Beta
Executive Summary
Key Takeaways
- ✓ Beta measures a stock's systematic (market-related) risk, not its total volatility or company-specific risk.
- ✓ A beta of 1.0 moves in line with the market; above 1.0 indicates higher systematic risk; below 1.0 indicates lower systematic risk.
- ✓ Beta is the risk input to CAPM, used to build the cost of equity component of the discount rate.
- ✓ Beta can be estimated by regressing a stock's historical returns against a market index, or sourced from published data services.
- ✓ Beta observed for a listed company reflects that company's own capital structure: it is a levered (equity) beta, and must be unlevered before being compared across companies with different leverage.
- ✓ For private companies or specific projects, beta is typically built from a set of comparable unlevered betas re-levered to the subject's target capital structure.
Definition¶
Beta (β) is a measure of a stock's systematic risk — the portion of its return volatility that is correlated with, and cannot be diversified away from, movements in the broader market. Beta is the risk input to the Capital Asset Pricing Model (CAPM), which is the standard methodology for estimating cost of equity in a DCF valuation.
Formula¶
β = Cov(Rstock, Rmarket) / Var(Rmarket)
In practice, beta is most commonly estimated as the slope coefficient of a linear regression of a stock's periodic returns against the returns of a broad market index over a historical window (commonly two to five years of monthly or weekly data).
Interpreting Beta¶
- β = 1.0 — the stock's returns move, on average, in line with the market
- β > 1.0 — the stock is more sensitive to market-wide movements than the market average (amplified upside and downside)
- β < 1.0 — the stock is less sensitive to market-wide movements than the market average
- β < 0 — rare; the stock tends to move opposite to the market
Sourcing Beta¶
Two approaches are used in practice:
- Direct regression. For a listed, reasonably liquid stock, beta can be regressed directly from the company's own historical returns against a market index. This is only reliable where sufficient trading history and liquidity exist.
- Comparable company approach. For private companies, specific projects, or thinly traded stocks, beta is built from a set of comparable listed companies: each comparable's observed (levered) beta is unlevered to strip out its own capital-structure effect (see Unlevered Beta), the resulting asset betas are averaged, and the average is then re-levered at the subject's target capital structure using the Hamada equation.
Published data services also provide beta estimates, though the underlying regression window, return frequency, and index choice vary by provider and should be disclosed.
Role in a DCF Valuation¶
Beta feeds directly into CAPM: Cost of Equity = Risk-free rate + β × Equity Risk Premium. A higher beta produces a higher cost of equity and, through WACC, a higher discount rate — meaning beta has a direct and often material effect on the resulting enterprise or equity value.
Audit Considerations¶
- Verify the source of beta: regression window, return frequency, market index used, and (for the comparable-company approach) the composition of the comparable set
- Confirm whether the beta used is levered or unlevered, and whether it has been correctly re-levered to the subject's target capital structure
- Confirm the target capital structure used for re-levering is consistent with the capital structure assumed elsewhere in the WACC build
- Check for stale or overly short regression windows that may not reflect the company's current business or leverage
Common Errors¶
| Error | Description | Risk |
|---|---|---|
| Using a levered comparable beta directly | Comparable companies' observed betas applied without unlevering for capital structure differences | Beta, and therefore cost of equity, is distorted by comparables' leverage rather than the subject's |
| Inconsistent target capital structure | Beta re-levered at a different capital structure than the one used elsewhere in WACC | Internal inconsistency between the discount rate build and the model's financing assumptions |
| Undisclosed beta source | Beta figure used without stating source, window, or index | Cannot be independently assessed or replicated |
Continue Reading¶
Prerequisites¶
- Discounted Cash Flow (DCF) Valuation — the parent pillar
- CAPM (Capital Asset Pricing Model)
Related Glossary¶
Related Technical Guides¶
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Frequently Asked Questions
What is the formula for beta?
Beta is formally defined as the covariance of the stock's returns with the market's returns, divided by the variance of the market's returns: β = Cov(Rstock, Rmarket) / Var(Rmarket). In practice, beta is most commonly estimated as the slope coefficient of a linear regression of a stock's historical returns against the returns of a broad market index.
What does a beta above or below 1.0 mean?
A beta of 1.0 means the stock's returns move, on average, in line with the market. A beta above 1.0 indicates the stock is more sensitive to market movements than the market average (amplified swings in both directions); a beta below 1.0 indicates lower sensitivity. A negative beta, while rare, indicates the stock tends to move opposite to the market.
Where does beta come from in a DCF model?
Beta is either regressed directly from a company's own historical stock returns (if listed and liquid), or, more commonly for private companies, specific projects, or thinly traded stocks, estimated from a set of comparable listed companies whose betas are unlevered, averaged, and then re-levered to the subject's target capital structure.
Why can't listed company betas be compared directly across companies?
Because an observed (levered) beta reflects both the company's underlying business risk and the financial risk added by its own capital structure. Two companies in the same industry with different leverage will have different levered betas even if their underlying business risk is identical. Unlevering removes the capital-structure effect, allowing betas to be compared on a like-for-like basis.
How many years of data are typically used to estimate beta by regression?
Common convention uses two to five years of monthly or weekly return data, though the appropriate window and return frequency involve a trade-off between having enough observations for statistical reliability and using a period that still reflects the company's current business and capital structure.
Related Articles
CAPM (Capital Asset Pricing Model)
The Capital Asset Pricing Model (CAPM) is the standard methodology for estimating the cost of equity — the return equity investors require to hold a company's stock, given its systematic risk relative to the broader market. CAPM expresses cost of equity as the risk-free rate plus the company's beta multiplied by the equity risk premium (the excess return the market as a whole is expected to earn over the risk-free rate). CAPM is the most widely used cost-of-equity methodology in institutional valuation practice and is the standard input to the cost-of-equity component of WACC.
Unlevered Beta (Asset Beta)
Unlevered beta, also called asset beta, is a company's observed (levered) beta adjusted to remove the effect of its financial leverage, leaving only the systematic risk attributable to the underlying business. Because an observed beta reflects both business risk and the financial risk added by a company's own capital structure, comparing levered betas directly across companies with different leverage is misleading. Unlevering allows betas from a set of comparable companies to be placed on a like-for-like basis, averaged, and then re-levered at the subject company's or project's target capital structure using the Hamada equation, producing a beta appropriate for the subject's own financing.
Hamada Equation
The Hamada equation is a formula, developed by Robert Hamada, that relates a company's observed levered equity beta to its underlying unlevered (asset) beta, adjusting for the effect of financial leverage and the corporate tax rate. It is used to strip out the effect of capital structure from an observed beta — unlevering it — so that betas from different comparable companies with different debt levels can be meaningfully compared or averaged, and then to relever the resulting average unlevered beta back to the subject company's own target capital structure. The Hamada equation is a standard step in building a bottom-up cost of equity estimate from a set of comparable companies.
Cost of Equity
Cost of equity is the rate of return equity investors require to compensate them for the risk of holding a company's stock, given its systematic risk relative to the broader market. It is most commonly estimated using the Capital Asset Pricing Model (CAPM), which expresses cost of equity as the risk-free rate plus a beta-adjusted equity risk premium. Cost of equity serves two roles in a DCF valuation: it is one of the two components blended into WACC (alongside the after-tax cost of debt), and it is used as the sole discount rate when valuing a levered cash flow (FCFE) directly.
Equity Risk Premium (ERP)
The equity risk premium (ERP) is the additional return equity investors require, above the risk-free rate, for bearing the risk of holding equities as an asset class rather than a risk-free instrument. ERP is not directly observable and must be estimated, typically from long-run historical average equity returns in excess of government bond yields, from implied ERP models that back the premium out of current market prices, or from surveys of practitioner expectations. ERP is a required input to the Capital Asset Pricing Model (CAPM), where it is multiplied by beta to determine the equity-risk component of cost of equity. Because reasonable ERP estimates can differ materially between sources, the ERP figure used in a valuation should always be disclosed alongside its source and date.