FIN5330-Homework 1 Solved

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.
0
18542 19990104
CAT 47.3750 -0.000822 0.011409
1
18542 19990105
CAT 47.2500 0.011879 0.009512
2
18542 19990106
CAT 48.5000 0.021143 0.014866
3
18542 19990107
CAT 48.9375 -0.000798 0.003560
4
18542 19990108
CAT 51.0000 0.004602 0.009410
(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:

2515
59176 19990104
AXP 101.5000 -0.000822 0.011409
2516
59176 19990105
AXP 99.5625 0.011879 0.009512
2517
59176 19990106
AXP 103.6250 0.021143 0.014866
2518
59176 19990107
AXP 104.8750 -0.000798 0.003560
2519
59176 19990108
AXP 108.0625 0.004602 0.009410
[7]:      PERMNO    date TICKER  PRC   vwretd   ewretd

5025
59176 20081224
AXP 17.97 0.004514 0.005042
5026
59176 20081226
AXP 17.91 0.007191 0.011107
5027
59176 20081229
AXP 17.70 -0.004365 -0.015163
5028
59176 20081230
AXP 18.00 0.024764 0.021418
5029
59176 20081231
AXP 18.55 0.017404 0.034456
2510
18542 20081224
CAT 41.91 0.004514 0.005042
2511
18542 20081226
CAT 42.72 0.007191 0.011107
2512
18542 20081229
CAT 42.34 -0.004365 -0.015163
2513
18542 20081230
CAT 43.66 0.024764 0.021418
2514
18542 20081231
CAT 44.67 0.017404 0.034456
[6]:    PERMNO    date TICKER    PRC   vwretd   ewretd

0
18542 19990104
CAT 47.3750 -0.000822 0.011409
1
18542 19990105
CAT 47.2500 0.011879 0.009512
2
18542 19990106
CAT 48.5000 0.021143 0.014866
3
18542 19990107
CAT 48.9375 -0.000798 0.003560
4
18542 19990108
CAT 51.0000 0.004602 0.009410
[8]:      PERMNO    date TICKER  PRC   vwretd   ewretd

[9]:      PERMNO    date TICKER    PRC   vwretd   ewretd

5030
77702 19990104
SBUX 53.8750 -0.000822 0.011409
5031
77702 19990105
SBUX 52.0000 0.011879 0.009512
5032
77702 19990106
SBUX 51.5625 0.021143 0.014866
5033
77702 19990107
SBUX 51.7500 -0.000798 0.003560
5034
77702 19990108
SBUX 52.8750 0.004602 0.009410
[10]:     PERMNO    date TICKER  PRC   vwretd   ewretd

7540
77702 20081224
SBUX 9.34 0.004514 0.005042
7541
77702 20081226
SBUX 9.35 0.007191 0.011107
7542
77702 20081229
SBUX 9.03 -0.004365 -0.015163
7543
77702 20081230
SBUX 9.36 0.024764 0.021418
7544
77702 20081231
SBUX 9.46 0.017404 0.034456
You can access the price time series as (for example for AXP):

[11]: 2515
101.5000
2516
99.5625
2517
103.6250
2518
104.8750
2519
108.0625
2520
106.2500
2521
102.3750
2522
98.6875
2523
96.0000
2524
104.3750
2525
100.5000
2526
102.0000
2527
102.5000
2528
98.5000
2529
101.5000
2530
101.7500
2531
99.4375
2532
100.4375
2533
102.8750
2534
100.7500
2535
99.6875
2536
100.5000
2537
100.2500
2538
98.1250
2539
97.0625
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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