Portfolio Risk and Return: Part II | Free CFA Level I Lesson

A portfolio manager pitches you two funds with identical 12% returns but different volatilities. Part II builds the toolkit that says which one earned that 12% the smart way.

A risk-free asset has zero variance and zero correlation with any risky portfolio. Combine it with risky portfolio P and the result has a linear risk-return profile. The weighted variance collapses to a single term because the cross-product disappears.

Let w be the weight in risky portfolio P and (1 − w) in the risk-free asset.

$E (R_{p}) = w \cdot E (R_{P}) + (1 - w) R_{f}, σ_{p} = w \cdot σ_{P}$

Solve for w in the σ equation, substitute back, and you get the Capital Allocation Line (CAL).

$E (R_{p}) = R_{f} + (\frac{E ( R _{P} ) - R _{f}}{σ _{P}}) σ_{p}$

KEY: The slope of the CAL is the Sharpe ratio of the risky portfolio. Steeper CAL means better risk-adjusted opportunity.

A CAL exists for any risky portfolio P combined with the risk-free asset. Each investor's optimal CAL touches their best feasible risky portfolio.

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Common mistakes

Mixing up CML and SML axes. The CML x-axis is total risk (σ) and applies only to efficient portfolios. The SML x-axis is beta and applies to any asset. Trap: using the CML to evaluate an individual stock.
Believing nonsystematic risk is priced. It is not. Diversification removes it for free, so the market refuses to pay a premium. Trap: "the stock has high idiosyncratic risk, so its required return should rise."
Forgetting to subtract the risk-free rate. Sharpe, Treynor, M², and Jensen's α all use excess return (Rp − Rf). Trap: dividing raw return by σ instead of excess return.

Bottom line

CAPM: $E (R_{i}) = R_{f} + β_{i} (E (R_{m}) - R_{f})$ . Beta is the only priced risk.
Nonsystematic risk earns zero premium because diversification eliminates it for free.
The CAL runs from Rf through any risky portfolio, with slope equal to that portfolio's Sharpe ratio.
The CML is the specific CAL through the market portfolio under homogeneous expectations; it uses total risk (σ) and applies only to efficient portfolios.

Exam shortcut

Beta from correlation. If the exam gives you ρ, σi, and σm, compute β instantly as ρ × (σi / σm). Skip the covariance route entirely. CML vs. SML disambiguator. If the x-axis is σ, it is the CML and only efficient portfolios sit on it. If the x-axis is β, it is the SML and every asset sits on it (or off it if mispriced). Performance measure picker.

The full lesson (about 2,776 words, 19 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

portfolio risk and return part II

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