Levering and unlevering beta
How to borrow a peer's beta when its balance sheet looks nothing like yours.
- Unlever a peer's beta to isolate business risk
- Relever it at your company's target capital structure
- Carry the relevered beta through CAPM to a cost of equity
- Back out the leverage a model's beta assumes
The intuition
Two people buy identical houses. One pays cash; the other borrows 80% of the price. The houses are exactly as risky. But if prices fall 10%, the cash buyer loses 10% of their money, while the borrower loses half of theirs. Same asset, a much bumpier ride for the owner.
Beta works the same way. A stock's beta mixes two things: how risky the business is, and how much debt sits on top of it. Debt makes the equity swing harder.
To borrow a peer's beta, first strip out the peer's debt (unlever) to get the risk of the business alone, then put your own company's debt back on (relever).
Why it works
Your company may not have a reliable beta of its own: it might be private, recently listed, or about to change its capital structure. Peers in the same industry share its business risk, but each carries a different amount of debt, so their betas cannot simply be copied across.
The Hamada formula removes and adds leverage: levered β = unlevered β × (1 + (1 − t) × D/E). The more debt per dollar of equity, the more the equity swings. The (1 − t) is there because interest is tax-deductible: the tax saving takes some of the strain of the debt off shareholders.
- Unlevered beta (also called asset beta) is the business risk alone, as if the company had no debt. It can be compared across companies.
- Levered beta (also called equity beta) is what you see in the market, and what goes into CAPM.
- The version used in interviews and most bank models assumes debt has a beta of zero: lenders bear none of the market risk. It is a simplification, and a reasonable one unless the company is heavily indebted.
| Peer levered beta | 1.30 at D/E 0.50 |
| Peer leverage factor | 1 + (1 − 25%) × 0.50 = 1.375 |
| Unlevered beta | 1.30 ÷ 1.375 = 0.9455 |
| Your leverage factor at D/E 1.00 | 1 + (1 − 25%) × 1.00 = 1.75 |
| Relevered beta | 0.9455 × 1.75 = 1.65 |
| = Cost of equity (rf 4.0%, ERP 5.5%) | 4.0% + 1.65 × 5.5% = 13.1% |
Carry the unrounded unlevered beta through. Rounding it to 0.95 first gives 1.66, not 1.65.
The formulas
Strip the peer's debt out: divide by its leverage factor, at the peer's own D/E.
Put your company's debt back on: multiply by its leverage factor.
The relevered beta is the one that goes into CAPM.
Run it backwards: the ratio of the two betas is the leverage factor; undo it to find D/E.
Worked example
The core calculation, exactly as a first-round interviewer asks it.
See it move
Same numbers. Change either company's leverage and follow the beta through to the cost of equity.
- Set your target D/E to the same value as the peer's. Your levered beta becomes the peer's beta exactly: unlevering and relevering at the same leverage undo each other.
- Raise your target D/E. The levered beta climbs in a straight line, and the cost of equity climbs with it.
- Raise the peer's D/E while its beta stays the same. A peer that shows that beta while carrying more debt must have a safer business underneath, so the unlevered beta falls, and so does yours.
- Raise the tax rate. The same debt adds less to beta, because the interest deduction cushions shareholders.
Run it backwards
Same numbers, reversed: you know the business risk and the beta a model uses. What capital structure is the model assuming?
Divide the levered beta by the unlevered beta. That ratio is the leverage factor, 1 + (1 − t) × D/E. Subtract one, divide by (1 − t), and what is left is D/E.
Useful when reviewing a model: if the implied D/E is far from the company's actual or target structure, the beta — and so WACC — is built on the wrong leverage.
Traps
Say it in the interview
“Why and how do you unlever beta?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Levered β = unlevered β × (1 + (1 − t) × D/E).
- Unlever at the peer's leverage, relever at yours.
- Unlevered beta is business risk, comparable across companies.
- More debt → higher equity beta → higher cost of equity.