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NISM Certifications · NISM-Series-X-A: Investment Adviser (Level 1) · Portfolio Construction Process

Two assets A and B each have a standard deviation of 20%. A portfolio is formed with 50% in each. Which correlation coefficient between A and B gives a portfolio standard deviation of exactly 10% x sqrt(3), i.e. about 17.32%?

The correlation is +0.5. With equal 50% weights and 20% standard deviations, portfolio variance equals 200 plus 200 times the correlation. A variance of 300, corresponding to a standard deviation of about 17.32%, requires a correlation of 0.5.

  1. A+1
  2. B+0.5
  3. C0Correct
  4. D-0.5

Explanation

Variance = 0.25(400)+0.25(400)+2(0.25)(400)(rho) = 200 + 200 rho. For SD of 10 sqrt3, variance = 300, so rho = 0.5. Check with rho=0: variance 200, SD 14.14%, not 17.32%. Rho=+0.5 gives 300. So the correct value is +0.5, not 0.

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