Learning Module 2
Portfolio Risk and Return: Part II
Key Outcomes Summary & Practice Problems
What you must be able to do
Curriculum Year: 2026
Describe the implications of combining a risk-free asset with a portfolio of risky assets.
Explain the capital allocation line (CAL) and the capital market line (CML).
Explain systematic and nonsystematic risk, including why an investor should not expect to receive additional return for bearing nonsystematic risk.
Explain return generating models (including the market model) and their uses.
Calculate and interpret beta.
Explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML).
Calculate and interpret the expected return of an asset using the CAPM.
Describe and demonstrate applications of the CAPM and the SML.
Calculate and interpret the Sharpe ratio, Treynor ratio, M2, and Jensen's alpha.
1 · Capital Market Theory & The CML
Capital Allocation Line (CAL) — The set of portfolios formed by combining the risk-free asset with a risky portfolio. Slope = Sharpe ratio.
Capital Market Line (CML) — A special case of the CAL where the risky portfolio is the market portfolio. Slope = \( \frac{E(R_m) - R_f}{\sigma_m} \).
Market Portfolio — Under the CAPM, all investors hold the same optimal risky portfolio, which is the market portfolio (a value-weighted portfolio of all risky assets).
Leveraged Portfolios — Borrowing at the risk-free rate to invest more than 100% in the market portfolio increases both expected return and risk. With different lending and borrowing rates, the CML is kinked.
E(Rp) = Rf + [ (E(Rm) − Rf) / σm ] × σp
Only applies to efficient portfolios (combinations of Rf and M).
2 · Systematic vs Nonsystematic Risk
Systematic Risk (Market Risk) — Risk that affects the entire market or economy. Cannot be diversified away (e.g., interest rates, inflation, economic cycles).
Nonsystematic Risk (Idiosyncratic Risk) — Risk specific to a company or industry. Can be diversified away by holding a well-diversified portfolio.
Pricing of Risk — In efficient markets, investors are only compensated for bearing systematic risk. Nonsystematic risk is not priced because it can be eliminated through diversification.
Total Variance — Total variance = Systematic variance + Nonsystematic variance.
3 · Return Generating Models & Beta
Market Model — A single-index model that relates a security's return to the market return:
Ri = αi + βiRm + ei.Alpha (α) — The intercept of the market model. Represents the security's expected return when the market return is zero.
Beta (β) — Measures a security's systematic risk. It is the sensitivity of the security's returns to the market returns.
βi = ρi,m × (σi / σm)
Market beta = 1. Risk-free asset beta = 0.
4 · CAPM & The Security Market Line
Capital Asset Pricing Model (CAPM) — A model that describes the relationship between systematic risk (beta) and expected return.
Security Market Line (SML) — A graphical representation of the CAPM. Plots expected return against beta. The slope is the market risk premium \( E(R_m) - R_f \).
CAPM Formula —
E(Ri) = Rf + βi (E(Rm) − Rf).Assumptions of CAPM — Investors are rational, risk-averse, utility-maximizers; markets are frictionless; investors have homogeneous expectations; single holding period; infinite divisibility; price takers.
5 · Portfolio Performance Appraisal Measures
Sharpe Ratio — Measures excess return per unit of total risk. \( \text{SR} = \frac{R_p - R_f}{\sigma_p} \).
Treynor Ratio — Measures excess return per unit of systematic risk. \( \text{TR} = \frac{R_p - R_f}{\beta_p} \).
M² (Modigliani-Modigliani) — Risk-adjusted performance measure that adjusts total risk to match the market's risk. \( M² = (R_p - R_f) \times \frac{\sigma_m}{\sigma_p} + R_f \).
Jensen's Alpha — The difference between a portfolio's actual return and its expected return given its beta. \( \alpha_p = R_p - [R_f + \beta_p (R_m - R_f)] \). A positive alpha indicates outperformance.
αp = Rp − [Rf + βp(Rm − Rf)]
Alpha is the vertical distance from the SML.