Capital Market Line and Capital Asset Pricing Model (CAPM) for CMA Final

Understand Capital Market Line and Capital Asset Pricing Model

Key rules to remember

CAPM (required return)

E(Ri) = Rf + βi × (Rm − Rf)

Rm − Rf is the market risk premium. Use Rm as the expected market return unless the question gives the premium directly.

Capital Market Line

E(Rp) = Rf + [(E(Rm) − Rf) ÷ σm] × σp

Applies to efficient portfolios only. The slope is the Sharpe ratio of the market portfolio.

Beta of a security

β = Cov(Ri, Rm) ÷ σm² = ρim × σi ÷ σm

Market beta is 1. Risk-free asset beta is 0.

Beta of a portfolio

βp = Σ (wi × βi)

Weights are proportions of investment value and must sum to 1. A risk-free holding contributes a beta of 0.

Systematic and total risk

Systematic variance = β² × σm²; Total variance = β² × σm² + unsystematic variance

Beta captures only the systematic part.

SML decision rule

Expected return > CAPM return: undervalued (buy). Expected return < CAPM return: overvalued (sell).

You can also use alpha = expected return − required return.

Implied price from CAPM

Fair price = (Expected dividend + Expected price at year end) ÷ (1 + required return)

For a one-year holding period.

How to solve Capital Market Line and Capital Asset Pricing Model questions

1. 1Identify what risk the question gives: standard deviation (think CML, efficient portfolios) or beta (think SML, CAPM).
2. 2List Rf, Rm or the market premium, and betas or the data to compute beta.
3. 3If beta is needed, compute it from covariance ÷ market variance, or correlation × σi ÷ σm. For a portfolio, take the weighted average of betas.
4. 4Check weights carefully. If money is borrowed at Rf, the weight in Rf is negative and the weight in the market is above 1.
5. 5Apply CAPM to get the required return, or the CML to get the expected return at a given σ.
6. 6Compare required return with expected return, and classify the security as undervalued, overvalued or fairly priced.
7. 7State a clear recommendation (buy, sell, hold) with the reason in one line.

Quickest way: Beta-first shortcut with alpha check

Common mistakes in Capital Market Line and Capital Asset Pricing Model

• Using Rm instead of (Rm − Rf) as the multiplier of beta.

  Students remember the formula as Rf + β × Rm.

  Fix: Always write the premium first. Required return = Rf + β × (Rm − Rf).

• Applying the CML to individual shares or using beta on its x-axis.

  CML and SML look alike, both straight lines starting at Rf.

  Fix: CML: standard deviation, efficient portfolios only. SML: beta, every asset. Say this in every comparison answer.

• Treating a share as overvalued because its return is high.

  Students judge on expected return alone and ignore risk.

  Fix: Compare expected return with CAPM required return. Only a gap above the SML means undervalued.

• Wrong weights when the investor borrows at the risk-free rate.

  Students force weights to stay between 0 and 1.

  Fix: With borrowing, the risk-free weight is negative and the market weight exceeds 1. Total weights still equal 1.

• Dividing covariance by σm instead of σm², or mixing percentages with decimals in variance.

  Confusing standard deviation with variance.

  Fix: Beta = Cov ÷ Variance of market. If σm = 20%, variance is 400 (in %²) or 0.04 in decimals. Keep covariance in the same units.

• Averaging betas by simple mean instead of by weights.

  Rushing when securities look similar.

  Fix: Weight each beta by its share of portfolio value.

Worked examples