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IAI Actuarial Core Principles · Economic Modelling · Mean-variance portfolio theory

Two risky assets have a correlation of +1 between their returns. An investor forms portfolios by varying the proportions held in the two assets, with no short selling. Which statement best describes the resulting set of portfolios in expected return–standard deviation space?

The portfolios lie on a straight line joining the two assets. When correlation is +1, portfolio standard deviation is the weighted average of the individual standard deviations, so there is no diversification benefit beyond simple averaging, and the curve cannot bulge to the left.

  1. AA straight line joining the two assets, so diversification gives no risk reduction beyond averagingCorrect
  2. BA curve bulging to the left of the straight line joining the two assets
  3. CA single point, since both assets must have the same expected return
  4. DA curve that lies entirely below the straight line joining the two assets
  5. A horizontal line, since the portfolio risk is independent of the weights

Explanation

With correlation +1, portfolio standard deviation equals the weighted average of the two standard deviations, so risk and return are both linear in the weights. The portfolio set is therefore a straight line. A curve bulging left needs correlation below 1, which is what produces diversification benefit.

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