NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory
Stock A and Stock B each have a standard deviation of 20%. A portfolio is made with 50% in each stock. If the correlation between them is +1, the portfolio standard deviation is:
The portfolio standard deviation is 20%. With a correlation of +1, portfolio risk equals the weighted average of the individual standard deviations, which is 0.5x20% + 0.5x20%. Perfect positive correlation gives no diversification benefit, so risk is not reduced below 20%.
- A10%
- B14.14%
- C20%Correct
- D40%
Explanation
Variance = 0.25x400 + 0.25x400 + 2x0.5x0.5x1x20x20 = 100+100+200 = 400. The square root is 20%. With perfect positive correlation there is no diversification benefit, so risk is just the weighted average, 20%. The 14.14% figure would be correct for zero correlation (variance 200).
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