CFA Level I · CFA Level I Exam · Statistical Characteristics of Asset Returns
A portfolio manager compares two return series with identical means and standard deviations. Series X has a sample skewness of -0.9 and Series Y has a sample skewness of +0.9. An investor focused on avoiding large losses would most likely view:
Series X looks riskier to a loss-averse investor. Its negative skewness means a longer left tail and a greater chance of large negative returns, even though the mean and standard deviation match Series Y. Y's longer tail holds large gains, not losses.
- ASeries X as less risky because its mean is below its median
- BSeries X as more risky because of its greater likelihood of large negative returnsCorrect
- CSeries Y as more risky because its right tail is longer
Explanation
Negative skew means a longer left tail, so large losses are more likely than under a positively skewed series with the same mean and variance. Series Y's long tail is on the gain side, which is not a concern for downside risk. Standard deviation alone misses this difference.
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