CFA Level 1 portfolio risk and return measures
Expected portfolio return is the weighted average of asset expected returns. Portfolio variance also depends on covariance: diversification depends on how the assets move together, not only on how many assets you hold.
The key ideas, at a glance
Expected return
Read the visual, then follow the worked example below. Use the stated case assumptions.
Illustrative worked case
% volatility
- Asset A
- 10
- Asset B
- 10
- 50/50 portfolio
- 7.07
Both assets have 10% volatility, equal weights and zero correlation. Portfolio volatility is √0.005 = 7.07%; this is a modeled case.
| Concept | Rule or decision | Common mistake |
|---|---|---|
| Expected return | E(Rp) = sum of weight × expected return; check that weights sum to one. | Expected return is an estimate, not a promised outcome. |
| Two-asset variance | σp² = wA²σA² + wB²σB² + 2wAwBσAσBρAB. | Volatilities cannot simply be averaged to obtain portfolio volatility. |
| Correlation | Lower correlation can reduce portfolio risk for the same asset weights and volatilities. | Correlations can change; historical diversification may weaken under stress. |
| Risk-adjusted return | Sharpe uses excess return divided by total return volatility. | Do not compare ratios calculated over incompatible periods or with different conventions. |
01Expected return
E(Rp) = sum of weight × expected return; check that weights sum to one.
Watch for: Expected return is an estimate, not a promised outcome.
02Two-asset variance
σp² = wA²σA² + wB²σB² + 2wAwBσAσBρAB.
Watch for: Volatilities cannot simply be averaged to obtain portfolio volatility.
03Correlation
Lower correlation can reduce portfolio risk for the same asset weights and volatilities.
Watch for: Correlations can change; historical diversification may weaken under stress.
04Risk-adjusted return
Sharpe uses excess return divided by total return volatility.
Watch for: Do not compare ratios calculated over incompatible periods or with different conventions.
Selected 2026 study concepts. Match your preparation to your registered exam-year curriculum. These notes are not complete curriculum coverage.
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Put the method to work
One worked example, from facts to answer
Given
Two assets each have 10% volatility, equal 50% weights and zero correlation.
Method
Variance = 0.5² × 0.1² + 0.5² × 0.1² = 0.005. Volatility = √0.005.
Answer and interpretation
Portfolio volatility is about 7.07%, below either asset’s 10%. Zero correlation creates the reduction in this example.
Original independent teaching example. Assumptions are stated above; this is not an official exam question or scoring key.
Apply the framework, step by step
Calculate portfolio expected return and two-asset risk, then distinguish total-risk and market-risk measures. Use Portfolio Management for investor objectives and the broader portfolio process.
Before you start: Asset weights, variance versus standard deviation, covariance, correlation and a common return measurement period.
METHOD 01
Expected return
E(Rp) = sum of weight × expected return; check that weights sum to one.
Use each asset’s portfolio weight at the point specified by the question, multiply by its expected return and add the products. A fully invested long-only example normally has weights summing to one. Expected return is a model input or estimate rather than a guaranteed outcome. Do not use the expected-return weighted-average formula to average standard deviations; risk requires joint behavior.
Avoid this mistake: Expected return is an estimate, not a promised outcome.
METHOD 02
Two-asset variance
σp² = wA²σA² + wB²σB² + 2wAwBσAσBρAB.
For two assets, variance includes the squared-weight variance terms and twice the covariance term. Convert correlation into covariance with correlation × volatility A × volatility B. Enter volatilities in matching units, keep variance separate from standard deviation, and take the square root only at the end. Forgetting the cross term or squaring an already squared variance changes the result.
Avoid this mistake: Volatilities cannot simply be averaged to obtain portfolio volatility.
METHOD 03
Correlation
Lower correlation can reduce portfolio risk for the same asset weights and volatilities.
With fixed positive weights and volatilities, lower correlation reduces portfolio variance. Perfect positive correlation provides no volatility reduction below the weighted-average volatility. Negative correlation can provide a larger reduction, but the weights still matter. Historical correlation is an estimate and can change, particularly under stress; diversification is a portfolio property, not a promise that losses cannot occur.
Avoid this mistake: Correlations can change; historical diversification may weaken under stress.
METHOD 04
Risk-adjusted return
Sharpe uses excess return divided by total return volatility.
Sharpe compares excess return with total volatility. Measures using beta address exposure to market risk instead, so they answer a different comparison question. Use consistent horizons, risk-free assumptions and return definitions. A ratio derived from a short noisy sample should not be interpreted as proof of skill. Choose the measure from the portfolio context and the risk the question asks you to evaluate.
Avoid this mistake: Do not compare ratios calculated over incompatible periods or with different conventions.
Apply it to a different case
- New facts
- Weights are 60% and 40%; expected returns are 8% and 4%. Both assets have 10% volatility and correlation 0.50.
- Working
- Expected return = 0.60 × 8% + 0.40 × 4% = 6.4%. Variance = 0.60² × 0.10² + 0.40² × 0.10² + 2 × 0.60 × 0.40 × 0.10 × 0.10 × 0.50 = 0.0076.
- Conclusion
- Portfolio volatility is √0.0076, approximately 8.72%. Return is a weighted average; volatility requires the covariance term.
Original teaching case under the stated assumptions, rather than an official exam question.
Questions about this method
- Can I average asset volatilities to get portfolio volatility?
- Generally no. Portfolio variance depends on weights, asset variances and covariances. Calculate variance first and then its square root. A simple weighted average is only a special-case result under matching positive exposures and perfect positive correlation.
- How do covariance and correlation differ?
- Correlation is a unitless measure of association bounded between -1 and +1. Covariance retains the units of the return measures and equals correlation times the two standard deviations.
- Does diversification guarantee a positive return?
- No. It can reduce risk arising from assets moving differently, but a diversified portfolio can still suffer losses and remains exposed to risks shared across its holdings.
Sources and curriculum scope
Official outlines establish curriculum scope. The explanations and worked examples are independent teaching material; the sources do not verify or endorse them.
- 2026 CFA Level 1 curriculum outline
- Official Level 1 format and curriculum
- 2026 portfolio risk and return
- 2027 CFA Level 1 curriculum outline
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