NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory
Two assets have equal weights of 50% each. Asset X has standard deviation 10% and Asset Y has standard deviation 20%. Their correlation is 0.5. What is the standard deviation of the portfolio (to two decimals)?
The portfolio standard deviation is 13.23%. Portfolio variance is 25 plus 100 plus 50, which equals 175, including the covariance term at correlation 0.5. The square root of 175 is 13.23%, lower than the 15% weighted average because correlation is below one.
- A15.00%
- B12.91%
- C13.23%Correct
- D10.00%
Explanation
Variance = 0.25×100 + 0.25×400 + 2×0.5×0.5×0.5×10×20 = 25 + 100 + 50 = 175. Standard deviation = √175 = 13.23%. The 15% option is the simple weighted average, which assumes correlation of 1. 12.91% results from omitting the covariance term incorrectly scaled.
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