Do You Use Levered or Unlevered Beta in CAPM?

The Capital Asset Pricing Model (CAPM) is a widely recognized framework for estimating an investment’s expected return, helping investors determine an appropriate rate of return for an asset based on its risks. Beta, a central CAPM component, quantifies an asset’s systematic risk or its volatility relative to the overall market. Understanding whether to employ a levered or unlevered beta in CAPM is a frequent question for investors.

What Beta Represents

Beta measures systematic risk, the non-diversifiable risk inherent to the entire market or economy. This risk stems from macroeconomic factors like inflation, interest rate changes, or broad economic downturns that affect all investments. Unlike unsystematic risk, which is company-specific and diversifiable, systematic risk cannot be eliminated by holding a diverse portfolio. Beta indicates how sensitive a security’s returns are to market movements.

Beta for publicly traded companies is derived through regression analysis, comparing historical stock returns against a market benchmark like the S&P 500 index. The regression line’s slope represents the beta coefficient. A beta of 1 suggests the stock’s price moves with the market; greater than 1 indicates higher volatility, and less than 1 suggests lower volatility.

The beta observed for a company with financial debt is known as “levered beta” or “equity beta.” This beta reflects both the company’s business and financial risk from debt. Financial databases commonly report levered beta, making it readily available.

The Impact of Financial Leverage

Financial leverage, using borrowed funds to finance assets, significantly impacts a company’s equity risk and beta. Debt amplifies equity return volatility, making levered beta higher than without debt. More debt commits a larger portion of earnings to servicing, increasing uncertainty for equity holders. This heightened financial risk translates into a higher levered beta.

To isolate a company’s operational or business risk, independent of its capital structure, “unlevered beta” is used. Also known as asset beta, it represents the systematic risk of a company’s assets as if it had no debt. It strips away leverage’s financial effects, providing a clearer view of risk from core operations.

To “unlever” a company’s observed (levered) beta and arrive at its unlevered beta, adjusting for the impact of debt and taxes is involved. The Hamada equation is used for this purpose, theoretically linking levered and unlevered betas. While specific formulas can vary, a general form for unlevering beta involves dividing the levered beta by a factor that accounts for the debt-to-equity ratio and the company’s tax rate. For instance, the simplified Hamada equation can be expressed as: Unlevered Beta = Levered Beta / [1 + (1 – Tax Rate) (Debt / Equity)].

Conversely, to “relever” an unlevered beta, the process is reversed, adding back the financial risk for a specific capital structure. This allows analysts to adjust an unlevered beta to reflect a target company’s or project’s unique debt-to-equity ratio. These adjustments are performed to compare companies with differing capital structures or to evaluate the risk of a project or private entity using comparable public company data.

Choosing the Right Beta for CAPM

The decision to use levered or unlevered beta in the Capital Asset Pricing Model depends on the specific application and the nature of the asset being valued. For valuing the equity of a publicly traded company, its observed levered beta is the appropriate choice for use in the CAPM. This market-derived levered beta incorporates the company’s existing capital structure and reflects the financial risk borne by its equity investors. Using the company’s own levered beta directly in the CAPM accounts for its current financial leverage.

However, unlevered beta is indispensable when valuing projects, divisions, private companies, or comparing companies with dissimilar capital structures. Since private companies and new projects do not have readily observable market betas, an unlevered beta can be estimated by analyzing comparable publicly traded companies in the same industry. The levered betas of these comparable firms are first “unlevered” to remove the effect of their respective debt levels, yielding an average unlevered beta that represents the industry’s business risk.

This average unlevered beta is then “relevered” to reflect the specific debt-to-equity ratio and tax rate of the project or private company being valued. This process ensures that the beta used in the CAPM accurately reflects the financial risk of the target entity’s intended capital structure. The goal is to match the beta to the specific equity or project being valued, considering its unique financial leverage profile.