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CMA Final · Strategic Financial Management · Portfolio Theory and Practice

Securities A and B have expected returns of 10% and 16% and standard deviations of 12% and 18% respectively. Their returns are perfectly negatively correlated (ρ = −1). If the investor combines them to eliminate all portfolio risk, what is the expected return of that zero-variance portfolio?

The zero-risk portfolio returns 12.4%. With perfect negative correlation, risk vanishes when A gets 18/30 = 60% and B gets 40%. The weighted return is 0.6 × 10% plus 0.4 × 16%, giving 12.4%.

  1. A13.6%
  2. B12.4%Correct
  3. C13.0%
  4. D11.2%

Explanation

Zero variance needs wA = σB/(σA+σB) = 18/30 = 60% and wB = 40%. Return = 0.6×10 + 0.4×16 = 6 + 6.4 = 12.4%. Option 13.6% comes from swapping the weights (40% in A, 60% in B), and 13.0% from equal weights.

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