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

Two assets X and Y have weights of 50% each. Both have a standard deviation of 10%. The correlation between them is 0.2. What is the variance of the portfolio, in (%)² terms?

The portfolio variance is 60 (%)². Each asset contributes 0.25 times 100, equal to 25, and the covariance term adds 2 × 0.5 × 0.5 × 0.2 × 100, equal to 10. Together this gives 25 plus 25 plus 10, which is 60.

  1. A60Correct
  2. B100
  3. C50
  4. D80

Explanation

Variance = w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2 = 0.25×100 + 0.25×100 + 2×0.25×0.2×100 = 25 + 25 + 10 = 60. Option 100 assumes perfect correlation of 1 (2×0.25×100 = 50 giving 100). Option 50 ignores the covariance term. Option 80 wrongly uses correlation of 0.6.

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