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CFA Level I Exam · Basics of Portfolio Planning and Construction

Portfolio Approach and Diversification: How Diversification Reduces Risk

Updated 7 October 2026 · Fact-checked

The portfolio approach judges each holding by how it changes the risk and return of the whole portfolio, not by its own risk alone. Diversification lowers portfolio risk when assets are not perfectly correlated. It reduces nonsystematic risk but cannot remove systematic risk, and it can fail in crises.

Understand Portfolio Approach and Diversification

An individual asset approach asks: is this security good or bad on its own? The portfolio approach asks a different question: what does this security do to the risk and return of everything I own? The second question matters because investors live with the total result of their holdings, not with each holding in isolation.

Here is why it works. Portfolio expected return is just the weighted average of the asset returns. Portfolio risk is not. Risk depends on how the assets move together, measured by correlation. If two assets do not move in perfect lockstep, a loss in one is partly offset by a gain or smaller loss in the other. So portfolio standard deviation is lower than the weighted average of the individual standard deviations. This is diversification.

The lower the correlation, the larger the benefit. With a correlation of +1, there is no risk reduction from combining the assets (the portfolio standard deviation equals the weighted average). With a correlation below +1, there is a benefit. With a correlation of -1, risk can be reduced to zero with the right weights.

Diversification has limits. It removes nonsystematic (firm-specific) risk, which is unique to a company or sector. It cannot remove systematic (market) risk, which affects all assets, such as recessions or interest rate shocks. Adding more securities gives smaller and smaller benefits. In market stress, correlations often rise, so benefits shrink just when you need them. Diversification also does not guarantee a profit or protect against loss in a falling market. It also has costs, such as transaction costs and monitoring effort.

The portfolio perspective also means a risky asset can be a good addition if its correlation with the existing holdings is low. An asset's standalone risk is not the whole story.

Key formulas to remember

Portfolio expected return
E(Rp) = Σ wi × E(Ri)
Weighted average of asset expected returns. Weights sum to 1. Diversification does not change this calculation.
Two-asset portfolio variance
σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ12 σ1 σ2
Portfolio standard deviation is √σp². The correlation term drives the diversification benefit.
Covariance and correlation
Cov(1,2) = ρ12 × σ1 × σ2
Correlation ranges from -1 to +1.
Perfect positive correlation case
σp = w1σ1 + w2σ2 when ρ12 = +1
No diversification benefit. For ρ < +1, σp is less than the weighted average of the standard deviations.
Risk decomposition
Total risk = Systematic risk + Nonsystematic risk
Diversification reduces nonsystematic risk only. Systematic risk remains.

How to solve Portfolio Approach and Diversification questions

Use this method for both conceptual and numerical questions on the portfolio approach and diversification.

  1. 1Identify what is asked: a concept (why diversify, limits) or a calculation (portfolio return or risk).
  2. 2For concept questions, check whether the statement is about the portfolio as a whole or a single asset. The portfolio view looks at contribution to total risk.
  3. 3Look for the correlation. If it is below +1, a risk reduction exists. If it is exactly +1, there is none.
  4. 4Decide which type of risk is involved. Firm-specific risk can be diversified away. Market-wide risk cannot.
  5. 5For calculations, compute expected return first as a weighted average using weights that sum to 1.
  6. 6For risk, plug into the two-asset variance formula, then take the square root at the end.
  7. 7Sanity check: portfolio standard deviation should not exceed the weighted average of the individual standard deviations, and should equal it only when ρ = +1.
  8. 8Eliminate two options: remove any that claim diversification removes all risk or guarantees returns.

Quickest way: Quick check using the correlation bounds

When to use it: Use when a numerical question gives standard deviations, weights and a correlation below +1 and the three options are far apart.

  1. Compute the weighted average of the standard deviations. This is the upper bound for portfolio risk.
  2. Any option above that bound is wrong when ρ < +1.
  3. If ρ is 0 or negative, expect the answer to sit well below the bound.
  4. Only compute the full formula if two options remain below the bound.
  5. On the BA II Plus, enter the variance terms with parentheses, then press 2nd then √x... (the √x key) at the end. On the HP 12C, compute the variance and press g then √x.

Common mistakes in Portfolio Approach and Diversification

  • Averaging the standard deviations to get portfolio risk

    Expected return is a weighted average, so students assume risk is too.

    Fix: Use the variance formula with the correlation term. The weighted average of standard deviations holds only when ρ = +1.

  • Saying diversification eliminates all risk

    The benefit sounds complete.

    Fix: Diversification removes nonsystematic risk only. Systematic risk stays, and the correlation is rarely -1.

  • Judging an asset only by its standalone risk

    The individual asset habit is strong.

    Fix: Ask how the asset's correlation with the existing portfolio changes total risk. A volatile asset with low correlation can reduce portfolio risk.

  • Forgetting to take the square root

    The formula gives variance, and students stop there.

    Fix: Finish with σp = √σp². Check whether the options are in variance or standard deviation terms.

  • Assuming diversification always works in a crisis

    Textbook correlations are treated as fixed.

    Fix: Remember correlations tend to rise in market stress, which reduces the benefit when it is most needed.

  • Using weights that do not sum to 1

    Mixing percentages and amounts.

    Fix: Convert amounts to weights first and confirm they add to 1.

Worked examples

Example 1

Asset A has an expected return of 8% and a standard deviation of 12%. Asset B has an expected return of 12% and a standard deviation of 20%. The portfolio holds 60% A and 40% B, and the correlation is 0.25. What is the portfolio standard deviation? Options: A) 11.5%, B) 12.0%, C) 14.4%.

Show the solution
  1. Weights: wA = 0.6, wB = 0.4.
  2. wA²σA² = 0.36 × 0.0144 = 0.005184.
  3. wB²σB² = 0.16 × 0.04 = 0.0064.
  4. Covariance term: 2 × 0.6 × 0.4 × 0.25 × 0.12 × 0.20 = 0.48 × 0.25 × 0.024 = 0.00288.
  5. Variance = 0.005184 + 0.0064 + 0.00288 = 0.014464.
  6. Standard deviation = √0.014464 = 0.12027, about 12.0%.
  7. Check against the bound: weighted average = 0.6 × 12 + 0.4 × 20 = 15.2%, so the answer must be below 15.2%.

Answer: B) 12.0%. The computed value is well below the 15.2% weighted average, which confirms the diversification benefit.

Example 2

Which statement about diversification is most accurate? A) It removes systematic risk when enough assets are held. B) It reduces portfolio risk when assets are less than perfectly positively correlated. C) It raises the expected return of the portfolio above the weighted average of the asset returns.

Show the solution
  1. Test A: systematic risk affects all assets, so adding assets cannot remove it. A is wrong.
  2. Test C: expected return is the weighted average of asset expected returns. Diversification does not lift it above that. C is wrong.
  3. Test B: with a correlation below +1, the portfolio standard deviation is below the weighted average of the standard deviations. B is correct.

Answer: B

Exam tips

  • Expect conceptual items on what diversification can and cannot do. Wrong options usually say it removes all risk or guarantees returns.
  • For numerical items, compute the weighted-average bound first. It often eliminates one or two options quickly.
  • Remember the three correlation cases: +1 gives no benefit, 0 gives some benefit, -1 allows zero risk with the right weights.
  • Read whether the question asks for variance or standard deviation, and whether returns are given in percent or decimals.
  • Link this topic to systematic and nonsystematic risk questions, which often test the same idea from another angle.

Practice questions from Basics of Portfolio Planning and Construction

Portfolio Approach and Diversification in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Portfolio Approach and Diversification: frequently asked questions

What is the difference between the portfolio approach and the individual asset approach?

The individual asset approach judges each security on its own risk and return. The portfolio approach judges it by its effect on the whole portfolio. The key input is correlation with the other holdings.

How does diversification reduce risk in a portfolio?

When assets do not move perfectly together, their individual ups and downs partly offset each other. This lowers portfolio standard deviation below the weighted average of the asset standard deviations. The lower the correlation, the stronger the effect.

Can diversification remove all risk?

No. It reduces nonsystematic risk, which is specific to a firm or sector. Systematic market risk remains, and correlations can rise in a crisis.

Does diversification change expected return?

No. Portfolio expected return is the weighted average of the asset expected returns. Diversification changes risk, not that average.