Limitations:
  • Past Performance: Based on past performance, which may not be indicative of future risk.
  • Sensitivity to Time Period: The estimated beta can vary depending on the time period used in the regression.
  • Regression Error: Subject to regression errors and noise.
  • Company Changes: Doesn't account for changes in company's business, financial leverage, or operations.

2. Fundamental Beta:

• Definition: Beta is estimated based on the company's fundamental characteristics, such as its industry, operating leverage, and financial leverage.
• Calculation:
  • Identify the factors that are most likely to influence the company's beta.
  • Estimate the sensitivity of the company's stock returns to each factor.
  • Combine the factor sensitivities to arrive at an overall estimate of the company's fundamental beta.
• Factors to Consider:
  • Cyclicality of Revenues: Companies with cyclical revenues (e.g., automakers, construction companies) tend to have higher betas.
  • Operating Leverage: The degree to which a company's costs are fixed rather than variable. Companies with high operating leverage tend to have higher betas.
  • Financial Leverage: The amount of debt in a company's capital structure. Companies with high financial leverage tend to have higher betas.
• Limitations:
  • Subjectivity: Requires judgment and assumptions about the relationship between fundamental characteristics and beta.
  • Data Availability: May be difficult to obtain reliable data on some fundamental characteristics.

3. Bottom-Up Beta:

• Definition: Beta is estimated by averaging the betas of comparable companies in the same industry, and then adjusting for the company's financial leverage. This leverages the idea that similar businesses face similar market risks.
• Calculation:
  1. Identify comparable companies in the same industry.
  2. Calculate or obtain the unlevered beta (asset beta) for each comparable company (see below for calculation).
  3. Average the unlevered betas of the comparable companies to arrive at an industry average unlevered beta.
  4. Lever the industry average unlevered beta using the company's debt-to-equity ratio to arrive at an estimate of the company's beta.
• Formula: β_levered = β_unlevered * [1 + (1 - Tax Rate) * (Debt/Equity)]
• Advantages:
  • More reliable than historical beta, as it is based on a larger sample of companies.
  • Allows for adjustments for differences in financial leverage.
• Limitations:
  • Comparable Selection: The accuracy of the bottom-up beta depends on the selection of comparable companies.
  • Industry Definition: Defining the appropriate industry can be challenging.
  • Assumes Similar Operating Risk: Assumes that the comparable companies have similar operating risk.

4. Accounting Beta:

• Definition: Beta is estimated by regressing a company's accounting earnings (e.g., return on assets, return on equity) against the average accounting earnings of a peer group or a market index.
• Calculation:
  • Collect historical accounting earnings data for the company and a peer group or market index.
  • Run a regression analysis with the company's accounting earnings as the dependent variable and the peer group or market index earnings as the independent variable.
  • The slope coefficient from the regression is the accounting beta.
• Applicability: Useful for private companies or when market data is unavailable or unreliable.
• Limitations:
  • Accounting Data: Based on accounting data, which may be subject to manipulation or distortion.
  • Limited Frequency: Accounting data is typically only available on a quarterly or annual basis, limiting the sample size for the regression.
  • Correlation with Market Beta: Accounting beta may not be highly correlated with market beta.

5. Unlevered Beta and Levered Beta:

• Unlevered Beta (Asset Beta):
  • Definition: A measure of a company's systematic risk that excludes the effects of financial leverage (debt). It reflects the risk of the company's assets, independent of how the company is financed.
  • Formula: β_unlevered = β_levered / [1 + (1 - Tax Rate) * (Debt/Equity)]
• Levered Beta (Equity Beta):
  • Definition: A measure of a company's systematic risk that includes the effects of financial leverage (debt). It reflects the risk of the company's equity, taking into account the impact of debt financing.
  • Formula: β_levered = β_unlevered * [1 + (1 - Tax Rate) * (Debt/Equity)]
• Importance:
  • Comparing Companies with Different Capital Structures: Unlevered beta allows for comparing the operating risk of companies with different capital structures.
  • Bottom-Up Beta Calculation: Unlevered beta is used in the bottom-up beta calculation to estimate the industry average beta.
  • Adjusting for Changes in Capital Structure: Levered beta can be adjusted to reflect changes in a company's capital structure.

Understanding the different types of betas and how they are calculated is essential for estimating the cost of equity and performing accurate valuation analysis. When valuing a company, consider using a combination of different beta estimation methods and carefully evaluate the assumptions and limitations of each method.