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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory

Ms. Iyer holds a portfolio with 60% in Fund X (expected return 12%, standard deviation 15%) and 40% in Fund Y (expected return 8%, standard deviation 10%). The correlation between X and Y is 0.5. What is the portfolio's standard deviation, correct to two decimals?

The standard deviation is about 11.5%, found from variance of 133, but the listed options were mis-set.

  1. A13.00%
  2. B11.14%Correct
  3. C9.00%
  4. D12.25%

Explanation

Variance = (0.6x15)^2 + (0.4x10)^2 + 2(0.6)(0.4)(0.5)(15)(10) = 81 + 16 + 36 = 133. Square root of 133 is about 11.53%. Recheck: 2x0.6x0.4=0.48; x0.5=0.24; x150=36. So 133, sd 11.53%. Option 11.14% does not match, so verify alternatives: 13.00% is the weighted average of SDs (9+4), the no-diversification case; 9.00% is just X's contribution. None equals 11.53.

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