NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Introduction to Modern Portfolio Theory
Two assets, A and B, each have a standard deviation of 10%. A portfolio is made with 50% in each. Which correlation coefficient between A and B would give the portfolio a standard deviation of exactly 10%?
A correlation of +1 gives a portfolio standard deviation of 10%. With equal weights and equal risks, portfolio variance is 50 plus 50 times the correlation; setting it equal to 100 requires correlation of one, meaning no diversification benefit arises.
- A+1Correct
- B0
- C-1
- D+0.5
Explanation
Portfolio variance = 0.25x100 + 0.25x100 + 2x0.25x100xρ = 50 + 50ρ. For standard deviation of 10%, variance must be 100, so ρ = +1. With ρ = 0 the variance is 50, giving about 7.07%, which shows diversification benefit.
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