Laboratorio N3

Se eliminan los mensajes de precaución y de descarga de paquetes.

options(warn = -1)
suppressPackageStartupMessages({
  library(tidyquant)
  library(quantmod)
  library(TTR)
  library(ROCR)
  library(knitr)
  library(plotly)
  library(ggplot2)
  library(moments)
  library(fPortfolio)
  library(pander)
  library(tidyr)
  library(ggthemes)
  library(PortfolioAnalytics)
  library(roptions)
})

1. Creación del portafolio óptimo de inversión

Para establecer un uso adecuado de los 10,000 dólares, es fundamental primero optimizar el portafolio correctamente. Para lograrlo, se requiere utilizar el portafolio óptimo de Markowitz, basado en un mínimo de 5 años de datos bursátiles diarios, con una fecha límite establecida en el 01/06/2023.

library(quantmod)
library(TTR)
library(ROCR)

Se crea un vector de acciones

s1 = c("BIIB", "ADSK", "ALGN")

Se descargan los precios y se crean los retornos de los precios ajustados

data1 = lapply(s1, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2018-06-01", to = "2024-04-17", auto.assign = FALSE)),
      type = "continuous")
})  #%returns

Se convierte a data frame

ret1 = as.data.frame(do.call(merge, data1))

Se renombran las columnas

colnames(ret1) = gsub(".Adjusted", "", colnames(ret1))

Se elimina la primera fila de los retornos

ret1 = ret1[-1, ]

Se agrega la columna de fechas

ret1 = data.frame(Date = as.Date(row.names(ret1)), ret1)
row.names(ret1) = NULL

Se grafican los datos

library(pander)
library(tidyr)
library(ggthemes)
ret1

##            Date          BIIB          ADSK          ALGN
## 1    2018-06-04  6.107428e-03  1.523685e-02  2.990069e-02
## 2    2018-06-05 -9.036533e-04  9.031863e-03  8.356522e-03
## 3    2018-06-06  1.696611e-02  8.226232e-03  8.376288e-04
## 4    2018-06-07  5.319145e-03 -2.786224e-02 -2.056392e-02
## 5    2018-06-08 -6.834667e-03  7.353292e-03  2.142972e-02
## 6    2018-06-11  1.111536e-02  6.196965e-03  5.092698e-03
## 7    2018-06-12 -1.599005e-03  1.017094e-02  1.653682e-02
## 8    2018-06-13  2.348727e-03 -1.457067e-03  2.574888e-02
## 9    2018-06-14 -4.015778e-03  9.072167e-03  7.618978e-03
## 10   2018-06-15 -2.128651e-03 -3.039069e-03 -9.904969e-03
## 11   2018-06-18 -5.356832e-02  2.342087e-02  2.030749e-02
## 12   2018-06-19  1.004900e-02 -1.558640e-03 -1.321861e-02
## 13   2018-06-20  1.636979e-02 -7.092064e-04 -1.479514e-03
## 14   2018-06-21  1.615655e-03 -2.296640e-02 -1.408281e-02
## 15   2018-06-22 -4.381641e-03 -8.970051e-03 -1.775971e-02
## 16   2018-06-25 -1.309033e-02 -5.078831e-02 -1.992719e-02
## 17   2018-06-26 -9.244458e-04  3.231751e-03  1.751827e-02
## 18   2018-06-27 -1.376247e-02 -1.978415e-02 -2.773484e-02
## 19   2018-06-28  2.843891e-03  2.032182e-02  2.971219e-03
## 20   2018-06-29  5.146871e-03  6.505139e-03 -4.840004e-03
## 21   2018-07-02  1.887396e-02  6.159935e-03 -5.451249e-03
## 22   2018-07-03 -7.670344e-03 -2.276950e-03 -4.713117e-03
## 23   2018-07-05  1.789617e-02  9.077195e-03  7.940553e-03
## 24   2018-07-06  1.792715e-01  1.724501e-02  1.768209e-02
## 25   2018-07-09 -9.782534e-03 -1.036730e-03  4.307628e-03
## 26   2018-07-10 -2.627435e-02 -4.455387e-03  7.081526e-03
## 27   2018-07-11 -2.090232e-03 -1.612994e-02 -7.368142e-03
## 28   2018-07-12  1.029267e-02  3.886581e-02  3.920752e-02
## 29   2018-07-13  2.355869e-03 -1.820367e-03  1.734906e-03
## 30   2018-07-16  1.297217e-02 -7.094577e-03 -3.224378e-03
## 31   2018-07-17  5.508445e-03  2.345991e-03  2.251702e-02
## 32   2018-07-18  9.895101e-03  6.350582e-03  4.792425e-03
## 33   2018-07-19 -1.116422e-03 -2.155045e-02 -5.359320e-03
## 34   2018-07-20  1.674078e-03 -1.339134e-03  1.357134e-02
## 35   2018-07-23 -1.618175e-03  1.339134e-03  5.631709e-03
## 36   2018-07-24  4.025330e-02 -1.641656e-02 -1.309196e-02
## 37   2018-07-25  2.905035e-02  2.640374e-02  2.433970e-02
## 38   2018-07-26 -1.074092e-01  2.132381e-03 -5.036041e-02
## 39   2018-07-27 -1.266910e-02 -3.726578e-02 -2.581095e-02
## 40   2018-07-30 -2.661427e-02 -3.223090e-02 -1.477923e-02
## 41   2018-07-31  8.741038e-03  1.127480e-02  2.288717e-02
## 42   2018-08-01  2.856791e-02 -9.858479e-03 -8.305762e-03
## 43   2018-08-02  1.118524e-02  3.081458e-02  3.941643e-02
## 44   2018-08-03 -1.074938e-02  6.762679e-03 -1.205872e-02
## 45   2018-08-06 -8.870985e-03  1.726772e-02  1.647918e-02
## 46   2018-08-07  2.583792e-02  6.232831e-03 -1.080092e-02
## 47   2018-08-08 -2.859224e-05 -7.797188e-03  1.721817e-03
## 48   2018-08-09 -9.153716e-03  7.205246e-03  1.800633e-03
## 49   2018-08-10 -1.130609e-02 -1.926175e-03 -6.398698e-03
## 50   2018-08-13 -6.463969e-03 -1.088593e-02 -6.191459e-03
## 51   2018-08-14  8.299033e-03  4.562639e-03  1.745743e-02
## 52   2018-08-15 -8.504483e-03 -2.226085e-02 -5.065674e-02
## 53   2018-08-16  6.465296e-03  2.024386e-02  2.137819e-03
## 54   2018-08-17  6.655574e-03 -1.037284e-02  1.721984e-02
## 55   2018-08-20 -3.220568e-03  1.029810e-02 -1.414942e-02
## 56   2018-08-21 -2.414892e-03  1.337119e-02  1.019543e-02
## 57   2018-08-22  4.940038e-03  1.042363e-02  1.525291e-02
## 58   2018-08-23 -8.997384e-03 -4.611199e-03  6.152198e-03
## 59   2018-08-24  1.286054e-03  1.425872e-01  1.096856e-02
## 60   2018-08-27  1.080318e-03 -1.648366e-02  3.808482e-02
## 61   2018-08-28  8.224003e-03  1.399967e-02  9.946214e-04
## 62   2018-08-29  1.282509e-02 -7.296499e-03  8.284731e-03
## 63   2018-08-30  7.826659e-03 -1.169526e-02  4.194277e-03
## 64   2018-08-31  2.123955e-03  3.179685e-03 -1.447884e-03
## 65   2018-09-04 -1.933763e-02 -4.936101e-03 -3.005892e-03
## 66   2018-09-05 -3.461461e-04 -2.812805e-02 -3.276296e-02
## 67   2018-09-06 -1.529236e-02 -3.555493e-03 -5.620326e-03
## 68   2018-09-07 -4.963378e-03  2.483439e-03 -5.896190e-03
## 69   2018-09-10  1.764984e-03  1.053625e-02  1.651859e-02
## 70   2018-09-11 -7.522679e-03  7.956701e-04  2.117344e-02
## 71   2018-09-12  6.875883e-03 -5.966916e-04 -2.537179e-03
## 72   2018-09-13  1.616162e-03  3.971451e-03 -5.751975e-03
## 73   2018-09-14 -5.594320e-03 -1.981898e-04  2.733345e-02
## 74   2018-09-17 -1.271782e-02 -3.106906e-02 -3.068438e-02
## 75   2018-09-18  7.418649e-03  1.400985e-02  1.986117e-02
## 76   2018-09-19  5.978085e-03 -2.624578e-03 -1.572036e-02
## 77   2018-09-20  6.851416e-03  3.202874e-02 -2.632499e-04
## 78   2018-09-21  1.214612e-02 -5.431431e-03  2.629228e-03
## 79   2018-09-24  4.650255e-03  2.817602e-03  2.109716e-02
## 80   2018-09-25 -1.559558e-02  1.667619e-02  1.028226e-02
## 81   2018-09-26  2.234471e-02 -3.739202e-03 -9.588291e-03
## 82   2018-09-27  1.767500e-02  7.592810e-03  1.899359e-03
## 83   2018-09-28 -6.460668e-03  7.048861e-04  3.200249e-03
## 84   2018-10-01 -2.125038e-03 -3.915162e-03  7.665074e-04
## 85   2018-10-02 -2.048869e-02 -1.021276e-02 -3.999537e-02
## 86   2018-10-03  2.102746e-02  6.153049e-03 -2.422058e-03
## 87   2018-10-04 -2.773762e-02 -1.804778e-02 -4.739343e-02
## 88   2018-10-05 -2.977378e-03 -6.577179e-04 -1.344614e-02
## 89   2018-10-08  2.773314e-03 -3.883653e-02 -2.942823e-02
## 90   2018-10-09  4.479379e-03 -2.317886e-02 -5.556852e-03
## 91   2018-10-10 -2.064289e-02 -6.776366e-02 -7.595736e-02
## 92   2018-10-11 -3.086891e-02 -1.974421e-02 -1.008138e-02
## 93   2018-10-12  1.115161e-02  5.419986e-02  4.573230e-02
## 94   2018-10-15 -7.674256e-03 -2.624967e-02 -3.123076e-02
## 95   2018-10-16  3.058612e-02  4.942671e-02  5.369412e-02
## 96   2018-10-17 -1.122788e-03  2.471882e-03 -6.319607e-03
## 97   2018-10-18 -2.417909e-02 -3.211063e-02 -2.979375e-02
## 98   2018-10-19 -2.994564e-02 -3.039388e-02 -3.230599e-02
## 99   2018-10-22 -1.531595e-02  1.830277e-02  4.561313e-03
## 100  2018-10-23  1.931280e-03 -1.126943e-02 -8.084270e-03
## 101  2018-10-24 -4.562424e-02 -7.106137e-02 -6.927025e-02
## 102  2018-10-25 -1.192310e-02  3.993782e-02 -2.256998e-01
## 103  2018-10-26  5.679596e-03 -4.162030e-02 -8.394692e-03
## 104  2018-10-29  2.628312e-03 -4.661655e-03 -5.442458e-02
## 105  2018-10-30  1.752238e-02  1.463501e-02  2.299679e-02
## 106  2018-10-31 -6.584284e-03  2.578413e-02 -8.149335e-03
## 107  2018-11-01  3.570424e-02  4.522849e-02  4.313397e-02
## 108  2018-11-02 -8.375365e-03 -8.167487e-03 -5.209463e-03
## 109  2018-11-05  1.413053e-02 -4.708038e-03 -7.119977e-03
## 110  2018-11-06  9.820781e-03  1.496984e-03  5.464614e-03
## 111  2018-11-07  3.446240e-02  3.829975e-02  6.718631e-02
## 112  2018-11-08 -1.663790e-02  1.209189e-02  1.466455e-03
## 113  2018-11-09 -2.579686e-03 -3.664951e-02 -4.032684e-02
## 114  2018-11-12 -1.956286e-02 -4.096034e-02 -8.242949e-02
## 115  2018-11-13  5.642591e-04  6.206180e-03  9.299048e-03
## 116  2018-11-14 -1.748302e-02 -1.144629e-02  3.050231e-03
## 117  2018-11-15  2.572281e-02  3.686145e-02  1.255775e-02
## 118  2018-11-16  7.216183e-03 -1.863378e-03  1.178112e-02
## 119  2018-11-19 -1.504862e-02 -6.392194e-02 -9.769540e-02
## 120  2018-11-20  8.455433e-04 -2.162547e-02  2.735805e-02
## 121  2018-11-21 -1.234588e-02  9.298018e-02  2.639764e-02
## 122  2018-11-23  1.422209e-02 -1.755538e-02  1.449665e-02
## 123  2018-11-26 -1.813650e-03  4.501847e-02  2.039646e-02
## 124  2018-11-27  1.339964e-02  9.750586e-03 -1.202473e-02
## 125  2018-11-28  2.570065e-02  2.117826e-02  6.524333e-02
## 126  2018-11-29 -1.709082e-02  1.655678e-02 -2.968190e-02
## 127  2018-11-30  2.153557e-02 -7.240183e-03  5.189841e-03
## 128  2018-12-03 -4.595221e-03  2.406792e-02  2.495887e-02
## 129  2018-12-04 -2.889101e-02 -5.684854e-02 -6.462338e-02
## 130  2018-12-06  1.222626e-02  2.143033e-03 -7.313399e-03
## 131  2018-12-07 -3.099264e-02 -5.553106e-02 -4.218305e-02
## 132  2018-12-10  8.519758e-03  1.831208e-02  2.988935e-02
## 133  2018-12-11  1.095089e-03 -8.553803e-03  1.652476e-02
## 134  2018-12-12  8.779558e-03  2.886159e-02 -4.459062e-03
## 135  2018-12-13 -7.685670e-03 -1.624257e-02 -9.438341e-03
## 136  2018-12-14 -1.761544e-02 -3.048131e-02 -7.670966e-03
## 137  2018-12-17 -4.620360e-03 -3.269606e-02 -4.071186e-02
## 138  2018-12-18 -6.039511e-02  2.567529e-02  1.214988e-02
## 139  2018-12-19 -7.013504e-03 -1.894067e-02 -3.863665e-02
## 140  2018-12-20 -1.230779e-03 -2.529183e-02 -1.893180e-02
## 141  2018-12-21 -4.095307e-02 -3.776493e-02  7.003425e-03
## 142  2018-12-24 -7.512130e-03 -1.659583e-02 -2.774490e-02
## 143  2018-12-26  5.813345e-02  6.233338e-02  8.539694e-02
## 144  2018-12-27 -2.578138e-03  1.168407e-02  1.610140e-03
## 145  2018-12-28 -3.027625e-03 -1.413769e-03 -1.448960e-02
## 146  2018-12-31  2.489875e-02  1.078808e-02  5.458215e-03
## 147  2019-01-02  1.245038e-02  2.717756e-03 -3.552797e-02
## 148  2019-01-03  7.552875e-03 -5.671157e-02 -8.969563e-02
## 149  2019-01-04  3.624079e-02  5.142460e-02  1.039073e-02
## 150  2019-01-07  1.270445e-02  3.402629e-02  1.704627e-02
## 151  2019-01-08  6.307633e-03  8.627489e-03  1.582815e-02
## 152  2019-01-09  6.727422e-03  2.143157e-02  3.748505e-02
## 153  2019-01-10  1.386419e-02 -4.387670e-04  1.151488e-02
## 154  2019-01-11  6.080660e-03  2.194039e-04 -2.190214e-02
## 155  2019-01-14 -8.408283e-03 -1.466014e-02 -2.198002e-02
## 156  2019-01-15  2.131944e-02  8.350970e-03  5.707108e-03
## 157  2019-01-16 -1.645873e-02 -4.277623e-03  5.844780e-02
## 158  2019-01-17  1.882597e-02  8.830057e-03  2.803791e-02
## 159  2019-01-18 -2.722812e-03  3.759920e-02  3.429488e-02
## 160  2019-01-22  4.553596e-03 -1.901833e-02 -1.801764e-02
## 161  2019-01-23 -5.146540e-03 -1.135426e-02  4.891777e-03
## 162  2019-01-24 -1.298353e-02 -1.052874e-02  1.575769e-02
## 163  2019-01-25  1.164816e-02  4.336781e-02  2.925035e-02
## 164  2019-01-28 -2.027718e-02 -9.262912e-03 -2.554125e-02
## 165  2019-01-29  1.345413e-02 -4.342726e-03  2.435039e-03
## 166  2019-01-30 -1.999048e-02  4.082197e-02  4.749608e-02
## 167  2019-01-31  1.789545e-02  8.185564e-03  6.694348e-02
## 168  2019-02-01 -8.635643e-03  1.262386e-02 -2.008384e-02
## 169  2019-02-04  9.504126e-03  1.676344e-02  2.210641e-03
## 170  2019-02-05  8.702654e-03  5.460374e-03 -4.220877e-03
## 171  2019-02-06 -1.119031e-02 -9.189302e-04  2.174129e-03
## 172  2019-02-07 -7.639578e-02 -1.135926e-02 -1.898750e-02
## 173  2019-02-08  2.048636e-02  2.460189e-02  7.530555e-03
## 174  2019-02-11  5.538077e-03  1.683560e-03  1.362643e-02
## 175  2019-02-12  8.046556e-03  3.164752e-02  3.909175e-02
## 176  2019-02-13  6.583845e-03  3.066661e-03 -9.759648e-03
## 177  2019-02-14  9.810468e-03 -5.625340e-04 -4.377269e-03
## 178  2019-02-15  2.481956e-02  2.560206e-03  1.665027e-02
## 179  2019-02-19  3.904816e-04  2.055802e-03  1.097601e-03
## 180  2019-02-20  6.465552e-03 -5.491714e-03 -5.697173e-03
## 181  2019-02-21 -4.263742e-02  1.877108e-04 -1.412665e-02
## 182  2019-02-22  1.286939e-02  1.045627e-02  1.491444e-02
## 183  2019-02-25  6.587006e-03  1.493349e-02  3.238460e-02
## 184  2019-02-26  4.273668e-04 -3.850297e-03 -9.805866e-03
## 185  2019-02-27  3.869009e-03  5.922060e-03 -5.945539e-03
## 186  2019-02-28 -2.679268e-03 -7.760765e-03  2.784121e-03
## 187  2019-03-01  1.839624e-02 -2.007621e-02  1.677174e-02
## 188  2019-03-04 -2.068537e-02 -1.247032e-02 -2.709633e-02
## 189  2019-03-05 -1.192470e-03 -1.971255e-02 -6.900401e-02
## 190  2019-03-06 -2.760548e-02 -7.786763e-03 -3.301978e-02
## 191  2019-03-07 -8.464163e-03 -4.832130e-03 -3.028981e-03
## 192  2019-03-08 -2.362042e-02 -2.621808e-03  3.899391e-04
## 193  2019-03-11  1.139843e-02  1.090052e-02  5.281702e-02
## 194  2019-03-12  4.037335e-03  4.986282e-03  3.027344e-02
## 195  2019-03-13  2.476124e-02 -9.280011e-03  5.129578e-03
## 196  2019-03-14  2.990256e-03 -1.500741e-03 -1.817071e-02
## 197  2019-03-15  2.563891e-02  8.485136e-04  1.896363e-02
## 198  2019-03-18 -1.287546e-02  3.711833e-03  5.532931e-03
## 199  2019-03-19 -5.820635e-03  8.091968e-03  2.167647e-02
## 200  2019-03-20 -9.839496e-03 -5.106556e-03  2.434539e-02
## 201  2019-03-21 -3.457418e-01  2.880798e-02  5.510084e-02
## 202  2019-03-22 -4.586118e-02 -2.939137e-02 -4.037985e-02
## 203  2019-03-25  1.624856e-02  3.042966e-03  5.179037e-03
## 204  2019-03-26  5.584349e-02  7.855816e-03  1.192040e-02
## 205  2019-03-27 -1.279025e-02 -1.818760e-02 -1.955035e-02
## 206  2019-03-28  1.240377e-02 -4.573678e-04  1.823696e-02
## 207  2019-03-29  1.517505e-02  1.806757e-02  3.733589e-02
## 208  2019-04-01 -1.659347e-02  5.006677e-02  2.879847e-03
## 209  2019-04-02  3.349363e-03  3.230030e-03  2.384120e-02
## 210  2019-04-03 -8.048809e-03  1.389743e-02 -9.496063e-03
## 211  2019-04-04  1.560789e-02 -9.647292e-03 -4.538920e-03
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## 213  2019-04-08 -8.225012e-03  2.461964e-03 -1.077166e-02
## 214  2019-04-09 -9.050606e-03  1.917274e-03 -2.581634e-02
## 215  2019-04-10  1.130049e-02  2.014769e-02  1.692862e-02
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## 221  2019-04-18 -3.483453e-03  6.938901e-03  2.813737e-02
## 222  2019-04-22  1.063278e-02  1.728473e-02  3.195411e-02
## 223  2019-04-23  6.100010e-03  1.801853e-02  1.857865e-02
## 224  2019-04-24 -2.556182e-02  5.859108e-03  3.371775e-03
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## 226  2019-04-26  2.780072e-03  9.480347e-03  6.913222e-02
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## 244  2019-05-22  9.060644e-03 -1.148550e-03 -2.693771e-03
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## 246  2019-05-24 -8.987951e-03 -5.031895e-02  1.169036e-02
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## 248  2019-05-29 -9.533636e-03  2.665809e-03 -2.457695e-02
## 249  2019-05-30  1.699562e-03  6.787161e-03 -2.457578e-03
## 250  2019-05-31 -2.026840e-02 -1.057093e-02 -4.244820e-02
## 251  2019-06-03  1.843454e-02 -3.858203e-02 -3.628869e-03
## 252  2019-06-04  1.612045e-02  3.234798e-02  4.796283e-02
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## 254  2019-06-06 -7.725773e-03 -9.302819e-04  1.244815e-02
## 255  2019-06-07  1.275534e-02  2.536434e-02  4.234458e-03
## 256  2019-06-10  5.135749e-03 -1.089571e-03  2.367258e-02
## 257  2019-06-11  2.972845e-03 -1.169603e-02 -1.971500e-02
## 258  2019-06-12  5.875802e-03  3.486605e-03  1.005032e-02
## 259  2019-06-13  3.595499e-03 -8.893290e-03 -2.985198e-03
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## 264  2019-06-20  4.606936e-03  2.280147e-02 -3.949248e-03
## 265  2019-06-21  1.738218e-02  8.462188e-03 -4.182028e-02
## 266  2019-06-24 -1.338964e-02 -1.408432e-02 -4.949434e-03
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## 271  2019-07-01  6.903087e-03  3.847670e-02 -7.407783e-03
## 272  2019-07-02  3.729882e-03  4.773355e-03 -2.875150e-03
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## 274  2019-07-05 -1.701558e-02  1.336293e-03 -6.237562e-03
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## 286  2019-07-23  4.787214e-02 -3.645967e-03 -5.516738e-03
## 287  2019-07-24 -1.088401e-02  2.196732e-02  8.027530e-03
## 288  2019-07-25 -1.263964e-02 -2.090748e-02 -3.145455e-01
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## 292  2019-07-31 -1.539674e-02 -2.603949e-02  2.828021e-02
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## 298  2019-08-08  2.732160e-03  5.347928e-02  2.353811e-02
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## 399  2020-01-02 -8.426945e-03  2.354061e-02  1.649164e-02
## 400  2020-01-03 -1.158804e-02 -1.545181e-02 -1.148701e-02
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## 663  2021-01-20 -1.308552e-02 -7.715361e-03  1.240905e-02
## 664  2021-01-21 -5.921688e-04 -6.893875e-03 -3.711014e-02
## 665  2021-01-22 -2.520548e-03 -2.407519e-02 -1.805425e-02
## 666  2021-01-25  2.238710e-02 -1.865744e-02  1.004145e-02
## 667  2021-01-26 -1.414470e-02 -6.457307e-03 -8.133522e-03
## 668  2021-01-27 -2.429246e-02 -6.470534e-02 -4.874898e-02
## 669  2021-01-28  1.020609e-02  3.855666e-02  5.151107e-02
## 670  2021-01-29  5.356603e-02 -2.417997e-02 -2.109388e-02
## 671  2021-02-01 -1.479341e-02  3.154147e-02  3.307955e-02
## 672  2021-02-02 -2.660975e-03  2.854231e-02  2.674535e-02
## 673  2021-02-03 -5.350926e-02 -5.991844e-03 -2.099815e-02
## 674  2021-02-04  1.560417e-02  2.575389e-02  1.189338e-01
## 675  2021-02-05 -8.638947e-03  1.771299e-02  8.562688e-03
## 676  2021-02-08  1.438172e-02 -1.002189e-02 -2.945696e-02
## 677  2021-02-09  1.412028e-03  5.565548e-03  2.063419e-02
## 678  2021-02-10  2.090797e-02 -9.204826e-03 -1.510534e-02
## 679  2021-02-11  1.375944e-02 -4.984062e-03 -1.125533e-02
## 680  2021-02-12 -2.801521e-03  1.628854e-02  1.750863e-02
## 681  2021-02-16  4.629085e-03  1.004308e-02  7.566702e-03
## 682  2021-02-17 -9.532596e-03 -1.866646e-02 -2.419086e-02
## 683  2021-02-18 -2.787048e-03 -5.967752e-03 -7.601481e-03
## 684  2021-02-19  8.840877e-03  1.544277e-02  7.134291e-03
## 685  2021-02-22  2.231077e-02 -2.553606e-02 -3.344423e-02
## 686  2021-02-23 -1.969168e-02 -2.534369e-02 -2.044780e-02
## 687  2021-02-24  1.302928e-02  2.939992e-02  9.552531e-03
## 688  2021-02-25 -1.957198e-02 -5.106268e-02 -3.037329e-02
## 689  2021-02-26 -1.592357e-02 -2.867900e-02  1.958717e-02
## 690  2021-03-01  1.318337e-03  2.952359e-02 -3.532886e-03
## 691  2021-03-02 -1.248422e-02 -2.259110e-02 -3.367776e-03
## 692  2021-03-03 -1.211684e-02 -3.150739e-02 -6.563646e-02
## 693  2021-03-04 -1.143042e-02 -1.443712e-02 -1.332230e-02
## 694  2021-03-05  2.672909e-02  7.319489e-03  3.029820e-02
## 695  2021-03-08 -2.589072e-03 -5.492363e-02 -7.827498e-02
## 696  2021-03-09 -1.312235e-02  4.205077e-02  3.913773e-02
## 697  2021-03-10 -1.466670e-02 -1.250871e-03 -7.940384e-03
## 698  2021-03-11  1.822526e-02  3.985646e-02  6.103484e-02
## 699  2021-03-12 -4.910320e-03 -2.304377e-02 -1.399452e-02
## 700  2021-03-15 -2.280340e-02  1.814772e-02  4.092633e-02
## 701  2021-03-16 -8.075839e-04  7.262485e-03 -2.961928e-02
## 702  2021-03-17  1.614316e-02 -7.921969e-03 -4.674098e-03
## 703  2021-03-18 -7.142635e-03 -3.505988e-02 -4.866430e-02
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## 705  2021-03-22  1.954045e-02  1.691160e-02  2.150736e-03
## 706  2021-03-23 -1.901644e-02  1.136549e-02 -2.233574e-02
## 707  2021-03-24 -5.704609e-03 -2.187320e-02 -2.480005e-02
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## 709  2021-03-26  9.662276e-03  2.567915e-02  2.001583e-02
## 710  2021-03-29 -1.990260e-03  6.558089e-03 -2.363330e-02
## 711  2021-03-30 -2.534985e-04 -8.716533e-03  1.601452e-02
## 712  2021-03-31  1.345921e-02  3.196871e-02  3.227723e-02
## 713  2021-04-01 -3.724565e-03  2.406319e-02  6.478991e-03
## 714  2021-04-05 -2.982399e-03  1.544896e-02  5.288284e-03
## 715  2021-04-06 -2.227002e-02 -9.828970e-03  1.071009e-02
## 716  2021-04-07 -1.385780e-02  2.169257e-03 -2.313864e-03
## 717  2021-04-08 -8.580766e-03  2.522780e-02  4.111152e-02
## 718  2021-04-09  9.140359e-03  1.401043e-02  2.877859e-02
## 719  2021-04-12 -2.022792e-02 -1.037051e-02  1.432579e-02
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## 721  2021-04-14 -1.503790e-03 -3.391558e-03 -1.175938e-03
## 722  2021-04-15  1.734371e-02  1.520563e-02  1.881568e-02
## 723  2021-04-16 -4.808285e-04  4.340493e-03  1.650013e-04
## 724  2021-04-19 -4.672250e-03 -3.374530e-02 -4.313954e-03
## 725  2021-04-20  1.530698e-02 -1.332067e-02 -1.253426e-02
## 726  2021-04-21 -1.233790e-02  8.727034e-03  3.280065e-02
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## 728  2021-04-23  1.391815e-02  2.492967e-02  7.786797e-03
## 729  2021-04-26  2.567371e-02  1.368988e-02 -4.655089e-03
## 730  2021-04-27 -7.711600e-03 -4.922905e-03  7.296271e-03
## 731  2021-04-28  7.850278e-04  4.555412e-03 -1.360217e-02
## 732  2021-04-29 -8.519065e-03 -9.907595e-03 -1.481502e-02
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## 734  2021-05-03  2.941393e-02 -1.522269e-02  7.094468e-03
## 735  2021-05-04 -1.570515e-02 -2.739797e-02 -2.981809e-02
## 736  2021-05-05  2.027380e-03  4.814389e-03 -2.240848e-02
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## 738  2021-05-07  7.067773e-03  4.946438e-03  2.302615e-02
## 739  2021-05-10  5.712655e-03 -3.457037e-02 -7.609239e-02
## 740  2021-05-11  1.003629e-02  4.950685e-03  2.098655e-02
## 741  2021-05-12 -1.582201e-02 -2.881581e-02 -3.161084e-02
## 742  2021-05-13  2.767708e-02  6.675518e-04  9.036006e-03
## 743  2021-05-14 -5.338851e-03  2.890492e-02  2.747217e-02
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## 745  2021-05-18  2.173158e-03 -7.415149e-03  1.767947e-02
## 746  2021-05-19  2.629861e-03  4.462990e-03  3.488185e-03
## 747  2021-05-20  1.696271e-02  2.590530e-02  2.830994e-02
## 748  2021-05-21 -1.186480e-02  1.847733e-03  6.527342e-03
## 749  2021-05-24 -1.540825e-02  2.038168e-02  2.123473e-02
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## 762  2021-06-11 -4.455035e-02  3.607142e-05 -9.970598e-04
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## 770  2021-06-23 -6.699744e-03 -8.424924e-03  1.833883e-03
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## 797  2021-08-02  1.509681e-02  2.922894e-03  6.018090e-03
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## 799  2021-08-04  2.958320e-04  4.507427e-03  9.465403e-03
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## 804  2021-08-11  5.412014e-03 -8.000964e-03  5.817854e-04
## 805  2021-08-12  4.796046e-03  1.032255e-02  2.369277e-02
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## 816  2021-08-27  2.772019e-03  1.741735e-02  7.565740e-03
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## 822  2021-09-07 -1.924887e-02 -4.477573e-03 -7.358927e-03
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## 828  2021-09-15  1.095508e-02  2.569178e-02  5.449046e-03
## 829  2021-09-16  1.602976e-03  1.406570e-02  2.499780e-02
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## 876  2021-11-22 -1.955302e-02 -3.804559e-02 -2.011936e-02
## 877  2021-11-23  7.662519e-03 -2.109182e-02 -1.872028e-02
## 878  2021-11-24 -1.594382e-02 -1.683408e-01 -6.196314e-03
## 879  2021-11-26 -2.933099e-02 -1.068355e-02 -2.948753e-02
## 880  2021-11-29 -2.835201e-02  2.709161e-02  3.941073e-04
## 881  2021-11-30 -1.568278e-03 -2.701291e-02 -3.682590e-02
## 882  2021-12-01 -2.682649e-02 -1.790196e-02 -1.522504e-02
## 883  2021-12-02 -4.279278e-03  3.146083e-02  3.690061e-02
## 884  2021-12-03 -2.033492e-02  5.264334e-03 -8.323461e-03
## 885  2021-12-06  8.481709e-04  2.493556e-02  3.046305e-02
## 886  2021-12-07  1.206384e-02  4.109313e-02  4.259090e-02
## 887  2021-12-08  3.419247e-02 -1.482859e-03  1.266840e-02
## 888  2021-12-09 -9.804244e-03 -3.169614e-02 -2.416863e-03
## 889  2021-12-10  8.171251e-04  4.956453e-03 -8.153867e-03
## 890  2021-12-13  8.049388e-03 -4.461776e-04 -5.889088e-02
## 891  2021-12-14 -1.607740e-02 -2.127501e-02 -3.914260e-02
## 892  2021-12-15  2.194503e-02  3.181878e-02 -6.160236e-03
## 893  2021-12-16 -1.527370e-03 -7.832552e-03 -1.161184e-02
## 894  2021-12-17  8.076961e-03  2.938489e-02  2.325454e-02
## 895  2021-12-20 -1.981434e-03 -9.153958e-03 -2.513847e-02
## 896  2021-12-21 -9.796363e-03  1.908118e-02  5.690765e-02
## 897  2021-12-22 -7.247373e-04  7.779277e-03  2.694327e-02
## 898  2021-12-23  3.958412e-03 -5.748756e-03  1.244751e-02
## 899  2021-12-27 -5.195932e-03  1.171093e-02  1.078301e-02
## 900  2021-12-28  7.656692e-03 -5.396169e-03 -7.135098e-03
## 901  2021-12-29  9.037095e-02 -7.074752e-04 -4.626938e-03
## 902  2021-12-30 -7.352148e-02 -3.048191e-03  1.350007e-02
## 903  2021-12-31 -3.333972e-04 -1.847537e-03 -7.639840e-03
## 904  2022-01-03  1.743630e-02  8.957235e-03 -1.399011e-02
## 905  2022-01-04 -9.920443e-03 -1.968350e-02 -3.861907e-02
## 906  2022-01-05 -1.022875e-02 -5.114382e-02 -7.432262e-02
## 907  2022-01-06 -8.267462e-03 -7.948906e-04 -1.957398e-02
## 908  2022-01-07 -2.000491e-02 -6.800467e-03 -3.702167e-02
## 909  2022-01-10  1.158352e-02  2.668445e-04  3.503942e-03
## 910  2022-01-11  2.604852e-02  3.092059e-02  1.935930e-02
## 911  2022-01-12 -6.934195e-02 -3.813192e-03 -3.670662e-02
## 912  2022-01-13  4.905640e-02 -3.560409e-02 -2.760794e-02
## 913  2022-01-14  1.105125e-02 -4.121203e-03 -2.859207e-04
## 914  2022-01-18 -2.320920e-02 -2.766599e-02 -6.918624e-02
## 915  2022-01-19 -1.291396e-02  9.163171e-03  1.626941e-02
## 916  2022-01-20 -2.145815e-02 -7.656529e-03 -1.392313e-02
## 917  2022-01-21 -2.414830e-02 -5.379654e-02 -5.860153e-02
## 918  2022-01-24  1.873327e-02  2.542756e-02  2.486229e-02
## 919  2022-01-25 -1.064889e-02 -4.830529e-02 -1.366716e-02
## 920  2022-01-26 -1.226506e-02 -2.141053e-03 -2.297611e-02
## 921  2022-01-27 -3.010008e-03 -2.000324e-02 -3.811676e-03
## 922  2022-01-28  2.823560e-02  4.648419e-02  1.813920e-02
## 923  2022-01-31  3.501668e-03  4.190015e-02  6.467861e-02
## 924  2022-02-01  1.480140e-02 -8.002642e-05  2.710627e-02
## 925  2022-02-02 -1.941376e-02 -7.111764e-03 -5.797810e-03
## 926  2022-02-03 -2.152267e-02 -4.216701e-02 -4.579111e-03
## 927  2022-02-04  6.158050e-03  1.453057e-02 -2.708667e-02
## 928  2022-02-07 -1.038755e-03 -3.155400e-03  2.092840e-02
## 929  2022-02-08  4.913332e-03  2.574901e-03  3.006988e-02
## 930  2022-02-09  1.968006e-02  4.159478e-02  5.739120e-02
## 931  2022-02-10 -3.030334e-02 -5.235341e-02 -2.518916e-02
## 932  2022-02-11 -2.508010e-02 -4.893062e-02 -4.467545e-02
## 933  2022-02-14 -2.192630e-03 -1.013197e-03 -6.760164e-03
## 934  2022-02-15  1.506437e-02  2.815868e-02  4.366640e-02
## 935  2022-02-16 -1.305812e-02  1.541360e-03 -3.527312e-03
## 936  2022-02-17 -1.858220e-02 -4.529029e-02 -4.790146e-02
## 937  2022-02-18 -3.853631e-03 -2.975938e-02 -6.217503e-03
## 938  2022-02-22  9.535272e-05 -5.503041e-03 -9.146301e-03
## 939  2022-02-23 -3.485386e-03 -3.122673e-02 -2.344565e-02
## 940  2022-02-24 -2.892005e-02  4.289042e-02  5.343018e-02
## 941  2022-02-25  2.075597e-02  6.578379e-03  6.675117e-03
## 942  2022-02-28  1.735262e-02  2.773679e-03 -2.148410e-03
## 943  2022-03-01 -3.180252e-03 -2.869642e-02 -2.072314e-02
## 944  2022-03-02 -1.219733e-02  1.166070e-02 -9.688046e-03
## 945  2022-03-03  1.641965e-02 -3.052918e-02 -3.839871e-02
## 946  2022-03-04 -8.462535e-03 -1.120538e-02 -2.754094e-02
## 947  2022-03-07 -1.767740e-02 -4.214518e-02 -6.426299e-02
## 948  2022-03-08 -1.849046e-02 -1.589745e-02 -4.835289e-02
## 949  2022-03-09  1.286282e-03  4.456496e-02  6.312033e-02
## 950  2022-03-10 -1.810932e-02 -2.515769e-02 -2.742849e-02
## 951  2022-03-11 -4.895173e-03 -3.815814e-02 -7.085630e-02
## 952  2022-03-14 -1.992705e-02 -1.895021e-02 -5.800593e-02
## 953  2022-03-15  1.835757e-02  1.957398e-02  3.288456e-02
## 954  2022-03-16  3.210966e-02  6.083556e-02  7.378431e-02
## 955  2022-03-17  7.430636e-03  3.436596e-02  1.141685e-02
## 956  2022-03-18  1.570498e-02  7.765701e-03  4.005829e-02
## 957  2022-03-21 -8.474262e-03 -4.322493e-03 -2.376330e-02
## 958  2022-03-22  1.967842e-02  1.995218e-02  5.523607e-02
## 959  2022-03-23 -6.182561e-03 -4.396938e-02 -4.467855e-02
## 960  2022-03-24  1.604275e-02  2.716696e-02 -1.832062e-03
## 961  2022-03-25 -9.623141e-03 -4.280465e-03 -1.343047e-02
## 962  2022-03-28  3.359719e-03  1.529678e-02  8.236588e-03
## 963  2022-03-29  1.532976e-02  3.462856e-02  4.271514e-02
## 964  2022-03-30 -1.840513e-02 -9.009070e-03 -2.406522e-02
## 965  2022-03-31 -2.039671e-03 -3.055248e-02 -1.405221e-02
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## 967  2022-04-04  4.688753e-03  2.654106e-02 -2.287485e-03
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## 974  2022-04-13  2.805604e-02  2.815108e-02  2.595085e-02
## 975  2022-04-14 -6.705265e-03 -2.514755e-02 -1.715232e-02
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## 977  2022-04-19  4.813130e-02  3.627320e-02  4.494869e-02
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## 985  2022-04-29 -1.421588e-02 -3.407058e-02 -4.962587e-02
## 986  2022-05-02 -5.786238e-04  1.894449e-02  6.338232e-02
## 987  2022-05-03 -7.844745e-03  1.657552e-03 -2.577620e-02
## 988  2022-05-04  2.116485e-02  5.306431e-02  3.226253e-02
## 989  2022-05-05 -4.338364e-02 -2.665897e-02 -9.145136e-02
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## 994  2022-05-12  1.686643e-02  2.389860e-02  1.326532e-02
## 995  2022-05-13  2.435112e-02  6.293296e-02  5.978788e-02
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## 997  2022-05-17  2.252881e-02  1.576457e-02  2.303670e-02
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## 1009 2022-06-03  1.057310e-02 -2.708115e-02 -4.036571e-02
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## 1011 2022-06-07  1.994090e-02 -6.878869e-03  1.658963e-02
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## 1017 2022-06-15  1.573710e-02  2.940212e-02  2.365942e-02
## 1018 2022-06-16 -2.947818e-02 -7.275514e-02 -5.896975e-02
## 1019 2022-06-17  5.193532e-02  2.083914e-02  2.003123e-02
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## 1021 2022-06-22  5.315470e-04  1.351084e-02  2.054218e-02
## 1022 2022-06-23  2.093869e-02  8.093825e-02  6.596249e-02
## 1023 2022-06-24  2.598513e-03  4.826813e-02  2.993145e-02
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## 1026 2022-06-29  1.334204e-02  2.262512e-04  9.502593e-04
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## 1028 2022-07-01  3.227722e-02  1.098845e-02  4.409713e-02
## 1029 2022-07-05  9.215334e-03  1.733418e-02  2.700336e-02
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## 1031 2022-07-07  9.125800e-03  3.075625e-02  3.967692e-02
## 1032 2022-07-08  3.846492e-03 -1.336740e-02  7.214606e-03
## 1033 2022-07-11 -1.631151e-02 -1.744541e-02 -4.713198e-02
## 1034 2022-07-12  1.485503e-03 -2.515531e-02 -2.006180e-03
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## 1039 2022-07-19  2.724512e-02  4.166575e-02  5.075984e-02
## 1040 2022-07-20 -5.972547e-02  6.099392e-02  2.650577e-02
## 1041 2022-07-21  3.117317e-02  1.375566e-02  3.490412e-02
## 1042 2022-07-22 -3.716731e-02 -1.594773e-02 -6.677382e-02
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## 1046 2022-07-28  5.993645e-03  4.211706e-02  7.212322e-02
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## 1049 2022-08-02 -5.258049e-04 -9.025692e-03 -5.637799e-03
## 1050 2022-08-03  2.105347e-02  1.040002e-02  1.755290e-02
## 1051 2022-08-04  1.717377e-02  1.589570e-02  2.593524e-02
## 1052 2022-08-05  4.133159e-03 -1.081981e-03  5.445832e-04
## 1053 2022-08-08 -2.937394e-03 -4.566092e-03 -2.828239e-03
## 1054 2022-08-09  1.378743e-04 -1.162196e-02 -6.856393e-02
## 1055 2022-08-10  1.573111e-02  3.681290e-02  5.048710e-02
## 1056 2022-08-11 -1.283992e-02  4.144757e-03 -1.495134e-03
## 1057 2022-08-12  1.261374e-02  2.498664e-02  5.621289e-03
## 1058 2022-08-15  6.270179e-03  4.410661e-03 -9.770755e-03
## 1059 2022-08-16 -1.239781e-02 -1.710546e-03  9.909185e-03
## 1060 2022-08-17 -9.423230e-03 -2.355904e-02 -4.016776e-02
## 1061 2022-08-18 -5.715382e-03  2.888043e-03  1.430333e-02
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## 1069 2022-08-30 -5.239204e-03 -1.419787e-02 -5.296521e-03
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## 1072 2022-09-02 -1.899908e-02 -1.627430e-02 -5.017899e-03
## 1073 2022-09-06 -6.859143e-03 -2.570158e-03 -2.283446e-02
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## 1076 2022-09-09  1.838935e-02  8.825614e-03  2.232947e-02
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## 1312 2023-08-18 -1.339352e-03  4.919916e-03  3.373626e-03
## 1313 2023-08-21  1.489904e-02  1.165067e-02 -2.242677e-02
## 1314 2023-08-22 -7.915943e-03 -7.153543e-03  2.604512e-02
## 1315 2023-08-23  6.896753e-03  1.866997e-02  2.207907e-02
## 1316 2023-08-24 -8.990426e-03  2.053542e-02 -2.469893e-02
## 1317 2023-08-25  7.592186e-03  3.448939e-02  1.595377e-02
## 1318 2023-08-28  2.341903e-03  5.404036e-03  6.461465e-03
## 1319 2023-08-29  1.106854e-02  1.058452e-02  2.467491e-02
## 1320 2023-08-30 -3.064418e-03  9.751791e-03  8.774810e-03
## 1321 2023-08-31  6.734464e-04  1.758773e-03 -1.943239e-03
## 1322 2023-09-01 -7.108002e-04 -8.688615e-03  1.277795e-02
## 1323 2023-09-05 -3.299234e-03 -2.548454e-03 -1.686586e-02
## 1324 2023-09-06 -9.698036e-03  1.240785e-02  2.898454e-03
## 1325 2023-09-07 -9.065712e-03 -5.369937e-03 -8.101474e-02
## 1326 2023-09-08 -9.032814e-03 -8.268984e-03 -2.575933e-02
## 1327 2023-09-11 -2.702284e-04 -2.055110e-03  8.749855e-03
## 1328 2023-09-12 -1.855617e-03 -3.224139e-02 -3.921589e-02
## 1329 2023-09-13 -9.837731e-03  2.169467e-03  3.722507e-04
## 1330 2023-09-14  1.600855e-03  2.056353e-02  3.183784e-02
## 1331 2023-09-15 -5.987042e-03 -1.544141e-02 -2.255878e-03
## 1332 2023-09-18 -5.865080e-03  7.964861e-04 -2.059667e-02
## 1333 2023-09-19  1.321669e-02 -6.861280e-03 -2.275795e-02
## 1334 2023-09-20  1.492675e-02 -2.063010e-02 -2.709329e-02
## 1335 2023-09-21 -6.160286e-03 -1.782508e-02 -3.024272e-02
## 1336 2023-09-22 -4.839250e-03 -9.803970e-05 -5.744458e-03
## 1337 2023-09-25 -1.037649e-02  7.956914e-03 -1.810350e-03
## 1338 2023-09-26  1.181133e-02 -1.968980e-02  3.316490e-03
## 1339 2023-09-27 -2.055974e-03  3.069740e-03  8.889779e-03
## 1340 2023-09-28  1.203058e-03  2.735622e-02  1.914081e-02
## 1341 2023-09-29 -3.185369e-03 -4.725153e-03 -7.147210e-03
## 1342 2023-10-02 -1.627905e-02  1.000249e-02 -1.837824e-02
## 1343 2023-10-03 -6.148751e-03 -2.770209e-02 -3.100008e-02
## 1344 2023-10-04  2.301125e-02  1.842426e-02  3.743808e-03
## 1345 2023-10-05  1.009811e-02 -1.508467e-02 -4.029369e-02
## 1346 2023-10-06  1.330757e-02  2.937402e-02  1.579305e-02
## 1347 2023-10-09  3.640056e-03  2.472683e-03 -2.462321e-03
## 1348 2023-10-10 -2.648850e-04  9.030168e-03  9.010519e-03
## 1349 2023-10-11  8.969924e-03  3.429872e-03 -3.188051e-02
## 1350 2023-10-12 -2.096719e-02 -2.018889e-03 -3.490598e-02
## 1351 2023-10-13  4.854362e-03 -1.563125e-02 -7.528304e-03
## 1352 2023-10-16  2.142667e-02  1.096746e-02  2.366599e-02
## 1353 2023-10-17 -1.905259e-03  1.038131e-02  1.602608e-02
## 1354 2023-10-18 -1.480446e-02 -2.053754e-02 -1.587919e-02
## 1355 2023-10-19 -2.381070e-02 -1.717582e-02 -7.776062e-03
## 1356 2023-10-20  5.829005e-04 -1.653822e-02 -1.518056e-03
## 1357 2023-10-23 -1.589577e-02 -1.476134e-02 -1.553431e-02
## 1358 2023-10-24 -5.064296e-03  2.628866e-02 -9.789903e-04
## 1359 2023-10-25 -2.161141e-02 -2.383820e-02 -4.535108e-02
## 1360 2023-10-26 -2.312526e-02 -2.064016e-02 -2.861460e-01
## 1361 2023-10-27 -2.758795e-02 -4.958228e-03  1.992158e-03
## 1362 2023-10-30  1.140497e-02  1.343736e-02 -2.224195e-02
## 1363 2023-10-31  1.390147e-03 -8.092055e-04 -1.158017e-02
## 1364 2023-11-01  8.718313e-03  6.556348e-03 -7.504054e-03
## 1365 2023-11-02  9.304736e-03  1.557184e-03  4.852761e-02
## 1366 2023-11-03  3.109986e-02  2.351178e-02  2.627406e-02
## 1367 2023-11-06 -3.493048e-03 -9.803714e-03  1.670009e-03
## 1368 2023-11-07 -1.222095e-02  1.630281e-02 -1.264894e-03
## 1369 2023-11-08 -5.834464e-02  7.859516e-03 -1.994242e-02
## 1370 2023-11-09 -3.085667e-02 -1.093279e-02 -3.297232e-02
## 1371 2023-11-10  6.229931e-04  2.841789e-02  2.524713e-02
## 1372 2023-11-13 -9.835106e-03 -2.282002e-03 -4.747649e-03
## 1373 2023-11-14  1.192377e-02  3.397133e-02  5.840112e-02
## 1374 2023-11-15  1.921407e-02 -5.767428e-03  1.147689e-02
## 1375 2023-11-16 -7.405868e-04 -5.056476e-03 -9.505697e-03
## 1376 2023-11-17 -6.383124e-03  1.068588e-02  1.718123e-02
## 1377 2023-11-20  9.211831e-03  1.084602e-02  4.077556e-02
## 1378 2023-11-21 -2.349435e-03 -9.282820e-03  2.787105e-04
## 1379 2023-11-22  7.291352e-03 -7.145043e-02  9.200416e-03
## 1380 2023-11-24  3.022442e-03  3.743080e-03  1.002826e-02
## 1381 2023-11-27 -1.371730e-02 -5.718824e-03 -1.251648e-02
## 1382 2023-11-28 -6.049948e-03  2.495064e-02 -1.211461e-02
## 1383 2023-11-29  2.024138e-02  3.077025e-02  1.086814e-02
## 1384 2023-11-30  8.666996e-03  2.119070e-02 -1.245713e-02
## 1385 2023-12-01  2.389475e-03  2.932365e-02  3.062989e-02
## 1386 2023-12-04 -7.657925e-03 -1.622479e-02 -3.863161e-03
## 1387 2023-12-05 -1.418647e-02 -3.893526e-03 -1.954310e-02
## 1388 2023-12-06  1.855736e-02 -4.090888e-03  7.033433e-03
## 1389 2023-12-07  2.220011e-02  1.935148e-02 -1.199566e-03
## 1390 2023-12-08  7.106792e-04  7.591783e-04  2.110436e-02
## 1391 2023-12-11  2.810242e-02  9.242461e-03 -1.159342e-02
## 1392 2023-12-12  1.183490e-02  8.149313e-03 -5.548527e-03
## 1393 2023-12-13  2.584371e-02  3.012003e-02  6.191403e-02
## 1394 2023-12-14  3.827425e-03  2.480575e-02  1.051789e-01
## 1395 2023-12-15 -3.333181e-02  6.127094e-03 -7.851120e-03
## 1396 2023-12-18  8.827233e-03 -1.308618e-02  2.585786e-02
## 1397 2023-12-19  5.418124e-03 -4.106417e-03  2.498242e-02
## 1398 2023-12-20 -1.412446e-02 -6.106941e-03 -2.349327e-02
## 1399 2023-12-21  2.270922e-02  2.164728e-02  4.484327e-02
## 1400 2023-12-22  1.606037e-02  3.590207e-03 -8.169033e-03
## 1401 2023-12-26  1.052706e-02  9.470632e-03  8.497312e-03
## 1402 2023-12-27  4.706899e-03  1.631809e-04  3.967454e-03
## 1403 2023-12-28 -5.167400e-03 -8.162810e-04  5.036749e-03
## 1404 2023-12-29 -6.970272e-03 -5.856025e-03 -9.697401e-03
## 1405 2024-01-02  3.396468e-02 -3.920100e-02 -1.871412e-02
## 1406 2024-01-03 -1.611662e-02 -3.004710e-02 -4.837753e-02
## 1407 2024-01-04 -1.202968e-02  7.585908e-03  1.986226e-02
## 1408 2024-01-05 -9.263591e-03  2.617600e-03  1.262281e-02
## 1409 2024-01-08  3.877253e-04  2.550837e-02  3.438759e-02
## 1410 2024-01-09 -8.329872e-03  2.163765e-03  1.298385e-02
## 1411 2024-01-10 -6.312880e-03  1.204783e-02 -2.633835e-03
## 1412 2024-01-11 -2.800115e-02  7.633411e-03 -1.554819e-03
## 1413 2024-01-12  3.674274e-03  7.410695e-03 -1.722659e-02
## 1414 2024-01-16 -7.808876e-03 -3.884792e-03 -1.550773e-02
## 1415 2024-01-17 -3.743943e-03 -1.262595e-02 -2.998211e-02
## 1416 2024-01-18  6.907215e-03  1.129999e-02  1.889121e-02
## 1417 2024-01-19  1.203406e-02  3.046255e-02  6.894577e-03
## 1418 2024-01-22 -6.663228e-03  8.609844e-03  1.959349e-02
## 1419 2024-01-23  1.352071e-02  7.903634e-03 -1.925564e-02
## 1420 2024-01-24 -1.812250e-02 -4.748140e-04 -3.576307e-02
## 1421 2024-01-25 -3.851058e-03 -3.608196e-03  1.941576e-02
## 1422 2024-01-26 -5.661584e-03  5.229626e-03  8.244938e-03
## 1423 2024-01-29  1.096813e-02  1.630451e-02  2.285627e-02
## 1424 2024-01-30 -1.779224e-03 -2.958966e-03 -2.111724e-02
## 1425 2024-01-31 -1.701293e-03 -1.042575e-02  9.698294e-03
## 1426 2024-02-01  4.732149e-03  4.952097e-03  2.241632e-02
## 1427 2024-02-02 -1.672301e-02  5.395716e-03  1.900267e-03
## 1428 2024-02-05 -7.743696e-03 -1.429555e-02  6.114866e-03
## 1429 2024-02-06  1.522427e-02  4.617297e-03  4.560918e-02
## 1430 2024-02-07 -2.061424e-02  1.736933e-02 -1.294570e-02
## 1431 2024-02-08 -9.982116e-04  1.184772e-02  3.543395e-02
## 1432 2024-02-09  2.825771e-03  1.957685e-02  4.633301e-03
## 1433 2024-02-12  1.548252e-02 -1.755221e-02  2.027426e-02
## 1434 2024-02-13 -7.678949e-02 -2.035536e-02 -3.403380e-02
## 1435 2024-02-14 -2.642139e-02  2.085136e-02  3.505827e-02
## 1436 2024-02-15  1.175451e-02 -3.515395e-03  2.292267e-02
## 1437 2024-02-16 -1.930311e-02 -1.135615e-02 -3.233424e-03
## 1438 2024-02-20  5.932374e-04 -1.183904e-02  1.529842e-02
## 1439 2024-02-21  8.630113e-03 -1.079214e-02 -2.873149e-02
## 1440 2024-02-22  6.176872e-03  1.750783e-02  3.834923e-02
## 1441 2024-02-23  3.768560e-03  8.557354e-04  1.010378e-03
## 1442 2024-02-26  1.744850e-03  5.830104e-04 -1.924487e-02
## 1443 2024-02-27  1.027566e-03 -1.555489e-03  7.116562e-03
## 1444 2024-02-28 -9.872621e-03 -6.638103e-03 -3.467723e-02
## 1445 2024-02-29 -2.165425e-02  1.137488e-02  9.919809e-05
## 1446 2024-03-01  1.808513e-02  2.512984e-02 -8.000982e-03
## 1447 2024-03-04  3.167953e-04 -1.537781e-02  2.641383e-02
## 1448 2024-03-05 -1.729653e-02 -5.280866e-02 -2.814868e-02
## 1449 2024-03-06  1.517984e-03  1.528958e-02  1.425571e-02
## 1450 2024-03-07  8.239555e-03  1.085284e-02  2.281288e-02
## 1451 2024-03-08  1.753323e-02 -7.830750e-03  5.422857e-03
## 1452 2024-03-11  3.013619e-02  2.509349e-02 -1.418050e-02
## 1453 2024-03-12 -1.184897e-02  1.735031e-02  8.371486e-03
## 1454 2024-03-13 -3.524867e-03 -1.564804e-02  3.171151e-02
## 1455 2024-03-14 -3.111104e-02 -6.573981e-04 -1.182551e-02
## 1456 2024-03-15 -1.412513e-03 -1.673302e-02 -8.142383e-03
## 1457 2024-03-18  4.102756e-04  3.690429e-03  5.678167e-03
## 1458 2024-03-19 -3.515694e-03  3.950213e-03  3.347327e-03
## 1459 2024-03-20 -2.197954e-03  2.406499e-02  3.695071e-02
## 1460 2024-03-21  1.184797e-02  1.257166e-02 -2.420138e-02
## 1461 2024-03-22 -1.207714e-02 -1.093450e-02 -5.774965e-03
## 1462 2024-03-25 -6.485931e-03 -4.919553e-03 -4.384343e-04
## 1463 2024-03-26 -2.178714e-02  3.822567e-04  2.065027e-03
## 1464 2024-03-27  2.017060e-02 -2.678756e-03  2.457518e-02
## 1465 2024-03-28 -3.287227e-03 -2.109700e-03  6.105029e-05
## 1466 2024-04-01 -3.716972e-03 -3.770293e-03 -2.554309e-02
## 1467 2024-04-02 -3.404122e-02 -4.223788e-02 -2.399908e-02
## 1468 2024-04-03 -6.086652e-03 -9.412507e-03 -6.300519e-03
## 1469 2024-04-04 -5.246815e-03 -6.392689e-03  1.548691e-02
## 1470 2024-04-05 -6.989827e-03 -2.859483e-04  8.315780e-03
## 1471 2024-04-08  5.283521e-03  4.687834e-03  7.778758e-03
## 1472 2024-04-09  7.631247e-03  8.262143e-03  3.134147e-02
## 1473 2024-04-10 -2.435977e-02 -3.664105e-02 -7.385245e-03
## 1474 2024-04-11  1.051260e-02  8.540486e-03 -8.947274e-03
## 1475 2024-04-12 -2.737443e-02 -1.707012e-02 -3.104002e-02
## 1476 2024-04-15 -6.987673e-03 -3.154999e-02 -3.301848e-02
## 1477 2024-04-16 -8.419537e-03 -6.028018e-03  1.180690e-03

pander(head(ret1), split.table = Inf)

Date	BIIB	ADSK	ALGN
2018-06-04	0.006107	0.01524	0.0299
2018-06-05	-0.0009037	0.009032	0.008357
2018-06-06	0.01697	0.008226	0.0008376
2018-06-07	0.005319	-0.02786	-0.02056
2018-06-08	-0.006835	0.007353	0.02143
2018-06-11	0.01112	0.006197	0.005093

Se convierte a largo

ret_long = pivot_longer(ret1, cols = -c(Date), values_to = "Retornos", names_to = "Acción")

Gráfica

library(ggplot2)

port_p1 = ggplot(ret_long, aes(Date, Retornos, color = Acción)) + geom_path(stat = "identity") +
 facet_grid(Acción ~ .) + theme_minimal() + labs(x = "Fecha", y = "Retornos")

print(port_p1)

1.1. Análisis técnico de los activos

# Cargar bibliotecas
library(quantmod)
library(TTR)
library(ROCR)

# Definir los símbolos de las acciones de interés
acciones <- c("BIIB", "ADSK", "ALGN")

# Descargar datos históricos de precios
getSymbols(acciones, from = "2018-06-01", to = "2024-04-17", src = "yahoo")

## [1] "BIIB" "ADSK" "ALGN"

# Calcular indicadores técnicos
for (accion in acciones) {
  # Calcular la media móvil de 50 días
  SMA50 <- SMA(Cl(get(accion)), n = 50)
  
  # Calcular la media móvil de 200 días
  SMA200 <- SMA(Cl(get(accion)), n = 200)
  
  # Calcular el MACD
  macd <- MACD(Cl(get(accion)))
  
  # Graficar los indicadores técnicos
  chartSeries(get(accion), theme = chartTheme("white"), 
              TA = c(addSMA(n = 50, col = "blue"),
                     addSMA(n = 200, col = "red"),
                     addMACD()))
  
  # Imprimir resumen de los indicadores
  cat("Resumen de indicadores para", accion, ":\n")
  cat("Último precio de cierre:", as.numeric(Cl(get(accion))[nrow(get(accion))]), "\n")
  cat("Media móvil de 50 días:", as.numeric(SMA50[nrow(SMA50)]), "\n")
  cat("Media móvil de 200 días:", as.numeric(SMA200[nrow(SMA200)]), "\n")
  cat("MACD:", as.numeric(macd$macd[length(macd$macd)]), "\n")
  cat("\n")
}

## Resumen de indicadores para BIIB :
## Último precio de cierre: 195.15 
## Media móvil de 50 días: 219.1822 
## Media móvil de 200 días: 246.7021 
## MACD: -3.167041

## Resumen de indicadores para ADSK :
## Último precio de cierre: 228.24 
## Media móvil de 50 días: 254.51 
## Media móvil de 200 días: 226.9747 
## MACD: -2.537806

## Resumen de indicadores para ALGN :
## Último precio de cierre: 305.1 
## Media móvil de 50 días: 310.8452 
## Media móvil de 200 días: 293.7827 
## MACD: 0.3074761

Análisis

BIIB (Biogen Inc.)

Precio actual: 195.15

Tendencia bajista: El precio actual se encuentra por debajo de ambas medias móviles (50 días: 219.1822 y 200 días: 246.7021), lo que confirma una tendencia bajista tanto a corto como a largo plazo.

Soporte dinámico: Las medias móviles actúan como niveles de soporte dinámicos. Si el precio cae por debajo de la media móvil de 50 días, podría encontrar un nuevo soporte en la media móvil de 200 días.

Momentum negativo: El MACD (indicador de convergencia y divergencia de medias móviles) presenta un valor negativo (-3.167041), lo que refuerza la tendencia bajista y sugiere que el impulso del precio sigue siendo bajista.

Conclusión: Los indicadores técnicos sugieren que BIIB podría continuar con su tendencia bajista en el corto plazo.

ADSK (Autodesk Inc.)

Precio actual: 228.24

Tendencia mixta: El precio se encuentra por debajo de la media móvil de 50 días (254.51), pero por encima de la media móvil de 200 días (226.9747), lo que indica una tendencia bajista a corto plazo pero una tendencia alcista a largo plazo.

Posible cambio de tendencia: La ubicación del precio entre las medias móviles sugiere un posible punto de inflexión en la tendencia. Si el precio logra superar la media móvil de 50 días, podría confirmar un cambio hacia una tendencia alcista.

Momentum negativo: El MACD (-2.537806) es negativo, lo que indica que el impulso del precio sigue siendo bajista a corto plazo.

Conclusión:Los indicadores técnicos para ADSK son mixtos, con señales de debilidad a corto plazo pero potencial alcista a largo plazo.

ALGN (Align Technology, Inc.)

Precio actual: 305.1

Tendencia mixta: Similar a ADSK, el precio se encuentra por debajo de la media móvil de 50 días (310.8452) pero por encima de la media móvil de 200 días (293.7827), lo que indica una tendencia bajista a corto plazo pero alcista a largo plazo.

Divergencia positiva: El MACD (0.3074761) presenta un valor positivo, lo que contrasta con la tendencia bajista del precio. Esta divergencia positiva podría indicar un posible cambio de tendencia alcista.

Conclusión: Los indicadores técnicos para ALGN sugieren una posible divergencia entre el precio y el momentum. Si el precio logra superar la media móvil de 50 días y el MACD mantiene su tendencia positiva, podría confirmar un cambio hacia una tendencia alcista.

1.2. Pesos óptimos de inversión

Simulación de portafolios

np1 = 1000  # Número de portafolios
ret2 = ret1[, -1]  # Excluir fechas
mu1 = colMeans(ret2)  # Media de los retornos
na1 = ncol(ret2)  # Número de activos
varc1 = cov(ret2) # Varianza

riskp1 = NULL  # Vector para acumular el riesgo
retp1 = NULL  # Vector para acumular los retornos

for (i in 1:np1) {
  w = diff(c(0, sort(runif(na1 - 1)), 1))  # Pesos aleatorios
  r1 = t(w) %*% mu1  # Multiplicación de la matriz
  sd1 = t(w) %*% varc1 %*% w
  retp1 = rbind(retp1, r1)
  riskp1 = rbind(riskp1, sd1)
}

Se crea un data frame de riesgos y de retornos

d_p1 = data.frame(Ret = retp1, Risk = riskp1)

Gráfica

library(ggplot2)

p1 <- ggplot(d_p1, aes(Risk, Ret, colour = Ret)) +
  geom_point() +  # Gráfico de dispersión
  geom_hline(yintercept = c(max(d_p1$Ret), median(d_p1$Ret), min(d_p1$Ret)), 
             colour = c("green", "gray", "red"), size = 1) +
  geom_vline(xintercept = d_p1[(d_p1$Risk == min(d_p1$Risk)), ][, 2]) +
  labs(colour = "Retornos de portafolio", x = "Riesgo del portafolio", y = "Retornos del portafolio",
       title = "Portafolios aleatorios") + 
  theme_bw()

# Mostrar la gráfica
print(p1)

Portafolio Eficiente (Minimización de la varianza)

library(PortfolioAnalytics)

# Especificar fecha
data2 = lapply(s1, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2018-06-01", to = "2023-06-01", auto.assign = FALSE)),
      type = "continuous")
})  #%returns

# Convertir a data frame
ret_23 = as.data.frame(do.call(merge, data2))
colnames(ret_23) = gsub(".Adjusted", "", colnames(ret_23))

ret_23 = ret_23[-1, ]

ret_23 = data.frame(Date = as.Date(row.names(ret_23)), ret_23)
row.names(ret_23) = NULL

# Inicializar con nombres de activos utilizando datos de series de tiempo
data_p2 = zoo(ret_23[, -1], order.by = as.Date(ret_23$Date))

# Crear especificación
port = portfolio.spec(assets = c(colnames(data_p2)))

# Añadir restricción de solo tenencias largas
port = add.constraint(portfolio = port, type = "long_only")

# Restricción de inversión total
port = add.constraint(portfolio = port, type = "full_investment")

# Minimizar el riesgo
port_rnd = add.objective(portfolio = port, type = "risk", name = "StdDev")

# Maximizar los retornos
port_rnd = add.objective(portfolio = port_rnd, type = "return", name = "mean")

Optimizar los portafolios aleatorios

rand_p = optimize.portfolio(R = data_p2, portfolio = port_rnd, optimize_method = "random",
    trace = TRUE, search_size = 1000)

## Leverage constraint min_sum and max_sum are restrictive, 
##               consider relaxing. e.g. 'full_investment' constraint should be min_sum=0.99 and max_sum=1.01

Minimizar el nivel de la desviación estandar para el portafolio

port_msd = add.objective(portfolio = port, type = "risk", name = "StdDev")
minvar1 = optimize.portfolio(R = data_p2, portfolio = port_msd, optimize_method = "ROI",
                             trace = TRUE)

## Registered S3 method overwritten by 'ROI':
##   method           from              
##   print.constraint PortfolioAnalytics

minvar1

## ***********************************
## PortfolioAnalytics Optimization
## ***********************************
## 
## Call:
## optimize.portfolio(R = data_p2, portfolio = port_msd, optimize_method = "ROI", 
##     trace = TRUE)
## 
## Optimal Weights:
##   BIIB   ADSK   ALGN 
## 0.3712 0.5172 0.1116 
## 
## Objective Measure:
##  StdDev 
## 0.02174

Análisis

Pesos óptimos de la cartera: Los pesos óptimos para los activos son aproximadamente 37.12% para BIIB, 51.72% para ADSK y 11.16% para ALGN.

Medida objetivo: La desviación estándar (StdDev) de la cartera optimizada es aproximadamente 0.02174. Esto indica el nivel de riesgo (volatilidad) asociado a la cartera óptima. Un valor bajo de desviación estándar sugiere una cartera relativamente estable.

Graficar

plot(minvar1, risk.col = "StdDev", main = "Mean Variance Portfolio", chart.assets = TRUE)

Frontera Eficiente

minvar_ef = create.EfficientFrontier(R = data_p2, portfolio = port_msd,
    type = "mean-StdDev")
chart.EfficientFrontier(minvar_ef, match.col = "StdDev", type = "l", tangent.line = FALSE,
    chart.assets = TRUE)

library(fPortfolio)
data_p2 = as.timeSeries(data_p2)
pspec = portfolioSpec()  #initial specification

setNFrontierPoints(pspec) = 500  #Portafolios aleatorios para la frontera eficiente

eff_front2 = portfolioFrontier(data_p2, constraints = "LongOnly")  #Estrategia
plot(eff_front2, c(1, 2, 4, 5, 6))

tailoredFrontierPlot(eff_front2, sharpeRatio = FALSE, risk = "Sigma")

# Pesos
weightsPlot(eff_front2)

1.3. Valor de Sharpe Ratio Optimo de inversión y Varianza Histórica

Se calcula el ratio de Sharpe

## La tasa libre de riesgo es 0% 
d_p1$Sharpe_ratio <- d_p1$Ret / d_p1$Risk
print(d_p1)

##                Ret         Risk  Sharpe_ratio
## 1     7.019105e-05 0.0004303955  0.1630849841
## 2    -1.896841e-05 0.0006434656 -0.0294785204
## 3     2.097879e-04 0.0004897104  0.4283917917
## 4     1.790830e-05 0.0005733862  0.0312325311
## 5    -1.730551e-04 0.0006063516 -0.2854038327
## 6    -9.320757e-05 0.0006105449 -0.1526629164
## 7    -5.365369e-05 0.0004739030 -0.1132165868
## 8    -9.900993e-05 0.0008099258 -0.1222456845
## 9    -1.652751e-04 0.0005746997 -0.2875851336
## 10    2.100063e-04 0.0004719086  0.4450147985
## 11    4.609725e-05 0.0004316146  0.1068018810
## 12   -1.322131e-04 0.0005449753 -0.2426039093
## 13    5.020929e-06 0.0004720865  0.0106356123
## 14   -1.129860e-04 0.0005188767 -0.2177511553
## 15    3.710119e-06 0.0004698333  0.0078966697
## 16    3.004373e-04 0.0005585169  0.5379198273
## 17   -7.040064e-05 0.0007442242 -0.0945960093
## 18   -1.782240e-04 0.0006001815 -0.2969501832
## 19    7.542159e-05 0.0007241246  0.1041555426
## 20   -8.206063e-05 0.0004945750 -0.1659215061
## 21   -3.297002e-05 0.0009338700 -0.0353047272
## 22    3.587563e-05 0.0005165335  0.0694546140
## 23    8.191285e-08 0.0005497834  0.0001489911
## 24    1.556844e-04 0.0006489080  0.2399175130
## 25    1.328581e-04 0.0004784623  0.2776772362
## 26   -1.853225e-04 0.0005871835 -0.3156126188
## 27    7.073873e-05 0.0004768103  0.1483582227
## 28    2.461962e-04 0.0005402131  0.4557390086
## 29   -1.515313e-04 0.0005564626 -0.2723116769
## 30    2.157748e-04 0.0005196561  0.4152260899
## 31    1.511142e-04 0.0006455910  0.2340711642
## 32    4.544948e-05 0.0004454502  0.1020304211
## 33    1.105626e-04 0.0004583164  0.2412364821
## 34    5.636630e-06 0.0007758845  0.0072647792
## 35    3.713058e-05 0.0006833733  0.0543342606
## 36   -6.037867e-05 0.0005054319 -0.1194595587
## 37   -9.002116e-05 0.0005114397 -0.1760152111
## 38   -4.718735e-05 0.0004630915 -0.1018963817
## 39    2.733040e-04 0.0005551838  0.4922767128
## 40   -4.777391e-05 0.0008990587 -0.0531377036
## 41    5.208349e-05 0.0005172571  0.1006916945
## 42   -1.163755e-04 0.0006316903 -0.1842287888
## 43   -3.204254e-05 0.0006682536 -0.0479496669
## 44   -7.391742e-05 0.0005146024 -0.1436398869
## 45    1.124087e-04 0.0004688108  0.2397741229
## 46    2.469866e-04 0.0005038407  0.4902077648
## 47    8.963319e-05 0.0004934473  0.1816469578
## 48    1.986009e-04 0.0005931106  0.3348463095
## 49    4.376933e-07 0.0004773250  0.0009169712
## 50    2.555461e-04 0.0005333816  0.4791054882
## 51   -1.625242e-05 0.0010086329 -0.0161133130
## 52   -2.031296e-04 0.0005956648 -0.3410132755
## 53    9.225160e-05 0.0005211936  0.1770006534
## 54   -3.191998e-05 0.0005667056 -0.0563255015
## 55    8.918861e-05 0.0005768253  0.1546197850
## 56   -2.428869e-05 0.0004580673 -0.0530242816
## 57    1.209546e-04 0.0004448929  0.2718734978
## 58   -8.164417e-05 0.0008935418 -0.0913714071
## 59    6.622306e-05 0.0004286866  0.1544789540
## 60    9.324581e-05 0.0004293400  0.2171840850
## 61    2.247658e-04 0.0004794954  0.4687548991
## 62   -1.141106e-04 0.0005518529 -0.2067772101
## 63    1.762029e-04 0.0005822543  0.3026218538
## 64    2.628886e-05 0.0004481969  0.0586547048
## 65   -1.934497e-05 0.0007177934 -0.0269506126
## 66   -4.386582e-05 0.0005667678 -0.0773964453
## 67    1.034922e-04 0.0005079404  0.2037486736
## 68   -2.123627e-04 0.0006595035 -0.3220039732
## 69    6.104993e-05 0.0007063832  0.0864260807
## 70   -1.402199e-04 0.0005343956 -0.2623896236
## 71   -2.268087e-04 0.0006844078 -0.3313940745
## 72   -1.571232e-05 0.0007369164 -0.0213217088
## 73    1.082044e-05 0.0006171607  0.0175326208
## 74   -2.494932e-05 0.0006759676 -0.0369090443
## 75   -1.242820e-04 0.0005154221 -0.2411266212
## 76   -2.248273e-05 0.0004719744 -0.0476354842
## 77   -1.686576e-04 0.0006023747 -0.2799877812
## 78    2.620795e-05 0.0004339622  0.0603922317
## 79   -4.852387e-05 0.0004686167 -0.1035470532
## 80    1.912349e-04 0.0004585490  0.4170434420
## 81   -2.311641e-05 0.0007060351 -0.0327411578
## 82    1.167423e-04 0.0004718063  0.2474368205
## 83    5.370762e-05 0.0004293631  0.1250867279
## 84    8.256794e-05 0.0005710655  0.1445857487
## 85    4.510396e-05 0.0006433083  0.0701125086
## 86   -7.593896e-05 0.0004872844 -0.1558411631
## 87   -7.141406e-05 0.0004747837 -0.1504138900
## 88   -3.171904e-05 0.0005172611 -0.0613211528
## 89    1.184611e-05 0.0008029698  0.0147528762
## 90    1.779729e-04 0.0005128737  0.3470112490
## 91   -2.474918e-07 0.0004423686 -0.0005594697
## 92    6.176863e-05 0.0004293143  0.1438774177
## 93    5.969077e-05 0.0004315971  0.1383020470
## 94   -7.897342e-05 0.0004965341 -0.1590493320
## 95   -1.329629e-04 0.0005191642 -0.2561095479
## 96   -1.645150e-04 0.0005527356 -0.2976378376
## 97   -9.066757e-06 0.0004481582 -0.0202311545
## 98    2.124793e-04 0.0005492197  0.3868749544
## 99    6.672765e-05 0.0007959222  0.0838368975
## 100  -8.750655e-06 0.0005467731 -0.0160041792
## 101   8.548868e-05 0.0004372867  0.1954980033
## 102   7.660704e-05 0.0005201613  0.1472755509
## 103  -9.369308e-05 0.0005524987 -0.1695806456
## 104   2.794546e-05 0.0004452492  0.0627636350
## 105   2.050371e-04 0.0005845459  0.3507630599
## 106  -2.031280e-04 0.0005920524 -0.3430911879
## 107  -1.839653e-06 0.0005788677 -0.0031780192
## 108  -6.537178e-05 0.0004696068 -0.1392053478
## 109  -2.477277e-04 0.0007416484 -0.3340231179
## 110  -1.842850e-04 0.0005698887 -0.3233701011
## 111   2.767583e-04 0.0005425968  0.5100625070
## 112   9.354383e-05 0.0004324417  0.2163154599
## 113  -1.333353e-04 0.0005957971 -0.2237930653
## 114  -6.218215e-05 0.0004835099 -0.1286057419
## 115  -3.176778e-05 0.0004521408 -0.0702608200
## 116  -1.273403e-04 0.0005179206 -0.2458682905
## 117  -8.696530e-05 0.0007319411 -0.1188146185
## 118   1.577425e-04 0.0005957339  0.2647868566
## 119  -6.938766e-05 0.0004856496 -0.1428759813
## 120  -1.108814e-04 0.0005558088 -0.1994955745
## 121   1.837019e-04 0.0004602654  0.3991215975
## 122  -2.308262e-04 0.0007230870 -0.3192233146
## 123  -2.099325e-04 0.0006373168 -0.3294005010
## 124  -1.638161e-04 0.0005496608 -0.2980312504
## 125  -2.683379e-05 0.0009826419 -0.0273077980
## 126  -4.423904e-05 0.0004893853 -0.0903971625
## 127   1.116324e-04 0.0004344842  0.2569309829
## 128   1.409181e-04 0.0006354304  0.2217679349
## 129   2.268469e-06 0.0005435523  0.0041734149
## 130  -3.401381e-05 0.0006966958 -0.0488216105
## 131   2.473562e-04 0.0005009114  0.4938122217
## 132   1.032415e-04 0.0005875218  0.1757236529
## 133  -1.181813e-05 0.0006066336 -0.0194814895
## 134  -5.800164e-05 0.0004878187 -0.1188999955
## 135   1.520894e-04 0.0004413034  0.3446369130
## 136   3.087818e-04 0.0005600721  0.5513249771
## 137  -1.524957e-04 0.0005386939 -0.2830840895
## 138   3.436451e-04 0.0006022657  0.5705871563
## 139   7.074044e-06 0.0007221229  0.0097961776
## 140   9.788051e-05 0.0006401785  0.1528956483
## 141   1.550515e-04 0.0005556315  0.2790546537
## 142  -4.573302e-05 0.0005965662 -0.0766604322
## 143   2.273847e-04 0.0005128269  0.4433945734
## 144   1.109221e-04 0.0005934272  0.1869178385
## 145  -1.860565e-04 0.0005821286 -0.3196141085
## 146  -5.380083e-05 0.0009581763 -0.0561491931
## 147   1.020218e-04 0.0004381825  0.2328294095
## 148  -1.405917e-04 0.0005404726 -0.2601273599
## 149   2.109084e-04 0.0005558318  0.3794463604
## 150   7.546265e-05 0.0004312458  0.1749875368
## 151   2.487433e-04 0.0004982967  0.4991871127
## 152  -1.889606e-04 0.0005856746 -0.3226374637
## 153  -2.173673e-05 0.0006289938 -0.0345579410
## 154  -7.384783e-05 0.0005332901 -0.1384758877
## 155  -7.265569e-06 0.0005825825 -0.0124713141
## 156   1.700297e-04 0.0005779353  0.2942019310
## 157   1.101647e-04 0.0005338903  0.2063433404
## 158   1.412740e-04 0.0004584720  0.3081409729
## 159  -1.544893e-04 0.0005445220 -0.2837153713
## 160  -1.165235e-04 0.0006991626 -0.1666614828
## 161   2.072708e-05 0.0004521798  0.0458381493
## 162   1.105050e-04 0.0005196182  0.2126658020
## 163   2.191528e-04 0.0004746537  0.4617109792
## 164  -1.239184e-04 0.0007054078 -0.1756691275
## 165   4.148813e-05 0.0004383515  0.0946457922
## 166  -5.076457e-05 0.0004768159 -0.1064657611
## 167  -1.175883e-04 0.0005311974 -0.2213645292
## 168   2.230483e-04 0.0004769652  0.4676406523
## 169  -2.001605e-04 0.0006164491 -0.3246992341
## 170   5.063581e-05 0.0004295101  0.1178920116
## 171  -5.667520e-05 0.0009655501 -0.0586973159
## 172   8.808125e-05 0.0004287047  0.2054590268
## 173   3.557055e-05 0.0007324838  0.0485615471
## 174   1.116152e-05 0.0004725805  0.0236182445
## 175   4.766326e-05 0.0006368250  0.0748451548
## 176   3.827482e-05 0.0006638801  0.0576532089
## 177  -7.559771e-05 0.0005110486 -0.1479266685
## 178   6.019787e-06 0.0004479228  0.0134393409
## 179  -1.469931e-04 0.0005947477 -0.2471519695
## 180   3.409142e-04 0.0005948166  0.5731417302
## 181   6.230497e-05 0.0004409180  0.1413073864
## 182  -5.602823e-05 0.0004764448 -0.1175964786
## 183  -7.193252e-05 0.0005023680 -0.1431868949
## 184   3.031813e-04 0.0005739069  0.5282761116
## 185  -5.651712e-05 0.0007064150 -0.0800055410
## 186  -1.925448e-04 0.0005893471 -0.3267086920
## 187  -1.335536e-04 0.0006869382 -0.1944185962
## 188   3.053782e-04 0.0005474742  0.5577947593
## 189  -1.671116e-04 0.0005556462 -0.3007519030
## 190  -6.042148e-05 0.0011095837 -0.0544541848
## 191  -1.123082e-04 0.0007311989 -0.1535946205
## 192   1.401675e-04 0.0004380954  0.3199474213
## 193   2.826979e-05 0.0008109124  0.0348617058
## 194  -2.383831e-04 0.0006798751 -0.3506277519
## 195  -3.015144e-05 0.0005692963 -0.0529626503
## 196  -2.485363e-04 0.0007454252 -0.3334154235
## 197  -1.288252e-05 0.0004559481 -0.0282543544
## 198  -2.202120e-04 0.0006768482 -0.3253491623
## 199  -6.357636e-05 0.0004683733 -0.1357386391
## 200   2.689815e-04 0.0005674494  0.4740185423
## 201   1.089166e-05 0.0006543889  0.0166440126
## 202  -2.096870e-04 0.0005990250 -0.3500471863
## 203   3.856169e-05 0.0004620845  0.0834515907
## 204  -2.968013e-05 0.0007025355 -0.0422471609
## 205  -6.736221e-05 0.0006570431 -0.1025232678
## 206   1.669058e-05 0.0006389268  0.0261228378
## 207   8.931676e-06 0.0004808140  0.0185761570
## 208   1.220792e-04 0.0004352224  0.2804985013
## 209  -1.241800e-04 0.0005839992 -0.2126372322
## 210   6.906780e-05 0.0004287720  0.1610827923
## 211  -1.653147e-04 0.0005850942 -0.2825437486
## 212   1.262462e-04 0.0004651054  0.2714357268
## 213   2.623056e-04 0.0005142525  0.5100716988
## 214   2.009070e-04 0.0004994086  0.4022897649
## 215   9.366501e-05 0.0004975154  0.1882655312
## 216   2.606391e-04 0.0005051139  0.5160006447
## 217   5.659764e-05 0.0004570209  0.1238403854
## 218   1.613132e-04 0.0004490521  0.3592304746
## 219  -1.371731e-04 0.0006591518 -0.2081054663
## 220   3.326253e-05 0.0004435462  0.0749922498
## 221  -1.172645e-04 0.0005119202 -0.2290678336
## 222   2.101882e-04 0.0005639084  0.3727346606
## 223  -1.443855e-04 0.0006166041 -0.2341624902
## 224  -1.496698e-05 0.0004591014 -0.0326005935
## 225  -1.975292e-04 0.0006093299 -0.3241745212
## 226   1.008781e-04 0.0004302632  0.2344566943
## 227   2.546396e-04 0.0005433795  0.4686219899
## 228   8.456152e-05 0.0006914280  0.1222998148
## 229  -6.122220e-05 0.0005929952 -0.1032423211
## 230  -2.433613e-05 0.0008083550 -0.0301057471
## 231  -1.001969e-04 0.0005647849 -0.1774072829
## 232   8.923711e-05 0.0005872062  0.1519689616
## 233   1.209987e-05 0.0004548802  0.0266001239
## 234  -9.257576e-05 0.0009147218 -0.1012064605
## 235  -9.018230e-05 0.0006226574 -0.1448345358
## 236   9.575052e-06 0.0004371928  0.0219012105
## 237  -1.109079e-04 0.0005023913 -0.2207599878
## 238  -2.394557e-04 0.0006536088 -0.3663594327
## 239  -1.370334e-04 0.0006315364 -0.2169841209
## 240  -4.864040e-05 0.0004602712 -0.1056776802
## 241   3.253207e-04 0.0005798808  0.5610131127
## 242  -1.037118e-04 0.0007440833 -0.1393819237
## 243  -1.349251e-04 0.0005207685 -0.2590884823
## 244  -7.471126e-05 0.0005022295 -0.1487591958
## 245   1.253422e-04 0.0005099881  0.2457747147
## 246   2.702341e-04 0.0005183907  0.5212942168
## 247   1.596698e-04 0.0006580761  0.2426312311
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## 858   2.870371e-04 0.0005367875  0.5347313752
## 859   1.254838e-04 0.0004345424  0.2887721986
## 860  -1.863439e-05 0.0007935087 -0.0234835330
## 861   7.581966e-05 0.0006183782  0.1226105022
## 862   1.910696e-05 0.0004347556  0.0439487420
## 863   1.565017e-04 0.0004484391  0.3489921860
## 864  -6.754015e-05 0.0009930962 -0.0680096749
## 865  -1.870737e-04 0.0005797947 -0.3226550674
## 866   2.027915e-04 0.0004743137  0.4275471164
## 867   7.222005e-05 0.0006018552  0.1199957263
## 868  -1.884318e-04 0.0005990887 -0.3145308136
## 869   8.812497e-05 0.0007274425  0.1211435543
## 870  -5.672174e-05 0.0004677729 -0.1212591528
## 871   1.182475e-04 0.0004420920  0.2674726431
## 872  -1.563814e-05 0.0006541872 -0.0239046845
## 873   1.333049e-04 0.0005138888  0.2594042444
## 874  -8.003781e-05 0.0009151362 -0.0874599940
## 875   8.628830e-05 0.0006202250  0.1391241844
## 876   3.700958e-05 0.0004446186  0.0832389237
## 877  -1.057834e-04 0.0005531673 -0.1912322959
## 878   1.076277e-04 0.0005282212  0.2037550102
## 879   3.221730e-05 0.0008494026  0.0379293621
## 880  -4.649596e-05 0.0006982054 -0.0665935201
## 881   1.978565e-04 0.0004651598  0.4253515897
## 882   1.629944e-04 0.0005522451  0.2951486886
## 883   2.007788e-04 0.0004631794  0.4334794281
## 884  -7.566755e-05 0.0005040796 -0.1501103268
## 885   1.574681e-04 0.0005040355  0.3124146423
## 886  -9.950895e-05 0.0005217610 -0.1907174771
## 887   1.770550e-04 0.0004683322  0.3780541546
## 888   1.488325e-04 0.0006204888  0.2398633058
## 889   7.659324e-06 0.0007143348  0.0107223160
## 890  -2.092089e-04 0.0005983381 -0.3496499572
## 891  -5.839219e-05 0.0009951473 -0.0586769345
## 892  -1.818909e-04 0.0005695112 -0.3193807147
## 893  -7.997067e-05 0.0007279360 -0.1098594931
## 894  -8.866510e-05 0.0005113040 -0.1734097626
## 895  -1.539376e-04 0.0005750690 -0.2676853788
## 896   1.010638e-04 0.0004384521  0.2305014643
## 897   2.493906e-04 0.0005080575  0.4908708258
## 898   9.617169e-05 0.0005254107  0.1830409604
## 899   1.008864e-04 0.0004316946  0.2336985676
## 900  -7.509518e-05 0.0005734863 -0.1309450397
## 901  -6.346868e-05 0.0009099383 -0.0697505260
## 902  -5.736186e-05 0.0005478200 -0.1047093184
## 903  -9.788431e-06 0.0004708326 -0.0207896188
## 904  -1.142548e-04 0.0006139746 -0.1860904085
## 905  -2.125358e-04 0.0006512832 -0.3263339615
## 906  -4.114969e-05 0.0008775047 -0.0468939776
## 907  -1.440127e-04 0.0005686328 -0.2532613216
## 908  -1.669272e-05 0.0005984842 -0.0278916574
## 909   2.236839e-04 0.0005042890  0.4435628642
## 910  -1.525769e-04 0.0005783223 -0.2638267962
## 911   2.549579e-05 0.0006969852  0.0365801036
## 912   1.724331e-04 0.0005267213  0.3273705478
## 913  -1.590970e-05 0.0005945649 -0.0267585572
## 914  -9.128228e-05 0.0005050992 -0.1807214797
## 915  -1.689027e-04 0.0005868598 -0.2878075979
## 916  -2.175052e-04 0.0006555961 -0.3317670473
## 917  -5.332347e-05 0.0005210406 -0.1023403257
## 918   1.546929e-04 0.0005115008  0.3024294369
## 919   9.910159e-06 0.0005671286  0.0174742723
## 920  -1.612872e-04 0.0006066181 -0.2658792151
## 921  -2.693284e-04 0.0007934054 -0.3394587425
## 922  -1.655731e-04 0.0005626391 -0.2942794873
## 923  -2.507390e-04 0.0007339515 -0.3416288270
## 924   1.663683e-05 0.0004504216  0.0369361365
## 925   2.752190e-05 0.0004392232  0.0626603912
## 926   2.044785e-04 0.0005441254  0.3757930049
## 927   8.156433e-05 0.0006205746  0.1314335729
## 928   1.364461e-04 0.0004366286  0.3124992954
## 929   1.714978e-04 0.0004499274  0.3811677932
## 930  -1.350644e-04 0.0005252891 -0.2571239701
## 931  -1.188536e-04 0.0006197262 -0.1917840812
## 932   1.014671e-04 0.0004666732  0.2174264851
## 933  -8.055285e-05 0.0005251405 -0.1533929551
## 934  -1.531859e-04 0.0005816622 -0.2633588647
## 935  -1.132092e-04 0.0005102969 -0.2218496020
## 936  -1.566196e-04 0.0005803525 -0.2698697473
## 937  -1.487521e-04 0.0005413459 -0.2747820558
## 938  -6.409850e-05 0.0004746044 -0.1350566700
## 939  -7.383604e-05 0.0004988739 -0.1480054321
## 940  -1.103732e-04 0.0005731928 -0.1925585821
## 941  -5.299486e-06 0.0005698655 -0.0092995374
## 942   1.773162e-04 0.0004644538  0.3817735202
## 943   2.629575e-05 0.0004441599  0.0592033367
## 944   1.901094e-05 0.0007520060  0.0252802961
## 945  -1.087750e-04 0.0005610929 -0.1938627418
## 946  -5.668433e-05 0.0010806372 -0.0524545468
## 947   2.065375e-04 0.0005291431  0.3903243881
## 948  -1.177479e-04 0.0005084661 -0.2315747444
## 949   1.205247e-04 0.0004457980  0.2703572257
## 950  -1.449707e-04 0.0005742100 -0.2524698065
## 951   1.904308e-04 0.0005882202  0.3237407214
## 952   1.149968e-04 0.0007156190  0.1606955421
## 953  -1.945717e-04 0.0005911736 -0.3291278882
## 954   7.462101e-05 0.0006306430  0.1183252907
## 955   1.265014e-04 0.0005408120  0.2339101640
## 956   3.889522e-05 0.0005550913  0.0700699493
## 957   9.976131e-05 0.0004771827  0.2090631450
## 958  -8.150620e-05 0.0004977677 -0.1637434606
## 959  -1.212438e-04 0.0005113443 -0.2371079548
## 960   8.312787e-05 0.0005255078  0.1581857808
## 961   5.523463e-05 0.0004314631  0.1280170480
## 962  -1.344336e-04 0.0005975221 -0.2249851239
## 963  -1.091301e-04 0.0006079827 -0.1794954507
## 964  -8.550978e-05 0.0004853563 -0.1761794072
## 965  -1.015354e-04 0.0005348576 -0.1898363544
## 966   1.350037e-04 0.0006310879  0.2139221213
## 967   1.932215e-04 0.0005666778  0.3409724372
## 968  -1.331828e-04 0.0005559827 -0.2395449397
## 969   2.096958e-04 0.0006099133  0.3438125276
## 970  -8.415962e-05 0.0004819991 -0.1746053643
## 971  -9.673804e-05 0.0005659882 -0.1709188184
## 972   2.038552e-04 0.0004733388  0.4306750951
## 973   2.082580e-04 0.0005814431  0.3581742945
## 974   1.870907e-05 0.0004406962  0.0424534352
## 975  -2.817722e-05 0.0009966941 -0.0282706839
## 976   1.067534e-04 0.0005594653  0.1908133144
## 977  -6.593374e-05 0.0004800125 -0.1373583887
## 978   2.109350e-04 0.0004682241  0.4505001035
## 979  -3.606951e-05 0.0005644865 -0.0638979208
## 980  -2.142567e-04 0.0006621099 -0.3235969005
## 981   3.499117e-05 0.0008563341  0.0408615916
## 982   2.465695e-04 0.0005200154  0.4741580153
## 983   1.747451e-04 0.0005807407  0.3009004111
## 984   1.417599e-04 0.0004386964  0.3231388213
## 985  -2.220245e-04 0.0006823020 -0.3254049585
## 986   9.941367e-05 0.0006406826  0.1551683583
## 987   1.382390e-04 0.0004388949  0.3149706365
## 988  -4.448931e-05 0.0007599561 -0.0585419494
## 989   1.455215e-04 0.0006567289  0.2215854082
## 990   2.171923e-05 0.0004342613  0.0500141999
## 991   1.088491e-04 0.0005257256  0.2070454231
## 992  -1.264855e-04 0.0005142777 -0.2459478086
## 993  -5.664391e-05 0.0011298526 -0.0501338919
## 994  -1.043366e-04 0.0006575568 -0.1586732181
## 995   4.070817e-05 0.0004665719  0.0872495185
## 996   1.888027e-04 0.0005654953  0.3338713698
## 997   2.923447e-04 0.0005461603  0.5352728223
## 998  -4.368931e-05 0.0008258173 -0.0529043253
## 999  -8.337641e-05 0.0009472775 -0.0880168861
## 1000 -6.202353e-05 0.0008986974 -0.0690149275

positivos <- sum(d_p1$Sharpe_ratio > 0)
print(positivos)

## [1] 500

negativos <- sum(d_p1$Sharpe_ratio < 0)
print(negativos)

## [1] 500

#Sharpe óptimo
max_sharpe <- max(d_p1$Sharpe_ratio)
print(max_sharpe)

## [1] 0.5811257

Un valor positivo en el índice de Sharpe indica que el portafolio ha generado un mayor retorno por unidad de riesgo en comparación con el activo libre de riesgo.

Sharpe_max <- data.frame(
  Ret = c(693),
  Risk = c(0.0003324367),
  Sharpe_ratio = c(0.0005791040)
)

print(Sharpe_max)

##   Ret         Risk Sharpe_ratio
## 1 693 0.0003324367  0.000579104

En este caso el índice de Sharpe se máximiza cuando el portafolio toma los valores de la tabla anterior.

Se calcula la varianza de los activos

var_hist <- var(ret2)
print(var_hist)

##              BIIB         ADSK         ALGN
## BIIB 0.0008394307 0.0001655036 0.0002168179
## ADSK 0.0001655036 0.0006189758 0.0004430757
## ALGN 0.0002168179 0.0004430757 0.0011722089

BIIB: La varianza de BIIB es 0.0008394307, lo que indica que sus valores están relativamente dispersos.

ADSK: La varianza de ADSK es 0.0006189758, lo que sugiere que sus valores están menos dispersos que los de la variable BIIB.

ALGN: La varianza de ALGN es 0.0011722089, lo que indica que sus valores son los más dispersos entre las tres variables.

Además las acciones de BIIB, ADSK y ALGN tienden a moverse en la misma dirección, con una relación más fuerte entre ADSK y ALGN.

2. Creación de Arboles binomiales a través del modelo Cox-Ross-Rubinstein (CRR)

Varianza forma 1: Volatilidad implícita

# Opciones BIIB
p_strike = 190
vol_imp = 0.6432

Varianza forma 2: Volatilidad del activo

op = c("BIIB")
data_op = lapply(op, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2023-06-01", to = "2024-04-19", auto.assign = FALSE)),
      type = "continuous")
})  #%returns
ret_op = as.data.frame(do.call(merge, data_op))
colnames(ret_op) = gsub(".Adjusted", "", colnames(ret_op))
ret_op = ret_op[-1, ]

# Volatilidad del activo original
var_op = var(ret_op)
desves_op = sqrt(var_op)
print(desves_op)

## [1] 0.01460798

Varianza forma 3:Volatilidad del portafolio

# Retornos BIIB
op_BIIB = c("BIIB")
data_op_BIIB = lapply(op_BIIB, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2023-06-01", to = "2024-04-19", auto.assign = FALSE)),
      type = "continuous")
})  #%returns
ret_op_BIIB = as.data.frame(do.call(merge, data_op_BIIB))
colnames(ret_op_BIIB) = gsub(".Adjusted", "", colnames(ret_op_BIIB))
ret_op_BIIB = ret_op_BIIB[-1, ]

# Retornos ADSK
op_ADSK = c("ADSK")
data_op_ADSK = lapply(op_ADSK, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2023-06-01", to = "2024-04-19", auto.assign = FALSE)),
      type = "continuous")
})  #%returns
ret_op_ADSK = as.data.frame(do.call(merge, data_op_ADSK))
colnames(ret_op_ADSK) = gsub(".Adjusted", "", colnames(ret_op_ADSK))
ret_op_ADSK = ret_op_ADSK[-1, ]

# Retornos ALGN
op_ALGN = c("ALGN")
data_op_ALGN = lapply(op_ALGN, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2023-06-01", to = "2024-04-19", auto.assign = FALSE)),
      type = "continuous")
})  #%returns
ret_op_ALGN = as.data.frame(do.call(merge, data_op_ALGN))
colnames(ret_op_ALGN) = gsub(".Adjusted", "", colnames(ret_op_ALGN))
ret_op_ALGN = ret_op_ALGN[-1, ]

ret_port <- cbind(ret_op_BIIB, ret_op_ADSK, ret_op_ALGN)
pesos <- c(0.3712, 0.5172, 0.1116)

# Calcular la matriz de varianza-covarianza
matriz_varianza_covarianza <- cov(ret_port)

# Calcular la varianza del portafolio
varianza_portafolio <- t(pesos) %*% matriz_varianza_covarianza %*% pesos

desves_port = sqrt(varianza_portafolio)
print(desves_port)

##           [,1]
## [1,] 0.0134236

2.1. Valuación de las opciones europeas call y put

S1 <- 194.50
sigma1 <- 0.6432
delta_t <- 0.25
N <- 4

build_stock_tree <- function(S, sigma, delta_t, N) {
  tree = matrix(0, nrow=N+1, ncol=N+1)
  U = exp(sigma*sqrt(delta_t))
  D = exp(-sigma*sqrt(delta_t))
  for (i in 1:(N+1)) {
    for (j in 1:i) {
      tree[i, j] = S * U^(j-1) * D^((i-1)-(j-1))
    }  }
  return(tree)
}

First_tree <- build_stock_tree(S1, sigma1, delta_t, N)

K <- 190

IntrinsecValue <- First_tree[5,]-K
IntrinsecValue[IntrinsecValue<0] <- 0
print(IntrinsecValue)

## [1]   0.0000   0.0000   4.5000 180.0478 514.0379

q_prob <- function(r, delta_t, sigma) {
  u = exp(sigma*sqrt(delta_t))
  d = exp(-sigma*sqrt(delta_t))
    return((exp(r*delta_t) - d)/(u-d))
}

value_binomial_option <- function(tree, sigma, delta_t, r, X, type) {
  q = q_prob(r, delta_t, sigma)
  option_tree = matrix(0, nrow=nrow(tree), ncol=ncol(tree))
  if(type == 'put') {
    option_tree[nrow(option_tree),] = pmax(X - tree[nrow(tree),], 0)
  } else {  option_tree[nrow(option_tree),] = pmax(tree[nrow(tree),] - X, 0)
  }
  for (i in (nrow(tree)-1):1) {
    for(j in 1:i) {
      # Calculamos los pesos dentro del ciclo
      peso_abajo = (1 - q) * exp(-r * delta_t)
      peso_arriba = q * exp(-r * delta_t)
      option_tree[i,j] = (peso_abajo * option_tree[i+1,j] + peso_arriba * option_tree[i+1,j+1])
    }
  }
  return(option_tree)
}

binomial_option <- function(type, sigma, T, r, X, S, N) {
  q <- q_prob(r=r, delta_t=T/N, sigma=sigma)
  tree <- build_stock_tree(S=S, sigma=sigma, delta_t=T/N, N=N)
  option <- value_binomial_option(tree, sigma=sigma, delta_t=T/N, r=r, X=X, type=type)
  return(list(q=q, stock=tree, option=option, price=option[1,1]))
}

La tasa libre de riesgo trimestral es 1/06/2023 = 5.50%

RESULTADOS FORMA 1: Volatilidad Implícita

results1 <- binomial_option(type='call', sigma=0.6432, T=1, r=0.055, X=190, S=194.5, N=4)


results1$q

## [1] 0.4414444

results1$stock

##           [,1]     [,2]     [,3]     [,4]     [,5]
## [1,] 194.50000   0.0000   0.0000   0.0000   0.0000
## [2,] 141.01019 268.2803   0.0000   0.0000   0.0000
## [3,] 102.23071 194.5000 370.0478   0.0000   0.0000
## [4,]  74.11605 141.0102 268.2803 510.4191   0.0000
## [5,]  53.73326 102.2307 194.5000 370.0478 704.0379

results1$option

##            [,1]       [,2]      [,3]     [,4]     [,5]
## [1,] 52.7832645   0.000000   0.00000   0.0000   0.0000
## [2,] 16.2728770 100.634965   0.00000   0.0000   0.0000
## [3,]  0.8531422  36.293693 185.20160   0.0000   0.0000
## [4,]  0.0000000   1.959372  80.87488 323.0137   0.0000
## [5,]  0.0000000   0.000000   4.50000 180.0478 514.0379

results1$price

## [1] 52.78326

RESULTADOS FORMA 2: Volatilidad del activo

results2 <- binomial_option(type='call', sigma=desves_op, T=1, r=0.055, X=190, S=194.5, N=4)


results2$q

## [1] 1.445933

results2$stock

##          [,1]     [,2]     [,3]     [,4]     [,5]
## [1,] 194.5000   0.0000   0.0000   0.0000   0.0000
## [2,] 193.0845 195.9258   0.0000   0.0000   0.0000
## [3,] 191.6794 194.5000 197.3621   0.0000   0.0000
## [4,] 190.2845 193.0845 195.9258 198.8089   0.0000
## [5,] 188.8997 191.6794 194.5000 197.3621 200.2663

results2$option

##           [,1]      [,2]      [,3]      [,4]     [,5]
## [1,] 14.709003  0.000000  0.000000  0.000000  0.00000
## [2,] 10.668974 13.603878  0.000000  0.000000  0.00000
## [3,]  7.046076  9.653810 12.515916  0.000000  0.00000
## [4,]  2.395140  5.679171  8.520448 11.403534  0.00000
## [5,]  0.000000  1.679400  4.500000  7.362105 10.26633

results2$price

## [1] 14.709

RESULTADOS FORMA 3: Volatilidad del Portafolio

results3 <- binomial_option(type='call', sigma=desves_port, T=1, r=0.055, X=190, S=194.5, N=4)


results3$q

##          [,1]
## [1,] 1.529705

results3$stock

##          [,1]     [,2]     [,3]     [,4]     [,5]
## [1,] 194.5000   0.0000   0.0000   0.0000   0.0000
## [2,] 193.1989 195.8098   0.0000   0.0000   0.0000
## [3,] 191.9066 194.5000 197.1285   0.0000   0.0000
## [4,] 190.6228 193.1989 195.8098 198.4560   0.0000
## [5,] 189.3477 191.9066 194.5000 197.1285 199.7925

results3$option

##           [,1]      [,2]      [,3]      [,4]     [,5]
## [1,] 14.716429  0.000000  0.000000  0.000000 0.000000
## [2,] 10.783945 13.487887  0.000000  0.000000 0.000000
## [3,]  7.238431  9.653810 12.282302  0.000000 0.000000
## [4,]  2.876641  5.793548  8.404456 11.050649 0.000000
## [5,]  0.000000  1.906556  4.500000  7.128492 9.792505

results3$price

## [1] 14.71643

Análisis

Al evaluar los 3 casos, se observa que todos los árboles presentan una tendencia a la baja, lo que indica que se encuentran en put.

Primer árbol: Posee el valor inicial más alto (194.5000) y genera ganancias constantes a lo largo de los cinco períodos.

Segundo árbol: Presenta un valor inicial menor (52.78326) comparado con el primer árbol, pero genera mayores ganancias en los últimos períodos.

Tercer árbol: Su valor inicial es similar al del segundo árbol (14.709) y genera ganancias consistentes a lo largo de los cinco períodos.

En cuanto a la volatilidad, se observa que la volatilidad implícita genera mayores ganancias, ya que el valor de la opción es mayor.

2.2. Escenarios con valores extremos

Resultados con valores extremos (precio más bajo)

results_pre_ba <- binomial_option(type='call', sigma=0.8413, T=1, r=0.055, X=190, S=180, N=4)

print(results_pre_ba)

## $q
## [1] 0.4123424
## 
## $stock
##           [,1]      [,2]     [,3]     [,4]     [,5]
## [1,] 180.00000   0.00000   0.0000   0.0000   0.0000
## [2,] 118.19158 274.13121   0.0000   0.0000   0.0000
## [3,]  77.60694 180.00000 417.4884   0.0000   0.0000
## [4,]  50.95826 118.19158 274.1312 635.8145   0.0000
## [5,]  33.46021  77.60694 180.0000 417.4884 968.3144
## 
## $option
##          [,1]      [,2]      [,3]     [,4]     [,5]
## [1,] 56.78003   0.00000   0.00000   0.0000   0.0000
## [2,] 15.30448 117.79619   0.00000   0.0000   0.0000
## [3,]  0.00000  37.62982 236.00199   0.0000   0.0000
## [4,]  0.00000   0.00000  92.52215 448.4091   0.0000
## [5,]  0.00000   0.00000   0.00000 227.4884 778.3144
## 
## $price
## [1] 56.78003

Resultados con valores extremos (precio más alto)

results_pre_al <- binomial_option(type='call', sigma=1.6372, T=1, r=0.055, X=190, S=255, N=4)

print(results_pre_al)

## $q
## [1] 0.3136419
## 
## $stock
##            [,1]      [,2]      [,3]     [,4]     [,5]
## [1,] 255.000000   0.00000    0.0000    0.000    0.000
## [2,] 112.467416 578.16746    0.0000    0.000    0.000
## [3,]  49.603607 255.00000 1310.8926    0.000    0.000
## [4,]  21.877606 112.46742  578.1675 2972.217    0.000
## [5,]   9.649089  49.60361  255.0000 1310.893 6738.978
## 
## $option
##            [,1]      [,2]      [,3]     [,4]     [,5]
## [1,] 166.953414   0.00000    0.0000    0.000    0.000
## [2,]  45.819691 439.40608    0.0000    0.000    0.000
## [3,]   6.220688 134.49875 1126.0464    0.000    0.000
## [4,]   0.000000  20.10833  390.7621 2784.812    0.000
## [5,]   0.000000   0.00000   65.0000 1120.893 6548.978
## 
## $price
## [1] 166.9534

Análisis

Precio más bajo (q = 0.4123424): Se observa una alta sensibilidad del valor de la opción a los cambios en el precio del activo, especialmente en los períodos posteriores. Un aumento en la probabilidad de éxito (q) implicaría un mayor valor de la opción.

Precio más alto (q = 0.3136419): Se observa una alta sensibilidad del valor de la opción a los cambios en el precio del activo, especialmente en los períodos posteriores. A pesar de la menor probabilidad de éxito (q), el valor de la opción es mayor debido al mayor precio inicial del activo.

3. Creación de coberturas

3.1. Estrategias de cobertura

Retornos trimestre 1

data_tri1 = lapply(s1, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2023-06-01", to = "2023-08-31", auto.assign = FALSE)),
      type = "continuous")
})  #%returns

# Convertir a data frame
ret_tri1 = as.data.frame(do.call(merge, data_tri1))
colnames(ret_tri1) = gsub(".Adjusted", "", colnames(ret_tri1))

ret_tri1 = ret_tri1[-1, ]

ret_tri1 = data.frame(Date = as.Date(row.names(ret_tri1)), ret_tri1)
row.names(ret_tri1) = NULL

peso_BIIB <- 0.3712
peso_ADSK <- 0.5172
peso_ALGN <- 0.1116

ret_tri1 <- ret_tri1 %>%
  mutate(BIIB_mult = BIIB * peso_BIIB,
         ADSK_mult = ADSK * peso_ADSK,
         ALGN_mult = ALGN * peso_ALGN)

suma_tri1 <- sum(ret_tri1[c("BIIB_mult", "ADSK_mult", "ALGN_mult")])

Gráfica

graf_tri1 <- ggplot(ret_tri1, aes(x = Date)) +
  geom_line(aes(y = BIIB_mult, color = "BIIB_mult")) +
  geom_line(aes(y = ADSK_mult, color = "ADSK_mult")) +
  geom_line(aes(y = ALGN_mult, color = "ALGN_mult")) +
  labs(title = "Rendimientos de acciones",
       x = "Fecha",
       y = "Rendimiento",
       color = "Acciones") +
  theme_minimal()

graf_tri1 <- ggplotly(graf_tri1, tooltip = c("y"))
graf_tri1

Retornos trimestre 2

data_tri2 = lapply(s1, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2023-09-01", to = "2023-11-30", auto.assign = FALSE)),
      type = "continuous")
})  #%returns

# Convertir a data frame
ret_tri2 = as.data.frame(do.call(merge, data_tri2))
colnames(ret_tri2) = gsub(".Adjusted", "", colnames(ret_tri2))

ret_tri2 = ret_tri2[-1, ]

ret_tri2 = data.frame(Date = as.Date(row.names(ret_tri2)), ret_tri2)
row.names(ret_tri2) = NULL

peso_BIIB <- 0.3712
peso_ADSK <- 0.5172
peso_ALGN <- 0.1116

ret_tri2 <- ret_tri2 %>%
  mutate(BIIB_mult = BIIB * peso_BIIB,
         ADSK_mult = ADSK * peso_ADSK,
         ALGN_mult = ALGN * peso_ALGN)

suma_tri2 <- sum(ret_tri2[c("BIIB_mult", "ADSK_mult", "ALGN_mult")])

Gráfica

graf_tri2 <- ggplot(ret_tri2, aes(x = Date)) +
  geom_line(aes(y = BIIB_mult, color = "BIIB_mult")) +
  geom_line(aes(y = ADSK_mult, color = "ADSK_mult")) +
  geom_line(aes(y = ALGN_mult, color = "ALGN_mult")) +
  labs(title = "Rendimientos de acciones",
       x = "Fecha",
       y = "Rendimiento",
       color = "Acciones") +
  theme_minimal()

graf_tri2 <- ggplotly(graf_tri2, tooltip = c("y"))
graf_tri2

Retornos trimestre 3

data_tri3 = lapply(s1, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2023-12-01", to = "2024-02-29", auto.assign = FALSE)),
      type = "continuous")
})  #%returns

# Convertir a data frame
ret_tri3 = as.data.frame(do.call(merge, data_tri3))
colnames(ret_tri3) = gsub(".Adjusted", "", colnames(ret_tri3))

ret_tri3 = ret_tri3[-1, ]

ret_tri3 = data.frame(Date = as.Date(row.names(ret_tri3)), ret_tri3)
row.names(ret_tri3) = NULL

peso_BIIB <- 0.3712
peso_ADSK <- 0.5172
peso_ALGN <- 0.1116

ret_tri3 <- ret_tri3 %>%
  mutate(BIIB_mult = BIIB * peso_BIIB,
         ADSK_mult = ADSK * peso_ADSK,
         ALGN_mult = ALGN * peso_ALGN)

suma_tri3 <- sum(ret_tri3[c("BIIB_mult", "ADSK_mult", "ALGN_mult")])

Gráfica

graf_tri3 <- ggplot(ret_tri3, aes(x = Date)) +
  geom_line(aes(y = BIIB_mult, color = "BIIB_mult")) +
  geom_line(aes(y = ADSK_mult, color = "ADSK_mult")) +
  geom_line(aes(y = ALGN_mult, color = "ALGN_mult")) +
  labs(title = "Rendimientos de acciones",
       x = "Fecha",
       y = "Rendimiento",
       color = "Acciones") +
  theme_minimal()

graf_tri3 <- ggplotly(graf_tri3, tooltip = c("y"))
graf_tri3

Retornos trimestre 4

data_tri4 = lapply(s1, FUN = function(x) {
  ROC(Ad(getSymbols(x, from = "2024-03-01", to = "2024-04-17", auto.assign = FALSE)),
      type = "continuous")
})  #%returns

# Convertir a data frame
ret_tri4 = as.data.frame(do.call(merge, data_tri4))
colnames(ret_tri4) = gsub(".Adjusted", "", colnames(ret_tri4))

ret_tri4 = ret_tri4[-1, ]

ret_tri4 = data.frame(Date = as.Date(row.names(ret_tri4)), ret_tri4)
row.names(ret_tri4) = NULL

peso_BIIB <- 0.3712
peso_ADSK <- 0.5172
peso_ALGN <- 0.1116

ret_tri4 <- ret_tri4 %>%
  mutate(BIIB_mult = BIIB * peso_BIIB,
         ADSK_mult = ADSK * peso_ADSK,
         ALGN_mult = ALGN * peso_ALGN)

suma_tri4 <- sum(ret_tri4[c("BIIB_mult", "ADSK_mult", "ALGN_mult")])

Gráfica

graf_tri4 <- ggplot(ret_tri4, aes(x = Date)) +
  geom_line(aes(y = BIIB_mult, color = "BIIB_mult")) +
  geom_line(aes(y = ADSK_mult, color = "ADSK_mult")) +
  geom_line(aes(y = ALGN_mult, color = "ALGN_mult")) +
  labs(title = "Rendimientos de acciones",
       x = "Fecha",
       y = "Rendimiento",
       color = "Acciones") +
  theme_minimal()

graf_tri4 <- ggplotly(graf_tri4, tooltip = c("y"))
graf_tri4

pyg <- data.frame(suma_tri1, suma_tri2, suma_tri3, suma_tri4)
print(pyg)

##    suma_tri1  suma_tri2  suma_tri3  suma_tri4
## 1 0.02319452 -0.1282955 0.07968275 -0.1209405

La suma de los rendimientos en el primer y tercer trimestre es positiva, lo que indica una expectativa de aumento moderado en el precio del activo subyacente. Debido a la perspectiva alcista, se utiliza la estrategia Bull Call Spread.

La suma de los rendimientos en el segundo y cuarto trimestre es negativa, lo que indica una expectativa de caída o movimiento bajista en el precio del activo subyacente. Debido a la perspectiva bajista, se utiliza la estrategia Bear Long Spread.

Bull Call Spread

Trimestre 1

accion = c("BIIB")
prices1 = lapply(accion, FUN = function(x) {
  getSymbols(x, from = "2023-06-01", to = "2023-08-30", auto.assign = FALSE)
})

pricestri1 = as.data.frame(do.call(merge, prices1))
prices_tri1 <- select(pricestri1, BIIB.Close)

library(roptions)
estrategia1 <- call.spread(-22, 12, 20, 20, llimit = 255, ulimit = 255)

## [1] "This is a Bull Call Spread because excercise price of long call (k1) is less than excercise price of short call (k2)"
##     stock_price_at_expiration long_call short_call profit_loss
## 1                        -277       -20         20           0
## 2                        -276       -20         20           0
## 3                        -275       -20         20           0
## 4                        -274       -20         20           0
## 5                        -273       -20         20           0
## 6                        -272       -20         20           0
## 7                        -271       -20         20           0
## 8                        -270       -20         20           0
## 9                        -269       -20         20           0
## 10                       -268       -20         20           0
## 11                       -267       -20         20           0
## 12                       -266       -20         20           0
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## 240                       -38       -20         20           0
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## 245                       -33       -20         20           0
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## 254                       -24       -20         20           0
## 255                       -23       -20         20           0
## 256                       -22       -20         20           0
## 257                       -21       -19         20           1
## 258                       -20       -18         20           2
## 259                       -19       -17         20           3
## 260                       -18       -16         20           4
## 261                       -17       -15         20           5
## 262                       -16       -14         20           6
## 263                       -15       -13         20           7
## 264                       -14       -12         20           8
## 265                       -13       -11         20           9
## 266                       -12       -10         20          10
## 267                       -11        -9         20          11
## 268                       -10        -8         20          12
## 269                        -9        -7         20          13
## 270                        -8        -6         20          14
## 271                        -7        -5         20          15
## 272                        -6        -4         20          16
## 273                        -5        -3         20          17
## 274                        -4        -2         20          18
## 275                        -3        -1         20          19
## 276                        -2         0         20          20
## 277                        -1         1         20          21
## 278                         0         2         20          22
## 279                         1         3         20          23
## 280                         2         4         20          24
## 281                         3         5         20          25
## 282                         4         6         20          26
## 283                         5         7         20          27
## 284                         6         8         20          28
## 285                         7         9         20          29
## 286                         8        10         20          30
## 287                         9        11         20          31
## 288                        10        12         20          32
## 289                        11        13         20          33
## 290                        12        14         20          34
## 291                        13        15         19          34
## 292                        14        16         18          34
## 293                        15        17         17          34
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## 295                        17        19         15          34
## 296                        18        20         14          34
## 297                        19        21         13          34
## 298                        20        22         12          34
## 299                        21        23         11          34
## 300                        22        24         10          34
## 301                        23        25          9          34
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## 305                        27        29          5          34
## 306                        28        30          4          34
## 307                        29        31          3          34
## 308                        30        32          2          34
## 309                        31        33          1          34
## 310                        32        34          0          34
## 311                        33        35         -1          34
## 312                        34        36         -2          34
## 313                        35        37         -3          34
## 314                        36        38         -4          34
## 315                        37        39         -5          34
## 316                        38        40         -6          34
## 317                        39        41         -7          34
## 318                        40        42         -8          34
## 319                        41        43         -9          34
## 320                        42        44        -10          34
## 321                        43        45        -11          34
## 322                        44        46        -12          34
## 323                        45        47        -13          34
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## 340                        62        64        -30          34
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## 342                        64        66        -32          34
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## 344                        66        68        -34          34
## 345                        67        69        -35          34
## 346                        68        70        -36          34
## 347                        69        71        -37          34
## 348                        70        72        -38          34
## 349                        71        73        -39          34
## 350                        72        74        -40          34
## 351                        73        75        -41          34
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## 356                        78        80        -46          34
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## 358                        80        82        -48          34
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## 360                        82        84        -50          34
## 361                        83        85        -51          34
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## 363                        85        87        -53          34
## 364                        86        88        -54          34
## 365                        87        89        -55          34
## 366                        88        90        -56          34
## 367                        89        91        -57          34
## 368                        90        92        -58          34
## 369                        91        93        -59          34
## 370                        92        94        -60          34
## 371                        93        95        -61          34
## 372                        94        96        -62          34
## 373                        95        97        -63          34
## 374                        96        98        -64          34
## 375                        97        99        -65          34
## 376                        98       100        -66          34
## 377                        99       101        -67          34
## 378                       100       102        -68          34
## 379                       101       103        -69          34
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## 388                       110       112        -78          34
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## 415                       137       139       -105          34
## 416                       138       140       -106          34
## 417                       139       141       -107          34
## 418                       140       142       -108          34
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## 426                       148       150       -116          34
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## 428                       150       152       -118          34
## 429                       151       153       -119          34
## 430                       152       154       -120          34
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## 452                       174       176       -142          34
## 453                       175       177       -143          34
## 454                       176       178       -144          34
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## 456                       178       180       -146          34
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## 458                       180       182       -148          34
## 459                       181       183       -149          34
## 460                       182       184       -150          34
## 461                       183       185       -151          34
## 462                       184       186       -152          34
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## 466                       188       190       -156          34
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## 473                       195       197       -163          34
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## 475                       197       199       -165          34
## 476                       198       200       -166          34
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## 478                       200       202       -168          34
## 479                       201       203       -169          34
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## 494                       216       218       -184          34
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## 497                       219       221       -187          34
## 498                       220       222       -188          34
## 499                       221       223       -189          34
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## 501                       223       225       -191          34
## 502                       224       226       -192          34
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## 506                       228       230       -196          34
## 507                       229       231       -197          34
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## 509                       231       233       -199          34
## 510                       232       234       -200          34
## 511                       233       235       -201          34

Trimestre 3

accion = c("BIIB")
prices3 = lapply(accion, FUN = function(x) {
  getSymbols(x, from = "2023-12-01", to = "2024-02-29", auto.assign = FALSE)
})

pricestri3 = as.data.frame(do.call(merge, prices3))
prices_tri3 <- select(pricestri3, BIIB.Close)

library(roptions)
estrategia3 <- call.spread(-33, 23, 20, 20, llimit = 255, ulimit = 255)

## [1] "This is a Bull Call Spread because excercise price of long call (k1) is less than excercise price of short call (k2)"
##     stock_price_at_expiration long_call short_call profit_loss
## 1                        -288       -20         20           0
## 2                        -287       -20         20           0
## 3                        -286       -20         20           0
## 4                        -285       -20         20           0
## 5                        -284       -20         20           0
## 6                        -283       -20         20           0
## 7                        -282       -20         20           0
## 8                        -281       -20         20           0
## 9                        -280       -20         20           0
## 10                       -279       -20         20           0
## 11                       -278       -20         20           0
## 12                       -277       -20         20           0
## 13                       -276       -20         20           0
## 14                       -275       -20         20           0
## 15                       -274       -20         20           0
## 16                       -273       -20         20           0
## 17                       -272       -20         20           0
## 18                       -271       -20         20           0
## 19                       -270       -20         20           0
## 20                       -269       -20         20           0
## 21                       -268       -20         20           0
## 22                       -267       -20         20           0
## 23                       -266       -20         20           0
## 24                       -265       -20         20           0
## 25                       -264       -20         20           0
## 26                       -263       -20         20           0
## 27                       -262       -20         20           0
## 28                       -261       -20         20           0
## 29                       -260       -20         20           0
## 30                       -259       -20         20           0
## 31                       -258       -20         20           0
## 32                       -257       -20         20           0
## 33                       -256       -20         20           0
## 34                       -255       -20         20           0
## 35                       -254       -20         20           0
## 36                       -253       -20         20           0
## 37                       -252       -20         20           0
## 38                       -251       -20         20           0
## 39                       -250       -20         20           0
## 40                       -249       -20         20           0
## 41                       -248       -20         20           0
## 42                       -247       -20         20           0
## 43                       -246       -20         20           0
## 44                       -245       -20         20           0
## 45                       -244       -20         20           0
## 46                       -243       -20         20           0
## 47                       -242       -20         20           0
## 48                       -241       -20         20           0
## 49                       -240       -20         20           0
## 50                       -239       -20         20           0
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## 52                       -237       -20         20           0
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## 61                       -228       -20         20           0
## 62                       -227       -20         20           0
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## 65                       -224       -20         20           0
## 66                       -223       -20         20           0
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## 100                      -189       -20         20           0
## 101                      -188       -20         20           0
## 102                      -187       -20         20           0
## 103                      -186       -20         20           0
## 104                      -185       -20         20           0
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## 146                      -143       -20         20           0
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## 176                      -113       -20         20           0
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## 180                      -109       -20         20           0
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## 182                      -107       -20         20           0
## 183                      -106       -20         20           0
## 184                      -105       -20         20           0
## 185                      -104       -20         20           0
## 186                      -103       -20         20           0
## 187                      -102       -20         20           0
## 188                      -101       -20         20           0
## 189                      -100       -20         20           0
## 190                       -99       -20         20           0
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## 192                       -97       -20         20           0
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## 194                       -95       -20         20           0
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## 196                       -93       -20         20           0
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## 200                       -89       -20         20           0
## 201                       -88       -20         20           0
## 202                       -87       -20         20           0
## 203                       -86       -20         20           0
## 204                       -85       -20         20           0
## 205                       -84       -20         20           0
## 206                       -83       -20         20           0
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## 209                       -80       -20         20           0
## 210                       -79       -20         20           0
## 211                       -78       -20         20           0
## 212                       -77       -20         20           0
## 213                       -76       -20         20           0
## 214                       -75       -20         20           0
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## 218                       -71       -20         20           0
## 219                       -70       -20         20           0
## 220                       -69       -20         20           0
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## 222                       -67       -20         20           0
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## 224                       -65       -20         20           0
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## 230                       -59       -20         20           0
## 231                       -58       -20         20           0
## 232                       -57       -20         20           0
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## 235                       -54       -20         20           0
## 236                       -53       -20         20           0
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## 239                       -50       -20         20           0
## 240                       -49       -20         20           0
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## 243                       -46       -20         20           0
## 244                       -45       -20         20           0
## 245                       -44       -20         20           0
## 246                       -43       -20         20           0
## 247                       -42       -20         20           0
## 248                       -41       -20         20           0
## 249                       -40       -20         20           0
## 250                       -39       -20         20           0
## 251                       -38       -20         20           0
## 252                       -37       -20         20           0
## 253                       -36       -20         20           0
## 254                       -35       -20         20           0
## 255                       -34       -20         20           0
## 256                       -33       -20         20           0
## 257                       -32       -19         20           1
## 258                       -31       -18         20           2
## 259                       -30       -17         20           3
## 260                       -29       -16         20           4
## 261                       -28       -15         20           5
## 262                       -27       -14         20           6
## 263                       -26       -13         20           7
## 264                       -25       -12         20           8
## 265                       -24       -11         20           9
## 266                       -23       -10         20          10
## 267                       -22        -9         20          11
## 268                       -21        -8         20          12
## 269                       -20        -7         20          13
## 270                       -19        -6         20          14
## 271                       -18        -5         20          15
## 272                       -17        -4         20          16
## 273                       -16        -3         20          17
## 274                       -15        -2         20          18
## 275                       -14        -1         20          19
## 276                       -13         0         20          20
## 277                       -12         1         20          21
## 278                       -11         2         20          22
## 279                       -10         3         20          23
## 280                        -9         4         20          24
## 281                        -8         5         20          25
## 282                        -7         6         20          26
## 283                        -6         7         20          27
## 284                        -5         8         20          28
## 285                        -4         9         20          29
## 286                        -3        10         20          30
## 287                        -2        11         20          31
## 288                        -1        12         20          32
## 289                         0        13         20          33
## 290                         1        14         20          34
## 291                         2        15         20          35
## 292                         3        16         20          36
## 293                         4        17         20          37
## 294                         5        18         20          38
## 295                         6        19         20          39
## 296                         7        20         20          40
## 297                         8        21         20          41
## 298                         9        22         20          42
## 299                        10        23         20          43
## 300                        11        24         20          44
## 301                        12        25         20          45
## 302                        13        26         20          46
## 303                        14        27         20          47
## 304                        15        28         20          48
## 305                        16        29         20          49
## 306                        17        30         20          50
## 307                        18        31         20          51
## 308                        19        32         20          52
## 309                        20        33         20          53
## 310                        21        34         20          54
## 311                        22        35         20          55
## 312                        23        36         20          56
## 313                        24        37         19          56
## 314                        25        38         18          56
## 315                        26        39         17          56
## 316                        27        40         16          56
## 317                        28        41         15          56
## 318                        29        42         14          56
## 319                        30        43         13          56
## 320                        31        44         12          56
## 321                        32        45         11          56
## 322                        33        46         10          56
## 323                        34        47          9          56
## 324                        35        48          8          56
## 325                        36        49          7          56
## 326                        37        50          6          56
## 327                        38        51          5          56
## 328                        39        52          4          56
## 329                        40        53          3          56
## 330                        41        54          2          56
## 331                        42        55          1          56
## 332                        43        56          0          56
## 333                        44        57         -1          56
## 334                        45        58         -2          56
## 335                        46        59         -3          56
## 336                        47        60         -4          56
## 337                        48        61         -5          56
## 338                        49        62         -6          56
## 339                        50        63         -7          56
## 340                        51        64         -8          56
## 341                        52        65         -9          56
## 342                        53        66        -10          56
## 343                        54        67        -11          56
## 344                        55        68        -12          56
## 345                        56        69        -13          56
## 346                        57        70        -14          56
## 347                        58        71        -15          56
## 348                        59        72        -16          56
## 349                        60        73        -17          56
## 350                        61        74        -18          56
## 351                        62        75        -19          56
## 352                        63        76        -20          56
## 353                        64        77        -21          56
## 354                        65        78        -22          56
## 355                        66        79        -23          56
## 356                        67        80        -24          56
## 357                        68        81        -25          56
## 358                        69        82        -26          56
## 359                        70        83        -27          56
## 360                        71        84        -28          56
## 361                        72        85        -29          56
## 362                        73        86        -30          56
## 363                        74        87        -31          56
## 364                        75        88        -32          56
## 365                        76        89        -33          56
## 366                        77        90        -34          56
## 367                        78        91        -35          56
## 368                        79        92        -36          56
## 369                        80        93        -37          56
## 370                        81        94        -38          56
## 371                        82        95        -39          56
## 372                        83        96        -40          56
## 373                        84        97        -41          56
## 374                        85        98        -42          56
## 375                        86        99        -43          56
## 376                        87       100        -44          56
## 377                        88       101        -45          56
## 378                        89       102        -46          56
## 379                        90       103        -47          56
## 380                        91       104        -48          56
## 381                        92       105        -49          56
## 382                        93       106        -50          56
## 383                        94       107        -51          56
## 384                        95       108        -52          56
## 385                        96       109        -53          56
## 386                        97       110        -54          56
## 387                        98       111        -55          56
## 388                        99       112        -56          56
## 389                       100       113        -57          56
## 390                       101       114        -58          56
## 391                       102       115        -59          56
## 392                       103       116        -60          56
## 393                       104       117        -61          56
## 394                       105       118        -62          56
## 395                       106       119        -63          56
## 396                       107       120        -64          56
## 397                       108       121        -65          56
## 398                       109       122        -66          56
## 399                       110       123        -67          56
## 400                       111       124        -68          56
## 401                       112       125        -69          56
## 402                       113       126        -70          56
## 403                       114       127        -71          56
## 404                       115       128        -72          56
## 405                       116       129        -73          56
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## 407                       118       131        -75          56
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## 409                       120       133        -77          56
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## 411                       122       135        -79          56
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## 413                       124       137        -81          56
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## 417                       128       141        -85          56
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## 420                       131       144        -88          56
## 421                       132       145        -89          56
## 422                       133       146        -90          56
## 423                       134       147        -91          56
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## 426                       137       150        -94          56
## 427                       138       151        -95          56
## 428                       139       152        -96          56
## 429                       140       153        -97          56
## 430                       141       154        -98          56
## 431                       142       155        -99          56
## 432                       143       156       -100          56
## 433                       144       157       -101          56
## 434                       145       158       -102          56
## 435                       146       159       -103          56
## 436                       147       160       -104          56
## 437                       148       161       -105          56
## 438                       149       162       -106          56
## 439                       150       163       -107          56
## 440                       151       164       -108          56
## 441                       152       165       -109          56
## 442                       153       166       -110          56
## 443                       154       167       -111          56
## 444                       155       168       -112          56
## 445                       156       169       -113          56
## 446                       157       170       -114          56
## 447                       158       171       -115          56
## 448                       159       172       -116          56
## 449                       160       173       -117          56
## 450                       161       174       -118          56
## 451                       162       175       -119          56
## 452                       163       176       -120          56
## 453                       164       177       -121          56
## 454                       165       178       -122          56
## 455                       166       179       -123          56
## 456                       167       180       -124          56
## 457                       168       181       -125          56
## 458                       169       182       -126          56
## 459                       170       183       -127          56
## 460                       171       184       -128          56
## 461                       172       185       -129          56
## 462                       173       186       -130          56
## 463                       174       187       -131          56
## 464                       175       188       -132          56
## 465                       176       189       -133          56
## 466                       177       190       -134          56
## 467                       178       191       -135          56
## 468                       179       192       -136          56
## 469                       180       193       -137          56
## 470                       181       194       -138          56
## 471                       182       195       -139          56
## 472                       183       196       -140          56
## 473                       184       197       -141          56
## 474                       185       198       -142          56
## 475                       186       199       -143          56
## 476                       187       200       -144          56
## 477                       188       201       -145          56
## 478                       189       202       -146          56
## 479                       190       203       -147          56
## 480                       191       204       -148          56
## 481                       192       205       -149          56
## 482                       193       206       -150          56
## 483                       194       207       -151          56
## 484                       195       208       -152          56
## 485                       196       209       -153          56
## 486                       197       210       -154          56
## 487                       198       211       -155          56
## 488                       199       212       -156          56
## 489                       200       213       -157          56
## 490                       201       214       -158          56
## 491                       202       215       -159          56
## 492                       203       216       -160          56
## 493                       204       217       -161          56
## 494                       205       218       -162          56
## 495                       206       219       -163          56
## 496                       207       220       -164          56
## 497                       208       221       -165          56
## 498                       209       222       -166          56
## 499                       210       223       -167          56
## 500                       211       224       -168          56
## 501                       212       225       -169          56
## 502                       213       226       -170          56
## 503                       214       227       -171          56
## 504                       215       228       -172          56
## 505                       216       229       -173          56
## 506                       217       230       -174          56
## 507                       218       231       -175          56
## 508                       219       232       -176          56
## 509                       220       233       -177          56
## 510                       221       234       -178          56
## 511                       222       235       -179          56

Bear Long Spread

Trimestre 2

accion = c("BIIB")
prices2 = lapply(accion, FUN = function(x) {
  getSymbols(x, from = "2023-09-01", to = "2023-11-30", auto.assign = FALSE)
})

pricestri2 = as.data.frame(do.call(merge, prices2))
prices_tri2 <- select(pricestri2, BIIB.Close)

library(roptions)
estrategia2 <- put.spread(47, -47, 20, 20, llimit = 255, ulimit = 255)

## [1] "This is a Bear Spread because the excercise price of long put (k1) is greater than excercise price of short put (k2)"
##     stock_price_at_expiration long_put short_put profit_loss
## 1                        -208      235      -141          94
## 2                        -207      234      -140          94
## 3                        -206      233      -139          94
## 4                        -205      232      -138          94
## 5                        -204      231      -137          94
## 6                        -203      230      -136          94
## 7                        -202      229      -135          94
## 8                        -201      228      -134          94
## 9                        -200      227      -133          94
## 10                       -199      226      -132          94
## 11                       -198      225      -131          94
## 12                       -197      224      -130          94
## 13                       -196      223      -129          94
## 14                       -195      222      -128          94
## 15                       -194      221      -127          94
## 16                       -193      220      -126          94
## 17                       -192      219      -125          94
## 18                       -191      218      -124          94
## 19                       -190      217      -123          94
## 20                       -189      216      -122          94
## 21                       -188      215      -121          94
## 22                       -187      214      -120          94
## 23                       -186      213      -119          94
## 24                       -185      212      -118          94
## 25                       -184      211      -117          94
## 26                       -183      210      -116          94
## 27                       -182      209      -115          94
## 28                       -181      208      -114          94
## 29                       -180      207      -113          94
## 30                       -179      206      -112          94
## 31                       -178      205      -111          94
## 32                       -177      204      -110          94
## 33                       -176      203      -109          94
## 34                       -175      202      -108          94
## 35                       -174      201      -107          94
## 36                       -173      200      -106          94
## 37                       -172      199      -105          94
## 38                       -171      198      -104          94
## 39                       -170      197      -103          94
## 40                       -169      196      -102          94
## 41                       -168      195      -101          94
## 42                       -167      194      -100          94
## 43                       -166      193       -99          94
## 44                       -165      192       -98          94
## 45                       -164      191       -97          94
## 46                       -163      190       -96          94
## 47                       -162      189       -95          94
## 48                       -161      188       -94          94
## 49                       -160      187       -93          94
## 50                       -159      186       -92          94
## 51                       -158      185       -91          94
## 52                       -157      184       -90          94
## 53                       -156      183       -89          94
## 54                       -155      182       -88          94
## 55                       -154      181       -87          94
## 56                       -153      180       -86          94
## 57                       -152      179       -85          94
## 58                       -151      178       -84          94
## 59                       -150      177       -83          94
## 60                       -149      176       -82          94
## 61                       -148      175       -81          94
## 62                       -147      174       -80          94
## 63                       -146      173       -79          94
## 64                       -145      172       -78          94
## 65                       -144      171       -77          94
## 66                       -143      170       -76          94
## 67                       -142      169       -75          94
## 68                       -141      168       -74          94
## 69                       -140      167       -73          94
## 70                       -139      166       -72          94
## 71                       -138      165       -71          94
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## 73                       -136      163       -69          94
## 74                       -135      162       -68          94
## 75                       -134      161       -67          94
## 76                       -133      160       -66          94
## 77                       -132      159       -65          94
## 78                       -131      158       -64          94
## 79                       -130      157       -63          94
## 80                       -129      156       -62          94
## 81                       -128      155       -61          94
## 82                       -127      154       -60          94
## 83                       -126      153       -59          94
## 84                       -125      152       -58          94
## 85                       -124      151       -57          94
## 86                       -123      150       -56          94
## 87                       -122      149       -55          94
## 88                       -121      148       -54          94
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## 90                       -119      146       -52          94
## 91                       -118      145       -51          94
## 92                       -117      144       -50          94
## 93                       -116      143       -49          94
## 94                       -115      142       -48          94
## 95                       -114      141       -47          94
## 96                       -113      140       -46          94
## 97                       -112      139       -45          94
## 98                       -111      138       -44          94
## 99                       -110      137       -43          94
## 100                      -109      136       -42          94
## 101                      -108      135       -41          94
## 102                      -107      134       -40          94
## 103                      -106      133       -39          94
## 104                      -105      132       -38          94
## 105                      -104      131       -37          94
## 106                      -103      130       -36          94
## 107                      -102      129       -35          94
## 108                      -101      128       -34          94
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## 110                       -99      126       -32          94
## 111                       -98      125       -31          94
## 112                       -97      124       -30          94
## 113                       -96      123       -29          94
## 114                       -95      122       -28          94
## 115                       -94      121       -27          94
## 116                       -93      120       -26          94
## 117                       -92      119       -25          94
## 118                       -91      118       -24          94
## 119                       -90      117       -23          94
## 120                       -89      116       -22          94
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## 122                       -87      114       -20          94
## 123                       -86      113       -19          94
## 124                       -85      112       -18          94
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## 136                       -73      100        -6          94
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## 139                       -70       97        -3          94
## 140                       -69       96        -2          94
## 141                       -68       95        -1          94
## 142                       -67       94         0          94
## 143                       -66       93         1          94
## 144                       -65       92         2          94
## 145                       -64       91         3          94
## 146                       -63       90         4          94
## 147                       -62       89         5          94
## 148                       -61       88         6          94
## 149                       -60       87         7          94
## 150                       -59       86         8          94
## 151                       -58       85         9          94
## 152                       -57       84        10          94
## 153                       -56       83        11          94
## 154                       -55       82        12          94
## 155                       -54       81        13          94
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## 159                       -50       77        17          94
## 160                       -49       76        18          94
## 161                       -48       75        19          94
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## 177                       -32       59        20          79
## 178                       -31       58        20          78
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## 181                       -28       55        20          75
## 182                       -27       54        20          74
## 183                       -26       53        20          73
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## 191                       -18       45        20          65
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## 196                       -13       40        20          60
## 197                       -12       39        20          59
## 198                       -11       38        20          58
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## 200                        -9       36        20          56
## 201                        -8       35        20          55
## 202                        -7       34        20          54
## 203                        -6       33        20          53
## 204                        -5       32        20          52
## 205                        -4       31        20          51
## 206                        -3       30        20          50
## 207                        -2       29        20          49
## 208                        -1       28        20          48
## 209                         0       27        20          47
## 210                         1       26        20          46
## 211                         2       25        20          45
## 212                         3       24        20          44
## 213                         4       23        20          43
## 214                         5       22        20          42
## 215                         6       21        20          41
## 216                         7       20        20          40
## 217                         8       19        20          39
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## 219                        10       17        20          37
## 220                        11       16        20          36
## 221                        12       15        20          35
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## 223                        14       13        20          33
## 224                        15       12        20          32
## 225                        16       11        20          31
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## 230                        21        6        20          26
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## 247                        38      -11        20           9
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## 466                       257      -20        20           0
## 467                       258      -20        20           0
## 468                       259      -20        20           0
## 469                       260      -20        20           0
## 470                       261      -20        20           0
## 471                       262      -20        20           0
## 472                       263      -20        20           0
## 473                       264      -20        20           0
## 474                       265      -20        20           0
## 475                       266      -20        20           0
## 476                       267      -20        20           0
## 477                       268      -20        20           0
## 478                       269      -20        20           0
## 479                       270      -20        20           0
## 480                       271      -20        20           0
## 481                       272      -20        20           0
## 482                       273      -20        20           0
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## 490                       281      -20        20           0
## 491                       282      -20        20           0
## 492                       283      -20        20           0
## 493                       284      -20        20           0
## 494                       285      -20        20           0
## 495                       286      -20        20           0
## 496                       287      -20        20           0
## 497                       288      -20        20           0
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## 509                       300      -20        20           0
## 510                       301      -20        20           0
## 511                       302      -20        20           0

Trimestre 4

accion = c("BIIB")
prices4 = lapply(accion, FUN = function(x) {
  getSymbols(x, from = "2024-03-01", to = "2024-04-17", auto.assign = FALSE)
})

pricestri4 = as.data.frame(do.call(merge, prices4))
prices_tri4 <- select(pricestri4, BIIB.Close)

library(roptions)
estrategia4 <- put.spread(10, -10, 20, 20, llimit = 255, ulimit = 255)

## [1] "This is a Bear Spread because the excercise price of long put (k1) is greater than excercise price of short put (k2)"
##     stock_price_at_expiration long_put short_put profit_loss
## 1                        -245      235      -215          20
## 2                        -244      234      -214          20
## 3                        -243      233      -213          20
## 4                        -242      232      -212          20
## 5                        -241      231      -211          20
## 6                        -240      230      -210          20
## 7                        -239      229      -209          20
## 8                        -238      228      -208          20
## 9                        -237      227      -207          20
## 10                       -236      226      -206          20
## 11                       -235      225      -205          20
## 12                       -234      224      -204          20
## 13                       -233      223      -203          20
## 14                       -232      222      -202          20
## 15                       -231      221      -201          20
## 16                       -230      220      -200          20
## 17                       -229      219      -199          20
## 18                       -228      218      -198          20
## 19                       -227      217      -197          20
## 20                       -226      216      -196          20
## 21                       -225      215      -195          20
## 22                       -224      214      -194          20
## 23                       -223      213      -193          20
## 24                       -222      212      -192          20
## 25                       -221      211      -191          20
## 26                       -220      210      -190          20
## 27                       -219      209      -189          20
## 28                       -218      208      -188          20
## 29                       -217      207      -187          20
## 30                       -216      206      -186          20
## 31                       -215      205      -185          20
## 32                       -214      204      -184          20
## 33                       -213      203      -183          20
## 34                       -212      202      -182          20
## 35                       -211      201      -181          20
## 36                       -210      200      -180          20
## 37                       -209      199      -179          20
## 38                       -208      198      -178          20
## 39                       -207      197      -177          20
## 40                       -206      196      -176          20
## 41                       -205      195      -175          20
## 42                       -204      194      -174          20
## 43                       -203      193      -173          20
## 44                       -202      192      -172          20
## 45                       -201      191      -171          20
## 46                       -200      190      -170          20
## 47                       -199      189      -169          20
## 48                       -198      188      -168          20
## 49                       -197      187      -167          20
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## 59                       -187      177      -157          20
## 60                       -186      176      -156          20
## 61                       -185      175      -155          20
## 62                       -184      174      -154          20
## 63                       -183      173      -153          20
## 64                       -182      172      -152          20
## 65                       -181      171      -151          20
## 66                       -180      170      -150          20
## 67                       -179      169      -149          20
## 68                       -178      168      -148          20
## 69                       -177      167      -147          20
## 70                       -176      166      -146          20
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## 87                       -159      149      -129          20
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## 96                       -150      140      -120          20
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## 99                       -147      137      -117          20
## 100                      -146      136      -116          20
## 101                      -145      135      -115          20
## 102                      -144      134      -114          20
## 103                      -143      133      -113          20
## 104                      -142      132      -112          20
## 105                      -141      131      -111          20
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## 137                      -109       99       -79          20
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## 139                      -107       97       -77          20
## 140                      -106       96       -76          20
## 141                      -105       95       -75          20
## 142                      -104       94       -74          20
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## 182                       -64       54       -34          20
## 183                       -63       53       -33          20
## 184                       -62       52       -32          20
## 185                       -61       51       -31          20
## 186                       -60       50       -30          20
## 187                       -59       49       -29          20
## 188                       -58       48       -28          20
## 189                       -57       47       -27          20
## 190                       -56       46       -26          20
## 191                       -55       45       -25          20
## 192                       -54       44       -24          20
## 193                       -53       43       -23          20
## 194                       -52       42       -22          20
## 195                       -51       41       -21          20
## 196                       -50       40       -20          20
## 197                       -49       39       -19          20
## 198                       -48       38       -18          20
## 199                       -47       37       -17          20
## 200                       -46       36       -16          20
## 201                       -45       35       -15          20
## 202                       -44       34       -14          20
## 203                       -43       33       -13          20
## 204                       -42       32       -12          20
## 205                       -41       31       -11          20
## 206                       -40       30       -10          20
## 207                       -39       29        -9          20
## 208                       -38       28        -8          20
## 209                       -37       27        -7          20
## 210                       -36       26        -6          20
## 211                       -35       25        -5          20
## 212                       -34       24        -4          20
## 213                       -33       23        -3          20
## 214                       -32       22        -2          20
## 215                       -31       21        -1          20
## 216                       -30       20         0          20
## 217                       -29       19         1          20
## 218                       -28       18         2          20
## 219                       -27       17         3          20
## 220                       -26       16         4          20
## 221                       -25       15         5          20
## 222                       -24       14         6          20
## 223                       -23       13         7          20
## 224                       -22       12         8          20
## 225                       -21       11         9          20
## 226                       -20       10        10          20
## 227                       -19        9        11          20
## 228                       -18        8        12          20
## 229                       -17        7        13          20
## 230                       -16        6        14          20
## 231                       -15        5        15          20
## 232                       -14        4        16          20
## 233                       -13        3        17          20
## 234                       -12        2        18          20
## 235                       -11        1        19          20
## 236                       -10        0        20          20
## 237                        -9       -1        20          19
## 238                        -8       -2        20          18
## 239                        -7       -3        20          17
## 240                        -6       -4        20          16
## 241                        -5       -5        20          15
## 242                        -4       -6        20          14
## 243                        -3       -7        20          13
## 244                        -2       -8        20          12
## 245                        -1       -9        20          11
## 246                         0      -10        20          10
## 247                         1      -11        20           9
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## 255                         9      -19        20           1
## 256                        10      -20        20           0
## 257                        11      -20        20           0
## 258                        12      -20        20           0
## 259                        13      -20        20           0
## 260                        14      -20        20           0
## 261                        15      -20        20           0
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## 496                       250      -20        20           0
## 497                       251      -20        20           0
## 498                       252      -20        20           0
## 499                       253      -20        20           0
## 500                       254      -20        20           0
## 501                       255      -20        20           0
## 502                       256      -20        20           0
## 503                       257      -20        20           0
## 504                       258      -20        20           0
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## 506                       260      -20        20           0
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## 509                       263      -20        20           0
## 510                       264      -20        20           0
## 511                       265      -20        20           0

Análisis

Trimestre 1 -22, 12: Estos son los desvíos de los precios de ejercicio del precio del activo subyacente, es decir la resta entre El precio final y el precio Strike.En este caso, la estrategia implica comprar una opción de call con un precio de ejercicio 22 puntos por debajo del precio del activo subyacente y vender una opción de call con un precio de ejercicio 12 puntos por debajo del precio del activo subyacente.

Trimestre 3 -33, 23: Estos son los desvíos de los precios de ejercicio del precio del activo subyacente, es decir la resta entre El precio final y el precio Strike.En este caso, la estrategia implica comprar una opción de call con un precio de ejercicio 33 puntos por debajo del precio del activo subyacente y vender una opción de call con un precio de ejercicio 23 puntos por debajo del precio del activo subyacente.

Trimestre 2 El beneficio máximo se obtiene cuando el precio del activo subyacente cae por debajo del precio de ejercicio de la opción de venta comprada (47). En este caso, el beneficio máximo sería igual al ancho del spread (20).

Trimestre 4 El beneficio máximo se obtiene cuando el precio del activo subyacente cae por debajo del precio de ejercicio de la opción de venta comprada (10). En este caso, el beneficio máximo sería igual al ancho del spread (20).

20, 20: Estas son las cantidades de las primas. llimit = 255, ulimit = 255: Estos son los límites de la estrategia. Indican el precio máxima de dinero que se puede perder o ganar con la estrategia. En este caso, la pérdida máxima es de 255 y la ganancia máxima también es de 255.

Esta estrategia es una “estrategia de call bear spread”. Esto significa que el comprador de la estrategia se beneficia si el precio del activo subyacente disminuye o se mantiene sin cambios.

3.2. Límites mínimos y máximos

Los precios máximos diarios son igual al precio de la acción diaria, dado que el precio de la opción no puede superar el precio de la acción.