Are Stock Return Normally Distributed?

Data

Security	SPX Index
Start Date	39080
End Date	42734
Period	M
Currency	USD
Date	Closing Price
12/30/16	2238.83
11/30/16	2198.81
10/31/16	2126.15
9/30/16	2168.27
8/31/16	2170.95
7/29/16	2173.6
6/30/16	2098.86
5/31/16	2096.96
4/29/16	2065.3
3/31/16	2059.74
2/29/16	1932.23
1/29/16	1940.24
12/31/15	2043.94
11/30/15	2080.41
10/30/15	2079.36
9/30/15	1920.03
8/31/15	1972.18
7/31/15	2103.84
6/30/15	2063.11
5/29/15	2107.39
4/30/15	2085.51
3/31/15	2067.89
2/27/15	2104.5
1/30/15	1994.99
12/31/14	2058.9
11/28/14	2067.56
10/31/14	2018.05
9/30/14	1972.29
8/29/14	2003.37
7/31/14	1930.67
6/30/14	1960.23
5/30/14	1923.57
4/30/14	1883.95
3/31/14	1872.34
2/28/14	1859.45
1/31/14	1782.59
12/31/13	1848.36
11/29/13	1805.81
10/31/13	1756.54
9/30/13	1681.55
8/30/13	1632.97
7/31/13	1685.73
6/28/13	1606.28
5/31/13	1630.74
4/30/13	1597.57
3/29/13	1569.19
2/28/13	1514.68
1/31/13	1498.11
12/31/12	1426.19
11/30/12	1416.18
10/31/12	1412.16
9/28/12	1440.67
8/31/12	1406.58
7/31/12	1379.32
6/29/12	1362.16
5/31/12	1310.33
4/30/12	1397.91
3/30/12	1408.47
2/29/12	1365.68
1/31/12	1312.41
12/30/11	1257.6
11/30/11	1246.96
10/31/11	1253.3
9/30/11	1131.42
8/31/11	1218.89
7/29/11	1292.28
6/30/11	1320.64
5/31/11	1345.2
4/29/11	1363.61
3/31/11	1325.83
2/28/11	1327.22
1/31/11	1286.12
12/31/10	1257.64
11/30/10	1180.55
10/29/10	1183.26
9/30/10	1141.2
8/31/10	1049.33
7/30/10	1101.6
6/30/10	1030.71
5/31/10	1089.41
4/30/10	1186.69
3/31/10	1169.43
2/26/10	1104.49
1/29/10	1073.87
12/31/09	1115.1
11/30/09	1095.63
10/30/09	1036.19
9/30/09	1057.08
8/31/09	1020.62
7/31/09	987.48
6/30/09	919.32
5/29/09	919.14
4/30/09	872.81
3/31/09	797.87
2/27/09	735.09
1/30/09	825.88
12/31/08	903.25
11/28/08	896.24
10/31/08	968.75
9/30/08	1166.36
8/29/08	1282.83
7/31/08	1267.38
6/30/08	1280
5/30/08	1400.38
4/30/08	1385.59
3/31/08	1322.7
2/29/08	1330.63
1/31/08	1378.55
12/31/07	1468.36
11/30/07	1481.14
10/31/07	1549.38
9/28/07	1526.75
8/31/07	1473.99
7/31/07	1455.27
6/29/07	1503.35
5/31/07	1530.62
4/30/07	1482.37
3/30/07	1420.86
2/28/07	1406.82
1/31/07	1438.24
12/29/06	1418.3

Histogram example

-0.17	Frequency	Cumulative %
-16.00%	1	0.84%
-15.00%	0	0.84%
-14.00%	0	0.84%
-13.00%	0	0.84%
-12.00%	0	0.84%
-11.00%	0	0.84%
-10.00%	1	1.68%
-9.00%	1	2.52%
-8.00%	3	5.04%
-7.00%	2	6.72%
-6.00%	3	9.24%
-5.00%	3	11.76%
-4.00%	2	13.45%
-3.00%	6	18.49%
-2.00%	4	21.85%
-1.00%	11	31.09%
0.00%	11	40.34%
1.00%	12	50.42%
2.00%	15	63.03%
3.00%	11	72.27%
4.00%	12	82.35%
5.00%	7	88.24%
6.00%	5	92.44%
7.00%	3	94.96%
8.00%	1	95.80%
9.00%	3	98.32%
10.00%	1	99.16%
11.00%	1	100.00%
More	0	100.00%

Histogram

Frequency -16.00% -15.00% -14.00% -13.00% -12.00% -11.00% -10.00% -9.00% -8.00% -7.00% -6.00% -5.00% -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 11.00% More 1 0 0 0 0 0 1 1 3 2 3 3 2 6 4 11 11 12 15 11 12 7 5 3 1 3 1 1 0 Cumulative % -16.00% -15.00% -14.00% -13.00% -12.00% -11.00% -10.00% -9.00% -8.00% -7.00% -6.00% -5.00% -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 11.00% More 8.4033613445378148E-3 8.4033613445378148E-3 8.4033613445378148E-3 8.4033613445378148E-3 8.4033613445378148E-3 8.4033613445378148E-3 1.680672268907563E-2 2.5210084033613446E-2 5.0420168067226892E-2 6.7226890756302518E-2 9.2436974789915971E-2 0.11764705882352941 0.13445378151260504 0.18487394957983194 0.21848739495798319 0.31092436974789917 0.40336134453781514 0.50420168067226889 0.63 025210084033612 0.72268907563025209 0.82352941176470584 0.88235294117647056 0.92436974789915971 0.94957983193277307 0.95798319327731096 0.98319327731092432 0.99159663865546221 1 1

-0.17

Frequency