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UNIVERSIDAD POLITECNICO GRANCOLOMBIANO

Gestión Integral del Riesgo Financiero ECOPETROL

Jhon Wilson Serrato Hernández - Cód.. 1611024807 Sandra Milena Martínez Higuita - Cód.. 1611025289 Yuri Paola Acero López - Cód.. 1621024896

Seminario Financiero Docente: Juan Carlos Rojas

Politécnico Gran Colombiano 2019

RESUMEN Realizamos el análisis de riesgo de mercado para la empresa ECOPETROL, con los valores de la acción comprendidos por un año, entre el 1º de Febrero de 2018 a 28 de Febrero de 2019, teniendo presente que el modelo se comprende con datos historicos de un año o un minimo de 250 dias habiles y asi procedemos a encontrar los retornos (dia Habil) y la desviacion estandar, con estos datos hallamos el valor de riesgo (VAR) el cual es nuestro eje para determinar el limite superior e inferior del año actual el cual nos entrega un margen de precio de la acción de acuerdo al nivel de confianza 99% para el dia siguiente.

Introducción En este trabajo analizaremos la acción de ECOPETROL para los siguientes riesgos en 3 etapas: 1. Riesgo de Mercado 2. Riesgo de Crédito 3. Riesgo Operativo

Marco Teórico y Marco Metodológico

Cotizaciones de la empresa: ECOPETROL Dia

Periodo

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

Feb/01/2018 Feb/02/2018 Feb/05/2018 Feb/06/2018 Feb/07/2018 Feb/08/2018 Feb/09/2018 Feb/12/2018 Feb/13/2018 Feb/14/2018 Feb/15/2018 Feb/16/2018 Feb/19/2018 Feb/20/2018 Feb/21/2018 Feb/22/2018 Feb/23/2018 Feb/26/2018 Feb/27/2018 Feb/28/2018 Mar/01/2018 Mar/02/2018 Mar/05/2018 Mar/06/2018 Mar/07/2018 Mar/08/2018 Mar/09/2018 Mar/12/2018 Mar/13/2018 Mar/14/2018 Mar/15/2018 Mar/16/2018 Mar/20/2018 Mar/21/2018 Mar/22/2018 Mar/23/2018 Mar/26/2018

Precio Cierre Retornos Distrubucion 2,770 2,665 2,485 2,500 2,430 2,335 2,455 2,420 2,385 2,500 2,490 2,485 2,480 2,485 2,475 2,565 2,625 2,655 2,630 2,510 2,480 2,480 2,510 2,505 2,450 2,475 2,505 2,480 2,505 2,505 2,535 2,590 2,670 2,750 2,620 2,700 2,775

-3.86% 4.0425735865 -6.99% 0.1525011363 0.60% 16.942109771 -2.84% 7.8685410416 -3.99% 3.6801012593 5.01% 1.6484305718 -1.44% 14.1465372961 -1.46% 14.0623093545 4.71% 2.17793111 -0.40% 17.1221196945 -0.20% 17.3503334589 -0.20% 17.3500019728 0.20% 17.4108443341 -0.40% 17.1185662555 3.57% 5.3101644828 2.31% 10.6736681612 1.14% 15.5731134526 -0.95% 15.8848226418 -4.67% 2.0790498434 -1.20% 15.0359268791 0.00% 17.4479855906 1.20% 15.3534661368 -0.20% 17.3516409008 -2.22% 10.6798813947 1.02% 15.9495568817 1.20% 15.3452520872 -1.00% 15.7092772474 1.00% 15.9855391464 0.00% 17.4479855906 1.19% 15.3938599864 2.15% 11.4395427988 3.04% 7.3908647257 2.95% 7.7754830151 -4.84% 1.774223571 3.01% 7.5368829851 2.74% 8.7126567532

38 39 40 41 42 43 44 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

Mar/27/2018 Mar/28/2018 Apr/02/2018 Apr/03/2018 Apr/04/2018 Apr/05/2018 Apr/06/2018 Apr/09/2018 Apr/10/2018 Apr/11/2018 Apr/12/2018 Apr/13/2018 Apr/16/2018 Apr/17/2018 Apr/18/2018 Apr/19/2018 Apr/20/2018 Apr/23/2018 Apr/24/2018 Apr/25/2018 Apr/26/2018 Apr/27/2018 Apr/30/2018 May/02/2018 May/03/2018 May/04/2018 May/07/2018 May/08/2018 May/09/2018 May/10/2018 May/11/2018 May/15/2018 May/16/2018 May/17/2018 May/18/2018 May/21/2018 May/22/2018 May/23/2018 May/24/2018 May/25/2018 May/28/2018 May/29/2018 May/30/2018 May/31/2018

2,645 2,615 2,690 2,730 2,740 2,740 2,730 2,745 2,790 2,980 2,955 2,835 2,760 2,870 2,935 3,030 3,030 3,085 3,060 3,045 3,010 3,070 3,100 3,105 3,100 3,095 3,030 3,085 3,160 3,100 3,135 3,290 3,205 3,170 3,150 3,125 3,110 3,025 3,070 2,955 2,900 3,030 3,120 3,090

-4.80% 1.8496089631 -1.14% 15.253608298 2.83% 8.3208346832 1.48% 14.3478203443 0.37% 17.2810553896 0.00% 17.4479855906 -0.37% 17.1715842946 0.55% 17.0348144616 1.63% 13.7409202043 6.59% 0.2904489794 -0.84% 16.1835575773 -4.15% 3.2505338076 -2.68% 8.5689880059 3.91% 4.18642899 2.24% 11.0100554164 3.19% 6.7938227917 0.00% 17.4479855906 1.80% 13.0037547564 -0.81% 16.2616250828 -0.49% 16.9768372316 -1.16% 15.2000909029 1.97% 12.2269898675 0.97% 16.0738784076 0.16% 17.4290738873 -0.16% 17.3803221855 -0.16% 17.3801433452 -2.12% 11.1310373878 1.80% 13.0037547564 2.40% 10.257998562 -1.92% 12.0728868631 1.12% 15.6173385968 4.83% 1.9600010191 -2.62% 8.8545743915 -1.10% 15.3992919171 -0.63% 16.699810343 -0.80% 16.3063081056 -0.48% 16.994543661 -2.77% 8.169418711 1.48% 14.3454419119 -3.82% 4.1846195223 -1.88% 12.2456091372 4.39% 2.8790423841 2.93% 7.8847868249 -0.97% 15.8237175178

82 83 84 85 86 87 88 89 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

Jun/01/2018 Jun/05/2018 Jun/06/2018 Jun/07/2018 Jun/08/2018 Jun/12/2018 Jun/13/2018 Jun/14/2018 Jun/15/2018 Jun/18/2018 Jun/19/2018 Jun/20/2018 Jun/21/2018 Jun/22/2018 Jun/25/2018 Jun/26/2018 Jun/27/2018 Jun/28/2018 Jun/29/2018 Jul/03/2018 Jul/04/2018 Jul/05/2018 Jul/06/2018 Jul/09/2018 Jul/10/2018 Jul/11/2018 Jul/12/2018 Jul/13/2018 Jul/16/2018 Jul/17/2018 Jul/18/2018 Jul/19/2018 Jul/23/2018 Jul/24/2018 Jul/25/2018 Jul/26/2018 Jul/27/2018 Jul/30/2018 Jul/31/2018 Aug/01/2018 Aug/02/2018 Aug/03/2018 Aug/06/2018 Aug/08/2018

3,110 3,080 3,015 3,060 3,045 3,005 3,010 3,005 2,985 2,985 2,905 2,875 2,845 2,880 2,820 2,885 2,970 2,985 3,005 2,930 2,930 2,895 2,935 3,000 3,020 2,955 2,945 2,965 2,940 2,960 2,965 2,950 2,970 2,965 3,000 3,005 2,985 3,080 3,070 3,125 3,130 3,095 3,140 3,175

0.65% 16.8610506881 -0.97% 15.8141431767 -2.13% 11.082780262 1.48% 14.3263218333 -0.49% 16.9768372316 -1.32% 14.5914182312 0.17% 17.4270656242 -0.17% 17.376781986 -0.67% 16.6224637546 0.00% 17.4479855906 -2.72% 8.4106778477 -1.04% 15.5973524106 -1.05% 15.5620023017 1.22% 15.2840019368 -2.11% 11.2103719255 2.28% 10.8284637201 2.90% 7.9864730952 0.50% 17.1041263695 0.67% 16.8165157852 -2.53% 9.2630840667 0.00% 17.4479855906 -1.20% 15.0383968616 1.37% 14.7461967607 2.19% 11.2366022688 0.66% 16.8231640892 -2.18% 10.884705413 -0.34% 17.2064446939 0.68% 16.7982905733 -0.85% 16.1717648179 0.68% 16.7959603039 0.17% 17.4260374054 -0.51% 16.9489283457 0.68% 16.8006090825 -0.17% 17.3751964787 1.17% 15.4507636717 0.17% 17.4269539347 -0.67% 16.6224637546 3.13% 7.0098394467 -0.33% 17.2235810794 1.78% 13.1048403841 0.16% 17.4295684325 -1.12% 15.3093683975 1.44% 14.4747840469 1.11% 15.6628929853

126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169

Aug/09/2018 Aug/10/2018 Aug/13/2018 Aug/14/2018 Aug/15/2018 Aug/16/2018 Aug/17/2018 Aug/21/2018 Aug/22/2018 Aug/23/2018 Aug/24/2018 Aug/27/2018 Aug/28/2018 Aug/29/2018 Aug/30/2018 Aug/31/2018 Sep/03/2018 Sep/04/2018 Sep/05/2018 Sep/06/2018 Sep/07/2018 Sep/10/2018 Sep/11/2018 Sep/12/2018 Sep/13/2018 Sep/14/2018 Sep/17/2018 Sep/18/2018 Sep/19/2018 Sep/20/2018 Sep/21/2018 Sep/24/2018 Sep/25/2018 Sep/26/2018 Sep/27/2018 Sep/28/2018 Oct/01/2018 Oct/02/2018 Oct/03/2018 Oct/04/2018 Oct/05/2018 Oct/08/2018 Oct/09/2018 Oct/10/2018

3,030 3,070 3,060 3,100 3,000 3,065 3,095 3,140 3,220 3,240 3,270 3,305 3,330 3,385 3,445 3,420 3,395 3,455 3,430 3,390 3,410 3,410 3,480 3,820 3,765 3,790 3,870 3,940 3,850 3,715 3,680 3,900 3,930 3,925 3,980 4,010 4,150 4,105 4,160 4,080 4,015 3,990 4,080 4,015

-4.67% 2.0708229033 1.31% 14.9700836813 -0.33% 17.2222832365 1.30% 15.016252488 -3.28% 6.061915519 2.14% 11.45285959 0.97% 16.0693737092 1.44% 14.4747840469 2.52% 9.7326985303 0.62% 16.9102816229 0.92% 16.2153523752 1.06% 15.8002784189 0.75% 16.6338332258 1.64% 13.6904970531 1.76% 13.1856698193 -0.73% 16.4798798642 -0.73% 16.4668012869 1.75% 13.2078104014 -0.73% 16.485036084 -1.17% 15.14054858 0.59% 16.9663066709 0.00% 17.4479855906 2.03% 11.9630922758 9.32% 0.0046364041 -1.45% 14.0888973095 0.66% 16.8284117341 2.09% 11.703715699 1.79% 13.0311453138 -2.31% 10.2600837302 -3.57% 4.9986927892 -0.95% 15.8832800097 5.81% 0.7290538181 0.77% 16.6049650427 -0.13% 17.4016876161 1.39% 14.6735441306 0.75% 16.6397759343 3.43% 5.8257231181 -1.09% 15.4254768718 1.33% 14.899209072 -1.94% 11.9601948113 -1.61% 13.4435965031 -0.62% 16.7177054812 2.23% 11.0514981941 -1.61% 13.4435965031

170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213

Oct/11/2018 Oct/12/2018 Oct/16/2018 Oct/17/2018 Oct/18/2018 Oct/19/2018 Oct/22/2018 Oct/23/2018 Oct/24/2018 Oct/25/2018 Oct/26/2018 Oct/29/2018 Oct/30/2018 Oct/31/2018 Nov/01/2018 Nov/02/2018 Nov/06/2018 Nov/07/2018 Nov/08/2018 Nov/09/2018 Nov/13/2018 Nov/14/2018 Nov/15/2018 Nov/16/2018 Nov/19/2018 Nov/20/2018 Nov/21/2018 Nov/22/2018 Nov/23/2018 Nov/26/2018 Nov/27/2018 Nov/28/2018 Nov/29/2018 Nov/30/2018 Dec/03/2018 Dec/04/2018 Dec/05/2018 Dec/06/2018 Dec/07/2018 Dec/10/2018 Dec/11/2018 Dec/12/2018 Dec/13/2018 Dec/14/2018

3,900 3,950 3,970 3,965 3,925 3,950 3,960 3,845 3,685 3,705 3,755 3,690 3,750 3,740 3,465 3,430 3,440 3,480 3,425 3,440 3,240 3,250 3,280 3,275 3,190 3,060 3,150 3,140 3,020 3,075 3,140 3,115 3,110 3,105 3,290 3,160 3,220 3,100 3,100 3,020 2,980 3,015 2,960 2,940

-2.91% 7.5832412037 1.27% 15.1050024411 0.51% 17.1022152876 -0.13% 17.4024230948 -1.01% 15.6746788959 0.63% 16.8807095179 0.25% 17.3797332354 -2.95% 7.4086256983 -4.25% 2.9857604287 0.54% 17.0456768876 1.34% 14.8640470634 -1.75% 12.8367547699 1.61% 13.7953046092 -0.27% 17.2891949756 -7.64% 0.0615515491 -1.02% 15.6705882585 0.29% 17.3509158214 1.16% 15.5086019481 -1.59% 13.4982184613 0.44% 17.1972648109 -5.99% 0.5349668276 0.31% 17.3365336916 0.92% 16.2230170831 -0.15% 17.3861119663 -2.63% 8.7998079395 -4.16% 3.2117798138 2.90% 8.0081132362 -0.32% 17.23233845 -3.90% 3.9457481008 1.80% 12.9779796074 2.09% 11.6902541686 -0.80% 16.2996036755 -0.16% 17.3806774778 -0.16% 17.380500228 5.79% 0.744455585 -4.03% 3.5576290693 1.88% 12.6425758 -3.80% 4.2466822524 0.00% 17.4479855906 -2.61% 8.8682009798 -1.33% 14.5492257352 1.17% 15.4703125112 -1.84% 12.4152505861 -0.68% 16.599206335

214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257

Dec/17/2018 Dec/18/2018 Dec/19/2018 Dec/20/2018 Dec/21/2018 Dec/24/2018 Dec/26/2018 Dec/27/2018 Dec/28/2018 Jan/02/2019 Jan/03/2019 Jan/04/2019 Jan/08/2019 Jan/09/2019 Jan/10/2019 Jan/11/2019 Jan/14/2019 Jan/15/2019 Jan/16/2019 Jan/17/2019 Jan/18/2019 Jan/21/2019 Jan/22/2019 Jan/23/2019 Jan/24/2019 Jan/25/2019 Jan/28/2019 Jan/29/2019 Jan/30/2019 Jan/31/2019 Feb/01/2019 Feb/04/2019 Feb/05/2019 Feb/06/2019 Feb/07/2019 Feb/08/2019 Feb/11/2019 Feb/12/2019 Feb/13/2019 Feb/14/2019 Feb/15/2019 Feb/18/2019 Feb/19/2019 Feb/20/2019

2,875 2,835 2,815 2,615 2,665 2,550 2,720 2,715 2,645 2,650 2,670 2,810 2,890 2,935 2,935 2,900 2,910 2,930 2,930 2,910 2,895 2,900 2,900 2,825 2,835 2,860 2,815 2,850 2,915 2,920 2,935 2,920 2,950 2,920 2,865 2,865 2,840 2,925 2,955 2,965 3,055 3,065 3,050 3,085

-2.24% 10.6075607087 -1.40% 14.2853123602 -0.71% 16.5289969369 -7.37% 0.0905826568 1.89% 12.5844971947 -4.41% 2.6096950369 6.45% 0.3430470707 -0.18% 17.3637766432 -2.61% 8.879213022 0.19% 17.4171068201 0.75% 16.6376606288 5.11% 1.4988481493 2.81% 8.4118449548 1.55% 14.0727144723 0.00% 17.4479855906 -1.20% 15.0457841551 0.34% 17.3029693369 0.68% 16.7817273033 0.00% 17.4479855906 -0.68% 16.5831323155 -0.52% 16.9315626188 0.17% 17.4244560913 0.00% 17.4479855906 -2.62% 8.8424400605 0.35% 17.2938078379 0.88% 16.3316128909 -1.59% 13.5284289148 1.24% 15.2392301249 2.26% 10.9381992321 0.17% 17.4249552729 0.51% 17.0911018586 -0.51% 16.939571988 1.02% 15.9290194425 -1.02% 15.6485282837 -1.90% 12.1429248756 0.00% 17.4479855906 -0.88% 16.0886608671 2.95% 7.7893324489 1.02% 15.9341912378 0.34% 17.3092312031 2.99% 7.6117532018 0.33% 17.3197260287 -0.49% 16.9782376521 1.14% 15.5580337087

258 259 260 261 262 263

Feb/21/2019 Feb/22/2019 Feb/25/2019 Feb/26/2019 Feb/27/2019 Feb/28/2019

3,060 3,080 3,145 3,195 3,230 3,120

-0.81% 16.2616250828 0.65% 16.8487912485 2.09% 11.7056353691 1.58% 13.9417903107 1.09% 15.7229369968 -3.46% 5.3679139052

esa: ECOPETROL Desviación estándar

2.29%

Valor en riesgo VAR al 99%

4.48%

VAR a 10 días VAR al 99%

Nº desvíos por nivel de confianza Nivel de confianza Desvíos 90% 1.645 95% 1.96 99% 2.576

14.17%

Limites Superior Inferior

medidas de tendecia central 3,260 2,980

media mediana

# veces que el precio de la accion rompe el limite Superior 58 Inferior 110

0.05% 0.00%

% de veces que el precio de la accion rompe el limite Superior 2% Inferior 4%

Distribucion Normal 20 18 16 Distribucion Normal

14 12 10 8 6 4 2 -10.00%

-5.00%

0 0.00%

5.00%

Retorno Diario

10.00%

15.00%

15.00%

Dia

Precio Cierre

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

2,770.000 2,665.000 2,485.000 2,500.000 2,430.000 2,335.000 2,455.000 2,420.000 2,385.000 2,500.000 2,490.000 2,485.000 2,480.000 2,485.000 2,475.000 2,565.000 2,625.000 2,655.000 2,630.000 2,510.000 2,480.000 2,480.000 2,510.000 2,505.000 2,450.000 2,475.000 2,505.000 2,480.000 2,505.000 2,505.000 2,535.000 2,590.000 2,670.000 2,750.000 2,620.000 2,700.000 2,775.000

Limite inferior

Limite Superior

Errores

2593.24322 2494.94339 2326.42939 2340.47222 2274.939 2186.00105 2298.34372 2265.57711 2232.8105 2340.47222 2331.11033 2326.42939 2321.74844 2326.42939 2317.0675 2401.3245 2457.49583 2485.5815 2462.17678 2349.83411 2321.74844 2321.74844 2349.83411 2345.15317 2293.66278 2317.0675 2345.15317 2321.74844 2345.15317 2345.15317 2373.23883 2424.72922 2499.62433 2574.51944 2452.81489 2527.71

2946.75678 2835.05661 2643.57061 2659.52778 2585.061 2483.99895 2611.65628 2574.42289 2537.1895 2659.52778 2648.88967 2643.57061 2638.25156 2643.57061 2632.9325 2728.6755 2792.50417 2824.4185 2797.82322 2670.16589 2638.25156 2638.25156 2670.16589 2664.84683 2606.33722 2632.9325 2664.84683 2638.25156 2664.84683 2664.84683 2696.76117 2755.27078 2840.37567 2925.48056 2787.18511 2872.29

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0

1

8 15 22 2

38 39 40 41 42 43 44 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

2,645.000 2,615.000 2,690.000 2,730.000 2,740.000 2,740.000 2,730.000 2,745.000 2,790.000 2,980.000 2,955.000 2,835.000 2,760.000 2,870.000 2,935.000 3,030.000 3,030.000 3,085.000 3,060.000 3,045.000 3,010.000 3,070.000 3,100.000 3,105.000 3,100.000 3,095.000 3,030.000 3,085.000 3,160.000 3,100.000 3,135.000 3,290.000 3,205.000 3,170.000 3,150.000 3,125.000 3,110.000 3,025.000 3,070.000 2,955.000 2,900.000 3,030.000 3,120.000 3,090.000

2597.92417 2476.21961 2448.13394 2518.34811 2555.79567 2565.15755 2565.15755 2555.79567 2569.8385 2611.967 2789.84289 2766.43817 2654.0955 2583.88133 2686.86211 2747.71439 2836.65233 2836.65233 2888.14272 2864.738 2850.69517 2817.92855 2874.09989 2902.18555 2906.8665 2902.18555 2897.50461 2836.65233 2888.14272 2958.35689 2902.18555 2934.95217 3080.06144 3000.48539 2967.71878 2948.995 2925.59028 2911.54744 2831.97139 2874.09989 2766.43817 2714.94778 2836.65233 2920.90933

2952.07583 2813.78039 2781.86606 2861.65189 2904.20433 2914.84245 2914.84245 2904.20433 2920.1615 2968.033 3170.15711 3143.56183 3015.9045 2936.11867 3053.13789 3122.28561 3223.34767 3223.34767 3281.85728 3255.262 3239.30483 3202.07145 3265.90011 3297.81445 3303.1335 3297.81445 3292.49539 3223.34767 3281.85728 3361.64311 3297.81445 3335.04783 3499.93856 3409.51461 3372.28122 3351.005 3324.40972 3308.45256 3218.02861 3265.90011 3143.56183 3085.05222 3223.34767 3319.09067

0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

82 83 84 85 86 87 88 89 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

3,110.000 3,080.000 3,015.000 3,060.000 3,045.000 3,005.000 3,010.000 3,005.000 2,985.000 2,985.000 2,905.000 2,875.000 2,845.000 2,880.000 2,820.000 2,885.000 2,970.000 2,985.000 3,005.000 2,930.000 2,930.000 2,895.000 2,935.000 3,000.000 3,020.000 2,955.000 2,945.000 2,965.000 2,940.000 2,960.000 2,965.000 2,950.000 2,970.000 2,965.000 3,000.000 3,005.000 2,985.000 3,080.000 3,070.000 3,125.000 3,130.000 3,095.000 3,140.000 3,175.000

2892.82367 2911.54744 2883.46178 2822.6095 2864.738 2850.69517 2813.24761 2817.92855 2813.24761 2794.52383 2794.52383 2719.62872 2691.54305 2663.45739 2696.224 2640.05267 2700.90494 2780.481 2794.52383 2813.24761 2743.03344 2743.03344 2710.26683 2747.71439 2808.56667 2827.29044 2766.43817 2757.07628 2775.80005 2752.39533 2771.11911 2775.80005 2761.75722 2780.481 2775.80005 2808.56667 2813.24761 2794.52383 2883.46178 2874.09989 2925.59028 2930.27122 2897.50461 2939.63311

3287.17633 3308.45256 3276.53822 3207.3905 3255.262 3239.30483 3196.75239 3202.07145 3196.75239 3175.47617 3175.47617 3090.37128 3058.45695 3026.54261 3063.776 2999.94733 3069.09506 3159.519 3175.47617 3196.75239 3116.96656 3116.96656 3079.73317 3122.28561 3191.43333 3212.70956 3143.56183 3132.92372 3154.19995 3127.60467 3148.88089 3154.19995 3138.24278 3159.519 3154.19995 3191.43333 3196.75239 3175.47617 3276.53822 3265.90011 3324.40972 3329.72878 3292.49539 3340.36689

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169

3,030.000 3,070.000 3,060.000 3,100.000 3,000.000 3,065.000 3,095.000 3,140.000 3,220.000 3,240.000 3,270.000 3,305.000 3,330.000 3,385.000 3,445.000 3,420.000 3,395.000 3,455.000 3,430.000 3,390.000 3,410.000 3,410.000 3,480.000 3,820.000 3,765.000 3,790.000 3,870.000 3,940.000 3,850.000 3,715.000 3,680.000 3,900.000 3,930.000 3,925.000 3,980.000 4,010.000 4,150.000 4,105.000 4,160.000 4,080.000 4,015.000 3,990.000 4,080.000 4,015.000

2972.39972 2836.65233 2874.09989 2864.738 2902.18555 2808.56667 2869.41894 2897.50461 2939.63311 3014.52822 3033.252 3061.33767 3094.10428 3117.509 3168.99939 3225.17072 3201.766 3178.36128 3234.53261 3211.12789 3173.68033 3192.40411 3192.40411 3257.93733 3576.24155 3524.75116 3548.15589 3623.051 3688.58422 3604.32722 3477.94172 3445.17511 3651.13666 3679.22233 3674.54139 3726.03178 3754.11744 3885.18389 3843.05539 3894.54578 3819.65066 3758.79839 3735.39366 3819.65066

3377.60028 3223.34767 3265.90011 3255.262 3297.81445 3191.43333 3260.58106 3292.49539 3340.36689 3425.47178 3446.748 3478.66233 3515.89572 3542.491 3601.00061 3664.82928 3638.234 3611.63872 3675.46739 3648.87211 3606.31967 3627.59589 3627.59589 3702.06267 4063.75845 4005.24884 4031.84411 4116.949 4191.41578 4095.67278 3952.05828 3914.82489 4148.86334 4180.77767 4175.45861 4233.96822 4265.88256 4414.81611 4366.94461 4425.45422 4340.34934 4271.20161 4244.60634 4340.34934

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213

3,900.000 3,950.000 3,970.000 3,965.000 3,925.000 3,950.000 3,960.000 3,845.000 3,685.000 3,705.000 3,755.000 3,690.000 3,750.000 3,740.000 3,465.000 3,430.000 3,440.000 3,480.000 3,425.000 3,440.000 3,240.000 3,250.000 3,280.000 3,275.000 3,190.000 3,060.000 3,150.000 3,140.000 3,020.000 3,075.000 3,140.000 3,115.000 3,110.000 3,105.000 3,290.000 3,160.000 3,220.000 3,100.000 3,100.000 3,020.000 2,980.000 3,015.000 2,960.000 2,940.000

3758.79839 3651.13666 3697.94611 3716.66989 3711.98894 3674.54139 3697.94611 3707.308 3599.64628 3449.85605 3468.57983 3515.38928 3454.537 3510.70833 3501.34644 3243.8945 3211.12789 3220.48978 3257.93733 3206.44694 3220.48978 3033.252 3042.61389 3070.69955 3066.01861 2986.44255 2864.738 2948.995 2939.63311 2827.29044 2878.78083 2939.63311 2916.22839 2911.54744 2906.8665 3080.06144 2958.35689 3014.52822 2902.18555 2902.18555 2827.29044 2789.84289 2822.6095 2771.11911

4271.20161 4148.86334 4202.05389 4223.33011 4218.01106 4175.45861 4202.05389 4212.692 4090.35372 3920.14395 3941.42017 3994.61072 3925.463 3989.29167 3978.65356 3686.1055 3648.87211 3659.51022 3702.06267 3643.55306 3659.51022 3446.748 3457.38611 3489.30045 3483.98139 3393.55745 3255.262 3351.005 3340.36689 3212.70956 3271.21917 3340.36689 3313.77161 3308.45256 3303.1335 3499.93856 3361.64311 3425.47178 3297.81445 3297.81445 3212.70956 3170.15711 3207.3905 3148.88089

0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257

2,875.000 2,835.000 2,815.000 2,615.000 2,665.000 2,550.000 2,720.000 2,715.000 2,645.000 2,650.000 2,670.000 2,810.000 2,890.000 2,935.000 2,935.000 2,900.000 2,910.000 2,930.000 2,930.000 2,910.000 2,895.000 2,900.000 2,900.000 2,825.000 2,835.000 2,860.000 2,815.000 2,850.000 2,915.000 2,920.000 2,935.000 2,920.000 2,950.000 2,920.000 2,865.000 2,865.000 2,840.000 2,925.000 2,955.000 2,965.000 3,055.000 3,065.000 3,050.000 3,085.000

2752.39533 2691.54305 2654.0955 2635.37172 2448.13394 2494.94339 2387.28167 2546.43378 2541.75283 2476.21961 2480.90055 2499.62433 2630.69078 2705.58589 2747.71439 2747.71439 2714.94778 2724.30967 2743.03344 2743.03344 2724.30967 2710.26683 2714.94778 2714.94778 2644.73361 2654.0955 2677.50022 2635.37172 2668.13833 2728.99061 2733.67155 2747.71439 2733.67155 2761.75722 2733.67155 2682.18117 2682.18117 2658.77644 2738.3525 2766.43817 2775.80005 2860.05705 2869.41894 2855.37611

3127.60467 3058.45695 3015.9045 2994.62828 2781.86606 2835.05661 2712.71833 2893.56622 2888.24717 2813.78039 2819.09945 2840.37567 2989.30922 3074.41411 3122.28561 3122.28561 3085.05222 3095.69033 3116.96656 3116.96656 3095.69033 3079.73317 3085.05222 3085.05222 3005.26639 3015.9045 3042.49978 2994.62828 3031.86167 3101.00939 3106.32845 3122.28561 3106.32845 3138.24278 3106.32845 3047.81883 3047.81883 3021.22356 3111.6475 3143.56183 3154.19995 3249.94295 3260.58106 3244.62389

0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

258 259 260 261 262 263

3,060.000 3,080.000 3,145.000 3,195.000 3,230.000 3,120.000

2888.14272 2864.738 2883.46178 2944.31405 2991.1235 3023.89011

3281.85728 3255.262 3276.53822 3345.68595 3398.8765 3436.10989

0 0 0 0 0 0 6

Retabilidad 12.64% nivel de confianza 99% VAR Modelo de Simulación H 6.38% total errores 6 error porcentual 2.3% eficiencia eficiente

BACKTESTING ECOPETROL 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0

1

8 15 22 29 36 43 50 57 64 71 78 85 92 99 06 13 20 27 34 41 48 55 62 69 76 83 90 97 04 11 18 25 32 39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2

Di a

Preci o Ci erre

Li mi te i nferi or

Li mi te Superi or

En esta grafica se puede observar la representacion del Backtesting. Se graficaron los valores de la ac ecopetrol del año bursatil anterior junto con los limites inferiores y superiores para cada dia. el morado representa el limite superior, el rojo el valor de accion en cada dia y el verde el limite inferior. Lo que aq puede observar es que la accion muy rara la vez sobrepasa estos limites.

OL

9 76 83 90 97 04 11 18 25 32 39 46 53 60 1 1 1 1 2 2 2 2 2 2 2 2 2

Li mi te Superi or

graficaron los valores de la accion de res para cada dia. el morado de el limite inferior. Lo que aqui se

Para un nivel de confianza del 99% las acciones de inversion de Ecopetrol presentan un VAR segun el modelo de Simulación Historica que puede ser positiva o negativa en un dia del 6.38%. Por otro lado se pudo corroborar la importancia de utilizar este tipo de calculos para saber cual sera el comportamiento a futuro de nuestras acciones y portafolios, utilizando de la manera correcta, estas herramientas y procedimientos nuestro dinero o el de otras personas que asesoremos, de alguna forma podra estar protegido.

Bibliografia https://www.ecopetrol.com.co/wps/portal/es/ecopetrol-web/historico-de-la-accion