How do I use the CAPM to estimate cost of equity, and when should I adjust beta?

The Capital Asset Pricing Model (CAPM) estimates a stock's required return based on its systematic risk (beta). Let's build up from the basics to the adjustments.

CAPM Formula:

> r_e = R_f + beta x ERP

where ERP = equity risk premium = E(R_m) - R_f

Worked Example — Basic CAPM:

Estimate cost of equity for Redfield Aerospace:

• Risk-free rate (R_f) = 4.0% (10-year government bond)
• Equity risk premium (ERP) = 5.5%
• Beta = 1.3

r_e = 4.0% + 1.3 x 5.5% = 4.0% + 7.15% = 11.15%

When to Adjust Beta:

1. Blume Adjusted Beta (Mean Reversion Adjustment)

Regression betas tend to revert toward 1.0 over time. The Bloomberg/Blume adjustment:

> Adjusted Beta = (2/3) x Raw Beta + (1/3) x 1.0

If Redfield's raw beta is 1.3:

> Adjusted beta = (2/3)(1.3) + (1/3)(1.0) = 0.867 + 0.333 = 1.20

Revised r_e = 4.0% + 1.20 x 5.5% = 10.60%

2. Re-Levering Beta (Hamada Equation)

When using a comparable's beta but the target has different leverage:

Step 1 — Unlever the comparable's beta:

> Beta_unlevered = Beta_levered / [1 + (1 - t) x (D/E)]

Step 2 — Re-lever at the target's capital structure:

> Beta_relevered = Beta_unlevered x [1 + (1 - t) x (D/E_target)]

Example:

Comparable (Skymark Defense) has beta = 1.4, D/E = 0.5, tax rate = 25%

Target (Redfield) has D/E = 0.8, same tax rate

Step 1: Beta_U = 1.4 / [1 + (0.75)(0.5)] = 1.4 / 1.375 = 1.018

Step 2: Beta_relevered = 1.018 x [1 + (0.75)(0.8)] = 1.018 x 1.60 = 1.629

Redfield's re-levered cost of equity = 4.0% + 1.629 x 5.5% = 12.96%

When to Use Which:

Common exam mistakes:

• Forgetting the (1 - t) tax shield in the Hamada equation
• Using D/E ratios at book value when market value is appropriate
• Applying Blume adjustment AND re-levering — you typically do one or the other based on the context

Build your CAPM skills with our CFA Level I equity practice questions.