Tail and Skew

Skewness and Kurtosis are statistical measures that provide insights about the shape of a distribution of returns. They are often used in finance, including stock return analyses, to understand the characteristics of the return distributions of different assets.

1. Skewness: Skewness measures the asymmetry of a distribution. In the context of stock returns, a positive skewness indicates that the returns have a right-leaning distribution, which means there's a greater likelihood of large positive returns than negative ones. Conversely, a negative skewness indicates a left-leaning distribution, suggesting a greater likelihood of large negative returns.

2. Kurtosis: Kurtosis measures the "tailedness" of a distribution. In the context of stock returns, a higher kurtosis implies a greater probability of extreme outcomes—both on the upside (large gains) and downside (large losses)—compared to a normal distribution (which has a kurtosis of 3). High kurtosis often indicates high investment risk because of the increased likelihood of extreme returns.

Excess kurtosis is often used in finance, which is the kurtosis of a distribution minus 3 (to give a comparison to the normal distribution). A positive excess kurtosis signifies a distribution with fat tails (more prone to extreme returns), while a negative excess kurtosis signifies a distribution with thin tails.

Both skewness and kurtosis provide valuable information about the distribution of returns. While average returns and standard deviation (volatility) are important, skewness and kurtosis provide additional insights about the potential for very large or very small returns, which are important considerations in risk management and portfolio optimization.

At Capital Market Laboratories (CML) we use a proprietary algorithm to compute a specific type of skew and kurtosis such that it has proven, using data from the past as a map to the future, to reflect stocks with a higher likelihood to outperform or underperform.

You can watch our webinar on the subject with historical results here: