Examen Aux I 2019.xlsx

S X r T Sigma d1 d2 N(d1) N(d2)

85 final 85 inicio 0.08% 12/8/2018 8/15/2021 2.69 12% 0.10929412 -0.0874353 0.5435154 N(-d1) 0.4564846 0.46516276 N(-d2) 0.53483724

Call Price Put price put price

t 981.00

6.74 6.56 6.562

12 10 8 6

6.74 6.56

4 2 0 0

20

40

60

80

100

120

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

call price put price 6.74 6.56

Problema 5. (20 pts.) Aplique el método binomial múltiples pasos a los datos siguientes, calculando el precio put y call tanto europeo y americano (genere la gráfica correspondiente): Bajo el esquema: VARIABLES Número de períodos 7 Precio del activo subyacente: 51,25 Precio de ejercicio: 50,00 Tasa de interés sin riesgo a corto plazo: 10,00% Movimiento multiplicativo al alza: 1,5024 Movimiento multiplicativo a la baja: 0,8976 Stock price

r*=r+1 P

(r*-d)/(u-d)

??? ??? ??? ??? 40 ??? ??? ??? ??? ???

n precio subya precio ejercic tasa de inter up u d down

p 1-p

r* 0.33465608 0.66534392

7 51.25 50 10% 150.24% call price 89.76%

115.681795 518.785246 76.998 471.622951 51.25 428.748137

69.1134048 297.447401 46.002 270.406728

110%

41.2913952 165.210414

0

1

2

115.681795 0.23387369 76.998 0.23308076 put price

51.25 0.23332199

69.1134048 0.23387369 46.002 0.23308076 41.2913952 0.23387369

885.508826 835.508826 589.396183 759.553478 392.303104 690.503162 261.117614 627.730147 173.800329 570.66377

529.042014 479.042014 352.131266 435.49274

234.379171 395.902491 156.003175 359.911356

103.835979 327.192141

316.073024 266.073024 210.378744 241.884568

140.02845 219.895062 93.2031751 199.904601

62.0361921 181.731456

188.83596 138.83596 125.689537 126.214509

83.65917 114.740463 55.6836861 104.309512

37.0631563 94.826829

112.818928 62.8189284 75.092471 57.1081167

49.9816766 51.9164697 33.2678891 759.553478

67.4030019 17.4030019 44.8635529 15.8209108

29.8612573 14.3826462

40.2695251 0 26.8034645 0 24.0587898 0

3

4

5

6

7 885.508826 0

589.396183 0.3042328 392.303104 0.21167521

529.042014 0

261.117614 0.23983426 173.800329 0.23126735

352.131266 0.3042328 234.379171 0.21167521

156.003175 0.23983426 103.835979 0.23126735

316.073024 0 210.378744 0.3042328

140.02845 0.21167521 93.2031751 0.23983426

62.0361921 0.23126735

188.83596 0 125.689537 0.3042328

83.65917 0.21167521 55.6836861 0.23983426

37.0631563 0.23126735

112.818928 0 75.092471 0.3042328

49.9816766 0.21167521 33.2678891 0.23983426

67.4030019 0 44.8635529 0.3042328

29.8612573 0.21167521

40.2695251 9.73047489 26.8034645 -2.6560969 24.0587898 25.9412102

Problema 4. (30Pts). Del vínculo siguiente: https://finance.yahoo.com/ Del índice de Bolsa Dow Jones Industrial Average, extraer la información histórica desde 02 de Enero del 2018 al 07 de Diciembre de 2018 (precio de cierre) de sus siguientes componentes: 1. JNJ Johnson & Johnson 2. CSCO Cisco Systems, Inc. 3. KO The Coca-Cola Company 4. MMM 3M Company 5. TRV The Travelers Companies, Inc. 6. PG The Procter & Gamble Company 7. AAPL Apple Inc. 8. WMT Walmart Inc. 9. JPM JPMorgan Chase & Co. 10. HD The Home Depot, Inc. Y con ellos conformar el portafolio correspondiente, además de la elaboración de la frontera eficiente.

fecha JNJ 49 Jan 01, 2018 48 Jan 08, 2018 47 Jan 15, 2018 46 Jan 22, 2018 45 Jan 29, 2018 44 Feb 05, 2018 43 Feb 12, 2018 42 Feb 19, 2018 41 Feb 26, 2018 40 Mar 05, 2018 39 Mar 11, 2018 38 Mar 18, 2018 37 Mar 25, 2018 36 Apr 01, 2018 35 Apr 08, 2018 34 Apr 15, 2018 33 Apr 22, 2018 32 Apr 29, 2018 31 May 06, 2018 30 May 13, 2018 29 May 20, 2018 28 May 27, 2018 27 Jun 03, 2018 26 Jun 10, 2018 25 Jun 17, 2018 24 Jun 24, 2018

CSCO 141.71 145.76 147.36 145.33 137.68 129.53 133.15 132.02 128.82 133.8 133.68 125.1 128.15 128.1 130.62 126.66 128.27 124.19 127.24 124.24 121.47 121.26 124.06 122.61 122.84 121.34

KO 39.53 40.87 41.29 42.56 40.93 39.53 44.33 44 44.06 45.37 45.01 42.42 42.89 40.73 43 44.09 44.71 45.3 45.93 43.21 43.26 43.66 43.48 44.25 43.2 43.03

MMM TRV 46.07 240.57 46.15 244.47 47.16 248.18 48.53 258.63 46.73 245.17 43.13 225.21 44.98 236.67 44.04 237.02 43.72 230.37 44.82 241.35 43.46 237.22 42.33 215.36 43.43 219.52 43.92 212.25 44.51 215.52 43.74 217.75 43.31 196.12 42.36 199.36 42.14 205.16 42.18 198.96 42.4 199.03 43.12 199.59 43.95 206.59 44.12 204.97 43.25 196.5 43.86 196.72

PG 132.16 134.73 137.85 149.42 147.95 137.08 141.16 139.74 137.88 142.3 141.32 134.9 138.86 137.25 136.29 136.84 133.19 129.71 131.25 129.85 131.03 129.29 131.32 129.37 124.41 122.34

91.24 89.61 91.07 87.73 84.25 79.92 82.6 81.05 79.5 80.29 78.97 75.91 79.28 78.43 78.37 73.8 72.81 72.43 73.37 73.45 74.31 73.45 77.18 77.38 77.43 78.06

23 Jul 01, 2018 22 Jul 08, 2018 21 Jul 15, 2018 20 Jul 22, 2018 19 Jul 29, 2018 18 Aug 05, 2018 17 Aug 12, 2018 16 Aug 19, 2018 15 Aug 26, 2018 14 Sep 02, 2018 13 Sep 09, 2018 12 Sep 16, 2018 11 Sep 23, 2018 10 Sep 30, 2018 9 Oct 07, 2018 8 Oct 14, 2018 7 Oct 21, 2018 6 Oct 28, 2018 5 Nov 05, 2018 4 Nov 12, 2018 3 Nov 19, 2018 2 Nov 26, 2018 1 Dec 03, 2018

125.75 125.93 125.85 131.55 131.95 130.75 134.47 135.95 134.69 137.32 139.49 142.88 138.17 139.1 133.87 139.05 136.97 140.68 145.34 145.99 142.23 146.9 145.91

42.71 41.78 42.01 42.57 42.83 43.78 45.87 46.32 47.77 47.05 47.4 48.56 48.65 48.13 45.71 45.34 44.25 45.48 47.11 46.35 44.54 47.87 48.39

44.64 44.74 45.28 46.21 46.62 46.08 46.6 45.63 44.57 45.72 45.99 46.58 46.19 45.88 44.68 46.33 45.92 48 49.68 50.17 49.02 50.4 49.38

197.46 201.18 201.95 207.42 207.29 201.96 204.77 205.29 210.92 212.57 207.88 216.33 210.71 213.19 198.23 199.85 184.95 192.81 201.1 209 196.8 207.92 202.68

123.18 126.63 125.2 130.73 129.7 128.87 130.42 130.51 131.6 130.09 130.01 134.44 129.71 130.13 123.65 126.07 121.29 124.9 131.03 128.77 126.6 130.37 125.41

79.31 79.31 78.68 80.58 82.33 81.43 83.69 83.36 82.95 81.91 83.61 85.82 83.23 82.15 79.06 87.3 87.86 89.81 92.41 93.82 91.54 94.51 93.55

AAPL

WMT 175 177.09 178.46 171.51 160.5 156.41 172.43 175.5 176.21 179.98 178.02 164.94 167.78 168.38 174.73 165.72 162.32 183.83 188.59 186.31 188.58 190.24 191.7 188.84 184.92 185.11

JPM 100.13 100.87 104.59 108.39 104.48 99.37 104.78 92.89 88.77 88.72 89.17 85.42 88.97 86.69 86.02 86.98 87.29 87.53 83.38 83.64 82.46 82.99 84.36 83.7 84.82 85.65

HD 108.34 112.67 113.01 116.32 114.28 110.04 114.68 117.31 113.32 118.04 115.44 107.01 109.97 109.09 110.3 111.47 109.4 108.43 113.86 111.13 110.66 108.4 111.11 107.9 105.75 104.2

192.5 196.42 201.33 207.23 193.97 184.12 186.97 188.35 178.46 182.16 178.96 171.8 178.24 174.45 172.8 177.01 186.46 185.03 190.31 187.42 186.85 187.35 198.33 200.54 197.41 195.1

a

b

c

JNJ

CSCO

KO

0.02857949 0.01097695 -0.0137758 -0.0526388 -0.0591952 0.02794719 -0.0084867 -0.0242388 0.03865859 -0.0008969 -0.0641831 0.0243805 -0.0003902 0.01967213 -0.0303169 0.0127112 -0.0318079 0.02455914 -0.0235775 -0.0222956 -0.0017288 0.02309088 -0.0116879 0.00187587 -0.012211

0.03389831 0.01027649 0.03075805 -0.0382989 -0.0342047 0.12142676 -0.0074442 0.00136364 0.02973218 -0.0079348 -0.0575428 0.01107968 -0.0503614 0.05573288 0.02534884 0.01406215 0.01319615 0.01390728 -0.0592206 0.00115714 0.00924642 -0.0041228 0.01770929 -0.0237288 -0.0039352

0.00173649 0.02188516 0.02905004 -0.0370905 -0.0770383 0.04289358 -0.0208982 -0.0072661 0.02516011 -0.0303436 -0.0260009 0.0259863 0.01128252 0.01343352 -0.0172995 -0.0098308 -0.0219349 -0.0051936 0.00094922 0.00521574 0.01698113 0.01924861 0.00386803 -0.0197189 0.01410405

187.97 191.33 191.44 190.98 207.99 207.53 217.58 216.16 227.63 221.3 223.84 217.66 225.74 224.29 222.11 219.31 216.3 207.48 204.47 193.53 172.29 178.58 174.72

84.51 87.7 88.06 88.13 89.6 90.18 97.85 94.95 95.86 95.83 94.59 95.9 93.91 93.31 94.81 97.15 98.94 101.34 105.56 97.69 95.1 97.65 94.77

104.06 106.36 111.28 116.03 117.09 115.73 114.77 114.68 114.58 114.32 113.5 117.85 112.84 114.62 106.95 107.91 103.42 108.38 111.29 109.99 106.65 111.19 105.19

194.48 198.69 202.45 197.14 195.64 196.3 195.56 201.3 200.77 206.23 209.07 212.39 207.15 196.38 192.47 179.85 172.23 179.93 185.99 177.02 168.85 180.32 175.96

0.03634416 0.00143141 -0.0006353 0.04529201 0.00304067 -0.0090944 0.02845124 0.01100617 -0.0092681 0.01952632 0.01580251 0.02430282 -0.0329647 0.00673084 -0.0375988 0.03869426 -0.0149586 0.02708622 0.03312482 0.00447227 -0.0257552 0.03283414 -0.0067393

-0.0074367 -0.0217748 0.00550503 0.01333016 0.00610759 0.02218071 0.04773869 0.00981033 0.03130397 -0.0150722 0.00743889 0.02447257 0.00185338 -0.0106886 -0.0502805 -0.0080945 -0.0240406 0.02779661 0.03583993 -0.0161325 -0.0390507 0.07476426 0.01086275

a

b

0.01778386 0.00224014 0.01206974 0.02053887 0.00887254 -0.011583 0.01128472 -0.0208155 -0.0232303 0.02580211 0.00590551 0.01282888 -0.0083727 -0.0067114 -0.0261552 0.03692927 -0.0088496 0.04529617 0.035 0.00986312 -0.0229221 0.02815177 -0.0202381

c

d

e

f

g

h

i

j

MMM

TRV

PG

AAPL

WMT

JPM

HD

0.01944613 0.02315743 0.08393181 -0.009838 -0.0734708 0.02976364 -0.0100595 -0.0133104 0.03205686 -0.0068869 -0.0454288 0.02935508 -0.0115944 -0.0069945 0.00403551 -0.0266735 -0.0261281 0.01187264 -0.0106667 0.00908741 -0.0132794 0.01570114 -0.0148492 -0.0383396 -0.0166385

-0.017865 0.01629282 -0.0366751 -0.0396672 -0.0513947 0.03353353 -0.0187651 -0.019124 0.00993711 -0.0164404 -0.0387489 0.04439468 -0.0107215 -0.000765 -0.0583131 -0.0134146 -0.0052191 0.01297805 0.00109036 0.01170865 -0.0115731 0.05078285 0.00259134 0.00064616 0.00813638

0.01194286 0.00773618 -0.0389443 -0.0641945 -0.0254829 0.10242312 0.01780433 0.00404558 0.02139493 -0.0108901 -0.0734749 0.01721838 0.00357611 0.03771232 -0.0515653 -0.0205165 0.13251602 0.02589349 -0.0120897 0.01218399 0.00880263 0.00767452 -0.0149191 -0.0207583 0.00102747

0.03996677 0.00301766 0.02928944 -0.0175378 -0.0371019 0.04216648 0.02293338 -0.0340124 0.04165196 -0.0220264 -0.0730249 0.02766097 -0.0080022 0.01109176 0.01060743 -0.01857 -0.0088665 0.05007839 -0.0239768 -0.0042293 -0.0204229 0.025 -0.0288903 -0.0199259 -0.0146572

0.02036364 0.02499745 0.02930512 -0.0639869 -0.050781 0.01547904 0.00738086 -0.0525086 0.02073294 -0.017567 -0.0400089 0.03748545 -0.0212635 -0.0094583 0.02436343 0.05338681 -0.0076692 0.02853591 -0.0151857 -0.0030413 0.00267594 0.05860689 0.01114304 -0.0156079 -0.0117015

0.0162115 0.01517569 0.04210654 -0.0520435 -0.0814129 0.05088584 0.00147885 -0.0280567 0.04766246 -0.0171121 -0.0921507 0.01931649 -0.0331177 0.01540636 0.01034707 -0.0993341 0.0165205 0.0290931 -0.0302203 0.00035183 0.00281365 0.0350719 -0.0078416 -0.0413231 0.00111959

0.00739039 0.03687915 0.03633235 -0.0360734 -0.0489089 0.05444299 -0.1134759 -0.0443535 -0.0005633 0.00507214 -0.0420545 0.04155935 -0.0256266 -0.0077287 0.0111602 0.00356404 0.00274946 -0.0474123 0.00311825 -0.0141081 0.00642736 0.01650801 -0.0078236 0.01338112 0.00978543

0.00376169 0.01883926 0.00382742 0.02708591 -0.0006267 -0.0257128 0.01391365 0.00253943 0.02742462 0.00782287 -0.0220633 0.04064845 -0.0259788 0.01176973 -0.0701721 0.00817233 -0.0745559 0.04249797 0.0429957 0.03928394 -0.0583732 0.05650407 -0.025202

d

0.00686611 0.02800779 -0.0112927 0.04416933 -0.0078788 -0.0063994 0.01202762 0.00069008 0.00835185 -0.0114742 -0.000615 0.0340743 -0.035183 0.00323799 -0.0497964 0.01957137 -0.0379154 0.02976338 0.04907926 -0.017248 -0.0168518 0.02977883 -0.0380456

0.01601332 0 -0.0079435 0.02414845 0.02171755 -0.0109316 0.0277539 -0.0039431 -0.0049184 -0.0125377 0.02075449 0.02643224 -0.0301794 -0.0129761 -0.0376141 0.10422464 0.00641466 0.0221944 0.02895001 0.01525809 -0.0243019 0.03244483 -0.0101577

0.01545027 0.01787519 0.00057492 -0.0024028 0.08906692 -0.0022116 0.04842673 -0.0065263 0.05306255 -0.0278083 0.01147763 -0.027609 0.03712212 -0.0064233 -0.0097196 -0.0126064 -0.0137249 -0.0407767 -0.0145074 -0.0535042 -0.1097504 0.03650821 -0.021615

e

f

g

-0.01331 0.03774701 0.0041049 0.00079491 0.0166799 0.00647321 0.08505212 -0.0296372 0.00958399 -0.000313 -0.0129396 0.01384924 -0.0207508 -0.0063891 0.01607545 0.02468094 0.01842512 0.02425713 0.041642 -0.0745548 -0.0265124 0.02681388 -0.0294931

h

-0.0013436 0.02210263 0.04625799 0.04268512 0.00913557 -0.011615 -0.0082952 -0.0007842 -0.000872 -0.0022692 -0.0071728 0.03832599 -0.0425117 0.01577455 -0.0669168 0.00897616 -0.0416087 0.04795978 0.02684997 -0.0116812 -0.0303664 0.04256915 -0.0539617

i

-0.0031779 0.02164747 0.01892395 -0.0262287 -0.0076088 0.00337354 -0.0037697 0.02935161 -0.0026329 0.0271953 0.01377103 0.01587985 -0.0246716 -0.0519913 -0.0199104 -0.0655687 -0.0423686 0.04470766 0.03367976 -0.0482284 -0.046153 0.06793012 -0.0241792

j

JNJ CSCO KO MMM TRV PG AAPL WMT JPM HD

rendiemiento riesgo 0.0009613819 0.02644873 0.0047611486 0.0331122 0.0017264187 0.02355819 -0.0028051939 0.03848973 -0.0006840206 0.0285764 0.0009210046 0.02846853 0.0008228106 0.04163297 -0.0005724712 0.03356092 -0.0001362882 0.03084033 -0.0013406718 0.03245977

A JNJ A B C D E F G H

JNJ CSCO KO MMM TRV PG AAPL WMT

B

C

JNJ CSCO KO MMM TRV PG AAPL WMT JPM HD suma

pesos 0.02130311 0.04776155 0.48997968 0 0.02819692 0.1294169 0.11330761 0.04455476 0 0.12547945 1

D

E

F

CSCO KO MMM TRV PG 0.0006995356 0.00048532 0.00046263 0.00067451 0.00049033 0.00055518 0.00048532 0.00109642 0.00038892 0.00083691 0.00052218 0.00031724 0.0004626332 0.00038892 0.00055499 0.00062207 0.00048353 0.0004608 0.000674509 0.00083691 0.00062207 0.00148146 0.00086699 0.00056001 0.0004903331 0.00052218 0.00048353 0.00086699 0.00081661 0.00037982 0.0005551786 0.00031724 0.0004608 0.00056001 0.00037982 0.00081046 0.0003098628 0.00070973 0.00021131 0.00062815 0.00015837 0.00038303 0.0003543809 0.00049077 0.00040806 0.00042037 0.00045803 0.0003902

I J

JPM HD

0.000580302 0.00059965 0.00044305 0.00095637 0.00070011 0.00039992 0.0004236123 0.0005712 0.00035445 0.00061041 0.00047265 0.0001996

RENDIMIENTO RIESGO

0.00109319 0.021342 RENDIMIENTRIESGO

TABAL RESUMEN PESOS IGUALES MAX REDIMIENTO MIN RIESGO

JNJ 0.00036541 0.02319312 0.00476115 0.0331122 0.00068564 0.02125492

0.1 0 0.0221341

CSCO

KO 0.1 0.1 1 0 0 0.42072525

0.005

1 MAX 2 3 4 5 6 7 8 9 10 11 MIN

RIESGO RENDIMIENTO 0.0331122 0.00476115 0.03036684 0.0043536 0.0279174 0.00394605 0.0258482 0.0035385 0.02423986 0.00313095 0.02310221 0.0027234 0.02235313 0.00231585 0.02188176 0.0019083 0.02154071 0.00150074 0.021342 0.00109319 0.02125492 0.00068564

0.0045 0.004 0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0 0.02

G

H

I

J

AAPL WMT JPM HD 0.00030986 0.00035438 0.0005803 0.00042361 0.00070973 0.00049077 0.00059965 0.0005712 0.00021131 0.00040806 0.00044305 0.00035445 0.00062815 0.00042037 0.00095637 0.00061041 0.00015837 0.00045803 0.00070011 0.00047265 0.00038303 0.0003902 0.00039992 0.0001996 0.0017333 0.00040203 0.00037091 0.00032731 0.00040203 0.00112634 0.00029155 0.00042159

0.00037091 0.00029155 0.00095113 0.00058069 0.00032731 0.00042159 0.00058069 0.00105364

MMM

TRV

PG

AAPL

WMT

JPM

0.1 0.1 0.1 0.1 0.1 0 0 0 0 0 0 0.07899815 0.14109815 0.12429115 0.05866308

HD 0.1 0.1 0 0 0 0.15409013

0.005

0.00068564 0.0045

RANGO 0.004

0.00040755

0.0035 0.003 0.0025 0.002 0.0015 0.001 0.0005 0 0.02

0.022

0.024

0.026

0.028

0.03

0.032

0.034