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%. Which correlation coefficient between them gives the greatest reduction in risk for an equally weighted portfolio?
A correlation of -0.5 gives the greatest risk reduction. Portfolio variance depends on the covariance term, which shrinks as correlation falls. With equal weights and 10% standard deviations, -0.5 gives 5% portfolio risk, lower than at 0, +0.5 or +1.
- A+1.0
- B+0.5
- C0
- D-0.5Correct
Explanation
Portfolio variance falls as correlation falls. At +1 there is no reduction (risk 10%). At -0.5 the variance is 0.25(100)+0.25(100)+2(0.25)(-0.5)(100)=25, giving 5% risk, lower than any higher correlation.
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