Analyzing the Skewness and Kurtosis of Stocks by: Philippe Tok
ANALYSIS OF DATA
Looking at the stock data provided by Yahoo Finance [1], corporations ranging from LMT (Lockheed Martin), MSFT (Microsoft), TWTR (Twitter), DIS (Disney), BAC (Bank of America), GM (General Motors), BA (Boeing), and JPM (JPMorgan) can be seen to have participated in fairly different industries. To have a fair comparison of the stocks price changes of these varying companies the stocks daily price changes were recalculated into the z scores (the amount of standard deviations from the mean price of the individual companies stock price over the 4 year period). When looking at the charts displaying the price of the stocks based on daily price changes, there seems to be a clear and strong positive trend in recent years (around the beginning of 2017) showing growth in basically every company. However, at the onset of 2019, there seems to be a slight dip within the price of every corporation observed as shown in Figures 1, 2, 3, and 4.
abstract Many people all over the world attempt to profit from the stock market using a plethora of strategies. The statistical concepts of skewness, kurtosis, and the normal distribution model can be used to analyze stocks. The standard model, which is pertinent to the analyses of both skewness and kurtosis, is the idea that a normal distribution of data will have means and medians that are one of the same while 68% of the data falls into 1 standard deviation from the mean, 95% of the data will fall within 2 standard deviations of the mean, and 99.7% of the data will fall within 3 standard deviations of the mean, which is all neatly displayed in a symmetrical bell curve. On one hand, skewness is essentially the measure of asymmetry within a data set and which side of the median contains the most values that are distorting the distribution the most from the normal model. While on the other hand, kurtosis is used to gauge the extremities of the tails of data distributions. Using these methods of statistical analysis and R studio, I analysed a series of different stock returns to uncover their relationships. 7 | JOURNYS | FALL 2020
In general, it could be assumed that the economy from 2016 to early 2018 was experiencing a steady growth, which then started to plateau around mid-2018, leading to a decline in growth around late 2018 to early 2019. Interestingly, this plateau in growth and eventual decline coincides with the start of the trade war between the U.S and China, which could signify that the tariffs enacted by the governments most likely had a somewhat significant effect on the growth of the economy. When examining the stock data of the companies individually, by looking at figure 5, a majority of the companies’ stock returns appear to have skewnesses that fall within the normal distribution (a skewness value between -0.5 and 0.5 as shown in Figure 6) with the exception of GM and DIS.
