STAT460 - Experimental Design
Homework #1 - Normality

The purpose of this homework assignment is to increase your mastery of the various tests for normality covered in class. We will do so by examining an important question in finance - namely, whether stock market returns are actually normally distributed (as is often claimed). The assignment is due at the beginning of class on Wednesday, March 2. It is worth 60 points toward your homework grade.

The data for this assignment are available in a file called DJIA.XLS. They consist of daily closing values of the Dow Jones Industrial Average, for the decade 2000-2009.

It is common in finance to treat stock market data as though returns follow a lognormal distribution - that is, as though the logarithm of the daily returns follows a normal distribution. Hence, you will want to begin your analysis by computing the log return for each day in the decade. For example, if the Dow went from 10,000 to 10,100 (a 1% gain), you would compute

logreturn = log(10100/10000) = 0.004321.

(Note that you will not be able to compute a return for the last day in the data set, 4 January 2010.)

Question 1: Find the skewness and kurtosis of the log returns. (You can use Excel's built-in function.) Give 95% confidence intervals for these values. What does this tell you about the (log-)normality of stock returns?

Question 2: Do a Kolmogorov-Smirnov test for normality of the log returns. (Sorry, there's no built-in function for this.) Again, interpret your result.

Question 3: Do an Anderson-Darling test for normality of the log returns. (Again, there's no built-in function for this.) Once again, interpret your result.

You should submit: (1) a brief writeup, outlining your answers to the three questions above. This should not run more than a couple of pages, and should be typed, and (2) an electronic version of a spreadsheet showing your work on Questions 2 and 3, which provides enough annotation that I can follow your work.