Cost of Capitaladvanced

Levered and Unlevered Beta

A reported equity (levered) beta mixes two risks, the firm’s business risk and the extra risk from financial leverage, so it is always at least as large as the unlevered (asset) beta that captures business risk alone. To compare firms with different leverage, unlever each peer’s beta to strip out debt, average the asset betas, then relever to the target’s own debt-equity mix. The basic algebra is the Hamada relation. The exact relevering formula depends on a financing assumption, where Miles-Ezzell and Harris-Pringle differ in how the tax shield is treated.

Try it yourself

Unlever & relever beta

An observed equity beta β_ecarries both business and financial risk. Strip the comparable's leverage to the unlevered (asset) beta β_u, then re-add leverage at your target D/E to get the relevered β_e*. More leverage raises equity beta. A positive debt beta β_d raises the asset beta you back out.

Relevered β_e* at target D/E = 40%1.26

Unlevered (asset) beta β_u 0.97Financial-risk add-on β_e* − β_u +0.29

Rebalancing method

Comparable equity (levered) beta β_e1.40

Comparable D/E60%

Tax rate T25%

Debt beta β_d0.00

Target D/E (relever to)40%

Try this

Unlevering β_e = 1.40 at the comparable's D/E of 60% gives an asset beta of 0.97. Relevering to the target D/E of 40% lifts it to 1.26, an added +0.29 of financial risk.

Hamada assumes a fixed dollar debt level, so the tax shield is as safe as the debt and carries the (1 − T) factor.

Discuss: why must you unlever a comparable's beta before applying it to a target with different leverage, and when is the β_d = 0 shortcut safe?

Why it matters

Leverage magnifies equity returns, both gains and losses, so a heavily indebted firm shows a higher equity beta even if its underlying business is no riskier than a debt-free rival. To see the pure business risk you have to remove the leverage, which is what unlevering does. This matters most for a private or young company with no usable return history. You borrow the asset beta from listed peers, then re-dress it in the target’s own leverage. A worked illustration of this peer method takes Pfizer against Abbott, Johnson and Johnson and Merck.

Formulas

Hamada, unlever to the asset beta

\beta_U = \dfrac{\beta_e}{1 + (1 - t)\,\frac{D}{E}}

This standard Hamada form assumes a zero debt beta. Here

\beta_e

is the levered equity beta,

\beta_U

the unlevered asset beta and

D/E

the debt-to-equity ratio. Higher leverage drives a larger gap between the two.

Relever to the target firm

\beta_e = \beta_U\,\left[1 + (1 - t)\,\dfrac{D}{E}\right]

After averaging peer asset betas, relever using the target’s own

D/E

. Harris-Pringle drops the

(1 - t)

term, treating the tax shield as risky, while Miles-Ezzell keeps a near-Hamada form for a rebalanced structure.

Worked examples

Scenario

A pharmaceutical peer has an equity beta of 1.20, a debt-to-equity ratio of 0.50 and faces a 20 percent tax rate. Unlever its beta, then relever it for a target firm with the same business risk but a debt-to-equity ratio of 0.25 and the same tax rate.

Solution

Unlever first. The denominator is $\,1 + (1 - 0.20)(0.50) = 1 + 0.40 = 1.40$ , so $\beta_U = 1.20 / 1.40 = 0.857$ . Now relever at $D/E = 0.25$ . The bracket is $\,1 + 0.80 \times 0.25 = 1.20$ , so $\beta_e = 0.857 \times 1.20 = 1.029$ . The target carries less debt, so its relevered equity beta of about 1.03 sits below the peer’s 1.20 even though the business risk is identical.

Common mistakes

✗Equity beta and asset beta are interchangeable. Equity beta includes financial leverage, asset beta does not, so equity beta is always greater than or equal to asset beta.
✗A higher equity beta always means a riskier business. It can simply mean more debt. Unlevering reveals whether the underlying operating risk is actually higher.
✗There is one correct relevering formula. Hamada, Harris-Pringle and Miles-Ezzell embed different assumptions about debt policy and the riskiness of the tax shield, so they relever differently.
✗You should unlever a single peer and stop. Average the unlevered betas of several comparables to smooth out firm-specific noise before relevering to the target.

Revision bullets

•Equity beta equals business risk plus financial leverage risk
•Unlevered (asset) beta strips out leverage to isolate business risk
•Levered beta is always at least the unlevered beta
•Method: unlever each peer, average, then relever to the target’s D/E
•Hamada gives the basic algebra, assuming a zero debt beta
•Miles-Ezzell and Harris-Pringle differ in how they treat the tax shield

Quick check

An equity beta of 1.50 comes from a firm with a debt-to-equity ratio of 1.0 and a 30 percent tax rate. Using the standard Hamada relation, the unlevered beta is closest to

Two firms operate the same business but one uses much more debt. Compared with the low-debt firm, the high-debt firm’s reported equity beta will be

Connected topics

WACC Cost of Equity (CAPM)Capital Weights Debt Beta Pure-Play Method

Sources

Hamada (1972)
Hamada, R. S. "The Effect of the Firm’s Capital Structure on the Systematic Risk of Common Stocks." Journal of Finance, 27(2), 1972, pp. 435-452.
Original relation linking levered and unlevered beta through leverage and the tax rate.
Miles & Ezzell (1980); Harris & Pringle (1985)
Miles, J. A. & Ezzell, J. R. Journal of Financial and Quantitative Analysis, 15(3), 1980; Harris, R. S. & Pringle, J. J. Journal of Financial Research, 8(3), 1985.
Two relevering conventions that differ in whether the interest tax shield is discounted at the cost of debt or the unlevered cost of equity.
Titman & Martin
Titman, S. & Martin, J. D. Valuation: The Art and Science of Corporate Investment Decisions. Pearson.
Chapter on estimating beta from comparable firms. The Pfizer peer example uses the unlever, average and relever procedure.

How to cite this page

Dr. Phil's Quant Lab. (2026). Levered and Unlevered Beta. Derivatives Atlas. https://phucnguyenvan.com/concept/sabv-levered-unlevered-beta

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