Charta is on Google Play: practise on the go. Get the app
Charta

Explain how correlation between assets changes the risk of a portfolio

CFA® Level I · Portfolio Management · Portfolio Risk and Return: Part I · PM.2.a

The idea

Correlation governs how much diversification reduces risk. At a correlation of +1 the assets move together and portfolio standard deviation is just the weighted average — no benefit. As correlation falls, risk reduction grows, and at -1 a weighting exists that eliminates volatility entirely. The practical implication is that benefit exists whenever correlation is below +1, so adding a volatile asset can lower total portfolio risk if it is weakly correlated with what you already hold. Correlations are unstable and tend to rise in crises, exactly when diversification is most needed.

Formulas

Correlation from covariance

ρ = Cov ÷ (σ₁ × σ₂)

Cov
the covariance of the two returns
σ₁, σ₂
the standard deviation of each return
ρ
the correlation, always between −1 and 1

Covariance says which way two assets move together but its size depends on the units. Dividing by both standard deviations scales that out, which is why correlation can be compared across pairs and covariance cannot.

A practice question

From the question bank, with the reason each wrong option is wrong.

A diversification benefit exists whenever the correlation between two assets is:

  1. below +1 — correct
  2. exactly +1Why not: The one case with no benefit at all: the portfolio's risk is simply the weighted average of the two.
  3. exactly zero and no other valueWhy not: Zero correlation gives a large benefit, but any value below +1 gives some, including a correlation of +0.8.

Any correlation short of perfect positive produces some offsetting movement. The benefit simply grows as correlation falls.

A harder one

At a correlation of exactly +1, portfolio standard deviation equals:

  1. the higher of the two standard deviationsWhy not: That would require the whole portfolio to sit in the riskier asset. Weights still apply.
  2. the weighted average of the component standard deviations — correct
  3. zeroWhy not: Zero risk needs a correlation of −1, where the movements cancel.

The assets move in lockstep, so nothing offsets and risk combines linearly — the one case where risk behaves like return.

The hardest tier

Adding a highly volatile asset that is weakly correlated with an existing portfolio most likely:

  1. raises total portfolio risk in proportion to its volatilityWhy not: Treats standalone volatility as the contribution. What an asset adds depends on its covariance with what is already held.
  2. leaves total portfolio risk unchangedWhy not: A weakly correlated addition changes the covariance structure, and in this case for the better.
  3. lowers total portfolio risk — correct

What matters is the asset's covariance with the rest of the portfolio, not its volatility in isolation — which is why risk cannot be judged asset by asset.

In the app: 21 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.

Take the free diagnostic →

More in Portfolio Risk and Return: Part I