NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory
Asset A has a weight of 60% and expected return of 15%; Asset B has a weight of 40% and expected return of 10%. Their standard deviations are 20% and 10%, and the correlation between them is 0.5. What is the portfolio standard deviation?
The portfolio standard deviation is about 14%. Variance is 0.0144 plus 0.0016 plus 0.0048, which equals 0.0208, and its square root is roughly 14.4%. The simple weighted average of 16% overstates risk because the correlation of 0.5 gives diversification benefit.
- AApproximately 14.0%Correct
- BApproximately 16.0%
- CApproximately 12.0%
- DApproximately 15.0%
Explanation
Variance = (0.6x0.2)^2 + (0.4x0.1)^2 + 2x0.6x0.4x0.5x0.2x0.1 = 0.0144 + 0.0016 + 0.0048 = 0.0208. Square root = 14.42%, so approximately 14.0% is the nearest option. The weighted average of 16% ignores diversification, since correlation is below 1.
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