Updated for the 2026-2027 CFA® Level I curriculum.
Portfolio expected return and risk bring several familiar statistics together. Expected return depends on how much you invest in each asset, while portfolio risk also depends on how the assets behave relative to one another.
For CFA Level I, you should be comfortable moving from asset weights, expected returns, standard deviations, and correlation to a complete portfolio calculation. The arithmetic is manageable once you keep the return and risk formulas separate.
Quick Answer
Portfolio expected return is the weighted average of the assets’ expected returns. Portfolio variance includes each asset’s weighted variance and the covariance between the asset returns. When correlation is below +1, the assets do not move together perfectly, which can lower portfolio risk through diversification.
Key Takeaways About Portfolio Expected Return and Risk
Portfolio expected return is calculated as a weighted average.
Portfolio variance is influenced by asset weights, individual variances, and covariance.
The weights in the individual variance terms must be squared.
Covariance can be calculated from correlation and the two asset standard deviations.
Lower correlation generally creates a larger diversification benefit, all else equal.
Portfolio standard deviation is the square root of portfolio variance.
A fully invested portfolio normally has weights that sum to 1.
Portfolio risk can be lower than the weighted average of the assets’ individual risks.
What You Need to Know for CFA Level I
When working with portfolio expected return and risk, you should be able to:
Calculate expected return using portfolio weights.
Confirm that the portfolio weights sum to 1.
Convert correlation into covariance.
Apply the two-asset portfolio variance formula.
Calculate portfolio standard deviation from variance.
Explain how correlation affects diversification.
Distinguish a weighted-average return calculation from a portfolio risk calculation.
Keep percentages and decimals consistent throughout the problem.
What Is Portfolio Expected Return?
Portfolio expected return is the probability-weighted return expected from the portfolio as a whole. Each asset contributes according to its portfolio weight.
For a portfolio with assets, the portfolio expected return formula is:
For a two-asset portfolio:
Expected return is linear. If Asset A represents 60% of the portfolio, then 60% of Asset A’s expected return contributes to the portfolio expected return.
Portfolio Expected Return Formula Breakdown
Where:
= expected return of the portfolio
= portfolio weight assigned to Asset
= expected return of Asset
= portfolio weight assigned to Asset A
= portfolio weight assigned to Asset B
= expected return of Asset A
= expected return of Asset B
= total number of assets in the portfolio
= the individual asset being evaluated
For a fully invested portfolio without borrowing or short selling, the asset weights should sum to 1:
What Is Portfolio Risk?
Portfolio risk measures how much the portfolio’s return may vary around its expected return. It depends on the risk of the individual assets and the way their returns move together.
This interaction is why portfolio risk cannot be calculated as a simple weighted average of asset standard deviations. Two risky assets may produce a less risky portfolio when their returns do not move together perfectly.
Portfolio Variance Formula
For a two-asset portfolio, the portfolio variance formula is:
The covariance between the two asset returns can be calculated from their correlation:
Substituting the correlation-based covariance formula gives:
Once you have portfolio variance, calculate portfolio standard deviation by taking the square root:
Portfolio Variance Formula Breakdown
Where:
= variance of the portfolio
= standard deviation of the portfolio
= portfolio weight assigned to Asset A
= portfolio weight assigned to Asset B
= variance of Asset A
= variance of Asset B
= standard deviation of Asset A
= standard deviation of Asset B
= covariance between the returns of Assets A and B
= correlation between the returns of Assets A and B
= covariance contribution to portfolio variance
The first two terms measure the weighted contribution of each asset’s own variance. The final term captures how the two asset returns move together.
How Do You Calculate Covariance From Correlation?
Correlation can be converted into covariance by multiplying the correlation coefficient by the standard deviation of each asset:
Suppose two assets have standard deviations of 15% and 8%, with a correlation of 0.25. Their covariance is:
The covariance is positive because the correlation is positive. The two measures always have the same sign because standard deviations cannot be negative.
Why Does Correlation Affect Portfolio Risk?
Correlation measures the strength and direction of the linear relationship between two asset returns. It determines the size and sign of the covariance term in the portfolio variance formula.
When correlation falls, the two assets move less closely together. One asset may therefore offset part of the other asset’s variability, reducing the portfolio’s overall standard deviation.
Correlation | General Effect on a Two-Asset Portfolio |
|---|---|
+1 | The assets move together perfectly, so there is no diversification benefit from imperfect co-movement |
Between 0 and +1 | The assets move in the same general direction but still provide some diversification |
0 | The returns have no linear relationship, creating a meaningful diversification benefit |
Between -1 and 0 | The asset returns tend to offset one another, producing a stronger diversification benefit |
-1 | Maximum potential diversification benefit; risk may be eliminated with the appropriate weights |
A lower correlation does not automatically make a portfolio appropriate for an investor. Expected return, individual asset risk, liquidity, time horizon, and the reliability of the correlation estimate still need to be considered.
Worked Example: Portfolio Expected Return and Risk
A portfolio invests:
60% in Asset A
40% in Asset B
The assets have the following expected returns and standard deviations:
Input | Asset A | Asset B |
|---|---|---|
Portfolio weight | 60% | 40% |
Expected return | 10% | 6% |
Standard deviation | 15% | 8% |
The correlation between Asset A and Asset B is 0.25.
Step 1: Confirm the Portfolio Weights
The weights sum to 1:
The portfolio is fully invested.
Step 2: Calculate Portfolio Expected Return
Apply the portfolio expected return formula:
The portfolio’s expected return is 8.4%.
Step 3: Calculate the Covariance
Convert the correlation into covariance:
Step 4: Calculate Portfolio Variance
Substitute the weights, standard deviations, and correlation into the portfolio variance formula:
Calculate each component:
The portfolio variance is 0.010564.
Step 5: Calculate Portfolio Standard Deviation
Take the square root of the variance:
The portfolio standard deviation is approximately 10.28%.
Step 6: Interpret the Diversification Benefit
The weighted average of the two individual standard deviations is:
The portfolio standard deviation is 10.28%, which is below the 12.2% weighted average of the individual standard deviations.
The assets have a correlation of only 0.25, so their returns do not move together closely. That imperfect relationship creates the diversification benefit.
How Does Correlation Change the Portfolio Standard Deviation?
Using the same weights and asset standard deviations, you can see how different correlations affect the portfolio’s risk.
Correlation | Approximate Portfolio Standard Deviation |
|---|---|
+1.00 | 12.20% |
+0.25 | 10.28% |
0.00 | 9.55% |
-0.50 | 7.91% |
-1.00 | 5.80% |
As correlation falls, portfolio standard deviation decreases. The expected return remains 8.4% because correlation affects portfolio risk rather than the weighted-average return calculation.
The exact relationship depends on the asset weights and standard deviations. Correlation alone does not determine the final risk level.
Multi-Asset Portfolio Risk
The expected return of a multi-asset portfolio still uses a weighted average:
Portfolio variance becomes more involved because it includes:
One weighted variance term for every asset
One weighted covariance relationship for every pair of assets
The matrix form of the multi-asset portfolio variance formula is:
Where:
= column vector containing the portfolio weights
= transpose of the portfolio-weight vector
= variance-covariance matrix of asset returns
= portfolio variance
You may not need to construct a large covariance matrix by hand in a basic CFA Level I question. You should still understand that every pairwise relationship contributes to the risk of a multi-asset portfolio.
Common Exam Traps
Common mistakes include:
Using unsquared weights in the individual variance terms.
Squaring the covariance term when the formula does not require it.
Using standard deviations where the individual terms require variances.
Forgetting the factor of 2 in the two-asset covariance term.
Treating portfolio standard deviation as a weighted average.
Using correlation directly without multiplying it by both standard deviations.
Forgetting to take the square root after calculating portfolio variance.
Mixing values such as 15 and 0.08 in the same calculation.
Assuming lower correlation changes the portfolio’s expected return.
Assuming negative correlation always eliminates portfolio risk.
Failing to check that the portfolio weights sum to 1.
Practice Question
A portfolio invests 50% in Asset X and 50% in Asset Y.
Asset X has:
Expected return of 12%
Standard deviation of 20%
Asset Y has:
Expected return of 6%
Standard deviation of 10%
The correlation between the two asset returns is 0.
Which pair is closest to the portfolio’s expected return and standard deviation?
9.0% and 11.2%
9.0% and 15.0%
18.0% and 11.2%
Correct Answer: A
First, calculate the portfolio expected return:
The expected return is 9.0%.
Because correlation is zero, the covariance term is also zero:
Calculate portfolio standard deviation:
The portfolio standard deviation is approximately 11.2%.
Option B treats portfolio risk too much like an average of the individual standard deviations.
Option C adds the two expected returns without applying their portfolio weights.
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FAQs About Portfolio Expected Return and Risk
What Is the Portfolio Expected Return Formula?
Portfolio expected return is the sum of each asset’s expected return multiplied by its portfolio weight:
The calculation is a weighted average, so the asset weights should normally sum to 1.
What Is the Two-Asset Portfolio Variance Formula?
The correlation-based two-asset portfolio variance formula is:
It combines the weighted variances of both assets with a covariance term that captures how their returns move together.
How Do You Calculate Portfolio Standard Deviation?
Calculate portfolio variance first, then take its square root:
Portfolio standard deviation expresses risk in the same units as the asset returns, making it easier to interpret than variance.
Can Portfolio Risk Be Lower Than the Risk of Both Assets?
Yes. When asset returns are sufficiently uncorrelated or negatively correlated, diversification can produce a portfolio standard deviation below the standard deviation of either individual asset.
The result depends on the correlation, asset weights, and individual standard deviations.
Does Correlation Affect Portfolio Expected Return?
No. Portfolio expected return depends on asset weights and expected returns.
Correlation affects portfolio variance and standard deviation because it determines how strongly the asset returns move together.