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CMA Final · Strategic Financial Management · Portfolio Theory and Practice

Two securities have standard deviations of 12% and 18%. Their covariance is -0.0108 (that is, -108 in %-squared terms). What is the correlation coefficient between them, and what does it imply for a portfolio?

Correlation equals covariance divided by the product of standard deviations: -108 divided by 216 gives -0.50. A negative correlation reduces portfolio variance below what the individual risks suggest, so there is a clear diversification benefit.

  1. A-0.50; diversification benefit is availableCorrect
  2. B-0.60; portfolio variance is higher than the weighted average of variances
  3. C+0.50; diversification benefit is nil
  4. D-0.50; portfolio risk equals the weighted average of risks

Explanation

Correlation = covariance / (s1 x s2) = -108 / (12 x 18) = -108/216 = -0.50. A negative correlation lowers portfolio variance through the covariance term, so diversification benefit is available. The -0.60 option divides incorrectly, and the risk-equals-average claim holds only at correlation +1.

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