Portfolio Risk and Return: Part II

Once a risk-free asset is added to the efficient frontier, portfolio choice reduces to holding the market portfolio and lending or borrowing. This module develops the capital market line, separates the risk that is rewarded from the risk that is not, introduces beta and return-generating models, and builds the capital asset pricing model and the security market line. It closes with the four performance measures that the exam tests every year: the Sharpe ratio, Treynor ratio, M-squared and Jensen's alpha.

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What you will learn

1. Describe the effect of combining a risk-free asset with a portfolio of risky assets and explain the capital allocation line and the capital market line, including lending and borrowing portfolios.

Two-fund separation: choose the optimal risky portfolio first, then the mix with the risk-free asset.
With homogeneous expectations, the optimal risky portfolio is the market portfolio and the CAL becomes the CML.
CML slope = (E(Rm) - Rf) / σm, the market price of risk.
Left of M: lending portfolios; right of M: borrowing (leveraged) portfolios with weight above 1.
A borrowing rate above the lending rate makes the CML kink and flatten beyond the market portfolio.

2. Explain systematic and nonsystematic risk and why an investor should not expect a higher return for bearing nonsystematic risk.

Total risk = systematic (market) risk + nonsystematic (company-specific) risk.
Nonsystematic risk diversifies away in a large portfolio; systematic risk does not.
Only systematic risk earns a risk premium in equilibrium, because diversifiable risk can be removed at little cost.
Concentrated positions carry extra risk with no extra expected return.
Total variance = beta² x market variance + nonsystematic (residual) variance.

3. Explain return-generating models, including the market model, and calculate and interpret beta.

Multi-factor models: excess return = sum of factor sensitivities x factor premiums.
Market model: Ri = αi + βi Rm + εi, estimated by regression on historical data.
β = Cov(Ri, Rm) / σm² = ρ σi / σm.
Market beta = 1, risk-free beta = 0; portfolio beta = weighted average of asset betas.
Beta measures systematic risk, not total risk.

4. Explain the capital asset pricing model, including its assumptions, and the security market line, and calculate an asset's expected return using the CAPM.

CAPM: E(Ri) = Rf + βi[E(Rm) - Rf]; beta is the only asset-specific risk input.
Key assumptions: risk-averse rational investors, frictionless markets, one holding period, homogeneous expectations, divisible assets, price takers.
SML: expected return versus beta; intercept Rf, slope = market risk premium, market at β = 1.
CML uses standard deviation and applies to efficient portfolios only; SML uses beta and applies to all assets.
A higher risk-free rate shifts the SML up, raising every asset's required return.

5. Apply the CAPM and the security market line to estimate required returns, evaluate capital projects and identify undervalued or overvalued securities.

Cost of equity / required return = Rf + β[E(Rm) - Rf].
Evaluate a project with the project's beta, not the company's average beta.
Forecast return above the CAPM return (positive alpha, above the SML) = undervalued; below = overvalued.
Market forces push mispriced assets back towards the SML.
Beta and the market risk premium are estimates; results are sensitive to them.

6. Calculate and interpret the Sharpe ratio, the Treynor ratio, M-squared and Jensen's alpha, and select the measure appropriate to a given situation.

Sharpe = (Rp - Rf) / σp: total risk; use for an investor's entire or undiversified portfolio.
M² = Rf + Sharpe x σm; M² alpha = M² - Rm; same ranking as Sharpe, in percentage terms.
Treynor = (Rp - Rf) / βp: systematic risk; use for well-diversified portfolios.
Jensen's alpha = Rp - [Rf + βp(Rm - Rf)]: distance above or below the SML.
Good Treynor/alpha but poor Sharpe/M² signals substantial nonsystematic risk.

Module at a glance

Two-fund separation: hold the market portfolio and lend or borrow at the risk-free rate; this traces the CML.
A borrowing rate above the lending rate flattens the CML beyond the market portfolio.
Only systematic risk is priced; nonsystematic risk diversifies away.
β = Cov(Ri, Rm) / σm² = ρσi/σm; portfolio beta is the weighted average of asset betas.
CAPM/SML: E(Ri) = Rf + βi[E(Rm) - Rf]; above the SML is undervalued, below is overvalued.
Judge projects with the project's own beta.
Sharpe and M² adjust for total risk; Treynor and Jensen's alpha adjust for beta.

This free module has 6 lessons, 20 practice questions with full explanations.

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