Portfolio Risk and Return: Part I

Combining a 20% volatility stock with a 12% volatility bond does not give you a 16% volatility portfolio. The math of correlation makes the whole less risky than the weighted average of the parts, and that single insight drives everything from utility-based selection to the efficient frontier.

Investors build portfolios from a small set of broad asset classes that differ in return, volatility, liquidity, and inflation sensitivity. The point of classification is not labeling, it is correlation, asset classes are useful precisely because their returns do not move together.

KEY: Equities deliver the highest expected return and the highest volatility. Cash sits at the opposite corner. Fixed income lives in between, with credit and duration as the main risk levers. Real estate and commodities are the classic inflation hedges. Alternatives are heterogeneous, their value is low correlation with traditional assets, not standalone return.

Three behavioral types matter for the exam:

• Risk averse. Demands compensation (a risk premium) to accept volatility. Given two portfolios with the same expected return, picks the one with lower variance.
• Risk neutral. Ranks portfolios purely on expected return. Indifferent to volatility.

Common mistakes

• Forgetting to square sigma in the utility function. Utility uses ${\sigma }^2$, not $\sigma$. If $\sigma =18\%$, use 0.0324 in the formula, not 0.18. The exam will leave a trap answer that used $\sigma$ instead of ${\sigma }^2$.
• Dropping the factor of 2 in portfolio variance. The cross-term is $2w_1{w}_2{\sigma }_1{\sigma }_2\rho$, not $w_1{w}_2{\sigma }_1{\sigma }_2\rho$. Halving the cross-term produces a portfolio variance that looks plausible but is wrong by a meaningful margin.
• Confusing covariance with correlation. Covariance is unbounded and depends on units. Correlation is bounded between -1 and +1. Saying "the covariance is 0.85, so the assets are highly correlated" is a unit error, 0.85 covariance could correspond to almost any correlation depending on the standard deviations.

Bottom line

• Portfolio variance depends on correlation, not just individual volatilities. The cross-term $2w_1{w}_2{\sigma }_1{\sigma }_2\rho$ is where diversification lives.
• Any correlation below +1 reduces portfolio risk below the weighted average of the component standard deviations. At $\rho =-1$, risk can be eliminated entirely with the right weights.
• Utility $U=E(R)-0.5A{\sigma }^2$ uses variance, not standard deviation, to rank portfolios. A typically ranges from 1 (aggressive) to 10 (very conservative); higher A means steeper indifference curves.
• The CAL combines the risk-free asset with a risky portfolio and its slope equals the Sharpe ratio. Higher risk aversion pulls the optimal mix down the CAL toward the risk-free asset; lower risk aversion pushes it up, possibly into leverage.

Exam shortcut

Memorize the utility formula with the half: $U=E(R)-0.5A{\sigma }^2$. The half is easy to drop and the exam will offer a wrong answer that forgot it. For diversification, the rule is "any $\rho <1$ helps", do not require negative correlation.

The full lesson (about 3,120 words, 21 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• portfolio risk and return part I

Browse all free CFA Level I lessons or jump into free CFA Level I practice questions.