VaR Estimation
/*--------------------------------------------------------------
SAS Sample Library
Name: copex01.sas
Description: Example program from SAS/ETS User's Guide,
The COPULA Procedure
Title: VaR Estimation
Product: SAS/ETS Software
Keys: copula joint distribution
PROC: COPULA
Notes:
--------------------------------------------------------------*/
ods graphics on;
data returns;
format date MMDDYY10.;
input date:MMDDYY10. price_ibm price_msft price_bp price_ko price_duk;
ret_msft = price_msft/lag(price_msft)-1;
ret_ko = price_ko/lag(price_ko)-1;
ret_ibm = price_ibm/lag(price_ibm)-1;
ret_duk = price_duk/lag(price_duk)-1;
ret_bp = price_bp/lag(price_bp)-1;
if ret_msft ^= .;
keep date ret_ibm ret_msft ret_bp ret_ko ret_duk;
datalines;
01/02/2008 99.91 33.48 62.78 56.91 17.13
01/03/2008 100.11 33.62 63.98 57.50 17.19
01/04/2008 96.52 32.68 63.05 57.61 17.18
01/07/2008 95.49 32.90 64.18 58.97 17.62
01/08/2008 93.14 31.80 63.15 59.22 17.57
01/09/2008 93.82 32.74 61.44 60.80 17.76
01/10/2008 95.36 32.64 61.17 61.07 17.73
01/11/2008 93.21 32.24 60.04 59.40 17.51
01/14/2008 98.23 32.69 60.11 59.90 17.57
01/15/2008 97.18 32.32 57.65 59.25 17.27
01/16/2008 96.99 31.59 56.42 58.36 17.31
01/17/2008 96.49 31.48 55.16 57.79 16.80
01/18/2008 98.68 31.38 55.65 56.58 16.62
01/22/2008 96.60 30.38 53.47 54.76 16.06
01/23/2008 101.26 30.35 52.53 54.84 16.47
01/24/2008 102.03 31.61 54.39 55.78 15.96
01/25/2008 99.75 31.31 54.15 54.41 15.57
01/28/2008 100.19 31.10 54.34 55.34 15.90
01/29/2008 101.26 30.99 54.47 54.54 15.92
01/30/2008 100.83 30.61 53.48 53.81 15.96
01/31/2008 102.22 30.99 54.73 54.96 16.18
02/01/2008 104.10 28.95 54.99 55.20 16.39
02/04/2008 103.01 28.70 55.12 54.62 16.69
02/05/2008 100.23 27.63 54.33 53.47 16.07
02/06/2008 99.24 27.11 54.53 53.76 16.34
02/07/2008 98.04 26.73 53.95 54.45 15.95
02/08/2008 98.94 27.15 55.03 55.19 15.95
02/11/2008 100.73 26.82 55.46 55.43 16.05
02/12/2008 102.06 26.94 56.11 55.82 16.22
02/13/2008 103.87 27.53 57.14 55.32 16.17
02/14/2008 101.68 27.09 56.85 54.54 15.94
02/15/2008 101.70 27.02 56.21 54.74 15.87
02/19/2008 100.59 26.88 57.33 54.12 15.95
02/20/2008 103.32 26.93 57.23 54.24 16.05
02/21/2008 102.44 26.82 55.81 54.02 15.72
02/22/2008 103.53 26.42 56.79 54.27 15.99
02/25/2008 105.46 26.57 57.86 54.75 16.15
02/26/2008 109.58 27.08 58.37 55.44 16.16
02/27/2008 111.57 26.97 57.57 55.94 16.02
02/28/2008 110.40 26.65 57.32 55.39 15.74
02/29/2008 109.08 25.96 56.20 54.46 15.40
03/03/2008 109.44 25.76 55.99 54.98 15.53
03/04/2008 110.85 26.33 55.53 55.30 15.54
03/05/2008 110.55 26.84 56.96 55.59 15.47
03/06/2008 107.80 26.31 55.24 55.05 15.15
03/07/2008 109.16 26.60 55.32 54.82 15.05
03/10/2008 109.22 26.77 55.89 54.64 15.03
03/11/2008 111.60 27.94 56.99 55.40 15.62
03/12/2008 112.16 27.32 57.11 55.49 15.39
03/13/2008 111.04 27.31 56.75 55.25 15.58
03/14/2008 110.39 26.68 55.65 53.93 15.36
03/17/2008 110.70 27.01 53.74 54.08 15.75
03/18/2008 113.44 28.08 54.85 55.70 15.92
03/19/2008 112.03 27.31 52.04 56.21 15.58
03/20/2008 113.36 27.85 51.89 57.23 16.01
03/24/2008 114.06 27.84 52.56 57.36 15.81
03/25/2008 113.02 27.81 53.50 57.57 15.63
03/26/2008 112.00 27.26 53.68 57.33 15.75
03/27/2008 110.67 26.77 52.55 57.48 15.63
03/28/2008 109.76 26.64 51.91 57.13 15.55
03/31/2008 110.31 27.08 52.54 57.07 15.67
04/01/2008 111.60 28.15 53.18 57.60 15.92
04/02/2008 109.99 27.83 54.03 56.68 16.06
04/03/2008 111.15 27.68 54.15 56.78 15.97
04/04/2008 110.90 27.83 54.56 56.49 15.91
04/07/2008 111.43 27.83 54.98 56.60 16.04
04/08/2008 111.39 27.44 55.32 56.73 16.16
04/09/2008 111.87 27.57 56.23 56.98 16.13
04/10/2008 113.79 27.78 56.26 57.50 16.11
04/11/2008 111.13 26.99 56.01 56.52 15.96
04/14/2008 112.36 26.78 56.84 57.19 15.84
04/15/2008 112.25 26.96 56.72 57.13 15.84
04/16/2008 115.41 27.63 58.30 57.33 16.20
04/17/2008 117.91 27.89 58.51 56.89 16.08
04/18/2008 119.18 28.63 59.08 56.35 16.14
04/21/2008 119.13 29.03 59.28 56.58 16.04
04/22/2008 118.48 28.87 59.63 56.15 15.87
04/23/2008 118.41 30.01 59.92 56.55 16.14
04/24/2008 118.98 30.35 58.75 56.49 15.99
04/25/2008 117.91 28.47 59.93 55.62 16.21
04/28/2008 116.58 27.67 59.76 55.29 16.05
04/29/2008 117.69 27.33 62.53 55.05 15.98
04/30/2008 115.63 27.22 63.06 55.19 16.07
05/01/2008 118.42 28.06 62.30 55.40 16.39
05/02/2008 118.01 27.90 62.57 55.10 16.67
05/05/2008 116.91 27.75 62.78 54.73 16.44
05/06/2008 117.66 28.34 63.10 54.63 16.47
05/07/2008 119.42 27.88 62.49 53.47 16.21
05/08/2008 120.17 27.93 62.98 52.77 16.28
05/09/2008 119.34 28.05 62.46 52.64 16.21
05/12/2008 120.47 28.62 63.24 52.88 16.42
05/13/2008 121.76 28.52 62.76 52.97 16.32
05/14/2008 122.67 28.67 63.11 53.01 16.58
05/15/2008 123.57 29.17 64.19 53.45 16.45
05/16/2008 122.96 28.73 65.52 53.50 16.47
05/19/2008 121.68 28.22 65.55 53.93 16.64
05/20/2008 120.42 27.55 65.65 53.52 16.51
05/21/2008 118.91 27.06 66.61 53.11 16.47
05/22/2008 119.95 27.27 66.69 54.63 16.55
05/23/2008 119.47 26.87 65.77 54.97 16.17
05/27/2008 122.47 27.24 64.45 54.93 16.25
05/28/2008 124.61 26.99 63.71 53.85 16.34
05/29/2008 124.77 27.12 63.13 54.25 16.36
05/30/2008 124.50 27.13 63.53 53.68 16.41
06/02/2008 122.51 26.63 62.23 53.44 16.09
06/03/2008 122.97 26.16 61.51 52.88 15.96
06/04/2008 122.70 26.38 59.14 53.16 16.12
06/05/2008 123.58 27.11 60.81 53.62 16.14
06/06/2008 120.18 26.33 60.36 52.31 15.71
06/09/2008 121.07 26.54 61.86 52.37 16.08
06/10/2008 121.15 26.71 60.02 54.38 15.91
06/11/2008 118.56 25.98 61.23 53.92 15.93
06/12/2008 119.14 27.05 60.57 53.92 15.85
06/13/2008 121.35 27.84 59.93 52.30 16.12
06/16/2008 121.89 27.71 60.35 51.13 16.17
06/17/2008 120.34 27.59 61.07 50.92 16.17
06/18/2008 119.43 27.26 60.08 50.17 16.08
06/19/2008 120.26 27.71 59.07 50.36 16.09
06/20/2008 118.07 27.04 59.01 50.64 15.69
06/23/2008 118.76 26.79 59.64 50.26 15.76
06/24/2008 118.76 26.56 58.94 50.36 15.60
06/25/2008 119.84 27.15 60.31 51.05 15.76
06/26/2008 116.52 26.58 59.54 50.22 15.30
06/27/2008 115.48 26.46 59.39 48.92 15.16
06/30/2008 114.02 26.35 60.95 49.05 15.44
07/01/2008 114.73 25.74 59.73 48.13 15.34
07/02/2008 114.57 24.79 57.42 48.48 15.33
07/03/2008 114.99 24.88 58.12 48.58 15.20
07/07/2008 116.88 24.93 58.22 48.40 15.26
07/08/2008 119.17 24.76 57.71 48.57 15.53
07/09/2008 115.82 24.17 56.47 48.02 15.55
07/10/2008 118.49 24.38 56.86 47.22 15.50
07/11/2008 117.47 24.19 56.54 47.44 15.45
07/14/2008 116.91 24.09 56.36 48.09 15.28
07/15/2008 118.51 25.05 54.59 48.87 15.33
07/16/2008 121.15 26.11 53.99 49.39 15.17
07/17/2008 121.70 26.36 53.89 47.51 15.26
07/18/2008 124.95 24.77 54.67 47.21 15.44
07/21/2008 123.76 24.56 55.19 46.81 15.42
07/22/2008 125.05 24.71 55.16 48.46 15.42
07/23/2008 124.59 25.32 54.29 49.54 15.29
07/24/2008 125.05 24.37 53.38 48.94 15.38
07/25/2008 123.64 25.06 53.95 49.13 15.27
07/28/2008 121.44 24.42 54.15 48.27 15.19
07/29/2008 122.80 25.01 52.78 48.67 15.34
07/30/2008 123.96 25.12 54.40 48.42 15.56
07/31/2008 123.11 24.64 53.83 48.60 15.61
08/01/2008 121.82 24.37 53.62 50.15 15.25
08/04/2008 122.70 24.21 52.75 50.87 15.43
08/05/2008 123.97 25.10 52.77 51.82 15.69
08/06/2008 124.73 25.88 53.96 52.24 15.49
08/07/2008 124.62 26.24 53.74 50.97 15.47
08/08/2008 124.39 26.94 52.59 52.29 16.15
08/11/2008 122.26 26.72 52.78 52.23 16.47
08/12/2008 120.92 26.93 53.42 51.70 15.85
08/13/2008 121.48 26.73 52.92 52.10 15.98
08/14/2008 122.58 26.73 52.26 51.92 15.81
08/15/2008 122.02 26.64 51.10 51.96 16.00
08/18/2008 120.31 26.52 51.10 51.27 16.10
08/19/2008 118.35 26.27 51.03 51.27 15.92
08/20/2008 118.31 26.24 51.04 51.29 15.93
08/21/2008 118.77 26.14 51.88 50.50 15.89
08/22/2008 120.64 26.77 50.76 51.31 16.04
08/25/2008 118.64 26.60 50.46 50.55 15.83
08/26/2008 118.30 26.22 50.55 50.51 15.93
08/27/2008 119.15 26.50 51.69 50.76 15.95
08/28/2008 120.31 26.87 51.20 50.13 16.05
08/29/2008 117.55 26.24 51.20 49.14 15.69
09/02/2008 114.35 26.06 47.98 49.03 15.60
09/03/2008 114.28 25.87 48.36 48.75 15.40
09/04/2008 111.05 25.34 48.20 48.80 15.56
09/05/2008 110.41 24.67 48.00 49.01 15.58
09/08/2008 113.27 25.12 48.32 50.37 16.08
09/09/2008 111.09 25.10 46.55 50.85 16.29
09/10/2008 113.99 25.43 47.52 50.78 16.08
09/11/2008 115.11 26.29 47.46 51.46 16.39
09/12/2008 114.89 26.56 48.68 51.80 16.47
09/15/2008 111.24 25.79 46.13 52.03 16.07
09/16/2008 112.07 24.99 46.48 52.13 16.23
09/17/2008 107.65 23.63 45.67 50.05 15.64
09/18/2008 111.17 24.29 45.72 50.74 16.73
09/19/2008 114.77 24.20 48.46 50.11 16.17
09/22/2008 112.22 24.43 49.00 48.83 16.17
09/23/2008 111.40 24.46 48.06 48.17 15.90
09/24/2008 112.46 24.73 47.57 47.70 16.06
09/25/2008 115.99 25.59 49.16 48.91 16.17
09/26/2008 115.32 26.35 48.46 49.88 16.22
09/29/2008 110.53 24.05 43.66 48.50 15.85
09/30/2008 112.95 25.67 44.57 50.26 15.68
10/01/2008 106.35 25.46 44.53 51.47 16.03
10/02/2008 101.15 25.24 41.79 50.94 15.78
10/03/2008 99.89 25.31 42.42 49.96 15.62
10/06/2008 97.17 23.95 40.56 48.39 15.40
10/07/2008 92.37 22.34 39.46 46.85 15.27
10/08/2008 87.44 22.13 39.71 45.06 15.23
10/09/2008 85.95 21.44 36.16 41.15 13.63
10/10/2008 84.74 20.68 36.02 39.44 12.98
10/13/2008 89.05 24.52 41.31 44.92 14.71
10/14/2008 90.39 23.18 41.50 41.56 14.14
10/15/2008 85.26 21.79 36.74 42.02 13.33
10/16/2008 88.38 23.26 39.48 43.51 13.97
10/17/2008 87.66 23.01 39.36 42.01 13.63
10/20/2008 89.34 23.77 45.25 44.16 15.01
10/21/2008 85.81 22.46 41.99 43.75 14.13
10/22/2008 80.73 20.70 38.42 43.13 13.90
10/23/2008 81.46 21.46 40.03 40.92 14.76
10/24/2008 79.25 21.12 37.84 39.55 14.06
10/27/2008 76.93 20.37 35.67 38.98 14.14
10/28/2008 84.29 22.21 41.33 43.01 15.01
10/29/2008 85.17 22.12 43.71 41.68 14.61
10/30/2008 87.58 21.76 44.05 42.45 15.14
10/31/2008 89.78 21.47 44.15 41.87 14.74
11/03/2008 89.50 21.75 43.06 43.20 15.00
11/04/2008 90.20 22.63 45.54 43.75 15.22
11/05/2008 86.85 21.23 43.49 42.51 14.05
11/06/2008 82.69 20.08 41.74 42.28 14.09
11/07/2008 83.78 20.68 43.97 43.96 14.62
11/10/2008 81.44 20.48 43.33 43.62 14.32
11/11/2008 80.35 20.39 41.82 42.24 14.25
11/12/2008 77.43 19.52 38.11 41.66 13.97
11/13/2008 81.78 20.44 40.35 43.98 14.71
11/14/2008 78.01 19.29 39.71 42.79 14.28
11/17/2008 75.24 18.58 39.61 41.79 14.05
11/18/2008 77.76 19.00 41.17 41.33 14.32
11/19/2008 73.77 17.71 39.24 40.17 13.61
11/20/2008 69.67 16.97 35.78 39.03 13.36
11/21/2008 72.71 19.05 39.20 41.82 13.73
11/24/2008 77.58 20.03 41.74 42.99 14.11
11/25/2008 78.32 19.35 42.88 42.83 14.00
11/26/2008 79.31 19.84 43.75 43.50 13.82
11/28/2008 79.24 19.58 44.04 44.92 14.21
12/01/2008 74.68 18.02 39.41 42.49 13.46
12/02/2008 77.53 18.54 41.50 42.11 13.24
12/03/2008 78.34 19.24 41.00 44.22 13.48
12/04/2008 75.20 18.50 39.19 42.89 13.32
12/05/2008 78.26 19.24 39.37 44.07 13.64
12/08/2008 82.41 20.34 41.58 44.07 13.64
12/09/2008 80.30 19.94 41.45 42.97 13.25
12/10/2008 80.46 19.95 41.76 43.43 13.44
12/11/2008 78.25 18.83 42.64 42.38 13.29
12/12/2008 79.82 18.74 42.55 42.72 13.35
12/15/2008 80.38 18.43 43.19 43.10 13.25
12/16/2008 83.90 19.47 44.63 44.53 13.64
12/17/2008 83.36 19.03 44.86 43.59 13.34
12/18/2008 81.57 18.69 42.02 43.30 13.49
12/19/2008 81.10 18.51 40.82 42.59 13.40
12/22/2008 79.62 18.57 40.61 42.81 13.55
12/23/2008 78.27 18.67 40.50 42.14 13.18
12/24/2008 78.19 18.56 39.95 42.27 13.34
12/26/2008 78.98 18.52 40.21 42.73 13.29
12/29/2008 78.90 18.36 40.99 42.57 13.38
12/30/2008 81.13 18.72 41.45 43.06 13.64
12/31/2008 81.73 18.82 42.28 43.39 13.71
01/02/2009 84.84 19.68 43.83 43.99 14.06
01/05/2009 84.31 19.87 44.35 43.55 14.40
01/06/2009 86.65 20.10 44.37 42.85 14.01
01/07/2009 85.25 18.89 42.93 43.06 14.04
01/08/2009 84.66 19.48 44.15 43.36 14.07
01/09/2009 82.25 18.90 42.63 42.75 13.94
01/12/2009 83.23 18.85 41.34 41.91 14.03
01/13/2009 82.87 19.19 40.90 42.19 13.84
01/14/2009 80.78 18.48 39.07 40.85 13.69
01/15/2009 81.69 18.63 39.35 41.56 13.57
01/16/2009 82.46 19.08 39.99 42.02 13.71
01/20/2009 79.61 17.89 37.33 41.10 13.59
01/21/2009 88.78 18.76 38.07 41.49 13.56
01/22/2009 87.47 16.57 37.48 41.33 13.57
01/23/2009 86.90 16.65 36.89 40.45 13.60
01/26/2009 88.95 17.07 38.62 41.24 13.84
01/27/2009 89.01 17.10 38.95 41.53 13.97
01/28/2009 92.08 17.47 39.30 42.04 14.06
01/29/2009 89.84 17.03 38.39 41.74 14.07
01/30/2009 89.00 16.56 38.42 40.95 13.83
02/02/2009 88.30 17.26 37.60 40.49 13.71
02/03/2009 90.78 17.91 38.25 41.52 13.74
02/04/2009 90.15 18.04 38.89 40.64 14.02
02/05/2009 89.74 18.43 40.03 40.92 14.13
02/06/2009 93.87 19.03 41.19 41.74 14.32
02/09/2009 94.53 18.82 41.12 40.55 14.30
02/10/2009 91.07 18.20 39.32 38.98 13.89
02/11/2009 92.91 18.60 39.47 39.56 13.85
02/12/2009 92.82 18.65 40.11 42.55 13.79
02/13/2009 91.62 18.48 39.66 42.03 13.67
02/17/2009 88.53 17.63 38.01 40.83 13.08
02/18/2009 89.35 17.66 37.58 40.91 13.36
02/19/2009 86.83 17.46 37.89 41.50 13.44
02/20/2009 86.69 17.55 37.01 41.06 13.13
02/23/2009 82.38 16.78 35.67 40.34 12.90
02/24/2009 84.36 16.74 36.98 41.27 13.27
02/25/2009 83.87 16.53 36.86 40.61 13.14
02/26/2009 86.87 16.01 36.00 39.36 12.78
02/27/2009 89.86 15.74 35.41 39.15 12.49
03/02/2009 86.95 15.39 32.44 38.04 11.98
03/03/2009 85.70 15.48 31.51 37.22 11.33
03/04/2009 87.38 15.71 33.06 38.08 11.51
03/05/2009 85.41 14.89 31.88 36.28 11.16
03/06/2009 83.78 14.90 32.60 37.48 11.26
03/09/2009 81.51 14.77 33.39 37.14 10.95
03/10/2009 85.19 16.06 34.36 37.53 11.49
03/11/2009 86.53 16.68 34.34 38.33 11.63
03/12/2009 88.26 16.58 35.30 39.56 11.73
03/13/2009 88.22 16.23 35.34 39.93 11.92
03/16/2009 89.06 15.84 35.46 39.98 12.20
03/17/2009 90.71 16.47 36.32 40.15 12.53
03/18/2009 89.78 16.53 36.87 40.34 12.97
03/19/2009 90.47 16.71 37.11 40.86 13.14
03/20/2009 90.32 16.63 36.37 41.30 13.18
03/23/2009 96.38 17.87 38.67 42.76 13.62
03/24/2009 95.98 17.48 38.11 42.64 13.16
03/25/2009 95.64 17.43 38.26 43.35 13.20
03/26/2009 96.45 18.36 38.51 43.44 13.41
03/27/2009 91.93 17.67 37.76 43.69 13.25
03/30/2009 92.29 17.04 36.39 42.54 13.08
03/31/2009 94.60 17.91 37.01 42.57 13.28
04/01/2009 95.30 18.82 37.31 43.45 13.22
04/02/2009 98.44 18.80 38.43 43.92 13.15
04/03/2009 99.80 18.28 38.15 43.56 13.16
04/06/2009 99.16 18.29 37.58 43.58 13.03
04/07/2009 96.42 18.29 36.59 43.22 12.76
04/08/2009 98.80 18.71 36.55 43.58 12.97
04/09/2009 99.30 19.17 36.93 43.58 12.94
04/13/2009 97.59 19.10 36.85 43.33 12.90
04/14/2009 96.92 18.86 36.17 42.82 12.72
04/15/2009 96.51 18.36 36.30 43.62 12.98
04/16/2009 99.03 19.26 36.93 43.69 12.86
04/17/2009 98.88 18.72 37.04 43.61 12.74
04/20/2009 98.06 18.14 35.90 42.94 12.72
04/21/2009 99.89 18.49 36.71 41.74 12.82
04/22/2009 100.13 18.31 36.10 41.58 12.72
04/23/2009 99.02 18.44 37.70 41.57 12.81
04/24/2009 97.71 20.38 38.82 41.45 12.75
04/27/2009 97.59 19.89 38.69 40.91 12.78
04/28/2009 99.53 19.43 39.34 40.95 12.84
04/29/2009 101.58 19.74 39.79 41.37 12.97
04/30/2009 100.77 19.75 39.19 41.70 12.80
05/01/2009 102.14 19.73 40.49 41.14 13.08
05/04/2009 103.68 19.68 41.55 41.82 13.19
05/05/2009 103.35 19.29 41.39 41.79 13.16
05/06/2009 102.68 19.29 42.58 41.59 12.97
05/07/2009 100.69 18.83 42.61 41.46 13.16
05/08/2009 99.61 18.93 44.62 41.57 13.15
05/11/2009 100.99 18.83 43.38 41.41 13.29
05/12/2009 102.01 19.39 44.25 43.01 13.35
05/13/2009 100.36 19.25 43.25 42.26 13.02
05/14/2009 99.18 19.55 43.42 43.49 12.94
05/15/2009 99.49 19.71 42.86 43.55 12.71
05/18/2009 102.64 20.08 44.40 44.62 12.77
05/19/2009 103.55 19.92 44.25 45.18 12.78
05/20/2009 102.12 19.99 44.89 45.53 12.65
05/21/2009 100.91 19.44 44.54 45.22 12.68
05/22/2009 100.00 19.37 44.72 45.82 12.90
05/26/2009 103.07 19.95 45.61 45.73 13.22
05/27/2009 101.02 19.75 45.17 45.17 12.96
05/28/2009 102.75 20.06 45.86 45.43 13.22
05/29/2009 104.31 20.49 46.50 47.62 13.34
06/01/2009 106.36 20.99 48.74 47.48 13.54
06/02/2009 104.85 20.99 49.15 48.10 13.29
06/03/2009 104.52 21.32 47.68 47.55 13.27
06/04/2009 104.36 21.42 47.83 48.20 13.26
06/05/2009 105.25 21.72 47.31 47.89 13.32
06/08/2009 105.50 21.63 48.24 47.83 13.28
06/09/2009 106.14 21.66 48.81 47.55 13.27
06/10/2009 106.34 22.12 49.00 46.89 13.33
06/11/2009 107.37 22.40 49.05 47.46 13.61
06/12/2009 106.20 22.89 48.10 47.76 13.83
06/15/2009 105.63 22.97 46.83 47.00 13.62
06/16/2009 105.33 23.00 46.32 46.73 13.41
06/17/2009 105.02 23.23 45.47 46.82 13.47
06/18/2009 104.36 23.05 44.83 48.41 13.80
06/19/2009 103.93 23.61 45.87 47.68 13.58
06/22/2009 102.58 22.84 44.01 46.88 13.81
06/23/2009 102.50 22.90 44.26 46.70 13.56
06/24/2009 102.22 23.02 44.13 46.40 13.57
06/25/2009 104.09 23.34 44.56 46.74 13.79
06/26/2009 103.72 22.91 44.38 47.02 13.58
06/29/2009 103.87 23.41 45.06 47.17 13.74
06/30/2009 102.48 23.32 44.79 46.88 13.75
07/01/2009 102.90 23.58 45.07 48.04 13.98
07/02/2009 99.84 22.93 44.21 47.75 13.57
07/06/2009 99.77 22.76 43.15 47.87 13.77
07/07/2009 98.33 22.10 42.59 47.52 13.50
07/08/2009 98.81 22.13 42.57 47.39 13.47
07/09/2009 100.19 22.01 42.78 47.58 13.41
07/10/2009 98.96 21.96 42.48 47.19 13.50
07/13/2009 101.70 22.79 43.40 47.92 13.73
07/14/2009 101.34 22.67 43.59 48.15 13.69
07/15/2009 105.23 23.66 45.40 49.36 13.91
07/16/2009 108.59 23.98 45.98 49.62 13.92
07/17/2009 113.28 23.83 45.77 49.16 13.88
07/20/2009 114.28 24.06 47.11 49.85 13.91
07/21/2009 114.87 24.36 46.93 49.19 14.03
07/22/2009 113.43 24.33 46.65 48.00 13.99
07/23/2009 114.89 25.07 47.63 48.04 14.28
07/24/2009 115.46 23.00 47.58 48.22 14.51
07/27/2009 115.45 22.67 48.23 48.38 14.56
07/28/2009 115.11 23.02 46.97 48.25 14.42
07/29/2009 115.09 23.35 46.66 48.14 14.47
07/30/2009 115.68 23.36 46.85 48.52 14.64
07/31/2009 115.74 23.07 47.01 48.69 14.59
08/03/2009 117.70 23.38 48.90 48.45 14.68
08/04/2009 117.38 23.32 48.59 48.36 14.68
08/05/2009 116.27 23.36 48.43 48.03 14.45
08/06/2009 115.74 23.01 47.45 48.25 14.56
08/07/2009 117.66 23.11 48.02 48.20 14.77
08/10/2009 117.04 22.97 48.10 48.30 14.63
08/11/2009 116.15 22.69 47.75 47.91 14.70
08/12/2009 117.63 23.08 48.05 47.34 14.63
08/13/2009 117.91 23.17 48.41 47.01 14.65
08/14/2009 116.92 23.24 48.17 47.35 14.72
08/17/2009 115.23 22.81 46.98 47.58 14.62
08/18/2009 115.99 23.26 47.82 47.49 14.60
08/19/2009 116.92 23.33 48.37 48.22 14.68
08/20/2009 117.29 23.35 48.86 48.28 14.83
08/21/2009 118.23 24.08 49.91 48.76 14.94
08/24/2009 117.65 24.31 49.56 47.93 15.03
08/25/2009 117.17 24.31 49.61 47.61 14.95
08/26/2009 117.80 24.22 49.07 48.04 14.97
08/27/2009 117.76 24.36 49.56 48.30 14.95
08/28/2009 116.57 24.35 49.65 47.93 14.94
08/31/2009 116.40 24.32 49.15 47.64 14.83
09/01/2009 115.06 23.68 48.21 47.41 14.64
09/02/2009 114.47 23.54 50.18 48.65 14.50
09/03/2009 114.71 23.78 50.44 48.43 14.66
09/04/2009 115.82 24.29 50.81 48.80 14.86
09/08/2009 115.53 24.49 51.74 49.25 14.86
09/09/2009 115.13 24.45 52.49 49.46 14.77
09/10/2009 116.03 24.66 52.58 49.41 14.77
09/11/2009 116.40 24.52 52.14 50.73 14.77
09/14/2009 117.22 24.66 51.86 51.37 14.98
09/15/2009 117.68 24.86 51.70 51.66 14.99
09/16/2009 120.12 24.86 52.20 51.87 15.17
09/17/2009 120.18 24.96 52.35 52.61 15.14
09/18/2009 120.41 24.92 52.34 52.95 15.28
09/21/2009 119.87 24.96 51.98 52.20 15.08
09/22/2009 119.91 25.42 52.91 52.05 15.04
09/23/2009 119.13 25.36 51.81 51.79 15.05
09/24/2009 119.25 25.59 50.81 51.55 15.13
09/25/2009 119.39 25.21 50.55 52.17 15.15
09/28/2009 117.66 25.48 51.16 52.33 15.26
09/29/2009 117.15 25.40 51.21 52.50 15.18
09/30/2009 117.94 25.37 50.85 52.89 15.07
10/01/2009 116.25 24.54 49.46 52.32 14.94
10/02/2009 117.36 24.62 48.46 53.06 14.72
10/05/2009 118.08 24.31 49.14 52.99 14.85
10/06/2009 119.66 24.77 50.15 53.50 14.95
10/07/2009 121.07 24.76 49.89 53.98 15.01
10/08/2009 120.58 25.32 50.40 53.76 14.92
10/09/2009 124.17 25.21 49.93 53.82 14.93
10/12/2009 125.27 25.37 50.28 53.96 14.97
10/13/2009 125.25 25.46 50.32 53.97 14.94
10/14/2009 126.56 25.61 51.26 54.01 15.11
10/15/2009 126.19 26.35 52.31 54.09 15.17
10/16/2009 119.94 26.14 52.55 54.18 15.11
10/19/2009 121.34 26.00 53.88 53.96 15.30
10/20/2009 121.11 26.01 53.67 53.25 15.27
10/21/2009 119.18 26.22 53.90 53.25 15.46
10/22/2009 120.98 26.23 54.11 53.33 15.50
10/23/2009 118.68 27.64 52.94 52.44 15.41
10/26/2009 118.43 28.29 53.00 52.43 15.26
10/27/2009 118.97 28.20 55.23 52.65 15.22
10/28/2009 119.80 27.64 54.28 52.70 15.16
10/29/2009 121.16 27.84 55.69 53.27 15.42
10/30/2009 118.93 27.36 54.09 52.50 15.14
11/02/2009 118.88 27.50 54.71 52.91 15.11
11/03/2009 119.47 27.16 54.97 52.32 15.05
11/04/2009 119.60 27.68 55.00 52.68 15.12
11/05/2009 121.38 28.09 55.91 53.58 15.36
11/06/2009 122.31 28.14 55.82 53.67 15.36
11/09/2009 124.80 28.60 57.25 54.64 15.61
11/10/2009 125.70 28.62 57.29 54.97 15.72
11/11/2009 125.98 28.73 56.51 55.28 15.68
11/12/2009 125.06 28.96 55.48 55.09 15.55
11/13/2009 125.82 29.23 56.53 55.61 15.58
11/16/2009 126.99 29.14 57.41 55.88 15.74
11/17/2009 127.40 29.73 57.65 56.01 15.73
11/18/2009 126.93 29.84 57.39 55.72 15.70
11/19/2009 126.32 29.51 56.80 56.02 15.64
11/20/2009 125.75 29.35 56.03 56.61 15.76
11/23/2009 126.98 29.67 56.81 57.36 15.99
11/24/2009 126.71 29.64 56.89 57.31 16.09
11/25/2009 126.07 29.52 57.37 57.23 16.27
11/27/2009 124.50 28.95 56.30 56.72 16.22
11/30/2009 125.15 29.14 55.40 56.74 16.21
12/01/2009 126.72 29.74 56.75 57.61 16.62
12/02/2009 126.00 29.51 56.81 57.49 16.76
12/03/2009 126.33 29.56 55.82 56.81 16.78
12/04/2009 126.04 29.71 56.06 57.02 16.65
12/07/2009 125.83 29.52 56.36 57.40 16.89
12/08/2009 125.59 29.30 55.26 57.21 16.95
12/09/2009 127.17 29.44 54.93 57.36 16.95
12/10/2009 128.11 29.60 54.63 58.10 17.17
12/11/2009 128.44 29.58 54.69 58.63 17.30
12/14/2009 128.69 29.84 55.00 58.56 17.20
12/15/2009 127.27 29.75 54.67 58.58 17.15
12/16/2009 127.48 29.83 55.26 57.95 17.05
12/17/2009 126.19 29.33 54.16 56.52 16.84
12/18/2009 126.69 30.08 54.43 56.46 16.90
12/21/2009 127.42 30.24 55.46 56.72 16.88
12/22/2009 128.69 30.54 55.69 56.81 16.77
12/23/2009 128.76 30.64 56.10 56.82 16.75
12/24/2009 129.33 30.72 56.42 56.97 16.78
12/28/2009 131.05 30.89 56.80 56.97 16.85
12/29/2009 130.59 31.10 56.24 57.27 16.90
12/30/2009 131.31 30.68 56.35 57.21 16.92
12/31/2009 129.65 30.20 56.16 56.54 16.72
01/04/2010 131.19 30.67 57.31 56.58 16.49
01/05/2010 129.60 30.68 57.71 55.89 16.22
01/06/2010 128.76 30.49 58.01 55.87 16.27
01/07/2010 128.32 30.17 57.99 55.73 16.35
01/08/2010 129.60 30.38 58.13 54.70 16.36
01/11/2010 128.25 29.99 59.96 55.81 16.53
01/12/2010 129.27 29.80 59.58 56.42 16.55
01/13/2010 128.99 30.07 59.87 56.57 16.58
01/14/2010 131.05 30.68 59.81 56.67 16.58
01/15/2010 130.52 30.58 59.72 55.83 16.42
01/19/2010 132.86 30.82 60.38 55.96 16.60
01/20/2010 129.01 30.31 59.16 55.05 16.45
01/21/2010 127.77 29.74 57.71 53.93 16.21
01/22/2010 124.30 28.70 56.07 53.80 16.08
01/25/2010 124.92 29.05 56.72 53.91 16.19
01/26/2010 124.55 29.23 56.67 53.70 16.33
01/27/2010 125.13 29.40 56.25 54.07 16.26
01/28/2010 122.57 28.89 55.54 53.74 16.15
01/29/2010 121.22 27.92 54.37 53.81 16.06
02/01/2010 123.48 28.15 55.45 53.94 16.18
02/02/2010 124.33 28.20 53.73 54.60 16.28
02/03/2010 124.46 28.37 53.45 54.42 16.17
02/04/2010 121.83 27.59 51.81 53.00 15.90
02/05/2010 122.34 27.76 51.52 52.66 15.86
02/08/2010 121.26 27.47 50.80 52.22 15.86
02/09/2010 122.58 27.75 51.94 53.57 16.09
02/10/2010 122.18 27.73 51.98 53.35 15.99
02/11/2010 123.10 27.86 53.09 53.78 15.98
02/12/2010 123.37 27.68 52.97 53.54 15.92
02/16/2010 124.59 28.22 54.21 54.37 16.02
02/17/2010 125.69 28.46 53.35 54.88 15.95
02/18/2010 127.16 28.84 53.84 55.46 16.10
02/19/2010 126.54 28.64 53.41 55.27 16.37
02/22/2010 126.20 28.60 53.36 54.93 16.20
02/23/2010 125.82 28.20 52.35 54.38 16.12
02/24/2010 126.94 28.50 52.70 54.71 16.22
02/25/2010 126.42 28.47 52.02 52.69 16.15
02/26/2010 126.51 28.54 52.34 52.29 16.12
03/01/2010 127.91 28.89 53.09 52.84 16.26
03/02/2010 126.77 28.33 53.11 52.87 16.21
03/03/2010 126.23 28.33 53.96 53.49 16.17
03/04/2010 126.07 28.50 54.19 54.03 16.10
03/05/2010 126.60 28.46 54.86 54.26 16.23
03/08/2010 125.77 28.50 55.25 54.02 16.30
03/09/2010 124.91 28.67 55.12 53.74 16.24
03/10/2010 124.98 28.84 55.27 53.76 16.24
03/11/2010 126.95 29.05 55.67 53.60 16.25
03/12/2010 127.29 29.14 55.93 53.35 16.10
03/15/2010 127.18 29.16 55.65 53.65 16.23
03/16/2010 128.01 29.24 56.24 53.70 16.37
03/17/2010 127.11 29.50 57.20 53.84 16.38
03/18/2010 127.73 29.48 57.20 53.95 16.35
03/19/2010 127.06 29.46 56.74 54.75 16.35
03/22/2010 127.33 29.47 56.41 54.54 16.21
03/23/2010 128.71 29.75 57.00 55.30 16.23
03/24/2010 127.87 29.52 56.29 54.62 16.09
03/25/2010 128.58 29.88 55.60 54.80 16.07
03/26/2010 128.60 29.53 55.76 54.65 16.19
03/29/2010 127.93 29.46 55.96 54.77 16.35
03/30/2010 128.11 29.64 55.90 54.87 16.17
03/31/2010 127.60 29.16 56.13 55.00 16.09
04/01/2010 127.60 29.03 56.79 55.30 16.18
04/05/2010 128.69 29.14 57.55 54.86 16.19
04/06/2010 128.27 29.19 58.39 54.29 16.32
04/07/2010 127.82 29.22 57.82 53.82 16.14
04/08/2010 126.96 29.79 58.00 53.76 16.01
04/09/2010 128.10 30.20 58.48 54.59 16.10
04/12/2010 127.71 30.18 58.37 54.76 16.03
04/13/2010 128.37 30.31 58.32 55.02 15.99
04/14/2010 130.58 30.68 59.02 54.95 15.98
04/15/2010 130.22 30.73 59.58 54.26 15.90
04/16/2010 129.96 30.53 58.90 54.97 15.78
04/19/2010 131.56 30.90 58.50 55.32 15.84
04/20/2010 129.03 31.22 59.49 54.47 16.12
04/21/2010 128.33 31.19 59.10 54.19 16.07
04/22/2010 128.47 31.25 58.57 54.31 15.98
04/23/2010 129.33 30.82 58.90 53.88 16.02
04/26/2010 130.06 30.97 56.96 53.73 16.01
04/27/2010 128.16 30.71 55.41 52.87 15.78
04/28/2010 129.44 30.77 56.40 53.36 16.40
04/29/2010 129.79 30.86 51.70 53.74 16.30
04/30/2010 128.34 30.40 51.29 53.45 16.54
05/03/2010 128.94 30.72 49.37 53.76 16.69
05/04/2010 127.47 29.99 50.36 53.18 16.47
05/05/2010 126.81 29.72 50.99 53.66 16.52
05/06/2010 123.92 28.85 50.33 52.30 16.25
05/07/2010 122.10 28.08 49.06 52.67 16.32
05/10/2010 126.27 28.81 48.75 54.04 16.66
05/11/2010 126.89 28.75 48.74 53.61 16.68
05/12/2010 132.68 29.31 48.50 54.02 16.74
05/13/2010 131.48 29.11 48.10 53.49 16.62
05/14/2010 131.19 28.80 46.87 53.34 16.54
05/17/2010 130.44 28.81 46.57 53.41 16.69
05/18/2010 129.95 28.60 45.38 53.10 16.70
05/19/2010 128.86 28.24 45.27 53.12 16.49
05/20/2010 123.80 27.11 44.58 51.54 15.97
05/21/2010 125.42 26.84 43.86 51.59 16.00
05/24/2010 124.45 26.27 41.86 51.46 15.97
05/25/2010 124.52 26.07 42.56 50.62 15.82
;
/* Printing first 10 observations of the data */
proc print data = returns(obs=10);
run;
/* Keep only the last 250 observations of the data */
data returns;
set returns nobs=observ;
if (_N_ > observ-250);
run;
/* Copula estimation and simulation of returns */
proc copula data = returns;
var ret_ibm ret_msft ret_bp ret_ko ret_duk;
* fit T-copula to stock returns;
fit T /
marginals = empirical
method = MLE
plots = (datatype = both);
* simulate 10000 observations;
* independent in time, dependent in cross-section;
simulate /
ndraws = 10000
seed = 1234
out = simulated_returns
plots(unpack) = (datatype = original);
run;
/* compute equally weighted portfolio return */
data port_ret (drop = i ret);
set simulated_returns;
array returns{5} ret_ibm ret_msft ret_bp ret_ko ret_duk;
ret =0;
do i =1 to 5;
ret = ret+ 0.2*exp(returns[i]);
end;
port_ret = ret-1;
run;
/* compute descriptive statistics */
/* quantile table will give Value-at-Risk estimates for the portfolio */
proc univariate data = port_ret;
var port_ret;
run;
