NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory
A two-asset portfolio has 50% in X (standard deviation 20%) and 50% in Y (standard deviation 20%). If the correlation between X and Y is -1, what is the portfolio standard deviation?
The portfolio standard deviation is 0%. With perfect negative correlation and equal weights in two equally volatile assets, the movements offset completely, so variance works out to 100 plus 100 minus 200, which is zero.
- A20%
- B10%
- C0%Correct
- D40%
Explanation
Variance = w1²s1² + w2²s2² + 2w1w2 rho s1 s2 = 0.25x400 + 0.25x400 + 2x0.25x(-1)x400 = 100 + 100 - 200 = 0. So standard deviation is 0%. With correlation +1 it would be 20%, which is the weighted average and the distractor for ignoring diversification.
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