Model Risk Data Analysis Questions

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WP96

Business Finance

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Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 Stock 1 100 100.10 99.63 98.33 97.68 98.33 98.21 98.91 98.81 99.21 99.30 99.19 100.70 101.27 100.47 100.54 100.13 99.93 100.11 100.41 99.95 100.07 100.07 99.47 99.53 99.45 99.53 98.40 98.93 98.96 99.28 97.77 96.70 96.61 96.65 95.87 96.66 97.38 97.49 97.49 97.23 96.48 96.72 97.64 Stock 2 100 99.33 98.23 98.70 98.42 99.30 99.12 99.26 99.81 100.17 99.67 99.15 98.58 98.17 97.88 98.24 98.58 98.36 98.92 98.51 99.71 100.37 100.56 100.06 100.00 100.22 99.78 100.25 100.68 100.86 101.26 100.68 100.72 101.06 101.54 101.54 101.91 102.33 102.58 102.45 102.28 102.47 102.69 102.69 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 96.57 97.12 96.85 97.48 98.44 98.37 98.93 97.24 96.92 96.52 95.47 95.96 96.71 96.45 96.15 96.07 96.01 95.82 94.81 95.67 95.12 95.68 96.33 96.72 96.22 95.15 95.87 94.77 94.97 93.89 93.58 93.26 94.44 94.88 93.89 93.84 93.48 93.00 92.50 93.63 94.35 94.15 94.82 94.25 95.58 94.77 95.05 103.59 103.33 103.20 102.79 102.64 103.43 104.11 103.99 104.65 106.17 106.61 107.34 108.48 108.18 106.80 106.64 107.64 108.02 107.32 108.02 107.72 107.30 107.84 107.89 108.92 109.73 109.91 109.65 108.67 108.01 108.81 109.21 110.64 110.94 110.26 108.81 108.86 109.18 110.20 109.56 109.99 110.02 111.30 110.96 112.00 112.24 111.20 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 95.03 93.87 93.95 94.45 93.35 93.23 92.85 93.18 92.38 91.92 91.42 90.12 90.07 89.61 89.03 89.02 88.41 88.29 86.93 86.74 85.85 84.91 85.04 85.28 85.61 86.53 86.89 86.55 86.80 87.59 87.57 89.64 88.76 88.21 88.69 88.01 88.74 88.62 88.24 86.84 87.13 86.17 85.67 85.60 85.76 86.09 85.72 110.99 112.26 111.90 111.94 112.24 112.05 112.18 112.76 113.03 113.76 114.32 114.73 115.41 114.89 113.92 114.01 113.22 112.78 111.77 111.89 113.93 114.71 116.01 115.43 116.42 117.19 117.74 117.54 117.31 117.23 117.18 116.87 116.90 117.74 117.59 117.13 117.31 118.23 118.70 118.77 118.89 119.74 119.55 121.23 122.16 121.69 121.79 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 87.53 86.93 85.75 85.19 84.34 84.91 84.87 85.72 85.30 85.14 86.05 86.12 85.94 85.40 85.21 85.06 84.44 83.73 83.49 82.96 82.57 83.08 84.17 85.18 85.12 84.49 84.41 83.38 83.49 83.65 83.65 83.11 83.31 84.03 84.24 85.02 84.44 83.58 83.36 83.74 83.99 84.70 83.16 83.47 82.94 82.38 83.04 121.37 120.95 120.39 120.28 120.51 121.30 120.70 120.96 120.75 121.01 120.51 120.32 120.23 120.93 121.08 121.70 120.67 122.30 121.91 122.54 123.36 124.18 124.45 125.24 124.78 124.75 124.65 124.68 125.65 125.88 125.70 126.12 126.84 126.43 126.51 125.74 127.18 127.26 127.22 127.42 126.51 127.71 128.62 127.90 128.26 129.39 129.60 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 82.78 82.34 82.87 82.42 83.41 82.84 82.15 81.56 82.16 81.42 81.97 81.51 80.88 82.15 81.49 82.27 82.13 82.22 82.21 82.51 81.39 81.00 79.45 78.48 77.99 77.51 76.49 77.86 77.20 76.85 77.77 77.60 78.87 78.42 78.38 78.47 77.81 78.00 77.58 77.78 77.86 77.53 77.32 75.64 75.19 74.13 73.64 129.41 128.81 128.77 128.93 128.79 128.82 128.80 129.56 129.97 130.48 129.06 129.05 129.78 129.54 128.76 129.21 129.66 129.02 129.22 129.37 128.42 129.01 128.51 128.58 128.63 128.71 129.51 130.91 130.85 129.50 128.64 128.66 128.27 128.54 127.95 128.40 128.66 129.35 128.74 127.90 129.05 129.37 129.89 130.59 130.37 130.54 130.20 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 73.16 72.79 72.42 72.05 72.31 72.31 72.31 72.52 72.17 71.39 71.44 71.53 70.99 70.56 69.87 69.49 69.46 68.93 68.49 130.18 130.54 131.13 131.60 131.03 130.15 129.94 128.69 128.42 128.34 128.07 127.43 127.41 128.21 128.11 128.36 127.89 128.44 128.81 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 TV radio newspaper sales 230.1 37.8 69.2 22.1 44.5 39.3 45.1 10.4 17.2 45.9 69.3 9.3 151.5 41.3 58.5 200 180.8 10.8 58.4 500 8.7 48.9 75 7.2 57.5 32.8 23.5 11.8 120.2 19.6 11.6 13.2 8.6 2.1 1 4.8 199.8 2.6 21.2 10.6 66.1 5.8 24.2 8.6 214.7 24 4 17.4 23.8 35.1 65.9 9.2 97.5 7.6 7.2 9.7 204.1 32.9 46 19 195.4 47.7 52.9 22.4 67.8 36.6 114 12.5 281.4 39.6 55.8 24.4 69.2 20.5 18.3 11.3 147.3 23.9 19.1 14.6 218.4 27.7 53.4 300 237.4 5.1 23.5 12.5 13.2 15.9 49.6 5.6 228.3 16.9 26.2 15.5 62.3 12.6 18.3 9.7 262.9 3.5 19.5 12 142.9 29.3 12.6 15 240.1 16.7 22.9 15.9 248.8 27.1 22.9 18.9 70.6 16 40.8 10.5 292.9 28.3 43.2 21.4 112.9 17.4 38.6 11.9 97.2 1.5 30 9.6 265.6 20 0.3 17.4 95.7 1.4 7.4 9.5 290.7 4.1 8.5 12.8 266.9 43.8 5 25.4 74.7 49.4 45.7 14.7 43.1 26.7 35.1 10.1 228 37.7 32 21.5 202.5 22.3 31.6 100 177 33.4 38.7 17.1 293.6 27.7 1.8 20.7 206.9 8.4 26.4 12.9 25.1 25.7 43.3 8.5 175.1 22.5 31.5 14.9 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 89.7 239.9 227.2 66.9 199.8 100.4 216.4 182.6 262.7 198.9 7.3 136.2 210.8 210.7 53.5 261.3 239.3 102.7 131.1 69 31.5 139.3 237.4 216.8 199.1 109.8 26.8 129.4 213.4 16.9 27.5 120.5 5.4 116 76.4 239.8 75.3 68.4 213.5 193.2 76.3 110.7 88.3 109.8 134.3 28.6 217.7 9.9 41.5 15.8 11.7 3.1 9.6 41.7 46.2 28.8 49.4 28.1 19.2 49.6 29.5 2 42.7 15.5 29.6 42.8 9.3 24.6 14.5 27.5 43.9 30.6 14.3 33 5.7 24.6 43.7 1.6 28.5 29.9 7.7 26.7 4.1 20.3 44.5 43 18.4 27.5 40.6 25.5 47.8 4.9 1.5 33.5 35.7 18.5 49.9 36.8 34.6 3.6 39.6 58.7 15.9 60 41.4 16.6 37.7 9.3 21.4 54.7 27.3 8.4 28.9 0.9 2.2 10.2 11 27.2 38.7 31.7 19.3 31.3 13.1 89.4 20.7 14.2 9.4 23.1 22.3 36.9 32.5 35.6 33.8 65.7 16 63.2 73.4 51.4 9.3 33 59 10.6 23.2 14.8 9.7 11.4 10.7 22.6 21.2 20.2 23.7 5.5 13.2 23.8 18.4 8.1 24.2 15.7 14 18 9.3 9.5 13.4 18.9 22.3 18.3 12.4 8.8 11 17 8.7 6.9 14.2 5.3 11 11.8 12.3 11.3 13.6 21.7 15.2 12 16 12.9 16.7 11.2 7.3 19.4 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 250.9 107.4 163.3 197.6 184.9 289.7 135.2 222.4 296.4 280.2 187.9 238.2 137.9 25 90.4 13.1 255.4 225.8 241.7 175.7 209.6 78.2 75.1 139.2 76.4 125.7 19.4 141.3 18.8 224 123.1 229.5 87.2 7.8 80.2 220.3 59.6 0.7 265.2 8.4 219.8 36.9 48.3 25.6 273.7 43 184.9 36.5 14 31.6 3.5 21 42.3 41.7 4.3 36.3 10.1 17.2 34.3 46.4 11 0.3 0.4 26.9 8.2 38 15.4 20.6 46.8 35 14.3 0.8 36.9 16 26.8 21.7 2.4 34.6 32.3 11.8 38.9 0 49 12 39.6 2.9 27.2 33.5 38.6 47 39 28.9 25.9 43.9 72.3 10.9 52.9 5.9 22 51.2 45.9 49.8 100.9 21.4 17.9 5.3 59 29.7 23.2 25.6 5.5 56.5 23.2 2.4 10.7 34.5 52.7 25.6 14.8 79.2 22.3 46.2 50.4 15.6 12.4 74.2 25.9 50.6 9.2 3.2 43.1 8.7 43 2.1 45.1 65.6 8.5 9.3 59.7 20.5 1.7 22.2 11.5 16.9 11.7 15.5 25.4 17.2 11.7 23.8 14.8 14.7 20.7 19.2 7.2 8.7 5.3 19.8 13.4 21.8 14.1 15.9 14.6 12.6 12.2 9.4 15.9 6.6 15.5 7 11.6 15.2 19.7 10.6 6.6 8.8 24.7 9.7 1.6 12.7 5.7 19.6 10.8 11.6 9.5 20.8 9.6 20.7 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 73.4 193.7 220.5 104.6 96.2 140.3 240.1 243.2 38 44.7 280.7 121 197.6 171.3 187.8 4.1 93.9 149.8 11.7 131.7 172.5 85.7 188.4 163.5 117.2 234.5 17.9 206.8 215.4 284.3 50 164.5 19.6 168.4 222.4 276.9 248.4 170.2 276.7 165.6 156.6 218.5 56.2 287.6 253.8 205 139.5 17 35.4 33.2 5.7 14.8 1.9 7.3 49 40.3 25.8 13.9 8.4 23.3 39.7 21.1 11.6 43.5 1.3 36.9 18.4 18.1 35.8 18.1 36.8 14.7 3.4 37.6 5.2 23.6 10.6 11.6 20.9 20.1 7.1 3.4 48.9 30.2 7.8 2.3 10 2.6 5.4 5.7 43 21.3 45.1 2.1 12.9 75.6 37.9 34.4 38.9 9 8.7 44.3 11.9 20.6 37 48.7 14.2 37.7 9.5 5.7 50.5 24.3 45.2 34.6 30.7 49.3 25.6 7.4 5.4 84.8 21.6 19.4 57.6 6.4 18.4 47.4 17 12.8 13.1 41.8 20.3 35.2 23.7 17.6 8.3 27.4 29.7 71.8 30 19.6 26.6 10.9 19.2 20.1 10.4 11.4 10.3 13.2 25.4 10.9 10.1 16.1 11.6 16.6 19 15.6 3.2 15.3 10.1 7.3 12.9 14.4 13.3 14.9 18 11.9 11.9 8 12.2 17.1 15 8.4 14.5 7.6 11.7 11.5 27 20.2 11.7 11.8 12.6 10.5 12.2 8.7 26.2 17.6 22.6 10.3 188 189 190 191 192 193 194 195 196 197 198 199 200 191.1 286 18.7 39.5 75.5 17.2 166.8 149.7 38.2 94.2 177 283.6 232.1 28.7 13.9 12.1 41.1 10.8 4.1 42 35.6 3.7 4.9 9.3 42 8.6 18.2 3.7 23.4 5.8 6 31.6 3.6 6 13.8 8.1 6.4 66.2 8.7 17.3 15.9 6.7 10.8 9.9 5.9 19.6 17.3 7.6 9.7 12.8 25.5 13.4 Assignment 1 (Short Answer Section: ~4-6 sentence responses expected) Problem #1: SR11-7 defines a model as ‘a quantitative method, system, or approach that applies statistical, economic, financial, or mathematical theories, techniques, and assumptions to process input data into quantitative estimates.’ This definition had the financial industry primarily in mind when formulated. With the growth in AI/ML models in other industries like automobiles, healthcare, etc., how you would expand this definition? (n.b. any part of the definition can be expanded on). Problem #2: Map the following MRM activities/situations to their appropriate ORM category. The ORM designations are: • • • • Process Control Model Risk Event Model Risk KRI The MRM activities/situations are: 1) Each validation report is approved by a senior validator (or model risk committee) before final issuance. 2) A high number (compared to the senior management threshold) of models are overdue for validation. 3) Each model goes through a series of testing steps during model validation. 4) A model calculated the wrong hedges due to a stale data source, causing a loss for the series of trades involved. (Numerical: ~4-6 sentence responses expected for short answer questions, numerical calculations with supporting code or xlsx to show the calculation for the numeric questions) Problem #3: Using Assignment1_Data_Issues.xlsx: Tab ‘Stationarity’, perform the following using your preferred computational environment (e.g. Python, R, Excel, MatLab, etc.): 1) Plot the variables against each other in time. 2) Run OLS regression on the time series (you can pick either variable to be the dependent variable (Y)) 3) Report the R2. 4) Now, first difference each time series. 5) Re-run the OLS regression 6) Report the R2 of the first-differenced series Using what you have learned about stationarity in class as a possible data risk in modeling (and using doing your own independent search on stationarity), do you trust the R2 found in step 3? What about the R2 found in step 6? Produce auxiliary charts to support your analysis as you find necessary. Problem #4: Using Assignment1_Data_Issues.xlsx: Tab ‘Outliers’, perform the following using your preferred computational environment (e.g. Python, R, Excel, MatLab, etc.): 1) Plot sales vs TV against each other, here is ‘sales’ is the amount of sales, ‘TV’ is the TV-related advertising costs. 2) Run OLS regression 3) Report the R2 and the β weight to ‘TV’ factor 4) Now, look for the outliers from Part 1) 5) Think of way to handle the outliers (i.e. this is outlier treatment) 6) Re-run the OLS regression 7) Report the updated R2 and β weight to ‘TV’ factor Give a summary analysis of how the outliers affected the regression statistics (by analyzing the R2 and β weight to ‘TV’ factor, you can ignore other metrics for now). Do the outliers look credible? What model risk would occur if an analyst used the data with the outliers?
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Explanation & Answer

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Time
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2
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43

Stock 1
100
100.10
99.63
98.33
97.68
98.33
98.21
98.91
98.81
99.21
99.30
99.19
100.70
101.27
100.47
100.54
100.13
99.93
100.11
100.41
99.95
100.07
100.07
99.47
99.53
99.45
99.53
98.40
98.93
98.96
99.28
97.77
96.70
96.61
96.65
95.87
96.66
97.38
97.49
97.49
97.23
96.48
96.72

Stock 2
100
99.33
98.23
98.70
98.42
99.30
99.12
99.26
99.81
100.17
99.67
99.15
98.58
98.17
97.88
98.24
98.58
98.36
98.92
98.51
99.71
100.37
100.56
100.06
100.00
100.22
99.78
100.25
100.68
100.86
101.26
100.68
100.72
101.06
101.54
101.54
101.91
102.33
102.58
102.45
102.28
102.47
102.69

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.976741
R Square
0.954023
Adjusted R Square
0.953838
Standard Error15.5987
Observations
251
ANOVA
df
Regression
Residual
Total

SS
MS
1 1257163 1257163
249 60586.56 243.3195
250 1317750

Coefficients
Standard Error t Stat
Intercept 860.4161 10.2646 83.82366
Stock 1
-8.35504 0.116236 -71.8799

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.978862
R Square
0.958172
Adjusted R Square
0.958004
Standard Error
14.87828
Observations
251
ANOVA
df
Regression
Residual
Total

SS
MS
1 1262631 1262631
249 55119.45 221.3633
250 1317750

Coefficients
Standard Error t Stat
Intercept
-633.351 10.09818 -62.7193
Stock 2
6.508864 0.086183 75.52407

44
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71
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81
82
83
84
85
86
87
88
89

97.64
96.57
97.12
96.85
97.48
98.44
98.37
98.93
97.24
96.92
96.52
95.47
95.96
96.71
96.45
96.15
96.07
96.01
95.82
94.81
95.67
95.12
95.68
96.33
96.72
96.22
95.15
95.87
94.77
94.97
93.89
93.58
93.26
94.44
94.88
93.89
93.84
93.48
93.00
92.50
93.63
94.35
94.15
94.82
94.25
95.58

102.69
103.59
103.33
103.20
102.79
102.64
103.43
104.11
103.99
104.65
106.17
106.61
107.34
108.48
108.18
106.80
106.64
107.64
108.02
107.32
108.02
107.72
107.30
107.84
107.89
108.92
109.73
109.91
109.65
108.67
108.01
108.81
109.21
110.64
110.94
110.26
108.81
108.86
109.18
110.20
109.56
109.99
110.02
111.30
110.96
112.00

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.976741
R Square
0.954023
Adjusted R Square
0.953838
Standard Error
1.823557
Observations
251
ANOVA
df
Regression
Residual
Total

SS
MS
1 17181.2 17181.2
249 828.0145 3.325359
250 18009.21

Coefficients
Standard Error t Stat
Intercept 102.2883 0.230893 443.0111
Time
-0.11419 0.001589 -71.8799
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.978862
R Square
0.958172
Adjusted R Square
0.958004
Standard Error
2.237532
Observations
251
ANOVA
df
Regression
Residual
Total

SS
MS
1 28556.78 28556.78
249 1246.631 5.006549
250 29803.41

Coefficients
Standard Error t Stat
Intercept
98.1156 0.28331 346.3193
Time
0.14721 0.001949 75.52407

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.935798

90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135

94.77
95.05
95.03
93.87
93.95
94.45
93.35
93.23
92.85
93.18
92.38
91.92
91.42
90.12
90.07
89.61
89.03
89.02
88.41
88.29
86.93
86.74
85.85
84.91
85.04
85.28
85.61
86.53
86.89
86.55
86.80
87.59
87.57
89.64
88.76
88.21
88.69
88.01
88.74
88.62
88.24
86.84
87.13
86.17
85.67
85.60

112.24
111.20
110.99
112.26
111.90
111.94
112.24
112.05
112.18
112.76
113.03
113.76
114.32
114.73
115.41
114.89
113.92
114.01
113.22
112.78
111.77
111.89
113.93
114.71
116.01
115.43
116.42
117.19
117.74
117.54
117.31
117.23
117.18
116.87
116.90
117.74
117.59
117.13
117.31
118.23
118.70
118.77
118.89
119.74
119.55
121.23

R Square
0.875718
Adjusted R Square
0.875218
Standard Error
2.998145
Observations
251
ANOVA
df
Regression
Residual
Total

SS
MS
1 15770.98 15770.98
249 2238.229 8.988871
250 18009.21

Intercept
Stock 2

Coefficients
Standard Error t Stat
172.7669
2.0349 84.90194
-0.72744 0.017367 -41.8868

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.935798
R Square
0.875718
Adjusted R Square
0.875218
Standard Error
3.856898
Observations
251
ANOVA
df
Regression
Residual
Total

SS
MS
1 26099.37 26099.37
249 3704.041 14.87567
250 29803.41

Coefficients
Standard Error t Stat
Intercept 222.4825
2.538 87.66056
Stock 1
-1.20384 0.02874 -41.8868

136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182

85.76
86.09
85.72
87.53
86.93
85.75
85.19
84.34
84.91
84.87
85.72
85.30
85.14
86.05
86.12
85.94
85.40
85.21
85.06
84.44
83.73
83.49
82.96
82.57
83.08
84.17
85.18
85.12
84.49
84.41
83.38
83.49
83.65
83.65
83.11
83.31
84.03
84.24
85.02
84.44
83.58
83.36
83.74
83.99
84.70
83.16
83.47

122.16
121.69
121.79
121.37
120.95
120.39
120.28
120.51
121.30
120.70
120.96
120.75
121.01
120.51
120.32
120.23
120.93
121.08
121.70
120.67
122.30
121.91
122.54
123.36
124.18
124.45
125.24
124.78
124.75
124.65
124.68
125.65
125.88
125.70
126.12
126.84
126.43
126.51
125.74
127.18
127.26
127.22
127.42
126.51
127.71
128.62
127...


Anonymous
This is great! Exactly what I wanted.

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