Question

Explain why skewness and kurtosis are important factors for portfolio managers to consider.

Answer 1

Skewness measures the asymmetry of a distribution. In terms of the market, the historical pattern of returns doesn’t resemble a normal distribution, and so demonstrates skewness. Negative skewness occurs when the values to the left of (less than) the mean are fewer but farther from it than values to the right of (greater than) the mean.
For example, the return series of -30 percent, 5 percent, 10 percent and 15 percent has a mean of 0 percent. There is only one return less than zero, and three that are higher. The single negative return is much farther from zero than the positive ones, so the return series has negative skewness. Positive skewness, on the other hand, occurs when values to the right of (greater than) the mean are fewer but farther from it than values to the left of (less than) the mean.

Kurtosis measures the degree to which exceptional values, those much larger or much smaller than the average, occur more frequently (high kurtosis) or less frequently (low kurtosis) than in a normal (bell shaped) distribution.

High kurtosis results in exceptional values that are called “fat tails.” Fat tails indicate a higher percentage of very low and very high returns than would be expected with a normal distribution. Low kurtosis results in “thin tails” and a wide middle to the curve. In other words, more values are closer to the average than would be found in a normal distribution, and tails are thinner.