Unlevered beta

Unlevered Beta: Definition, Formula, Example, and FAQs

What Is Unlevered Beta?

Unlevered beta, also known as asset beta, is a crucial metric in portfolio theory that measures the systematic risk of a company's assets without considering the impact of leverage or debt in its capital structure. It isolates the pure business risk inherent in a company's operations, making it possible to compare the risk profiles of different companies, irrespective of how they are financed. While Beta generally quantifies a security's sensitivity to overall market risk, unlevered beta strips away the additional volatility that comes from a company's borrowing.⁴⁵

History and Origin

The concept of beta, fundamental to unlevered beta, originated with the development of the Capital Asset Pricing Model (CAPM). William F. Sharpe, who shared the Nobel Memorial Prize in Economic Sciences in 1990 for his work on the CAPM, introduced the idea that a security's expected return is tied to its sensitivity to market movements.⁴⁴ His seminal 1964 paper, "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," laid the groundwork for quantifying systematic risk through beta.⁴², ⁴³

The distinction between levered and unlevered beta became particularly relevant with the advent of the Modigliani-Miller (MM) theorem. Franco Modigliani and Merton Miller's propositions, particularly their "irrelevance proposition" without taxes, posited that a firm's value is independent of its capital structure. This theoretical framework, developed in the 1950s, highlighted the importance of separating operational risk from financial risk, providing the conceptual basis for "unlevering" beta to reflect only the inherent business risk.³⁹, ⁴⁰, ⁴¹ The Federal Reserve Bank of San Francisco has also published on the Modigliani-Miller theorem's implications for capital structure and firm value. [External Link 1]

Key Takeaways

Unlevered beta measures a company's pure business risk, excluding the effects of financial leverage.³⁸
It is often referred to as "asset beta" because it reflects the volatility of a company's assets.³⁷
Unlevered beta is crucial for comparing the inherent risks of companies with different capital structures.³⁶
It is a key input in financial models such as discounted cash flow (DCF) analysis, especially when determining the cost of equity.³⁵
Unlevered beta helps in valuing private companies or projects by allowing analysts to use the beta of comparable publicly traded firms.³⁴

Formula and Calculation

The formula to calculate unlevered beta from levered beta is:

\beta_U = \frac{\beta_L}{1 + \left(1 - T\right) \times \left(\frac{D}{E}\right)}

Where:

(\beta_U) = Unlevered Beta (Asset Beta)
(\beta_L) = Levered beta (Equity Beta), which is the beta observed for a company's stock, including the effects of its debt-to-equity ratio.³², ³³
(T) = Corporate Tax Rate
(D) = Market Value of Debt
(E) = Market Value of Equity

This formula effectively removes the risk attributed to a company's debt, leaving only the risk associated with its core business operations.³⁰, ³¹

Interpreting the Unlevered Beta

Unlevered beta provides a clearer picture of a company's underlying operational risk. A higher unlevered beta indicates that the company's assets are more sensitive to overall market movements, implying greater inherent business volatility. Conversely, a lower unlevered beta suggests less sensitivity and a more stable business.²⁹ When analyzing companies for valuation or investment, comparing unlevered betas allows investors to focus on the operational aspects, free from the distortions introduced by varying levels of leverage across firms. For example, two companies in the same industry might have very different equity betas due to different debt levels, but their unlevered betas would reveal their comparable underlying business risk.²⁸

Hypothetical Example

Imagine an analyst is tasked with valuing a private technology startup, "InnovateTech," which has no debt. To estimate its cost of equity using the Capital Asset Pricing Model (CAPM), the analyst needs a beta. Since InnovateTech isn't publicly traded, its beta cannot be directly observed.

The analyst identifies a publicly traded comparable company, "TechGiant Corp.," which operates in a similar segment and has a publicly available levered beta of 1.3. TechGiant Corp. has a debt-to-equity ratio of 0.5 and faces a corporate tax rate of 25%.

First, the analyst "unlevers" TechGiant Corp.'s beta:

\beta_U = \frac{1.3}{1 + \left(1 - 0.25\right) \times 0.5} = \frac{1.3}{1 + 0.75 \times 0.5} = \frac{1.3}{1 + 0.375} = \frac{1.3}{1.375} \approx 0.945

The unlevered beta for TechGiant Corp. is approximately 0.945. Since InnovateTech has no debt, its unlevered beta is assumed to be the same as the comparable company's unlevered beta, reflecting its pure business risk. This unlevered beta of 0.945 can then be used in InnovateTech's CAPM calculation to determine its cost of equity.

Practical Applications

Unlevered beta finds extensive use in financial analysis, particularly in:

Company Valuation: When valuing private companies or divisions of public companies (e.g., in mergers and acquisitions), analysts often use the "pure play" method. This involves finding publicly traded comparable companies, unlevering their betas, averaging or taking the median of these unlevered betas, and then re-levering the average beta to match the target company's specific capital structure. This allows for a fair assessment of the target's cost of equity and subsequent valuation.²⁵, ²⁶, ²⁷ NYU Stern's Professor Aswath Damodaran provides extensive resources on using unlevered betas in valuation contexts. [External Link 4]
Investment Analysis: Investors can use unlevered beta to compare the intrinsic business risks of companies in the same industry but with different financing strategies. This helps in understanding the underlying volatility of a business, independent of its debt levels.²⁴
Capital Budgeting: For companies evaluating potential new projects, unlevered beta can be adjusted to reflect the specific business risk of the project itself, rather than the consolidated risk of the entire firm. This helps in determining the appropriate discount rate for project evaluation.
Weighted Average Cost of Capital (WACC) Calculations: Unlevered beta is a critical step in calculating the cost of equity component of WACC, especially when using comparable companies.²³

Limitations and Criticisms

While unlevered beta is a valuable tool, it has several limitations:

Assumption of Constant Capital Structure: The standard unlevering formula assumes a constant debt-to-equity ratio over time, which may not hold true for all firms, especially those undergoing significant changes in their financing strategy.²²
Exclusion of Non-Market Risks: Unlevered beta, like Beta in general, focuses solely on systematic risk (market risk) and does not account for company-specific risk (unsystematic risk), operational risk, or other non-market-related risks.¹⁹, ²⁰, ²¹
Reliance on Comparables: In practice, finding truly comparable companies with similar business risks can be challenging, and the choice of comparables can significantly impact the resulting unlevered beta.¹⁸
Sensitivity to Inputs: The calculated unlevered beta is sensitive to the inputs used, particularly the levered beta, the debt-to-equity ratio, and the corporate tax rate. Inaccurate estimates for these variables can lead to a misleading unlevered beta.
Debate on Beta's Predictive Power: There has been ongoing academic debate about the effectiveness of beta, including unlevered beta, in predicting future returns. Some research suggests that its predictive power can be weak over certain periods.¹⁶, ¹⁷ The CFA Institute has published on this "beta debate." [External Link 3]

Unlevered Beta vs. Levered Beta

The key distinction between unlevered beta and levered beta lies in the inclusion of financial leverage.

Levered beta (also known as equity beta or simply Beta) measures the sensitivity of a company's stock returns to overall market returns, taking into account both its operational risk and the financial risk arising from its debt. A company with higher debt will generally have a higher levered beta because debt amplifies the volatility of equity returns.¹⁴, ¹⁵ This is the beta figure typically reported by financial data providers.
Unlevered beta (or asset beta) removes the influence of debt, providing a measure of the company's inherent business risk as if it were financed entirely by equity. It focuses purely on the volatility stemming from the nature of the business itself.¹², ¹³

The primary use case for unlevered beta is to enable fair comparisons between companies with different capital structures, as it standardizes the risk measure by eliminating the effects of debt.¹⁰, ¹¹ Levered beta, on the other hand, is directly used in the Capital Asset Pricing Model (CAPM) to calculate the cost of equity for a company's actual equity investors, who are exposed to both business and financial risks.⁹

FAQs

What is the primary purpose of calculating unlevered beta?

The primary purpose of calculating unlevered beta is to assess a company's inherent business risk, independent of its financing choices. By removing the impact of leverage, it allows for a more accurate comparison of the operational risk of different companies, especially those with diverse capital structures.⁷, ⁸

Why is unlevered beta also called asset beta?

Unlevered beta is also known as asset beta because it reflects the sensitivity of a company's assets to market movements. It assumes the company is financed solely by equity, meaning the risk is solely attributable to the underlying assets and operations of the business, not its debt financing.⁵, ⁶

When is unlevered beta particularly useful?

Unlevered beta is particularly useful in valuation models, such as discounted cash flow (DCF) analysis, especially when valuing private companies or specific projects. It allows analysts to use the observed betas of publicly traded comparable companies and adjust them to the target company's or project's unique capital structure.³, ⁴ It is also important in calculating the Weighted Average Cost of Capital (WACC).

Does adding debt increase unlevered beta?

No, adding debt does not directly increase unlevered beta. Unlevered beta is designed to remove the effect of debt, reflecting only the pure business risk. However, adding debt will increase the company's levered beta (equity beta), as the increased financial leverage amplifies the volatility for equity holders.¹, ²

Can unlevered beta be negative?

While rare, unlevered beta can theoretically be negative if a company's business operations are inversely correlated with the overall market. This would imply that the company's asset returns tend to move in the opposite direction of the market. However, most companies exhibit a positive correlation with the broader market.