Consider the monthly stock returns of S&P composite index from January 1975 to December 2003 in Exercise 1.2. Answer the following questions:

(a) What is the average annual log return over the data span?

(b) Assume that there were no transaction costs. If one invested $1.00 on the S&P composite index at the beginning of 1975, what was the value of the investment at the end of 2003?

Exercise 1.2
Answer the same questions as Exercise 1.1 but using monthly stock returns for IBM, CRSP value-weighted index (VW), CRSP equal-weighted index (EW), and S&P composite index from January 1975 to December 2003. The returns of the indexes include dividend distributions. Data file is m-ibm3dx7503.txt.

Exercise 1.1
Consider the daily stock returns of American Express (axp), Caterpillar (cat), and Starbucks (sbux) from January 1994 to December 2003. The data are simple returns given in the file d-3stock.txt (date, axp, cat, sbux).

(a) Express the simple returns in percentages. Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the percentage simple returns.

(b) Transform the simple returns to log returns.

(c) Express the log returns in percentages. Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the percentage log returns.

(d) Test the null hypothesis that the mean of the log returns of each stock is zero. (Perform three separate tests.) Use 5% significance level to draw your conclusion.