Question

Below are returns on the stock A and S&P500 index. All numbers are in decimals (-0.0222 is equivalent to -2.22%). A S_P500 -0.0222 0.0032 -0.0048 -0.0058 0.1333 0.0434 0.0765 0.1081 -0.0161 -0.0121 0.1250 0.1400 0.0145 0.0368 -0.0475 -0.0454 0.0430 0.0577 -0.0260 -0.1374 0.0071 0.0064 0.0249 0.0186 0.0850 0.0215 -0.0624 -0.0752 0.0933 0.0365 0.0456 0.0528 -0.0632 -0.0131 0.0450 0.0009 0.0200 0.0017 0.0280 0.0985 What is the sample standard deviation of the S&P500 returns? Please write an answer in decimals. For example, 12.34% would be 0.1234. Also, round your answer to the fourth decimal

Answer 1

Numbers	(Xi - Xbar)^2
-0.0222	0.0019
0.0032	0.0003
-0.0048	0.0007
-0.0058	0.0007
0.1333	0.0126
0.0434	0.0005
0.0765	0.0031
0.1081	0.0076
-0.0161	0.0014
-0.0121	0.0011
0.125	0.0108
0.14	0.0142
0.0145	0.0000
0.0368	0.0003
-0.0475	0.0047
-0.0454	0.0044
0.043	0.0005
0.0577	0.0014
-0.026	0.0022
-0.1374	0.0251
0.0071	0.0002
0.0064	0.0002
0.0249	0.0000
0.0186	0.0000
0.085	0.0041
0.0215	0.0000
-0.0624	0.0069
-0.0752	0.0092
0.0933	0.0052
0.0365	0.0002
0.0456	0.0006
0.0528	0.0010
-0.0632	0.0071
-0.0131	0.0012
0.045	0.0006
0.0009	0.0004
0.02	0.0000
0.0017	0.0004
0.028	0.0001
0.0985	0.0060
Average (Xbar)= 0.0209	Sum = 0.1368

= Sample number given in first column

(Xbar)= Average of all sample numbers from first column

= sample number - average of number

Formula for sample standard deviation =S =

S=0.0592

Sample standard deviation of the S&P500 returns = 0.0592

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