Levered vs Unlevered Beta

A company's observed, or levered, beta reflects both its business risk and the financial risk added by debt. To compare betas across firms with different capital structures, you strip out the leverage to get an unlevered beta, also called asset beta. You then relever that asset beta to your target capital structure. The Hamada equation links the two.

Why unlever, and the formula

Debt magnifies equity risk, so a heavily levered firm shows a higher levered beta even if its underlying business is no riskier than a peer's. Unlevering removes that financial-risk component, leaving a clean measure of business risk that is comparable across companies.

The Hamada relationship to unlever is Bu = Bl / (1 + (1-tax)*D/E), where Bu is unlevered beta, Bl is levered beta, tax is the marginal tax rate, and D/E is the debt-to-equity ratio. To relever to a target structure you rearrange: Bl = Bu * (1 + (1-tax)*D/E) using the target D/E.

Worked example

A peer has a levered beta of 1.30, a debt-to-equity ratio of 0.50, and a 25 percent tax rate. You want to relever its asset beta to your firm's target debt-to-equity of 0.80 at the same tax rate.

1. Leverage factor for the peer: =1+(1-0.25)*0.50 returns 1.375.
2. Unlevered beta: =1.30/1.375 returns 0.945.
3. Leverage factor at target: =1+(1-0.25)*0.80 returns 1.60.
4. Relevered beta: =0.945*1.60 returns 1.512.

=(1.30/(1+(1-0.25)*0.50))*(1+(1-0.25)*0.80) returns 1.512.

Laying it out in a model

Unlevering and relevering is a two-step bridge, so build it with the peer inputs on the left and the target inputs on the right.

• Keep each peer's levered beta, D/E, and tax rate in their own cells.
• Compute unlevered beta per peer, then average the asset betas for a peer-group estimate.
• Put the target D/E and tax rate in a separate target block.
• Feed the relevered beta into the CAPM cell that drives cost of equity.

Pitfalls

Forgetting the tax term turns (1-tax) into 1 and overstates the leverage adjustment, because it ignores the tax shield on debt. Always include (1-tax) in both the unlever and relever steps at the relevant tax rate.

Using book equity for D/E instead of market equity distorts the ratio, since the formula assumes market values. Unlevering with one peer's D/E and forgetting to relever to your own target leaves you with an asset beta, not the equity beta CAPM needs; you must relever to your target structure before using the beta in cost of equity.