Beta (Levered vs Unlevered)
Beta measures a stock's sensitivity to broad market movements; levered beta reflects the volatility observed in the market and includes the amplifying effect of financial leverage, while unlevered beta strips out the leverage effect to isolate the underlying business risk.
Beta is the slope coefficient from a regression of a stock's excess returns on the market's excess returns over a historical period. A beta of 1.0 means the stock moves in line with the market; a beta of 1.5 means it historically moves 50% more in either direction; a beta below 1.0 implies lower volatility than the market. The beta observed from market data is called the 'levered' or 'equity' beta (Beta_L) because it reflects both the operating risk of the business and the financial risk introduced by debt.
When performing a comparable company analysis or valuing a private business, analysts need to estimate the beta for the target. They collect levered betas from public peers, but those peers have different capital structures, so the raw betas are not comparable. The solution is to unlever each peer's beta, stripping out the financial leverage effect, and then re-lever the unlevered beta at the target company's capital structure. The Hamada equation governs this transformation: Beta_Unlevered = Beta_Levered / [1 + (1 - Tc) x (D/E)], and the re-levering equation is Beta_Levered = Beta_Unlevered x [1 + (1 - Tc) x (D/E)].
Consider an example: a comparable company has an observed levered beta of 1.4, a D/E ratio of 0.5, and faces a 21% tax rate. Unlevered beta = 1.4 / [1 + (1 - 0.21) x 0.5] = 1.4 / 1.395 = 1.003. The target company has a D/E of 0.2, so its re-levered beta = 1.003 x [1 + (1 - 0.21) x 0.2] = 1.003 x 1.158 = 1.16. This re-levered beta is then plugged into CAPM to calculate the target's cost of equity.
Unlevered beta is also called 'asset beta' because it represents the riskiness of the firm's asset base regardless of how those assets are financed. Capital-intensive, cyclical businesses like steel producers have high asset betas; defensive, stable businesses like water utilities have very low asset betas. Companies that carry no debt at all have levered and unlevered betas that are identical, since there is no leverage to adjust for. Understanding the distinction is critical in any valuation involving peer comparisons, merger analysis, or a company going through a leveraged buyout that substantially changes its D/E ratio.