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CFA Level II Exam · Cost of Capital: Advanced Topics

Beta Estimation and Country Risk Premium Explained

Updated 7 October 2026 · Fact-checked

Beta is estimated by regressing a stock's returns on market returns; the slope is beta. You can adjust it toward 1 with the Blume formula, unlever it to remove financial leverage, relever it for a target capital structure, and add a country risk premium to the equity cost for emerging markets.

Understand Beta Estimation and Country Risk Premium

Beta measures how much a stock's return moves with the market. You estimate it by regression: stock returns are the dependent variable, market returns are the independent variable, and the slope is beta. The choices you make matter. A longer sample gives more data points but may include periods when the business was different. Shorter return intervals (daily) give more observations but can bring in noise and thin-trading bias. Longer intervals (monthly) reduce that noise. The choice of market index also changes the result.

A raw regression beta is only an estimate and has a standard error. Betas tend to drift toward the market average of 1 over time. The Blume adjustment reflects this by weighting the raw beta and 1. Many data providers publish adjusted betas using weights of two-thirds and one-third.

A company's observed beta mixes two risks: business risk and financial leverage. Debt makes equity riskier, so a levered firm's equity beta is higher than its asset beta. To use a comparable company's beta for your own project or firm, you unlever it to get the asset beta (the beta of the business with no leverage effect). Then you relever it using the target's own debt-to-equity ratio. A comparable firm that operates only in the project's business line is a pure play. Its unlevered beta is a good proxy for the project's business risk.

For firms in emerging markets, CAPM using a developed-market equity premium may understate risk. One fix is to add a country risk premium (CRP). A common estimate is the sovereign yield spread multiplied by the ratio of equity market volatility to bond market volatility. The CRP is added to the equity risk premium component, either multiplied by beta or added outside beta, depending on the form you are told to use.

Key formulas to remember

Regression beta
Rᵢ = α + β × Rₘ + ε; β = Cov(Rᵢ, Rₘ) ÷ Var(Rₘ)
Beta is the slope of the stock's returns regressed on market returns.
Blume adjusted beta
Adjusted β = (2/3) × raw β + (1/3) × 1.0
Pulls the raw beta toward 1. The 2/3 and 1/3 weights are the standard version; use other weights only if the question gives them.
Unlever beta (debt beta of zero)
β_asset = β_equity ÷ [1 + (1 − t) × (D ÷ E)]
Uses the comparable firm's own tax rate and D/E. This is the standard form when debt is assumed to have zero beta.
Relever beta
β_equity = β_asset × [1 + (1 − t) × (D ÷ E)]
Use the target's tax rate and target D/E.
Country risk premium
CRP = Sovereign yield spread × (σ_equity index ÷ σ_sovereign bond market)
Sovereign spread is the emerging-market government bond yield minus a comparable developed-market government bond yield.
Cost of equity with CRP
r_e = Rf + β × (ERP + CRP)
Some versions use r_e = Rf + β × ERP + CRP. Follow the form the question uses or implies.

How to solve Beta Estimation and Country Risk Premium questions

Work out first whether the question asks about estimating beta, adjusting it, transferring it between firms, or adding country risk.

  1. 1Read the vignette and list the given data: raw beta, D/E, tax rate, risk-free rate, equity risk premium and any sovereign spread or volatilities.
  2. 2Identify the task: regression issue, Blume adjustment, unlever and relever, or CRP.
  3. 3If beta must be adjusted, apply 2/3 × raw + 1/3 first, unless the question gives different weights. Check the order the question implies.
  4. 4To transfer beta from a comparable, unlever using the comparable's D/E and tax rate. This gives the asset beta.
  5. 5Relever using the target's D/E and tax rate. Be careful to use the target's figures, not the comparable's.
  6. 6If a CRP is needed, compute it as spread × (equity volatility ÷ bond volatility), unless it is given.
  7. 7Plug into CAPM with the CRP in the stated form and compute the cost of equity.
  8. 8Check that the answer is sensible: relevered beta should rise with more debt, and the cost of equity should exceed the risk-free rate.

Quickest way: Unlever, relever, then CAPM in three lines

When to use it: Use when the vignette gives a comparable firm's beta and capital structure and asks for a project or target cost of equity.

  1. Compute the multiplier for the comparable: 1 + (1 − t) × D/E. Divide beta by it.
  2. Compute the multiplier for the target the same way. Multiply the asset beta by it.
  3. Put the new beta into Rf + β × ERP, adding the CRP if required. Eliminate options that ignore tax or use the wrong D/E.

Common mistakes in Beta Estimation and Country Risk Premium

  • Using the target's D/E and tax rate when unlevering the comparable's beta.

    Vignettes list several capital structures and the numbers get mixed up.

    Fix: Label each figure Comparable or Target. Unlever with Comparable data, relever with Target data.

  • Forgetting the (1 − t) factor.

    Students memorise a no-tax version of the formula.

    Fix: Always write 1 + (1 − t) × D/E and check that a tax rate is given.

  • Applying Blume weights the wrong way round, such as 1/3 × raw + 2/3 × 1.

    The weights are easy to swap from memory.

    Fix: The raw beta gets the larger weight of 2/3. A raw beta of 1.5 should become 1.33, not 1.17.

  • Using D/(D+E) instead of D/E.

    Capital structure is often given as weights in WACC problems.

    Fix: If given debt weight w_d, compute D/E = w_d ÷ w_e before using the formula.

  • Adding the CRP at the wrong place or twice.

    Different forms of the model exist.

    Fix: Use the form stated in the question. In the form Rf + β × (ERP + CRP), the CRP is scaled by beta.

  • Treating the sovereign spread alone as the CRP.

    The spread is the most visible number.

    Fix: Scale it by the ratio of equity volatility to sovereign bond volatility, as equities are riskier than the bonds.

Worked examples

Example 1

A pure play comparable has an equity beta of 1.30, D/E of 0.50 and a tax rate of 30%. Your firm is entering the same business with a target D/E of 0.25 and a tax rate of 20%. Rf = 4%, ERP = 5%. Questions: (1) What is the comparable's asset beta? (2) What is the relevered beta? (3) What is the cost of equity?

Show the solution
  1. Comparable multiplier = 1 + (1 − 0.30) × 0.50 = 1 + 0.35 = 1.35.
  2. Asset beta = 1.30 ÷ 1.35 = 0.9630.
  3. Target multiplier = 1 + (1 − 0.20) × 0.25 = 1 + 0.20 = 1.20.
  4. Relevered beta = 0.9630 × 1.20 = 1.1556.
  5. Cost of equity = 4% + 1.1556 × 5% = 4% + 5.778% = 9.78%.

Answer: (1) Asset beta ≈ 0.963. (2) Relevered beta ≈ 1.156. (3) Cost of equity ≈ 9.78%.

Example 2

An analyst estimates a raw beta of 1.45 for an emerging-market company. Rf = 3%, ERP for developed markets = 5%. The sovereign yield spread is 3.0%, the emerging equity index volatility is 24% and the sovereign bond market volatility is 16%. Questions: (1) What is the Blume-adjusted beta? (2) What is the CRP? (3) What is the cost of equity using Rf + β × (ERP + CRP)?

Show the solution
  1. Adjusted beta = (2/3) × 1.45 + (1/3) × 1 = 0.9667 + 0.3333 = 1.30.
  2. CRP = 3.0% × (24 ÷ 16) = 3.0% × 1.5 = 4.5%.
  3. Cost of equity = 3% + 1.30 × (5% + 4.5%) = 3% + 1.30 × 9.5% = 3% + 12.35% = 15.35%.

Answer: (1) Adjusted beta = 1.30. (2) CRP = 4.5%. (3) Cost of equity = 15.35%.

Exam tips

  • Write Comparable and Target at the top of your scratch area and tag every number before calculating.
  • Questions often test the reasoning: more debt raises equity beta, and a short return interval can add noise or thin-trading bias. Know the direction of each effect.
  • Check which CRP form the vignette uses. If it does not say, scale it with beta only if the text puts it inside the premium.
  • Use the given weights for Blume if they differ from 2/3 and 1/3; read the exhibit footnotes.

Beta Estimation and Country Risk Premium in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Beta Estimation and Country Risk Premium: frequently asked questions

How do I unlever and relever beta in CFA Level II?

Divide the comparable's equity beta by 1 + (1 − t) × D/E using the comparable's figures to get the asset beta. Then multiply by 1 + (1 − t) × D/E using the target's figures. This assumes debt has a beta of zero.

What is the Blume adjusted beta formula?

Adjusted beta = 2/3 × raw beta + 1/3 × 1.0. It reflects the tendency of betas to move toward 1 over time. Use different weights only if the question provides them.

How is the country risk premium calculated?

A common method multiplies the sovereign yield spread by the ratio of the equity market's volatility to the sovereign bond market's volatility. You then add it to the equity risk premium in the cost of equity formula. Follow the form given in the question.

What is a pure play beta and why use it?

A pure play firm operates only in the same line of business as the project. Its unlevered beta reflects that business risk without the effect of its own debt. You relever it to the project's or target's capital structure to get the project's cost of equity.