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CMA Final · Strategic Financial Management · Portfolio Theory and Practice

Security A has a standard deviation of 10% and Security B has a standard deviation of 20%. The portfolio is split equally between them. The correlation coefficient between A and B is 0.5. What is the portfolio standard deviation, to two decimal places?

The portfolio standard deviation is 13.23%. Portfolio variance is 25 + 100 + 50 = 175 in %-squared terms, and its square root is 13.23%. The weighted average of 15% would be correct only if the two securities were perfectly positively correlated.

  1. A13.23%Correct
  2. B15.00%
  3. C17.50%
  4. D12.25%

Explanation

Variance = 0.25 x 100 + 0.25 x 400 + 2 x 0.5 x 0.5 x 0.5 x 10 x 20 = 25 + 100 + 50 = 175. The square root of 175 is 13.23%. The 15% option is the weighted average of the standard deviations, which holds only if the correlation is +1.

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