11 – M4 L3b 11 Skewness And Momentum Defining Skew V2

I hinted previously, that we could use skewness as a signal that stocks may be over bought in the short-term and may revert back soon afterwards. To help you understand skewness, I’ll first introduce a visual notion of skew. Then the common academic definition of skew, followed by the proxy for skewness that we will use when creating this Alpha factor. Skewness refers to the asymmetry in a distribution. When a distribution is negatively skewed, it has a longer tail on the left. When the distribution is positively skewed, it has a longer tail on the right. Skewness also means that the mean of a distribution is different than its medium. Negative skew, indicates that the mean is to the left of the median. You can imagine the small portion of extreme values on the left, pulling the mean to the left. While the median stays closer to the majority of observations. Similarly, a positive skew indicates that the mean is to the right of the median. You can imagine that the extreme values to the right, pull the mean to the right as well while the median stays closer to the majority of observations. If you learned about skewness in school, you may recall the concept of the first, second, third, and fourth moments of a distribution. The first moment is commonly known as the mean or average. The second moment is known as the variance. The third moment is skewness which we are discussing here. The fourth moment is kurtosis which measures the tails of the distribution. Stock returns generally exhibit excess kurtosis or fat tails compared to the normal distribution. For now though, we’ll focus on skewness. So, those were the visual and traditional interpretations of skewness. Now, let’s circle back to the definition of skewness used in this paper, and what we will implement in the Alpha factor. A useful proxy for skewness is the maximum daily return of a stock over the past 20 trading days. This definition is useful in part, because of how it captures how individual investors may perceive skewness. It’s possible to imagine that an investor may look at a recent stock high of a company as an indicator, upon which they will base their decision to buy or sell the stock.

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