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

Two risky assets have a correlation coefficient of +1 between their returns. An investor forms portfolios by varying the proportions held in the two assets (no short selling). In expected return–standard deviation space, the set of attainable portfolios is:

The attainable set is a straight line segment joining the two assets. With perfect positive correlation, portfolio standard deviation is the weighted average of the individual standard deviations, as is expected return, so both vary linearly with the weights and there is no diversification benefit.

  1. AA hyperbola bulging to the left of the straight line joining the two assets
  2. BA straight line segment joining the two assetsCorrect
  3. CA single point
  4. DA curve bulging to the right of the straight line joining the two assets
  5. A horizontal line at the higher of the two expected returns

Explanation

With rho = 1, portfolio standard deviation = w*s1 + (1-w)*s2, which is linear in w. Expected return is also linear in w, so the portfolios lie on a straight line. A curve bulging left appears only when correlation is below 1, giving diversification benefit.

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