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CMA Intermediate · Financial Management and Business Data Analytics · Risk and Return

Two securities have standard deviations of 10% and 20%. They are combined in a portfolio with weights of 50% each, and the correlation coefficient between them is +1. What is the portfolio standard deviation?

The portfolio standard deviation is 15%. When the correlation coefficient is +1, there is no diversification benefit, so portfolio risk equals the weighted average of the individual standard deviations: 0.5 x 10% plus 0.5 x 20%, which is 15%.

  1. A12.5%
  2. B15.0%Correct
  3. C10.0%
  4. D22.4%

Explanation

With correlation +1, portfolio SD is the weighted average of the SDs: 0.5 x 10 + 0.5 x 20 = 15%. 12.5% would be the answer by wrongly treating variances as zero-covariance (sqrt(0.0025x0.01+0.0025x0.04)... roughly 11.2%), and 22.4% is the square root of the sum of the variances, ignoring weights.

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