To unlever beta, divide a company’s observed equity beta by one plus its after-tax debt-to-equity ratio. Written out, the Hamada equation is βu = βl ÷ [1 + (1 − t) × (D/E)], where βl is the levered (market-observed) beta, t is the corporate tax rate as a decimal, and D/E is debt divided by equity at market values. The result, βu, is the unlevered beta: the volatility attributable to the business itself once financial leverage has been stripped out.
The reason to do this is that an equity beta pulled from Yahoo Finance or Bloomberg mixes two different risks together. Part of the number reflects the actual business (what it sells, how cyclical demand is, how fixed its costs are), and part reflects how the company is financed. Two identical retailers with different debt loads will show different equity betas even though the stores and margins are the same. Unlevering removes the financing effect so you can compare businesses on equal footing, or so you can average peer betas and relever them at a different capital structure.
The Formula and What Each Term Means
βu = βl ÷ [1 + (1 − t) × (D/E)]
βl is the levered beta, the equity beta as observed in the market. βu is the unlevered beta you’re solving for. The tax term (1 − t) is in the formula because interest on debt is deductible, so the tax shield reduces how much of the debt’s risk passes through to equity holders. The whole denominator measures how much financial leverage is inflating the observed equity beta above the underlying asset beta.
Gathering the Three Inputs
Levered Beta
The levered beta is reported on Yahoo Finance, Bloomberg, FactSet, and Capital IQ. Each service calculates it by regressing the stock’s returns against a market index, typically the S&P 500. The standard input is five years of monthly returns, though some providers use two years of weekly data. Longer windows give more observations but may reflect a business the company no longer resembles; shorter windows track the current business but are noisier.
One thing to watch. Bloomberg reports both a “raw” beta and an “adjusted” beta, where the adjusted version applies the Blume formula (0.67 × raw + 0.33) to shrink the number toward 1.0. For unlevering, use the raw beta. The Blume adjustment is a statistical smoothing that distorts the asset risk calculation.
Corporate Tax Rate
The U.S. federal corporate income tax rate is 21%, set by the Tax Cuts and Jobs Act of 2017 and in effect through 2026. For companies with meaningful foreign or state exposure, the effective tax rate from the 10-K income tax footnote is more accurate than the statutory rate. That footnote reconciles the 21% federal figure against state, foreign, and other adjustments to show what the company actually paid.
Debt-to-Equity Ratio
This is where most errors happen, and it dominates the error in the final answer. Two rules.
First, use market values for equity, not book values. The book equity on the balance sheet reflects historical accounting entries and rarely matches what investors think the company is worth. A firm with $3 billion in book equity and $11 billion in market capitalization has a very different risk profile than the book numbers imply. For equity, always use market capitalization: shares outstanding times the current share price. For debt, book value is usually close enough to market value for investment-grade issuers, so the balance sheet figure works in most cases.1NYU Stern. Estimating Risk Parameters
Second, decide between gross debt and net debt (gross minus cash). A company sitting on a large cash pile has effectively pre-funded some of its obligations, so its true leverage is lower than the gross number shows. Damodaran’s approach unlevers using gross D/E and then separately adjusts for cash as a share of firm value, since cash has a beta near zero and drags the asset beta upward when netted out.2NYU Stern. Backing Into a Pure Play Beta: Studio Entertainment For most companies the difference is small; for cash-heavy technology firms it is not.
Total debt should include all interest-bearing obligations: bonds, term loans, revolving credit balances, and capital leases. Exclude non-interest-bearing liabilities like accounts payable and deferred revenue.
Worked Example
Take a company with a levered beta of 1.20, an effective tax rate of 21%, total debt of $500 million, and market capitalization of $1 billion.
Step 1. Calculate D/E: $500 million ÷ $1 billion = 0.50.
Step 2. Calculate the after-tax factor: 1 − 0.21 = 0.79.
Step 3. Multiply by D/E: 0.79 × 0.50 = 0.395. This is how much debt is inflating the equity beta.
Step 4. Build the denominator: 1 + 0.395 = 1.395.
Step 5. Divide: 1.20 ÷ 1.395 = 0.86.
The unlevered beta is roughly 0.86. The drop from 1.20 to 0.86 is the share of observed volatility that came from leverage rather than the business. If the company retired all its debt, the equity beta would fall to about 0.86, holding everything else equal.3NYU Stern. Chapter 8 Estimating Risk Parameters and Costs of Financing
Relevering at a Target Capital Structure
Most analysts unlever beta only as a step toward relevering it. Once you have a clean unlevered beta, often the average of several peer companies, you relever it at the capital structure of the firm you’re actually valuing. The formula rearranges cleanly:
βl = βu × [1 + (1 − t) × (D/E)]
The D/E ratio here is the target company’s own leverage, not the peer average. If the target is deleveraging quickly, using today’s D/E can overstate long-run equity risk, so a forward or target ratio may fit better.4Oxera. Finding the Right Formula: De-levering and Re-levering the Beta in the CAPM The relevered beta then feeds CAPM: Cost of Equity = Risk-Free Rate + βl × Equity Risk Premium.
Unlevering for Private Companies
A private company has no traded stock and therefore no regression beta to unlever. The workaround, called a bottom-up beta, borrows business risk from public peers and applies it to the private firm’s own capital structure.
- Select six to eight comparable public companies in the same industry. If the sector is narrow, widen the definition or include global listings.
- Take a simple average of their levered betas.
- Unlever that average using the peer group’s average tax rate and average D/E ratio.
- If the peers hold significant cash, divide by (1 − cash/firm value) to strip out the cash drag, since cash has a beta near zero.
- Relever at the private firm’s actual or target D/E to get the beta used in CAPM.
Averaging first and then unlevering the average, rather than unlevering each peer and averaging afterward, reduces the compounding of estimation error.5NYU Stern. Ten Questions About Bottom-up Betas
When the Standard Formula Doesn’t Fit
The Hamada equation rests on assumptions that don’t always hold. Three cases to know.
The formula assumes debt is risk-free, meaning debt beta is zero. That works for investment-grade borrowers. For high-yield or distressed debt trading well below par and moving with equity, the debt itself carries market risk. A modified formula accounts for it: βl = βu × [1 + (1 − t) × (D/E)] − βd × (1 − t) × (D/E), where βd is the debt beta.6NYU Stern. Relative Risk Measures Ignoring debt beta on a CCC-rated issuer or a leveraged buyout candidate will materially understate the unlevered beta.
The Hamada equation also assumes a fixed dollar amount of debt. If the firm instead maintains a constant debt-to-value ratio, adjusting borrowing as the firm grows, the Harris-Pringle formula fits better. The two approaches give similar results at moderate leverage; the gap widens as D/E climbs above 1.0.4Oxera. Finding the Right Formula: De-levering and Re-levering the Beta in the CAPM
Preferred stock sits between debt and common equity. If preferred is less than about 5% of total firm value, folding it into debt makes no meaningful difference. Above that, treat preferred as a separate component with its own cost (the preferred dividend yield) rather than forcing it into either category.6NYU Stern. Relative Risk Measures
A final sanity check: compare the result against published sector unlevered betas from a source like Damodaran’s data page. If an unlevering calculation produces 1.4 for a regional utility or 0.3 for a semiconductor firm, something in the inputs is wrong, most often the equity value or the debt figure.7NYU Stern. Betas by Sector (US)