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NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Risk and Return

Asset A has a standard deviation of 10% and Asset B has 20%. They are combined 50:50 in a portfolio and their correlation coefficient is 0. What is the portfolio standard deviation (approximately)?

The portfolio standard deviation is about 11.18%. With zero correlation, variance is the sum of squared weighted standard deviations, 25 plus 100, equal to 125, and its square root is 11.18%. This is lower than the 15% weighted average, showing diversification benefit.

  1. A15.00%
  2. B11.18%Correct
  3. C7.50%
  4. D12.50%

Explanation

Variance = (0.5×10)^2 + (0.5×20)^2 = 25 + 100 = 125, so SD = sqrt(125) = 11.18%. The 15% answer assumes a correlation of +1 (simple weighted average). The 7.50% and 12.50% options come from wrong arithmetic on the weights.

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