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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

Which statement about diversification in a two-asset portfolio with positive weights is correct?

Portfolio volatility falls below the weighted average of the individual volatilities whenever correlation is less than 1. Only at perfect positive correlation do the two coincide. The benefit arises from imperfectly correlated returns, not from differences in expected returns.

  1. APortfolio volatility equals the weighted average of volatilities whenever correlation is below 1
  2. BPortfolio volatility is lowest when correlation is +1
  3. CPortfolio volatility is below the weighted average of volatilities whenever correlation is below 1Correct
  4. DDiversification benefits depend on the assets having different expected returns

Explanation

Volatility equals the weighted average only when correlation is exactly +1. For any correlation below 1, the covariance term is smaller, so portfolio volatility is strictly lower than the weighted average. Expected return differences are irrelevant to the diversification benefit.

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