[Solved] FIN5330 Homework 1

Consider the daily stock returns of American Express (AXP), Caterpillar (CAT), and Starbucks (SBUX) from January 1999 to December 2008. The data are daily prices in the file stock-datahwk1.txt.

• (a) Calculate simple returns for the three series.

• (b) Express the simple returns in percentages. Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the percentage simple returns.
• (c) Transform the simple returns to log returns.
• (d) Express the log returns in percentages. Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the percentage log returns.
• (e) Test the null hypothesis that the mean of the log returns of each stock is zero. That is, perform three separate tests. Use 5% significance level to draw your conclusion.
• (f) Plot histograms for each of the three series (both simple and log returns so six graphs

total).

• (g) Test the null hypothesis that the lag-2 autocorrelation is zero for log returns.

Here is some code to extract the price time series from the raw data in Python:

[7]: PERMNO date TICKER PRC vwretd ewretd

[6]: PERMNO date TICKER PRC vwretd ewretd

[8]: PERMNO date TICKER PRC vwretd ewretd

[9]: PERMNO date TICKER PRC vwretd ewretd

[10]: PERMNO date TICKER PRC vwretd ewretd

You can access the price time series as (for example for AXP):

• 9375
• 7500
• 0000
• 9375
• 1875

• 3800
• 7400
• 2300
• 6900
• 1800
• 3700
• 3000
• 3100
• 6400
• 7600
• 8700
• 8400
• 7800
• 4400
• 2900
• 5600
• 1300
• 3400
• 3400
• 0600
• 8100
• 9000
• 4300
• 4200
• 9600
• 9700
• 9100
• 7000
• 0000
• 5500

Name: PRC, Length: 2515, dtype: float64

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