Because(Y−μY)4cannot be negative, the kurtosis cannot be negative.The kurtosis of a normally distributed random variable is 3, so a random variable with kurtosisexceeding 3 has more mass in its tails than a normal random variable. A distribution with kurtosisexceeding 3 is called leptokurtic or, more simply, heavy-tailed. Like skewness, the kurtosis is unit free, sochanging the units ofYdoes not change its kurtosis.Graphically speaking, when the tails of a distribution are “fat,” there is more probability mass in the tailsof the distribution than predicted by the normal distribution. The figure below superimposes a “fat-tailed”distribution on a normal with the same mean and SD. Although symmetry is still preserved, the SD willunderestimate the likelihood of extreme events: large losses as well as large gains.Below each of the four distributions in Figure 2.3 is its kurtosis. The distributions in Figures 2.3b-d areheavy-tailed.

Example:Total CEO’s compensation in U.S. public companies is measured as salary, bonus, long-termincentive payouts, the value of stock options granted during the year, and other cash payments. TheFigure 2.4below plots the CEO pay distribution using the population of firms in the ExecuComp data setin 2003. Average annual remuneration is approximately $4.5 million ($4,517,935), with a median of $2.5million. See Table below.Figure 2.4 CEO pay distribution using the population of firms in the ExecuComp data set in 2003$2,000$4,000$6,000$8,000$10,000$12,000$14,000$16,000$18,000$20,000$22,000$24,000$26,000$28,000$30,000$32,000$34,000$36,000$38,000$40,000$42,000$44,000$46,000$48,000$50,000$52,000$54,000$56,000$58,000$60,000More0%5%10%15%20%25%30%35%40%45%CEO compensation ($000s)Source: ExecuComp.The distribution has two important characteristics: considerable pay dispersion (given by its Std. Dev of$6,058,352) and positive skewness of 3.9 (hence the long right tail). This means that most CEOs earnrelatively low compensation, and a few CEOs in the right tail receive excessively generous rewards. Thenotion that all CEOs receive stratospheric sums is incorrect. See Table below 2.4.Table 2.4 Descritive Statistics for CEO Compensation (2003)CEO Compensation (2003) ($000s)Mean4517.935Median2464.859Maximum74750.00Minimum0.000000Std. Dev.6058.352Skewness3.856944Kurtosis26.20666Observations1727EViews: Descriptive Statistics of an individual series

Before we start we need to learn to import Data into EviewsStep 1: Double click on the window below to access the DataStep 2: Select, and copy (Ctrl+C).Step 3: Open Eviews and press the mouse right-click button and “paste as a new work file” inan emptyspace inside EViewsStep 4: Click “Finish”Step 5: If you double-click on the series “high_bm” in the workfile window you’ll get a firstglance at the data.Step 6: To look at summary statistics for a series press “View\Descriptive Statistics &Tests/Histogram and Stats”.\

The more ways we can view our data, the better. EViews provides a collection of “Views” for each typeof object that can appear in a workfile.

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Term

Spring

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Probability theory