Empirical Analysis of S&P500 Returns

3. Empirical
Use S&P500 returns for September 1, 2017 through December 31, 2018. (1 point)
Plot the daily returns, and the histogram of daily returns and PDF of Normal distribution.
(1 point)
Plot of daily returns
01-09-17
17-09-17
03-10-17
19-10-17
04-11-17
20-11-17
06-12-17
22-12-17
07-01-18
23-01-18
08-02-18
24-02-18
12-03-18
28-03-18
13-04-18
29-04-18
15-05-18
31-05-18
16-06-18
02-07-18
18-07-18
03-08-18
19-08-18
04-09-18
20-09-18
06-10-18
22-10-18
07-11-18
23-11-18
09-12-18
25-12-18
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
Daily Returns
Days
Returns

Histogram of daily returns
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05
0
20
40
60
80
100
120
140
160
0
20
40
60
80
100
120
140
160
Histogram of Daily S&P 500 Returns and the
Normal Distribution
September 1, 2017 - December 31, 2018
Returns
Probability distribution
Plot autocorrelations, 1 to 100 lags. (1 point)
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Lag order
Autocorrelation of Daily Returns

Plot squared return autocorrelation. (1 point)
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Lag order
Autocorrelation of Squared Daily Returns
3.1. For each day, from September 1, 2018 through December 31, 2018, calculate the 10-
day 1% VaRs for S&P500 returns using the following methods: (a) RiskMetrics, that is,
normal distribution with an exponential smoother on variance using the weight, λ=0.94,
and (b) Historical Simulation. Use a 250-day moving sample. Compute the 10-day VaR
from 1-day VaR just by multiplying by square root of 10. Plot the VaRs. (10 points)
Calculations are shown in attached excel file.