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

The risk-free rate is 7%. The market portfolio has expected return 15% and standard deviation 10%. An investor holds a portfolio on the capital market line with expected return 23%. Which describes the position, and the standard deviation?

The investor borrows 100% of wealth at 7% and holds 200% in the market portfolio, giving standard deviation 20%. Solving 7% + w x 8% = 23% gives w = 2, and risk is then 2 x 10%.

  1. ALend 100% at risk-free; standard deviation 10%
  2. BHold 100% in market; standard deviation 10%
  3. CBorrow 100% of wealth at 7% and hold 200% in market; standard deviation 20%Correct
  4. DBorrow 50% of wealth at 7% and hold 150% in market; standard deviation 15%
  5. Borrow 200% of wealth at 7% and hold 300% in market; standard deviation 30%

Explanation

Let w be the market weight: 7 + w x 8 = 23, so w = 2. Borrowing is 1 (100% of wealth). Standard deviation = 2 x 10% = 20%. Check: 2x15 - 1x7 = 23. Other options give wrong returns, e.g. 1.5 gives 19%.

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