portfolio_var_calculation_and_correlation_monitoring.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "29e4131f",
   "metadata": {},
   "source": [
    "# Portfolio VaR Calculation and Correlation Monitoring\n",
    "**Bartłomiej Jamiolkowski 18.01.2022**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20d64fc9",
   "metadata": {},
   "source": [
    "# 1. Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6481b76",
   "metadata": {},
   "source": [
    "The aim of the work is to present the methods of monitoring the correlation along with the interpretation and to determine the VaR for the portfolio using specific methods. The calculations use the return prices of 3 well-known world stock exchange indexes (time period from 01/01/2006 to 31/12/2021) downloaded from the website stooq.pl. The project is implemented using the R language in Jupyter Notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c556cb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "options(warn=-1)\n",
    "library(SciViews)\n",
    "library(ggplot2)\n",
    "library(dplyr)\n",
    "library(gridExtra)\n",
    "\n",
    "library(fImport)\n",
    "library(tseries)\n",
    "library(quantmod)\n",
    "library(GGally)\n",
    "library(GAS)\n",
    "library(segMGarch)\n",
    "library(kableExtra)\n",
    "library(tidyr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb714a63",
   "metadata": {},
   "source": [
    "Data import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7c5e2967",
   "metadata": {},
   "outputs": [],
   "source": [
    "nasdaq_d <- read.csv(\"^NDQ.csv\", header = TRUE)\n",
    "nikkei_225_d <- read.csv(\"^NKX.csv\", header = TRUE)\n",
    "shanghai_d <- read.csv(\"^SHC.csv\", header = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f91d53d",
   "metadata": {},
   "source": [
    "Choice of closing prices of stock indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "513a6dab",
   "metadata": {},
   "outputs": [],
   "source": [
    "nasdaq_d_close <- nasdaq_d$Close\n",
    "nikkei_225_d_close <- nikkei_225_d$Close\n",
    "shanghai_d_close <- shanghai_d$Close"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "905dcace",
   "metadata": {},
   "source": [
    "Calculation of logarithmic rates of return for individual indexes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e848abf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "rate_of_return_nasdaq <- rep(0, 4028)\n",
    "for(i in 1:4028){\n",
    "  rate_of_return_nasdaq[i] = 100 * log(nasdaq_d_close[i + 1]/nasdaq_d_close[i])\n",
    "}\n",
    "\n",
    "rate_of_return_nikkei_225 <- rep(0, 3917)\n",
    "for(i in 1:3917){\n",
    "  rate_of_return_nikkei_225[i] = 100 * log(nikkei_225_d_close[i + 1]/nikkei_225_d_close[i])\n",
    "}\n",
    "\n",
    "rate_of_return_shanghai <- rep(0, 3888)\n",
    "for(i in 1:3888){\n",
    "  rate_of_return_shanghai[i] = 100 * log(shanghai_d_close[i + 1]/shanghai_d_close[i])\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da03d7d6",
   "metadata": {},
   "source": [
    "## 1.1 Extraction of negative returns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb6f9ff2",
   "metadata": {},
   "source": [
    "Due to the visualization of changes in the correlation value over time, at this stage of the extraction negative rates of return with assigned dates are subject. Data is stored in created data frames for each index."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "284136ed",
   "metadata": {},
   "source": [
    "### 1.1.1 Negative Nasdaq Composite index returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cf49483a",
   "metadata": {},
   "outputs": [],
   "source": [
    "data1 <- data.frame(\n",
    "  Date = nasdaq_d$Date[-1],\n",
    "  Return = rate_of_return_nasdaq\n",
    ")\n",
    "minus_date <- c()\n",
    "minus_return <- c()\n",
    "for(i in 1:length(data1$Return)){\n",
    "  if(data1$Return[i] < 0){\n",
    "    minus_date <- append(minus_date, data1$Date[i])\n",
    "    minus_return <-append(minus_return, data1$Return[i])\n",
    "  }\n",
    "}\n",
    "data1 <- data.frame(\n",
    "  Date = as.Date(minus_date),\n",
    "  Return = minus_return\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc9992cb",
   "metadata": {},
   "source": [
    "### 1.1.2 Negative rates of return for the Nikkei 225 index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "be6c7660",
   "metadata": {},
   "outputs": [],
   "source": [
    "data2 <- data.frame(\n",
    "  Date = nikkei_225_d$Date[-1],\n",
    "  Return = rate_of_return_nikkei_225\n",
    ")\n",
    "minus_date <- c()\n",
    "minus_return <- c()\n",
    "for(i in 1:length(data2$Return)){\n",
    "  if(data2$Return[i] < 0){\n",
    "    minus_date <- append(minus_date, data2$Date[i])\n",
    "    minus_return <-append(minus_return, data2$Return[i])\n",
    "  }\n",
    "}\n",
    "data2 <- data.frame(\n",
    "  Date = as.Date(minus_date),\n",
    "  Return = minus_return\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b47a017",
   "metadata": {},
   "source": [
    "### 1.1.3 Negative Shanghai Composite index returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f378222e",
   "metadata": {},
   "outputs": [],
   "source": [
    "data3 <- data.frame(\n",
    "  Date = shanghai_d$Date[-1],\n",
    "  Return = rate_of_return_shanghai\n",
    ")\n",
    "minus_date <- c()\n",
    "minus_return <- c()\n",
    "for(i in 1:length(data3$Return)){\n",
    "  if(data3$Return[i] < 0){\n",
    "    minus_date <- append(minus_date, data3$Date[i])\n",
    "    minus_return <-append(minus_return, data3$Return[i])\n",
    "  }\n",
    "}\n",
    "data3 <- data.frame(\n",
    "  Date = as.Date(minus_date),\n",
    "  Return = minus_return\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba5303d3",
   "metadata": {},
   "source": [
    "## 1.2 Transforming data to correlate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81bc1d54",
   "metadata": {},
   "source": [
    "In order to calculate the correlation, the vectors should be aligned to the same length. In addition, the time data needed for the subsequent visualization of changes in the correlation value should be taken into account. Therefore, the most sensible solution is to choose the time span for the longest vector. Based on this vector, 3 new data frames are created. In each frame, the dates are assigned negative phrases searched for based on the dates in the previous 3 frames. As a result, a negative return column appears with NA values ​​present. NA values ​​arise as a result of two events. The first reason is the non-negative rate of return not included. The second reason for this is, for example, the lack of data from stock exchanges, for example in Asia, due to their closing on a certain day for various reasons. Two methods of solving the NA problem in time series are popular. The first way is to delete the row. The second, and in this case better way, is to replace the missing values ​​with the top or bottom values. The result of these operations is 3 vectors capable of calculating the correlation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd666492",
   "metadata": {},
   "source": [
    "**negative returns on the Nasdaq Composite Index**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0ea13919",
   "metadata": {},
   "outputs": [],
   "source": [
    "nasdaq <- data.frame(\n",
    "  Date = nasdaq_d$Date[6:4029],\n",
    "  Return = rep(NA, length(nasdaq_d$Close[6:4029]))\n",
    ")\n",
    "for(i in 1:length(nasdaq$Date)){\n",
    "  for(j in 1:length(data1$Date)){\n",
    "    if(nasdaq$Date[i] == data1$Date[j]){\n",
    "      nasdaq$Return[i] = data1$Return[j]\n",
    "    }\n",
    "  }\n",
    "}\n",
    "minus_nasdaq <- nasdaq %>% fill(Return, .direction = 'downup')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0d5702b",
   "metadata": {},
   "source": [
    "**negative returns on the Nikkei 225 index**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6c169ddf",
   "metadata": {},
   "outputs": [],
   "source": [
    "nikkei_225 <- data.frame(\n",
    "  Date = nasdaq$Date,\n",
    "  Return = rep(0, 4024)\n",
    ")\n",
    "for(i in 1:length(nikkei_225$Date)){\n",
    "  for(j in 1:length(data2$Date)){\n",
    "    if(nikkei_225$Date[i] == data2$Date[j]){\n",
    "      nikkei_225$Return[i] = data2$Return[j]\n",
    "    }\n",
    "  }\n",
    "}\n",
    "minus_nikkei_225 <- nikkei_225 %>% fill(Return, .direction = 'downup')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9b1fc94",
   "metadata": {},
   "source": [
    "**negative returns of the Shanghai Composite index**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7a713f4f",
   "metadata": {},
   "outputs": [],
   "source": [
    "shanghai <- data.frame(\n",
    "  Date = nasdaq$Date,\n",
    "  Return = rep(0, 4024)\n",
    ")\n",
    "for(i in 1:length(shanghai$Date)){\n",
    "  for(j in 1:length(data3$Date)){\n",
    "    if(shanghai$Date[i] == data3$Date[j]){\n",
    "      shanghai$Return[i] = data3$Return[j]\n",
    "    }\n",
    "  }\n",
    "}\n",
    "minus_shanghai <- shanghai %>% fill(Return, .direction = 'downup')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95f8154a",
   "metadata": {},
   "source": [
    "# 2. Monitoring the correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c82f1599",
   "metadata": {},
   "source": [
    "As part of the correlation monitoring, the correlations are calculated using: a rolling observation window (T = 30) with the use of Pearson's correlation, EWMA with lambda = 0.94 and GARCH (1.1). For this purpose, three functions are created to automate these processes. The effects of the algorithms' work are presented in the diagrams of the correlation of negative returns of three indices in the project."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0085dfe7",
   "metadata": {},
   "source": [
    "**Pearson correlation (T = 30)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0078edd4",
   "metadata": {},
   "outputs": [],
   "source": [
    "pearson_corr <- function(x, y){\n",
    "  p_cor <- c()\n",
    "  for(i in 0:(length(x) - 31)){\n",
    "    x_cor <- rep(0, 30)\n",
    "    y_cor <- rep(0, 30)\n",
    "    for(j in 1:30){\n",
    "      x_cor[j] = x[j + i]\n",
    "      y_cor[j] = y[j + i]\n",
    "    }\n",
    "    c = cor(x_cor, y_cor, method = \"pearson\")\n",
    "    p_cor <- append(p_cor, c)\n",
    "  }\n",
    "  return(p_cor)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4941e38e",
   "metadata": {},
   "source": [
    "**EWMA correlation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6e27bfb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "ewma_corr <- function(x, y){\n",
    "  lambda = 0.94\n",
    "  covariance <- rep(0, length(x))\n",
    "  covariance[1] = cov(x, y)\n",
    "  for(i in 1:(length(x) - 1)){\n",
    "    covariance[i + 1] = covariance[i] * lambda + (1 - lambda) * x[i] * y[i]\n",
    "  }\n",
    "  variance_x <- rep(0, length(x))\n",
    "  variance_x[1] = var(x)\n",
    "  for(i in 1:(length(x) - 1)){\n",
    "    variance_x[i + 1] = variance_x[i] * lambda + (1 - lambda) * x[i]^2\n",
    "  }\n",
    "  variance_y <- rep(0, length(y))\n",
    "  variance_y[1] = var(y)\n",
    "  for(i in 1:(length(y) - 1)){\n",
    "    variance_y[i + 1] = variance_y[i] * lambda + (1 - lambda) * y[i]^2\n",
    "  }\n",
    "  sd_x <- rep(0, length(variance_x))\n",
    "  sd_y <- rep(0, length(variance_y))\n",
    "  for(i in 1:length(variance_x)){\n",
    "    sd_x[i] = sqrt(variance_x[i])\n",
    "    sd_y[i] = sqrt(variance_y[i])\n",
    "  }\n",
    "  ewma_cor <- rep(0, length(x))\n",
    "  for(i in 1:length(variance_x)){\n",
    "    ewma_cor[i] = covariance[i] / (sd_x[i] * sd_y[i])\n",
    "  }\n",
    "  return(ewma_cor)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb6fbc05",
   "metadata": {},
   "source": [
    "**correlation GARCH (1,1)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "02ca5f9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "garch_corr <- function(x, y){\n",
    "  gamma = 0.02\n",
    "  alpha = 0.15\n",
    "  beta = 0.83\n",
    "  long_run_vr = 0.00015\n",
    "  covariance <- rep(0, length(x))\n",
    "  covariance[1] = cov(x, y)\n",
    "  for(i in 1:(length(x) - 1)){\n",
    "    covariance[i + 1] = beta * covariance[i] + alpha * x[i] * y[i] + gamma * long_run_vr\n",
    "  }\n",
    "  variance_x <- rep(0, length(x))\n",
    "  variance_x[1] = var(x)\n",
    "  for(i in 1:(length(x) - 1)){\n",
    "    variance_x[i + 1] = beta * variance_x[i] + alpha * x[i]^2 + gamma * long_run_vr\n",
    "  }\n",
    "  variance_y <- rep(0, length(y))\n",
    "  variance_y[1] = var(y)\n",
    "  for(i in 1:(length(y) - 1)){\n",
    "    variance_y[i + 1] = beta * variance_y[i] + alpha * y[i]^2 + gamma * long_run_vr\n",
    "  }\n",
    "  sd_x <- rep(0, length(variance_x))\n",
    "  sd_y <- rep(0, length(variance_y))\n",
    "  for(i in 1:length(variance_x)){\n",
    "    sd_x[i] = sqrt(variance_x[i])\n",
    "    sd_y[i] = sqrt(variance_y[i])\n",
    "  }\n",
    "  garch_cor <- rep(0, length(x))\n",
    "  for(i in 1:length(variance_x)){\n",
    "    garch_cor[i] = covariance[i] / (sd_x[i] * sd_y[i])\n",
    "  }\n",
    "  return(garch_cor)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "042d32f6",
   "metadata": {},
   "source": [
    "# 2.1 Nasdaq Composite - Nikkei 225 correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f80bdf89",
   "metadata": {},
   "source": [
    "Vectors containing the calculated correlation values are created using 3 methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5780c1f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "pearson_nasdaq_nikkei_corr <- pearson_corr(minus_nasdaq$Return, minus_nikkei_225$Return)\n",
    "ewma_nasdaq_nikkei_corr <- ewma_corr(minus_nasdaq$Return, nikkei_225$Return)\n",
    "garch_nasdaq_nikkei_corr <- garch_corr(minus_nasdaq$Return, minus_nikkei_225$Return)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1cdb82a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QSwdoDVT78sKJy82mDZS4IVJu7IjRXAWstlwGI/yHNT6cFiOx1gASxfnpVDA0CL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\nhSDIZfL/qUdK88BuCdkAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data4 <- data.frame(\n",
    "  day = as.Date(nasdaq$Date),\n",
    "  value1 = rep(NA, 4024),\n",
    "  value2 = garch_nasdaq_nikkei_corr,\n",
    "  value3 = ewma_nasdaq_nikkei_corr\n",
    ")\n",
    "for(i in 31:4024){\n",
    "  data4$value1[i] = pearson_nasdaq_nikkei_corr[i - 30]\n",
    "}\n",
    "\n",
    "options(repr.plot.width=10, repr.plot.height=6)\n",
    "ggplot(data = data4, aes(x = day, y = value1)) + \n",
    "geom_line(color = \"#404788FF\", size = 0.8) +\n",
    "geom_line(aes(x = data4$day, y = data4$value2, color = '#29AF7FFF'), size = 0.8) +\n",
    "geom_line(aes(x = data4$day, y = data4$value3, color = '#FDE725FF'), size = 0.8) +\n",
    "ggtitle(\"Correlation between Nasdaq Composite and Nikkei 225 minus returns\") +\n",
    "ylab('correlation')+xlab('time') +\n",
    "scale_colour_manual(name = '',values =c('#404788FF'='#404788FF', '#29AF7FFF'='#29AF7FFF','#FDE725FF'='#FDE725FF'), labels = c('Pearson (T = 30)', 'GARCH','EWMA'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3a74559",
   "metadata": {},
   "source": [
    "# 2.2 Nasdaq Composite - Shanghai Composite correlation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d5245f9",
   "metadata": {},
   "source": [
    "Vectors containing the calculated correlation values are created using 3 methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f5242e95",
   "metadata": {},
   "outputs": [],
   "source": [
    "pearson_nasdaq_shanghai_corr <- pearson_corr(minus_nasdaq$Return, minus_shanghai$Return)\n",
    "ewma_nasdaq_shanghai_corr <- ewma_corr(minus_nasdaq$Return, minus_shanghai$Return)\n",
    "garch_nasdaq_shanghai_corr <- garch_corr(minus_nasdaq$Return, minus_shanghai$Return)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "4546835f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DXJO4OlI2A53zLRC+a6B7DUm4JFXvGRsfuxGWIO5LuYi9sHWKZQ3ivASkobsLxZ\nqZuDZVdrR2ApewocLHUeWHw1eyu6ACzTMLvWx4DFx4waYmDpHsASvQKspLQCS4W2uQutHCx9\nNFijBYuOtYuTnw21MtpfbrRgjWyup4Clrw+WorFVrcAat8Hi1ZwEFk0QeeaFAVheSoZRBaYl\nW1ApYNlVR5vNmlp0mTaPfLVngjXaRdUZWNqApcw++8AazQKkevU1wJI7nwSWjoElvrsDWAem\nE7D413jaGANLZYM1ZoI1HgmWmewGrPkwthznQ7bAWtZLY7AWgwAWNQCwDkw3YLnLYllO7rGM\ngPPAGsdSsMaRt7EfrLFDsKbWLFivoyuDpczAl4FF6x9gXT8AaxUs/lV97mzBYRUsul8cTXtx\nsMxhEqzxULBG1Qqs+Qci1GoRWOoiYPFxTAJrpJNyKsoPwPJSMoz2Sslt/rJQqjJYBMJCiD4d\nrKWgOFg6ESx746bfDiztgmUs0XwDG4pMsObmlqrNyCWBZYoAWEdmG6yPz/DP7YNDwBJrpQlY\n7DYnGSxb1Hlg2aIIrJHtyFaHMstuOctVsHQOWDoLLFUNrPEEsEbaGAZr3AJr6Y/PXPMIYBVn\nE6wP+x/2cU7JMNorJbfZOWNpMLMidKyqBZa6DFjLgjkerLkyOng0b2wT12w+1ux8OlgqEyy6\nPgDr4mkPlljyZ4OltF28psdtsIYssLRsZCn9WmCNYxis8T3BWk47ASyazACrTrLAkl4dAJZO\nBIsvKheskcAa7XXfBRbNzOpgjXRYKliW5QpgEZrmSe8P36SBRb2FwVp+UpAJFpekFlhL5aeD\nJQZJfO2lmQWwtpMHln0J6/9eKenv8yo8p2vBt9g8n58XjTbbB86xiyNuA89lJs2b58+oWZvn\ncvzc4GtmPpVpmnZ6so7mVTl39vnUYI4Xtc8LQs0VPamgp2JdP+fO1dM0TIdNT9uu531ZJ3Oz\ndqelhGEwu5k1Rv3z0aFPDFh0uk8qXo1mqOzB9vT5NVsOfjKwzPYZrKctYz655eO8M79kT1Mb\n/8ybGstJjmw43cPsDHnaDkwTtqHXUUvlz/kUxeUzRdNg2nG3H3kFdpzmcX3y0s1YyBMxj9hU\ntgdN50cj4Aw4siT/Dqv2i+58yhTeYZkv8orfHcyfUbM23h2Wdu+wtHOHZe8MMu+wlu+4WNfy\nDouBtZy5rWveN3iHZe4xXp8PnzbQl30zrkV3WEujsTusuRXeqj0rdj2dO6xB3mFpM47sgqfc\nYS03PZpfvZEfZo7iG/iNCl0f5w5LXL6lCS3usObiQ3dYNE6q5A5LdjsVhDus7eS9hiU/LxlG\nO334FnbtGoClt8FSe8EyrydoStIAACAASURBVNMfA5bBhlZpNlimnhhY9h2fyxN2cw2wWNti\nlfI1fSRYNEhhsEbzHSjAap47gDXuA2s8AixDUQ5Y+jywxihYfCFug8UGfzmAgaXp5AAW7wFg\nlafdt4RyRZlr1wKsZRnZhh2wzLLrCqxRgKWzwWJMbYFlRygA1jCkgGU+mpFuBNZYFSxF46RS\nwTLXAWAVJxssdrNVMoz2aoXActZKH2DRsls6ywRrtGrFwRrVghPAMmcqpoY+EyxDFJUowRKD\npUUr82kDrAOT/k73D/b5nJJhtFfr3cCal3gMrLEKWPI1ND68mq0qAsilqwQsdUewzAkvhdnu\nTgLLXq6NxbSatwUrnpJhtFerBVj2jsIDS7wKTWCx9WwWQBFY2oClDgZrPA+ssS5Y9r1O9cCi\ndW9nTQZY9EYsgNVRegXLPA4eewhYvIIjwFLmRd96YGkGljmPpX/Fhtd8Q7MMexZY1LACWACr\nfToDS49lYC3f1EXAUj5YxiTzWjdbUhcCa0gEa7SDlwzW0uOBYI2jBxY7UzE1dACsEWCtBmB5\nKRlGe7XeGqzpd65Hs5qbgsVqOB2sMQ4WvQBlNp0MljaFx8DSZWDxDlm3ACsx7wgWN+k4sEa1\nAZa6C1hWoaWz64HFzFU5YCmHvYUGc/YAq35uA9Y4roOlE8Cyq3UbrNdTG2CNAbDMeusArGU4\nHLBMS83BsovWfL4TrPl0w2DZ0zNNAKxucypYds3wyysW/B6w7Dv65s0Hg6WCYI13Acv0uAqW\nNmCZV6MUwNLZYNn5CrAS8tZg6WPBYn9G/qZg6SZgKfOXXWxJ5mz5Br7u7dUNgqUB1nVyN7DU\nLcAyK+RCYBlwksCy450IlpJgLfdLIbC0wVOsexUBy86OU8AaR4C1O2eCRWuGX16x3muAtWzu\nBixl52kuWGJVpYG1LKAysMzgCLA07bQTLNOyAxabEJwZMTVywBpLwVJmkul5B9a1AItGKh8s\nuyuLma8AKyH3BcuuU+WARSatgzWy7zwiYJlJTScQAksBLAbWeEWw1HIzCLBapzewDDh2IfvH\nKw6WUlGwFE07A5ayqyYKlmoDlkoCa1wDyyDSM1gqHywzgAKsWR1bkjlbBpbm6171CpadVwAr\nMSeDRTkNrOmbEAOWXZlxsJQHlj4ErOXfyBp9sOjM18HSlcCyL8vMreuDwRqPBGvsDyw2a5fP\n+EkArLw0A4uvKFrvB4Fl1p2duNPC3ATLCHAMWDobLFM596oKWPzHAzoG1rJmtTal6AKw1Alg\njRtgjVtgqWPBGmnaAKzc9AsWfWPEji8Ca7TrjoO1HN0XWHwXXRus6V4zDJbN3GsELHZbXAyW\nWq5TR2CNAOs66Q0sXRWsUYJFEzcDrCEK1ngAWGoLLF0PLPFxGSytAVYCWDQuNIUB1hkBWB5Y\nah9Y88wlBo4CS50Mljk5rVkpfYPF/3sEWKoiWGoEWCm5Gljs+7owWPYql4M1bbR7hsBSrcFS\nh4ClzgNr5O9W3wkWnW0SWBpgXTh3AkvcYXtgKQ6W3acQLMXA4tPPBUszsIRGq2DZEu22k8Ca\njzFrm8o5AixLC8AyEwtgbeeSYOnGYA1xsEYPLL6sHLB0EljEh9362v1osHg59kvETrCWHZLA\notvSPLD0QWCNAKuHvB1YtKz1Olim1RhYytw/JYOla4KlOFiqDli6BCyz3veCRbyEwDLD3QtY\ny1QcWTMA64xcGSzF9tsL1mindAAs9uKYB5Z5U2UxWFS7Ph4sdudIFZIec/oGy+xdGyz7FTAG\n1khg0VQ8Eiw5+3MDsLzkDmFjsNQqWPQehABYOgzWyMAyi6JPsKhgAZZRgIH1iU0BWKMBS+8F\niwSQYM1zQzBTE6xxA6zlz0BkgGUmNAfLzsBNsBTACufCYI25YNmvb3GwVDlYOgbW5zda0xH0\nOowFi1buaWCJt4tWAIv+IFYKWLoPsLQP1hgHa76oHlgKYDVIx2BxWcyeDlhKnQrWMpcXsEwV\nm2Dp24BFrZaDxe/wDgSL7nsTwDIe6zhYgw+Wmk5e54AlPgKsgrwfWPzGbTpas2/NliajYKlE\nsMzRHlhyexQs5YI16jpgUdHpYFnsEsAad4LFSNoLlr1kPYLF7TIjCrASArBe+8sFlA3WWB0s\n+xqXBlgEFn+2O7A0wDojfYGld4NlZ41mK2M/WGpZkjXAol8bqwsWvehnlvAy8+f9bUGm6FER\nWDQox4FlluM9wdL5YJm5Y0YUYCUEYBWDRXcpyWCpvWDpeetyIxkDi9byGljL2h3tsXoutQis\n0YKlt8DiZLUAa+wHrBFg5eZ6YLFVlwWWnTiFYI2ngjWfRjFYZtYng6XzwDI7hMBSFiwNsDTN\nO4BVIz2AZRZ9MlgjzT4O1ngsWOZn0nvAUuMOsEzd416w1DpYy762nFyw1P3AmmdpMlj8Yu8B\ny8zlkgAsL7lDGAeLLdkisOi+IQiWWRrvB5apxQFLbYClLS+Hg2UuYx2wltE9FCxidgUs06em\neQewaqQNWHbJ6SPBEmIdDZa5MdFyfRSAxb6zXVbOaNbYBlhqNGOYAZYycHCw7IJOB8uAsw6W\nDoK17NQlWIoaNDuae9d8sEYCi668LR1gbeciYC0Tomewhg7AsmN4DFh00UxJC1gqHSx5XSxY\ndHw9sOwt0TpYYwZYbC7VAmtcA2uHWADLS+4QroNlV+WytQCsMQ6W3gZLj+8JljK96LnUcrAM\nI8arS4BlruFo7wDTwBoAVovcHiyaiwGwtABLFYG1TMO2YGlW3jpY9KgdWHTaNcEiaVbB4vOs\nIlgj8bIK1mj+nhabxuZSA6zttAPLqLEGFttJl4GlaC6GwNKlYMkbBTX/2NsUkA2WNqfaBiy1\nCpZd1ppWkClpAUvXAGs61FyqGFh2HundYCmqRYJlBD8CrDEA1jy5AVZSugZLs500A0s/zexb\nB0ttgjXZUwSWqPtcsOzzBJZi5RWApQRYU94ALEUjZ8d4HSx7LZLBUgCrbvoFyxIyP9QCLJ0G\nljJgLW2sg7XMzPkH2QVg2QJWwNKj4mCZlWKK3ABrObOpTm3BMhB2ApZuANaCSBwsc6GOBMtc\nH4B1YG4Clp0EDlh8Ju0Cy76aEwGLToHm6qgCYCkJFl8IOgesuVkXLO2CpZT5qcDhYC3tUhPL\nffIWWOYHAWbQzbXrBSx1MFgjwMrIzcDSPYFlAdkCS62ANa6CNZm1CpYpsAgsszqTwdLVwdJl\nYJmzPhEse318sEwpyoAlArAycn+wNE1FrZU+GSwdBostPbNs7feIDljLQtFxsIZ8sHQFsOa9\newbLXJijwVqqXwdLA6wauT1Y2q7FxYBEsGxNO8Gy3ewAy/KxnJkLlpZgqQSwVBZYei9YBMJA\nD82ZKzOEEbAWZ3ywRnPBFLm6Byz2begClilsBSx7DqtgjdlgaYAVCsC6LVh2PY77wdLLcj0W\nLHttXLCMGoeBpawcDcAaAVZ6AJYBSwuwaHaGwbJ/08CdhBYsXQwWlZcOlsoFS22Apais/WDR\n5a0B1vx23z7AUnQO5WCNGmClpgVYZp2rZau4cC3BUgYsPjs3wbKvpi4imOVEXnUJFivzamBp\nByxjyn6wFDU3sibSwDLl5YE1NwGwEnMlsMZRgjVWB0sZsBTNzrpgqShY9rTLwFoQWgVLHwjW\nWA6WXbcNwTLv/gBYnacZWGMJWOYNS0GwzPyVvelTwVLLpPfAGhqAxQab1jIDS/cEFv2JKHPt\nzgVLHQzWyMGis/bBMt+ZAqxgXLB+fDzmJBybOYLOGoqCtUzZMQqWvhVYZsrbwTgPLF0A1nxO\nlp8AWIMDFo3OdIQHlrZDN7YCy96LWmA3wRpKwLIXlKZ8AKwRYMXjwPTj8WgBlrJ/GW03WG53\nOg7WtN6vBtaLp22wCC1W5LFgjQQWuwarYC2L1D6wezUDa9wAy0zTPLDssYlgjfb7SIDlxoHp\n4/Ez/djMEVwDy0yXq4L12m9Zddlg8b+VQOMwPzRLOBus8XJg2egmYBmLPLBGAZYyQ+KAxWfr\n01yNcQMsxQ4DWGlxwEq6szLJHME8sMQUSAOL3ZrovWDRQtoCS+8GS6WApdqCpe1i1lofDtbS\nUQWwxCVaBUsbSrLBshMhGyw12q9GACstDlDfHv/Sj80cwTPAEotF2VUpwFJsbdYAa5nbLcHS\niWDpNwLL/uTYOqNG87M6LcDS62CNNcGy93H2hwwAKysOWH8/vv5NPjZzBJcFtA7WYOwQU6AK\nWNqAZVotAWtkYAlkOVjz3CsDi24ANfNrNL+dshMsvRMsc9FcsIxYiWCZqoxZtcCy69/gIMAy\nGC3nEwNrbAGWAlhp8b4lPPhFdzZ92U1FRbAG0Z0Ay262a3MgsJQ207AMrGEFrKEcLDun7w+W\nvGU9CSwz3XLA0gCrXc4Dy66fbbDGg8FSFcFaOnDAGj2w9HXB0mYQ24E17gNrNB9qgjWo5VqY\nubsOljh+BFiFOe+NozGw7HoazwNrngdbYM011QJLF4Kl6oK1vL3nVLD49Y6CpWqDpY8Ga+Bg\naYB1Sq4P1kLJvKLrgjW9PcwFSx8Pliw2GSztgkV3LR2BxV51J7D0EWDpCmDpw8DSAKskLlj/\nfnx5PL78SPpZYd4AmrshZwJLsAYGlg6D9fo0AJaqBNb0F8kNWKoYrPmYpc92YJmvDqzZI8Fa\nriGrPwKWioJllD0KrDEKlloHy3xhjIOla4K1XLZyst4DrL/Lb+Z8pPysMG8At8H6fH6e/3bG\ntQBrfl8TA2sBwZS5CpbuCCz6ZZcaYCn2h5yTwfr8NBEsbTaGwDK335qqKQTL/IrzRcDac4/1\nHmB9f7ze1vD36+N7wrF5A5gKltoAa74YDCzzycFgKTuVOVimAwLLLKS7gaUkWGofWBYnBywd\nAMu+ql0JLB0BS7Fb01pgjetgKQEWG3MCq1SsDLD+31r26HJAIu90P+inhElgsbt/BpYKg6WP\nAkt5YKkAWKo/sOy6KwVrsP+w2SpYatnbfYk6ESzVECx25kGwRgYWqbMLLDVXC7D2pmuwhjWw\n1G6w9CpY5m2Fr8fm2xgfLHsKEixbs+2H990VWNOZhsGyK1EfAJa2YCn619rpt2g4WLZjCRZR\nQmDpEFjL7VwZWIp6MbPtdUAmWFoBrCrp5ltCtQMsajwIllkQzuaNO6xuwFIcrCENLJsgWNoF\nS9sKhhZgqVPAMi+H6eUMssAaHLB0LljaA4t9NQJYyenmRfd5QhwDlgqCNVwFrPkI0/f0W4ym\nXQtMFliDLW4dLLpIaWCphmApAZYBhIGl88Fadnpd5bnsU8GapyXAkunjbQ16+UuPWWCZ720I\nLHUmWDofLF0LLPstLQPmPLCWbpbduwaLDcJymQvAUiVgUeMSLGUqA1hFOfeNo1GwzFrOBGu0\nU3D5mnYwWCMHS4fAUqtg6ZPBoiW7CZbKAUsJsJYTaAjWuAKW7gwsM2MAVlEuBBaz4KlVA7A0\nwMoHi1/xeVMNsLR9jckDa+gZLO2CNY9dBCwNsLxwsB6Po3/5eZQxM8c87YE1xMFSB4E1SLDm\nJjPAUgeBNeaCpWJgLd/PWrCWzSVgDQ5YS4m2/iKwTFsBsBQNzYFgjQALYJ0Plplq7cEaCCxd\nDpbpuwgs+nF+I7Dsos4DSxNY5iRNjgZLhcDSAKtxTv2W0PHqYLB0Fljzc3lgKQGW/Y5mDSzz\nLuswWEMNsNiPxvaBpfLBWqoyYWCZAjLB0ptgLW2fBJb90lIRLGXmTedgpd/KBMJuhkLPLpuX\njyt99ASW1o3B0lGwBmU0EGCpfLDm/UvAGhewhnWwBFHngmWrMlkFS3cElg6ApTLAMj/7m566\nLVg7yFg/9rH8x3xc6SPyTvePj4Qi8gbQBcvM4J7A0lGwhgywSCPWKB+KVbDsktLZYOmaYKlE\nsIZisLQD1rKM50MYwPSN2HFg6QBYKgWs+RzEaNYDy7ZckDcA6+PxOPY1LAmWag6WPgYsu7pq\ng6W3wNIuWEo8Mm2mgcVORW+CxVZ+OVgqCpYdLz6IHYGlI2Atp7cOlu4ArCGcGFjet3CvD4GN\nD3ko48ZnhoMVF4s/8ZN5lfLPE+YNIAdLXROsZXofDBarlj8/v2AWBGsuxpYSAYvaPAIsxcbQ\n1n8OWONhYKkoWIMDlinp9cEBy+xwI7DcOyJ64Sm4MQRWkKJMsJ6H/ruEAMsmHyxlXs3IAEsl\ngEXvE7CDkgeWzgdLGwQuAJb5DYwAWHoLLDPsAizdKVh5L7oLUx7+Y2/jJlhuu6lgZSVj9JT9\n3SoXLHO1bwOWXQNVwTLbXbD08IyCZSq2a9C0ycBSrCtRa02wVDFYtsdSsNResHRlsGjP64HF\neRHf/j2WrbRbLljuIclg/TjmNSwXLHUGWLQqzwLL3keKbj2w+C57wdI3B0uPwyZY4wpYiggS\nYM33rM4ZWrA0gaXTwVrOcT9YY+9g8U8ezKPQt4b8gLqvYT2ZV9cBi08vgBUGy7mRoP1TwLKP\nBVj6LLCGCFgGm3KwxupgqTcDS9jkqpNxh+UfkgrWx+PP18fff18fv1fOzyRj9CRYugZYy19/\nrwKW/YtZ7cEaeLX5YPEvCgVgDelg2SFMAGtpbO5gGyx1Bliqa7DG/sF6mB8YOtCcCtZn7/97\n/Pf89/i6cn4mGaPXO1jqfmBp03B7sExjOgOscRMstR8s+8xyhqeCReNwObD4OxjoDiv0dnUD\n1sNrwnFHHLrywz8frP9eb2k47ltCXQqW6gIsrWuDpZPBMm0FweJNm0GuBtYwvCdYOgQWnXkS\nWOM2WGY1CLC0eUKXpa/fJcz84V58d+eZb49ffx9fnr8vCZbmYA38leXOwLJz1wNrOAesIRus\n4T3BsiNjR70ELNu7MwEAVv7uzjMvqb6+7ssq/013Axb7x0PodcVlj2uAtazRo8Aa6oClGVjm\nT4dRm+Vg0TmaAhLAMn9ZzANLr4E1HgIWG4YzweIXnX0eBkvZQ+4DVp5YKzu7T/335fUvUTx+\npDSbMXoGLPaPhyzX/npgDRtgKZqNrFExHMan48Ay/Y/zS95XAkudCpbiA3M2WPp9wKqVk984\nqnVrsPjazwZLrYKlysGy32y+N1hsBB2w1EFg2VPZAZZoU0uw2E1cCCy9CdYIsETeDyzrTBJY\ng9IcLBUDS9mFmw2WtmANnYGlTgeLRnA0vzVsDpDlpoKlDwWLqrBtagcs6rQQLDooL28AFv9j\nDUe86G5nzfIV8xJgDflgLe/qSgDL2sO4qAaWZmApvqomsHQKWKoCWEo1BUvXBWvgZx4CaxRg\naWV+HRJg1UkzsFRdsJYfQCeCZfaoBJZywFJng0XNc7CWniRYgwHLXBcxKulgDXYId4A1b2wK\nlmZbwmBpOzF1EVhmZPh1UTSxNcDKyZnfEh4K1rxXPlhDIVhsGS07ngDWMCSApfgcfwew1DpY\n8mUkByydABa/VACrcVqCRTJpD6zxNLDEHmlg6VSwBmpUDMd5YKlSsGjICSzVF1jKgKUcsMYz\nwVKyzUSw6JTNRQJYSfHA+vnt9VasPynHZoweA0sJsOxrCGeCZfeoBNbccSWwhnPBMp+HwVIS\nrLmdGaxBp4NFz0fAGqiGDLDMAjdgzT0oBtbCQRAsbe7QqMHGYGlzPuYQgOXFAevfl+n1q8ch\nv/ycB5a+EFjspSWA1TFYmuMy/wBzP1hqrATWMACszThgfX/8eP0e4a9Dfvm5NliqR7DYaiwE\nS5TaGiw1/8vXJ4OlisAao2CpMFhTqwDrymDNf0v+oF9+DoA1HgqW3geWBljKvnF2AUtFwHoe\nAtZYBSzF/gmO2mDNZdgWpmP3gDWOAGs1TcFSR4OlWdO8FrOHC5bZVBssHQRrOA8sWi1HgcV6\nCIGlOVhaaVUCFv9uOQUsNSq7owPWsFzONbD4FbNgqQBYVNJ0eDlYCmBtJfwt4Y+kX37OiFLP\n6Sq8Pl2u6PNpwFr2+NzyXMB6PqetL7DM8fNVfNKGZc9xNJumjcOwfG4/MU3zWuwey/5mj2H6\nC+nD3N20edrynLdNuy3Pv45T1PDiiC11+WSgVsVwjMvpmWPs2Q+D2HMxwzZqweLnKA6aweIt\njHMDZuMMFh8xPkisAgaWqXS5CgtY5syWcux1YGewDKU8Z3YRXi2xgZp3NYt9mTFspAd+Iefd\nnsqA9Vzm16DsNLHtUXFsGJan7WjRfBqpQjoTWcIyKcQkeM4dLfe0cznK1vVkE9WZkgSWIrCW\nJ/hRR+XCYP1b/m3Cj78Jx2Zw79xhma+lu+6wBvsVkXrJvMMyu5k96A7LfLEP32Hps++wlr4K\n7rDsqVS6wyKwtLzDYn+11fbO7rDonNlFoGFmNRiwku6wlFq7wzLt0d2NvMPiW/gdFlVIZyJL\niN9h6eUd9Obucf0Oy140D6zlieJbrPe4w3o+//fl8fjy41/KsRmj54KlLwXW4IGlE8AaDAYc\nrPmTqeYhB6zXg31gmWMOA0utg2X/XUV2EfLAGkJgjeY3jFfBspoWgjW/DKC3wdLmjVQhsKhF\nH6wRYCXl3DeOLhdBtwFLrJVDwDIzWJlt1KooqwgsfXGwTAfsImyANW6DNQqwnjoGljnyaLCU\nujNY/Jf26M8i00b7F4734xKL0+bXnNeuMkavB7AGgLWMcIdgscuQAZbaBZb49+X1PB/rg6XM\nFL8+WA/xX/GPRZh/jsL+y18BXKrE+1dzMo7NGL1NsMxLBOlgaYB1YbDMH4uIgqXMu6dWweIL\nPB8sscWCpaqDZb9V5MWz1i8ClvOPe/lg2U/PA+vP1x8pL7fPyRg9BpbuDiwiwAFLm9VqwbIM\nLctI294AVh5Ytg8zzJoBkw2WqgGWXsDy/1hgFbBUKli6AVgqnCBYywMXrIe35wlgHfznZabP\nBVjjOlhquWCNwBoOA0vVA0vzgy4JlumzACxl3xj7mgkzWGbSZIO1/IzP1MsKLQBLe2CxFrfA\nUr2D9XiKuyqAlQaWUseAJVZSdbBeN441weIKHAKW6VSCNQw9gGXdYmDpHLB4mzXBGneBZW7K\nuvuWkP2jgw8GhqQkA5HcnP9TQg6W7hUstn5zwbJT+AJgDf2Cpa8KloqDJYrnw3AhsJ7sbkr+\n885N7rBO+CmhVjcHi/U3sD6o03SwNE13TU02AUurIQ7WcBRYprlqYKkzwBrzwRqDYOluwTJ3\nUMyqJmCd8FNCvcyiBaxl45XAMgfngWXvtqbT2gOWPAMPLH0MWENLsHQ1sEyRAIuy9w5L3mLd\n7qeECWCpu4Nl7tWKwBrEGZwKli4Gy15ggKXF1NGXActlyv6o0L68ZT6914vuYbCGeT64YKkK\nYGkzx9qARf+R/V0LrAFgvT1YT/f19Qe/63q2eKf7cWDZ95bEwBrCYOkKYJktp4JlVrnpxwFr\nAFj3AsuMTylYKgSW6gusDnLaTwlTwRrOAst0eBxYukOwhnuCpU8Da4iDNewDS8XAKhMLYHnJ\nGD0PLC3BMutk/q9ZdClgaX5B64GluwVLnwPWALBYoQwsfh314WDxv5aalzcB69+Pg/68jAuW\n3gPWa3KEwGLrvT+w7HGHgqUqg0VeASxWvz2NDbA06VMGlrKv/WbmPcD6e9gf8AuCpcrBGgxY\n/Fe0ksASDwvAss3HwJpf5G8FlioDSzsVDJ5Xu8HyL0IVsMw5XxgsZcHSAGs93p9I/vpJ1d+v\nSX8iOWP0gmDpOmA5C3own7o1nAeWbOsiYNEAHgPWsAsszcCyO7NzuzhYeh2sErHeAyz6S1wJ\nx2aMHruZOhwsZ0bxJ/2HACsOlq4A1kBgUQeiOjY4dmUHwNIXBEvusQqWWgFLAywKwKoGlu4F\nLLUXrKnIBLBMNQDLnGsILDotcVk0fzQ1M1DpACuW874l3A3WPBEqgrX8d7gdWN4rPdNnpoX2\nYPFq08EadoClXZ4OBEuVgaUBVkrOe9E9H6yhBVhm9bCVtDQ6d3c9sLRcefcCSyeCRT3aM3e2\nvNIUrAFgJeS8tzXsBEufBZY2PNlPrw6WMwiJYA1pYOnGYOm6YL363AGWAlgH57w3jr6mlLk8\ndmsqWOOYCZaz8AOb6oOljwDLO7/TwNIJYC1dHAPWuAmWsUVXBcvfDrC6yalg2ctjP8sAS4fA\n0l2BJTpYjtwHVuD8ABYDyyYbrGEXWHQOa2AtOwGsinHB+jb/tvWXI17DostjP8sESwmwlvnL\nLv2hYOluwBp2gcV62QBLK9r/dmANzpa5lWpgjVlgKYCVGAesH8ufhzjkp4T2c9qaDtYYBYul\nPli6S7D4KRwJFts/CJbpAmAdDFaBWO8B1sfj9+vDn0Peh2U/p80BsIa+wGLFAawzwVIrYA26\nX7B0fbCKbrHeA6xD3zhqP6fN4ziaObgF1giw3gcstQHW4IM1MrD0qHh7YjRtY86WuZXKYMnT\n4mUArLI4MH17fP/3em/D42vCsRmjVwssRbtPk8jp5iiwdD5YwxZYAweLXjLz6z4arCHwdHOw\n1D6wpvXvnbwGWMFcGCz7xtE/CcdmjF41sJQAy825YD3XwTJd3gAsfUmwBvfkNcAKJhEs+8eI\n5V9A9v5Ocoo7xYm8cTTpX6LIGL1OwHK/ZUsDS9cFawiB5ZQvx06eQj9g2S7qgrWcRROwxlZg\n0XTvFyz5yYM+mr/ozjcflHPeh6W6BUsLNyJg6a7Acqo6ASzzwYA19geWuglY6gpgPblMjyfA\nCr4PywFL8rCE7j96BGuwFXYNlhjdEFhmMSaBpe0lC5ziHrDkqc11XRmsoSlYYziJYC3/thfA\nGsxx9wBreE+wvOHeBEungOWcJ39bQxws3SlY+nJgsf9zsB7Pfahs5Tpg6bPAWo49BayhOVja\nGZQNsHQYrCEdLKfaFLDsZVkFSyWBxSqzR9pwsPRbgZX1ovt7gzV9kgLW9FcZU8Cihpwns8Bi\n+xwIlldhOljLvhIs7YCl+wOL7ZAM1jKEp4Ild3fBck7hLcASnz6cDw/vn64/JFcCa5kQGmDx\n89kAKzAIDKwhGyx951RAeAAAIABJREFUPljskgqw9DZYa+NAR9ocA5b2wdJmHps2LgcW/0kh\nByv5n2EuzPlgDeVgDRGwuCv3A0tXBMt6ZZtoCpZeAUuHwOInLsfoYmDpu4K1W5WNAKx5USm5\nKdBwO7DcU+gTLOtqOVh6D1gqByzWxGFg6VWw+KBcDyz5XlF67eoR2LVuGoOlJFhDI7AGZ1Hl\ngrWs+9PA4qfYDVjizG1zu8ASg7IJluoMLC1P6/pgse/37g4W+52HEFiDWBcMrCEbLLMmNsCS\ns5+tJk3z7ACwhh1gWY09sCQBFwCLaREGS+sSsHQDsHQCWH5H1KxtQoClewSriwCsa4JF6/5o\nsLQtf2n4XLCoXICVFYDlJX3waoE1XBYsfV2wqPqlYQesAWAtTQqwaOdAR9SsbUKCJU4LYFHa\ngEVfnG8GFu9A1umAJdzgRQEsk/cBSwOs5JwG1rgBlrlFSQHLLFjTPMDKA0uzkxdgzQ9PBcu0\nzh4uaQRW8JjmYOWLBbC8pA/eHrDU/Gs5GmDVA4ufaVOwqCpTPKUNWOFj0sAajgKr5BYLYHlJ\nHzxFXp0Blvn7TTJHgWVWeQ9gTYsUYLUCSxeCZY7nb/9hpwWwKK3BUh2C5bRnCjRfCO0zaWDZ\nKR4Gaxg0a7RXsMxynB9kgSW39gcWz5uCdaU0B8u+iB4GSwMs1mInYL1+DZ2B9QrAAlinpHuw\nNMCiFrsBS9UEi846CJbZX1wyd5gkWMtrQtlgKYDVey4Glvmd0W2wtDcjOU1pYPEeqoBl0FrA\nsmXWBcv7x4TkGHQIlnk2Byw5TvcAa3DB0gDLyXlg2QvDwNLZYOll93KwaKnyraKdXLCo/D7A\nigdgsdPxY25oAvsfAJYsYjANAKy13AGsgX1GjV0ILLkSY4PogGX2rQUWjX8nYKndYMVvNVuA\nFfxXNOWjQbsFACwnAAtgiacOBMvcS6aCtbxeGQNLYjDt7YK1Og6BzXvBml5jVcr8C+WrJQCs\nonQK1giwtHsGVwfLNpsMljjrTbB0N2CpemBpgCUDsNqCNfDj7giW2KsMLJ0Alq4LlvvsClj6\nWLA0wBK5J1h8IdoArJ1gDT2DNaUWWN6za2Dxqg4AazoZgGXSAKzhNmDpC4LlcJQF1pALlnb2\nssN0LFjqVmC9BgJgmbQAi13JEFjDcBmwbAuZYA0XBYt9nTkeLL0Flo/GcxmC5mCpymAViAWw\nvKQPHn83XBpYy5Q7Ciy5kFLB0tXAkuhEwfLXdT5YopFLgWVbA1gAy+QcsPhwJ4ClBFhqeZeD\nXNengyW33QosZ9gOBMvW753Y0q52cyOw/EYBVnauCdbzUmDZInPAolpZiwlgBd6e6LXBB4pt\nss8ALPdpPmb+OVJVlcGanwdYLH2CpcrAoon9xmC5GZyqegZL/POi1NqbgKVXwMoXC2B5SR+8\nbLDUsWAJGHoGi0O0Ayx2Hn2D5Z/EwWDJnSqApQ8DK1MsgOUlffC2wRJrshFYLkrrYA19guWt\n0hywRE/OUBwFln+xKoAVHopAXZcBK/sWC2B5SR+8KFg6BSzt/C5pGVhsbW6D5c3mYrDYKrsX\nWHrgHQAsgHVKANYxYIlS5i1cmjuAJToAWADrlPQN1nwJ7wEW23MHWNK9ymCJnk4AixxyjhHl\nnwyWLFtUocUoOX1LsFR1sHLFAlhe0gdvAyy7hqqAxQThORgsvsrt/geAxWquDZbsaQ0srdyz\nygZLVJECljz9NbCGPWA5ZYsqqNUtsHSoBIBVIZcAS+eB5a+Bpd8VsIZwO+xogCVPRQ7s0WAN\nOWAN1wVLB8Aq+54QYHlJHzwJFl/ZaWDJ638IWEOwHXG408WJYFEHsmYXLG+hyXO9DFjOuGeD\nRVcgkkKwBmrc6xtgnZJewaJLGAWLLyb5STFY2m1HHO50cV+w2DFHgkVjdDWwQn0DrFNyOlhm\nsS0PAdbdwHJW4RZYtojAMaYjc2QzsMx0I7DcJ6uBxX49yT4PsCgAqyuw+Ln4YDnnNz+6Bljs\n1HsEy8qwEyx9IFiZYgEsL+mDlwiWmZxdgOUtI7eLQ8BiJ3UaWOLsDwWLToR1ewBYg1tHaFD4\ngWbf3WDpQ8HKEQtgeUkfvHcEyz4FsPggkT93BUsfBVaeWADLS/rguVeJXan5wtIFOxYsmsz9\ngyWL3ACLPREY8NuARdX5e+kKYOkksOSzlcHScbCyvikEWF7SB8+9StH5ALBCQvCl7dS8HyxW\nP7sWzoJuDZa8THS0U04JWGIqBUsoAUuXg+U/TzddGWIBLC/JY+ddheh8WAOLTbI+wXJk0O42\ngHUiWKGhWKsr/DRvPg8sbygAVpUALL4SNGsHYLHTdsGSZ3UWWO7hci99ElhO12zgANbx6R8s\nPb+3pQZYdiGyOccWfx2wDFX2qZuApWU7fGiuC5a8aOExo0GpAZa41AArOwCLFj/A0vIZMcZx\nsHRzsMznAIsCsLwkj513FSJXEmAdCxaN/ZuDZY+WFy00ZnxQ2oFV8GNCgOUleey8qxC+knai\neWCpHsAa2AeAdSZYujJYdLS8aLzTnsAqel8DwPKSPHbeVQhfSTvRTgaLRNBi243B4qMh12yX\nYLEhAFiJAVheksfOvQruZHLB0o3BMnIEwaKHEiwz+QGW0zuvwhGna7DcIpLBeir7DMCqHYD1\ntmBJMgCW2GEXWNFREnsngTVvAVg2fYKlOVjmz8ayRZQGljcJ24NlF/7A/tspWM75vhlY2iui\nMlhuOwArKZ2CZTYDLHs+PljzjpXB0tcDiz53wHIHQ44t/0zMp+PAon38dpLAyhALYHlJHTr/\nKnhXUouJRpv7AottGq4CFi+BjUscLHnQXrDEAtW2c5oFfNBYlaHjOwIreIYpYPEr5Z1oaP/p\nM4BlczWw5l2edJgWYFEfztWXa14u4gywxGHnguU/nndMAsuD/ESwnKvLigJYACs3VwBLC7CG\n+4PFlqU4H+fx3OjdwPLXMTUzsJHh88R8DrAoAMtL6tCJRC85m2i0uSuwBuewI8ESvdG+AIuN\ns1j6fCz2gGX/cyBY7vW1zcTAGgrEAlheEkdOJnrJ2USjzfwrjJ2mlcFiz/KCAJYc0ipgaUHG\nYFutB5Y4qwywSC26CPLAPsAy/6rwZgCWl5Rh8xK95Gyi0WZ3FV0OLGct9giWb8aBYHmj6XUe\nWMesxgSwxF5OLf7pyYYvANYkVgJZbwvWx2dCn/cNljtbqHGA1TtYvhWdgEUJtHogWPM/Lcx+\n5yeFrHcF68P+R37+vDlYQ6B3cVgKWFqcJsAKjKbXeddgid7cCg8Ea/7H0Jcfl78+bIsFsACW\nOCwClrPQnXNPBUv2xvdlj+cHFwBrECMuR9PpXJwaa44NFB3onWAuWPZY+Z/AePASvJOnETJV\nREbJ9pYNljb/toXN1neGAOtiYMmrL5eNWPzsWVaQP59E4UMJWJqDpQd+zraWVbDkSMwPSsGi\nJ9yz3wWWW8HSVHQ0nc7FqbEC2EDRgd4JPt0xdMfCOT17rPxPYDx4Cd7J0wiZKiKjZHsrAWsK\nu8sCWMGEwfq/V4o6pLXIt5kn5g+0We41baCN9HE5hm1gj+hguyfr3z7mB8wdDW7v4rBBPOPu\nIToXdTzFXqYsW4stk/VmzpwGRtb2FDu6HfrtOMW6Z887oD5F404/7JFbwdJUdDSdzgd+gVnT\nbKDoQO8EvTF0x8I5PXus/E9gPHgJ4ZN36g6Oku3NDoBsJrB/aEzfOc3usAb21cR+HSm+w3Jv\nB869w2K3iG4p/ulrsZcpy9aSeodlH8TusAI3IHYEvWI377DCjdPDq91hiUvGGu79Dis9uMO6\nMlg0Lw8By99jD1h8NYszzwSLugBYomrbhz3WNgywOg/AuiBYYvlfGCw9ACzRDMDaDMAqA0s3\nBYs/eDOwBtYia8oBy79+vGrbhz1WtA6wOk53YLGrsxMsd7EBLLbQnWJ9sLR3HrJx56y6Ait0\n/XjVtg97rGgdYHWc9He6f7DP5+QPorZXzVl+5hl6pF2waJoCrCywaCtb6E6xbw6WbB1gdZxm\nv0sol595hh5pByw2TYNgDXKDaOh+YLE5vA2WfJqNgFgQh4IVHk0JFl0ggEX7h8Y0KQDLS/4g\nuvOXLdR7gOWfhHf+1wGLD6nXuHNWZ4MlT8p8LsDy1znAun4AVk2wAifhnX9XYOlaYLnd+uMW\nGE26whysgBX3BWsQzQCszXQMlmsIm60Aix7sA4tXLluXQ+o17p2WV5gzboHRPAAsW/UOsCJF\nsCkEsJrlZLD49D0SLPG8ttdeTFS2L1vJZmNkibHHUbCche4MwGXBcgbIPS1/J9unOBm2tRQs\n76TM53XBkpgArC7SEiy2IM1z9KgaWFyoTsAiWOTaOBCsgbdjT0cs4E2wxNXwTssrzD6WJ8O2\n8nGoDJZ3SrxKW83A62AT7FSwnCFw9g+NaVIAlpf8QWwDFjliZjFbPm8GltnOl3k1sNx1TuPG\nToZtPQQsuy0dLD61bHP86BpgUUceWGzwvKHz2kkNwPKSP4itwdL9g8WHqD5Ydjtf5m8K1sCK\no6llm+NHA6xu8mZg2Yc1wBLdJIPlLNROwPJbD5xHb2ANrINlLHLAYmzQ1LLN8aO9gQu0CrBO\nyS3B0lXACs03/rgjsOSyFnsALL9+O5Gcyci2A6xOcy5Y/hzR5lpVBUuz5+1MPxoszTuKTjG5\nUOUil7XcCyyXIXlOrcBiMzIAlrhIAKuLAKxCsLTtE2BtgWUHXWytA5adE/NY1APLvUjs8hSD\nRedHFQCsrDQBi01Yba5VEVgDf6o5WHY3vxTnMGct8GVbDpazj1gHtwaLmgFYFIDlJX8QB3aR\n2JTilmSCxRorA0tfBKwAKXNuAVZAIdkTTRuAlRaA5SV/EAd2kdiUagqWaRxgydYD51EClr1K\nx4A18PO7AVjeIHntpAZgeckfxIFdJDalLg6Wd4auYu4ObcASBYsGg60HhvRdweIT05sHAOvU\nNAJLTqmjweKvy7IZI+t6Y7C8k6PhCIHljp6moT4BrGG4DVi2ejZ4AGs9PYGl/UdvARarjdfi\nguWu+OUzBpYo0VsHomC5s3tyNBx1wFr+io0zTIeCpYOliNOjD2yOyCnqDaWddCujArAOzFXA\nkrOqACxWQhgsudiDYGn3GO1NJnFesSFIA0vfCKzQKKyDJefE3cAaAFZh7gFWaHUdAZZ7Ltqb\nTOK8YkOQCJZYrXvAEsuajX93YNHsuDFY9F+AlR+AxVofxOOrgkUH8UG4GFj8CTts22CJFR4o\nRZyerWBw/+s4wYfSvRAA69ycDxYty9pg+aTIPu1B81FOXXyyiOpY6d65ACz+TA2w7PviUsCi\nC58NFrNDaMkGZhD7M7CCrdYFiyqMDeFWAJaX/EGkBcUuWCOw3Lr4kg2wM/itAyznmSpg2aed\nPvPBilTpg6UB1mXSFKxhkBPrTcASjd0IrOBF8HaVZ1QXLGeF82Hlnwzi+MH2bycYwOo2DcHi\nF8Q8zx8BrIPAYmcszl+2zvemWm3J7lmxUws8FRgFzkUJWKzKYRB7eedeEyz/fADWmekLLLMT\nu2bsSLrWMbDc3mSf1HoZWIFzaQiW+ewIsOj4w8Hiw7AOlg6cIhsyzT7pGyw6CYCVndPBspMb\nYJki42AJXXoAixa3uzM7tcBTgVHYAxb9hcYzwYqcD8A6Mw3ACl2Q0E4AawUs+iHn6WB5pQQr\nl08FRiENLPnRqTMPLK4BwLpqOgSLzYCzwHLW7xXAsrk7WE41ACsxAMtL/iB2AJYO7eku2T1g\n6SFGC7UjuqoPFi8MYEXAIkFsU0lgBc5FFAOwDk23YA3SoA2wggztA+v1IVi6s4/X1m6w6JcI\nc8Aa+BBRYXw5dQ0WfwywAFYkFwFrMMu4DCxnlqeCFS5d7lMdLAHCPrCYOPXACpbCBfCHIzgK\nYbD4I350BCxxqhlg2ceJYAVOwT1BDhb1KE8ZYO3OhcDStMxSwRrYMbz1ArBCrQ96COyZAJYe\n5N4OWPy8WXEAqzZY/Ii6YPnQpIJF5w2wAgFYdt8zwXL2BljOGXYBlnMVYtkAS3YPsHamFVj6\nJLBofvDWS8DSfuv9gSVgAlhdg+XsALCS0gwsuoangCVbD4MVexQ9l57BosXsdlMBrMDONCL+\ncARHoUOw7P/OAkuzHQBWUgCWLCX0KHoulwNLVt8dWPKhOPoAsCwKdnx6BGtgZ5AVgOUlfxDv\nCFbgiZpgsZm7Dyz/DLPBYssoBlZgQNqCNXhPHgnW9HldsFgTWQFYXvIH8QiwaMebgmVPMg0s\nmuSdgBUZBTl8g18QGxI2NLwDOsfaYIn99oBFrbHLImuKFAuwgukWLPPlSRxoLqEFi13Tu4MV\nWzdhsOxZ3wosfVOwaAYPTm3RWbYZgOUlfxCdkWezRW7WdH3FgeYKPul4cbn93pyFoAEWa7gU\nLP+088Fy2hn8gtiQsDp4B3SO/YNlr6E4U28GD05t0Vm2GYDlJX8QnZFns0VuZtdXHGiuIMCi\nlIMlFPDORBxOxVYDS9BwFFj8xyLUfA9gydMGWKm5NFjavdx+b85C0OE93dJS1l10KhWApfnZ\n1gCLzjoKlmYNhqQZ5C72qOBpA6xEsJwTZVcKYCXlMmDZA4ZjwNJynzSwgvutr1r3OYDFKtgP\nln2XmfnADWgB1sA/9wbJuVrmGgKsaM4Ey5vObLbIzXGw5mOOAMv9l9STzia03/qqdZ87EyzZ\n7T3BEjtdDSy9XEOAFc3ZYHlb5g/O1hhYppFDwFqtNLxPcL/1Ves+955g6WpgRfZOAcv8epjd\nMwLWxjmxOTzkgiWuF5VMlZuLulZAOADLS+4QBmbzCljOwhWN3BMsO2ffACxbs6jgKLDkXjrY\nRA2wdC2w5FXMGFQKwPKSO4SB2Xw0WHIy8Na3Kk06m+D6XF+17nNygvIi5SnoWNVvBpbznTvt\nLadLBKzBaewssPj1cC60M0cB1noAVqTSpLMJrs/1Ves+B7DEibKH1LBXhyjRgjXwYWNdDJcD\ny7mKGYNKAVhecocwMJu3wXL3mLa8G1iOLyK1wAqdxkXAsjUBLArA8pI7hIHZnAKWXKvThjyw\n5K/fNgfLe1wFLGdpsAUSLCoNrMHpcx0shkNKKoJl2gJYFIDlJXcIA7P5HLBCrW9VmnQ2wfW5\nvmovA5amjsVRcy+hs4oNSCRvDBaNn3O1ANZWAFak0rTTiS307sHS+8AKnZU5jeip+8dIoYbB\nL6gCWIIPt7FDwBp4jw5YzlgDrMx0DBb/K8o9gqVDrWu+MMIHeY+bgCVqyQMrclYtwTI3LkeA\ntXVOAOvMnPqrOZlgaYDVHVjuFtbSbcDSVIWoJX4e8r8A68A0ByuwEsvA8peSq4DXekahkb2i\nC33loNDubql7wGITXnsDGa6lFViygm7A4hWeBJYsGWBFczJY/paAH4VgBWg6FqwnwOItdQ2W\nKC4Ilt1LVog7rL5ybbBoIoRpCm+9AFjmuxKasqFD5yrYfgBLPlEJrOCfpff3Mv9lYJlOS8Gy\ns2OtgHAAlpfsMQRYyWCxQo4Di71Y0wAs/juTPljCgXKw2ADuAGv9NA4DSwMsLwArXOjFwOID\nkQHWasmHg6XZKUlw3hos5/IBLJErgCX2CIHFP3EavwlY8m1TsgrbSnuwNs49fByr70iwBAry\nJO1HgNV97gwWnyZiY59ghXoVmw8FK7jx/cByNIl27Z3DXrDkjAdYsQCscKGXB0vL7yPrgOXe\ngoiz2guWPgksUeOBYNkLK7nMA0vOgJwALC/ZY3gQWHxHr/UQWJsToE+wwj+sioElxbkCWOJh\nGlii2L7B0qInUfcaWBpgiQCscKFdghWuwrayBtZ6VbcHixsAsK4cgBUuFGC1AIv/Ukw9sDgC\n2qnxRLA074n1b6ukkgFWNAArXGgyWMGD145uB9ZKTb2A5fVTBpZ43203YMke6bwH92mAFc8b\ngJWy0d9n+2wKwQrufgZY6zVEC3O2XQMssbUHsGRN4hHAygnAChfaBqxgIQBLR8rPBUtvgeVp\nEu3aqwJgnROAFS60BViBnwK2BssX4DCwwv0cA5bcg32U5QOs/gKwwoU2AStcyJ3BEg2Ix4eB\n5YEBsK6Uy4Ol5Y5e65cBK1pIX2CFq6kOlqvFXcHi14tKBljRnAqW/z1PBKzAu1LEERwszXYM\ntA6wTEvrNUQquwVYdnSuCVbZoAIsL/mD6CUfLB0GK7iUisFa/wNIJj2DxVo2La3XEC3N27IB\n1lqtaxUEt7AvSOsHpYLlXv0qYNEcNmDZywCwKqdHsHQtsNIVK0ocrJxWaoKlbwtW8EvIKWBt\nnhK/gNMHgHVg7g1W6G4HYCWX3BNYGwcdBVbCZBEXEGAdnMZg6ePBCmx6I7DswQALYN0hrcGy\nU93ZlggWPwZgAaz9YDnttwBLlgmwRABWeQAW294CLC1mRaA2gMUe3yNXAYs/CbBEFbaV9wPL\nKawMLLun1x/A6i89gLWyLABWLlg6AtbqOzXeGSza1euvIVi0W/DEEgKwvGSPYSgAaxWlbQRc\nsOYhpW0pxdwGrNBW9uwKWKH+AFZ/AVjlqQjW2sosAYttA1g0OptgyfvQLLColXywRBkAay3v\nB1bKHExLTbDWd1itwrZyZbBCv7WltU5vbggN5DZYmknhtwmwuksHYK0tC4D1LmCFmsy7UOlg\nxfqLlLAbLHf+ZoOVAbcNwPKSPYahrIMVvuAAi1dhWwFYNwVrvf9IAJaXonF0EwNLPA2wVqqg\nVs4BK7wnwLKtAKwDA7DK0x1Y9gBqeS9Y/pbocr84WPESWoFFG0oCsLwUjaOb4BRaB8u/GLoZ\nWIHN7wxW6D6lMACLNpQEYHkpGkc3AAtgxVt8T7DEu+8Alkj/YLlzJgJWeHbfAayNvyZowWIt\nUstptdwCrEi5p4DFeHHB8uevbDAElgZYsVwALGcRxMCK4RTusaxYmbPA2qjC6xRg8U3NwXJO\nw28wCBa/iqn1igAsL0Xj6CYBLPc5gCWq8DrNBytyE3d9sPQdwEotVwZgeSkbSDe5YIUuhnPQ\n5rY6qyoCVtofhK9WThWwwrklWBklAqz+ArDKEwMrLwAr1nk+WP68GOwrQkQHwLpwAFZ5+ger\n+AUQ08AtwcotAWB1lD1g1cl0tf1t9rOMhoKNBztML2+9xwoN1SmHN2I+/fy4r+3ghQk3OPW1\no6tIi1lthifA8mFqKr/B0Oz09mI7TR/nwZg2+r36DYqxky1FzuqN0/4OK/Rlj3/BSfnqEd0V\nd1gn32HVS+07LF18h7W516F3WJkvidrgDstL2UB6Cc0JgJVehWmFtWg/HgBWbNfuwdIXBasw\nAMvLvgG1Wb0yAGuzCtMKa9F+vDRYCa8fOUeEfgPCNGbazGoQYPWWDsBaD8DaqsK0wlq0HwGW\nbcy0mdXgKWBpgJWe7sEKBmCxKkwrrEX7EWDZxkybWQ2eA1agUoAVCcDaUQXA4n0CLA2wDg/A\n2lFFp2BpgBV4zrSZ1WBDsPYGYHmpM7AlAVisCtNKoGWA5bWZVwLA6i0Aa0cVHYEVPnuA5bWZ\nV8IOsAaAdUQA1o4qegdr7/TPAqvaSuMtXhKsgYHlv10VYO0KwNpRxfuBFX3bdQ9g6S7AMndW\ncpvcvV6J8QAsL3UGtiQAi1Vhmok0vqPpjKO7ACs8L2SbeSXsA4vtIHevV2I8AMtLnYEtyS6w\nqs0JgCV2vQBY2X+qDGD1ltuDlbpnSRUAi+96BbCOKAFgnRmAtaMKgMV3BVgaYB0egLWjCoDF\ndwVYGmAdnpuDFX7RAmClBWClg+U8AFgH5e5gBfM+YO081fSDAZbzAGAdkxuBlfWPC1Sp4vZg\npQdgOQ8A1jG5E1jJuSNY0X9acE/b6TkCrPyhAVgUgOWlzsCWBGCxKjZa39N2euqDpQHWrgAs\nL3UGtiR7uwZYtXMAWAVDA7AoAMtLnYEtScOuWQAW7+cAsLJXL8CiACwvdQa2JACLVbHR+p62\nM6o4CKzMKmp3n3JWPljmE7ZN7r/eWlmxbgCWlzoDWxKAxarYaH1P2zlVACz7YP5E7CD3X2+t\npFQ/AMtLnYEtCcBiVewvoUIAFnswfyJ2kPuvt1ZSqh+A5aXOwJakk0UKsGwAFnswfyJ2kPuv\nt1ZSqh+A5aXOwJakk0UKsGwAFnswfyJ2kPuvt1ZSqh+A5aXOwJakk0UKsGwAln2gAdaBAVjl\nAVgUgGUfzFUArGMCsMoDsCgAyz4IgeXsv95aQaWBACwvdQa2JJ0sUoBlcwxYub+S0BFYGmAd\nEoBVHoBFOQis7CqqZhdYYoeVh+s7lwdgeakzsCXpZJHWmVwAq2IVVZPk1fw6O8A6KQCrPACL\nckuw0u5+AdaZAVjlAVgUgEUPANaBAVjlAVgUgEUPANaBAVjlAVgUgEUPANaBAVjlAVgUgEUP\ndoGV/d6zWACWlzoDW5JOFinAsgFY9GATrI3mciqMB2B5qTOwJelkkQIsG4BFDwDWgQFY5akE\n1s6/MN/JWAAs+wBgHRiAVZ5aYO2sonUBUwAWPQBYBwZglQdgUQAWPfDBWnvoN5dR4EoAlpc6\nA1uSThZpB0u0m7EAWPYBwDowAKs8AIvy5mBpgHVSAFZ5npX+QdZ96WYs3hos/mAfWLUmFcDy\nUmdgS9LLIu0hvVQBsMyDnWBVCsDycsq4B9PLIu0hvVQBsMwDgHVgAFZ5UAUFYNlHAOvIAKzy\noAoKwFqpAmDVC8AqD6qgAKzkKgDWngCs8qAKCsBKrgJg7QnAKg+qoACs5CoA1p4ArPKgCspt\nwUrZK7MKgLUjAKs8qILyzmAdXUVZAJaXJtdhHvx2XbOgCgrAOq6KsgAsL02uwzz47bpmQRUU\ngHVcFWUBWF6aXId58Nt1zYIqKM+zXprZqqJqAFZ3AVjlQRWUe1YBsLoLwCoPqqDctAqA1VsA\nVnlQBeWmVQCs3gKwyoMqKDetAmD1FoBVHlRBuWkVAKu3AKzyoArKTasAWL0FYJUHVVBuWgXA\n6i0AqzyognJ95swoAAAEXklEQVTTKgBWbwFY5UEVlJtWAbB6C8AqD6qg3LQKgNVbAFZ5UAXl\nplUArN4CsMqDKig3rQJg9RaAVR5UQblpFQCrtwCs8qAKCqqg9FlFNTLaBmCVB1VQUAWlzyqq\nkdE2AKs8qIKCKih9VlGNjLYBWOVBFRRUQemzimpktA3AKg+qoKAKSp9VVCOjbQBWeVAFBVVQ\n+qyiGhltA7DKgyooqILSZxXVyGgbgFUeVEFBFZQ+q6hGRtsArPKgCgqqoPRZRTUy2gZglQdV\nUFAFpc8qqpHRNgCrPKiCgioofVZRjYy2AVjlQRUUVEHps4pqZLQNwCoPqqCgCkqfVVQjo20A\nVnlQBQVVUPqsohoZbQOwyoMqKKiC0mcV1choG4BVHlRBQRWUPquoRkbbAKzyoAoKqqD0WUU1\nMtoGYJUHVVBQBaXPKqqR0TYAqzyogoIqKH1WUY2MtgFY5UEVFFRB6bOKamS0DcAqD6qgoApK\nn1VUI6NtAFZ5UAUFVVD6rKIaGW0DsMqDKiiogtJnFdXIaBuAVR5UQUEVlD6rqEZG2wCs8qAK\nCqqg9FlFNTLaBmCVB1VQUAWlzyqqkdE2AKs8qIKCKih9VlGNjLYBWOVBFRRUQemzimpktM0e\nsN49/9e6gI6CsaBgLA4MwCoPJiYFY0HBWBwYgFUeTEwKxoKCsTgwAKs8mJgUjAUFY3FgABaC\nIJcJwEIQ5DIBWAiCXCYAC0GQywRgIQhymQAsBEEuE4CVk4/P8I+fnz3l4/fJ2li822C4Y+GP\nDVIpACsjH8t/PujBB9/+TomNxbuNwyvuWPhjg9QKwMqINxE/ngDLPPh4AqzIR6ReAFZu5ER8\nW7CmxMbiHeMCBbAOCcDKDcCihMbiXV+3AVinBGBl5uMJsEwwFhRnLLzHSJ0ArMxgkVJCY+F8\n9jYBWOcEYOXFBeqdwQqOhfPZuwTz4qQArKx4ry6/8cTEWFDCA/CeY3FsAFZO2O3+2y/SlbF4\nt6HwxsIfG6RSAFZGPsyPwPBOd4wFizsWgbFBKgVgIQhymQAsBEEuE4CFIMhlArAQBLlMABaC\nIJcJwEIQ5DIBWAiCXCYAC0GQywRgIQhymQCst8/P15uxH5gIyBWCefr2mawCWMglgnn69oFV\nyHWCyfrueTxeYi3///b49vz75fHt3+cT/74/Ht//tS4PQXgA1ruHg/Xt8/NfXz7/8/3ziY/X\nM19al4cgPADr7WNfw3o59evx+PH6z/P5v89Pnj8eP1uXhyAsAOvtw8D6+/rPv/nRl2lqfH6L\niCD9BGC9fRhY8tGcxtUhCA/m49sHYCHXCebj2ycC1hdMDaS/YFa+fSJg/Xi96P7r8bVxdQjC\nA7DePo/HRwisf9PbGh5/WpeHICwA6+3zMwzW8+/3x+Pr78bFIYgIwEIQ5DIBWAiCXCYAC0GQ\nywRgIQhymQAsBEEuE4CFIMhlArAQBLlMABaCIJcJwEIQ5DIBWAiCXCYAC0GQywRgIQhymfx/\noECEHJ0ltYcAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data5 <- data.frame(\n",
    "  day = as.Date(nasdaq$Date),\n",
    "  value1 = rep(NA, 4024),\n",
    "  value2 = garch_nasdaq_shanghai_corr,\n",
    "  value3 = ewma_nasdaq_shanghai_corr\n",
    ")\n",
    "for(i in 31:4024){\n",
    "  data5$value1[i] = pearson_nasdaq_shanghai_corr[i - 30]\n",
    "}\n",
    "ggplot(data = data5, aes(x = day, y = value1)) + \n",
    "geom_line(color = \"#404788FF\", size = 0.8) +\n",
    "geom_line(aes(x = data5$day, y = data5$value2, color = '#29AF7FFF'), size = 0.8) +\n",
    "geom_line(aes(x = data5$day, y = data5$value3, color = '#FDE725FF'), size = 0.8) +\n",
    "ggtitle(\"Correlation between Nasdaq Composite and Shanghai Composite minus returns\") +\n",
    "ylab('correlation')+xlab('time') +\n",
    "scale_colour_manual(name = '',values =c('#404788FF'='#404788FF', '#29AF7FFF'='#29AF7FFF','#FDE725FF'='#FDE725FF'), labels = c('Pearson (T = 30)', 'GARCH', 'EWMA'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f488a49",
   "metadata": {},
   "source": [
    "# 2.3 Nikkei 225 correlation - Shanghai Composite"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35a3d00f",
   "metadata": {},
   "source": [
    "Vectors containing the calculated correlation values are created using 3 methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "62218310",
   "metadata": {},
   "outputs": [],
   "source": [
    "pearson_nikkei_225_shanghai_corr <- pearson_corr(minus_nikkei_225$Return, minus_shanghai$Return)\n",
    "ewma_nikkei_225_shanghai_corr <- ewma_corr(minus_nikkei_225$Return, minus_shanghai$Return)\n",
    "garch_nikkei_225_shanghai_corr <- garch_corr(minus_nikkei_225$Return, minus_shanghai$Return)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b2fd5a76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ArAYgFYFXNZsA5YQfdYHlEBWCwAq2IA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\nQZDTBGAhCHKaACwEQU4TgIUgyGny/xBdoT4AFF2gAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data6 <- data.frame(\n",
    "  day = as.Date(nasdaq$Date),\n",
    "  value1 = rep(NA, 4024),\n",
    "  value2 = garch_nikkei_225_shanghai_corr,\n",
    "  value3 = ewma_nikkei_225_shanghai_corr\n",
    ")\n",
    "for(i in 31:4024){\n",
    "  data6$value1[i] = pearson_nikkei_225_shanghai_corr[i - 30]\n",
    "}\n",
    "\n",
    "ggplot(data = data6, aes(x = day, y = value1)) + \n",
    "geom_line(color = \"#404788FF\", size = 0.8) +\n",
    "geom_line(aes(x = data6$day, y = data6$value2, color = '#29AF7FFF'), size = 0.8) +\n",
    "geom_line(aes(x = data6$day, y = data6$value3, color = '#FDE725FF'), size = 0.8) +\n",
    "ggtitle(\"Correlation between Nikkei 225 and Shanghai Composite minus returns\") +\n",
    "ylab('correlation')+xlab('time') +\n",
    "scale_colour_manual(name = '',values =c('#404788FF'='#404788FF', '#29AF7FFF'='#29AF7FFF','#FDE725FF'='#FDE725FF'), labels = c('Pearson (T = 30)', 'GARCH', 'EWMA'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f48db293",
   "metadata": {},
   "source": [
    "**Interpretation**\n",
    "\n",
    "The presented graphics show that the correlation for negative rates of return is not constant over time. Pearson's correlation indicates the lack of a strong linear relationship between the studied indices. EWMA and GARCH methods take higher positive values suggesting a stronger linear relationship. In this case, fluctuations in correlation may attract attention. The EWMA model is characterized by the smallest fluctuations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1de7e22",
   "metadata": {},
   "source": [
    "# 3. Influence of the considered correlation between loss rates on risk reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98e44f25",
   "metadata": {},
   "source": [
    "Considering the correlation between loss rates can reduce VaR because the correlation provides information about the strength and direction of the relationship between financial instruments and industries.\n",
    "This translates into a method of portfolio diversification and thus reduces the risk of losses. For example, if the portfolio consists of only aviation stocks (all eggs in the basket), then in the event of negative information from the aviation sector, stock prices will decrease and the portfolio will record a decrease in value. Therefore, the weakest possible correlations are desired, meaning that the portfolio manager has invested in a variety of industries, areas and companies."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82899284",
   "metadata": {},
   "source": [
    "# 4. Determining the VaR for the portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08586e7f",
   "metadata": {},
   "source": [
    "This part of the project aims to present the calculated 95% VaR of a portfolio consisting of 3 selected indices using 2 correlation monitoring models: EWMA and GARCH with a 250-day history.\n",
    "\n",
    "In this case, also create vectors of equal length in the same way as described in the section on monitoring correlations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "f54b44b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "data7 <- data.frame(\n",
    "  Date = nasdaq_d$Date[2:4029],\n",
    "  Return = rate_of_return_nasdaq\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "578a6224",
   "metadata": {},
   "outputs": [],
   "source": [
    "data8 <- data.frame(\n",
    "  Date = nasdaq_d$Date[2:4029],\n",
    "  Return = rep(0, 4028)\n",
    ")\n",
    "for(i in 1:length(data1$Date)){\n",
    "  for(j in 1:length(nikkei_225_d$Date)){\n",
    "    if(data8$Date[i] == nikkei_225_d$Date[j]){\n",
    "      data8$Return[i] = 1\n",
    "    }\n",
    "  }\n",
    "}\n",
    "j = 1\n",
    "a = 1\n",
    "for(i in 1:length(data2$Date)){\n",
    "  if(data8$Return[i] == 1 && a == 1){\n",
    "    data8$Return[i] = 0\n",
    "    a = 0\n",
    "  }\n",
    "  if(data8$Return[i] == 1){\n",
    "    data8$Return[i] = rate_of_return_nikkei_225[j]\n",
    "    j = j + 1\n",
    "  }\n",
    "  else{\n",
    "    data8$Return[i] = NA\n",
    "  }\n",
    "}\n",
    "data8 <- data8 %>% fill(Return, .direction = 'downup')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "9b84c181",
   "metadata": {},
   "outputs": [],
   "source": [
    "data9 <- data.frame(\n",
    "  Date = nasdaq_d$Date[2:4029],\n",
    "  Return = rep(0, 4028)\n",
    ")\n",
    "for(i in 1:length(data1$Date)){\n",
    "  for(j in 1:length(shanghai_d$Date)){\n",
    "    if(data9$Date[i] == shanghai_d$Date[j]){\n",
    "      data9$Return[i] = 1\n",
    "    }\n",
    "  }\n",
    "}\n",
    "j = 1\n",
    "a = 1\n",
    "for(i in 1:length(data3$Date)){\n",
    "  if(data9$Return[i] == 1 && a == 1){\n",
    "    data9$Return[i] = 0\n",
    "    a = 0\n",
    "  }\n",
    "  if(data9$Return[i] == 1){\n",
    "    data9$Return[i] = rate_of_return_shanghai[j]\n",
    "    j = j + 1\n",
    "  }\n",
    "  else{\n",
    "    data9$Return[i] = NA\n",
    "  }\n",
    "}\n",
    "data9 <- data9 %>% fill(Return, .direction = 'downup')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "120ddc0d",
   "metadata": {},
   "source": [
    "# 4.1 EWMA method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "5238a52b",
   "metadata": {},
   "outputs": [],
   "source": [
    "ewma_var <- function(x, y, z, a){\n",
    "  ewma_value_at_risk <- c()\n",
    "  for(i in 0:(length(x) - 251)){\n",
    "    window_x <- rep(0, 250)\n",
    "    window_y <- rep(0, 250)\n",
    "    window_z <- rep(0, 250)\n",
    "    for(j in 1:250){\n",
    "      window_x[j] = x[i + j]\n",
    "      window_y[j] = y[i + j]\n",
    "      window_z[j] = z[i + j]\n",
    "    }\n",
    "    lambda = 0.94\n",
    "    variance_x <- rep(0, length(window_x))\n",
    "    variance_y <- rep(0, length(window_y))\n",
    "    variance_z <- rep(0, length(window_z))\n",
    "    variance_x[1] = var(window_x)\n",
    "    variance_y[1] = var(window_y)\n",
    "    variance_z[1] = var(window_z)\n",
    "    for(i in 1:(length(window_x) - 1)){\n",
    "      variance_x[i + 1] = variance_x[i] * lambda + (1 - lambda) * window_x[i]^2\n",
    "      variance_y[i + 1] = variance_y[i] * lambda + (1 - lambda) * window_y[i]^2\n",
    "      variance_z[i + 1] = variance_z[i] * lambda + (1 - lambda) * window_z[i]^2\n",
    "    }\n",
    "    covariance_xy <- rep(0, length(window_x))\n",
    "    covariance_xz <- rep(0, length(window_x))\n",
    "    covariance_yz <- rep(0, length(window_x))\n",
    "    covariance_xy[1] = cov(window_x, window_y)\n",
    "    covariance_xz[1] = cov(window_x, window_z)\n",
    "    covariance_yz[1] = cov(window_y, window_z)\n",
    "    for(i in 1:(length(window_x) - 1)){\n",
    "      covariance_xy[i + 1] = covariance_xy[i] * lambda + (1 - lambda) * window_x[i] * window_y[i]\n",
    "      covariance_xz[i + 1] = covariance_xz[i] * lambda + (1 - lambda) * window_x[i] * window_z[i]\n",
    "      covariance_yz[i + 1] = covariance_yz[i] * lambda + (1 - lambda) * window_y[i] * window_z[i]\n",
    "    }\n",
    "    correlation_xy = tail(covariance_xy, 1) / (sqrt(tail(variance_x, 1)) * sqrt(tail(variance_y, 1)))\n",
    "    correlation_xz = tail(covariance_xz, 1) / (sqrt(tail(variance_x, 1)) * sqrt(tail(variance_z, 1)))\n",
    "    correlation_yz = tail(covariance_yz, 1) / (sqrt(tail(variance_y, 1)) * sqrt(tail(variance_z, 1)))\n",
    "\n",
    "    variance_portfolio = 1/9 * (tail(variance_x, 1) + tail(variance_y, 1) + tail(variance_z, 1))\n",
    "    + 2/9 * (correlation_xy * sqrt(tail(variance_x, 1)) * sqrt(tail(variance_y, 1)) + correlation_xz              *  sqrt(tail(variance_x, 1)) * sqrt(tail(variance_z, 1)) + correlation_yz *\n",
    "    sqrt(tail(variance_y, 1)) * sqrt(tail(variance_z, 1)))\n",
    "    sd_portfolio = sqrt(variance_portfolio)\n",
    "    q = qnorm(1 - a)\n",
    "    value_var = sd_portfolio * q\n",
    "    ewma_value_at_risk <- append(ewma_value_at_risk, value_var)\n",
    "  }\n",
    "  return(ewma_value_at_risk)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "dcde5f9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "ewma_95_portfolio_var <- ewma_var(data7$Return, data8$Return, data9$Return, 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "04aa6d22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9haYa27r8HvdvQLc1wawtKDISxgOdEU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\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data11 <- data.frame(\n",
    "  day = as.Date(data1$Date[251:4028]),\n",
    "  value1 = ewma_95_portfolio_var\n",
    ")\n",
    "\n",
    "ggplot(data = data11, aes(x = day, y = value1)) + \n",
    "  geom_line(color = \"darkblue\", size = 0.8) +\n",
    "  ggtitle(\"EWMA simulated portfolio with 95% VaR\") +\n",
    "  ylab('VaR')+xlab('Time')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "151cc0e4",
   "metadata": {},
   "source": [
    "# 4.2 GARCH method (1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "78122f71",
   "metadata": {},
   "outputs": [],
   "source": [
    "garch_var <- function(x, y, z, a){\n",
    "  garch_value_at_risk <- c()\n",
    "  for(i in 0:(length(x) - 251)){\n",
    "    window_x <- rep(0, 250)\n",
    "    window_y <- rep(0, 250)\n",
    "    window_z <- rep(0, 250)\n",
    "    for(j in 1:250){\n",
    "      window_x[j] = x[i + j]\n",
    "      window_y[j] = y[i + j]\n",
    "      window_z[j] = z[i + j]\n",
    "    }\n",
    "    gamma = 0.02\n",
    "    alpha = 0.15\n",
    "    beta = 0.83\n",
    "    long_run_vr = 0.00015\n",
    "    variance_x <- rep(0, length(window_x))\n",
    "    variance_y <- rep(0, length(window_y))\n",
    "    variance_z <- rep(0, length(window_z))\n",
    "    variance_x[1] = var(window_x)\n",
    "    variance_y[1] = var(window_y)\n",
    "    variance_z[1] = var(window_z)\n",
    "    for(i in 1:(length(window_x) - 1)){\n",
    "      variance_x[i + 1] = beta * variance_x[i] + alpha * window_x[i]^2 + gamma * long_run_vr\n",
    "      variance_y[i + 1] = beta * variance_y[i] + alpha * window_y[i]^2 + gamma * long_run_vr\n",
    "      variance_z[i + 1] = beta * variance_z[i] + alpha * window_z[i]^2 + gamma * long_run_vr\n",
    "    }\n",
    "    covariance_xy <- rep(0, length(window_x))\n",
    "    covariance_xz <- rep(0, length(window_x))\n",
    "    covariance_yz <- rep(0, length(window_x))\n",
    "    covariance_xy[1] = cov(window_x, window_y)\n",
    "    covariance_xz[1] = cov(window_x, window_z)\n",
    "    covariance_yz[1] = cov(window_y, window_z)\n",
    "    for(i in 1:(length(window_x) - 1)){\n",
    "      covariance_xy[i + 1] = beta * covariance_xy[i] + alpha * window_x[i] * window_y[i] + gamma *                 long_run_vr\n",
    "      covariance_xz[i + 1] = beta * covariance_xz[i] + alpha * window_x[i] * window_z[i] + gamma *                 long_run_vr\n",
    "      covariance_yz[i + 1] = beta * covariance_yz[i] + alpha * window_y[i] * window_z[i] + gamma *                 long_run_vr\n",
    "    }\n",
    "    correlation_xy = tail(covariance_xy, 1) / (sqrt(tail(variance_x, 1)) * sqrt(tail(variance_y, 1)))\n",
    "    correlation_xz = tail(covariance_xz, 1) / (sqrt(tail(variance_x, 1)) * sqrt(tail(variance_z, 1)))\n",
    "    correlation_yz = tail(covariance_yz, 1) / (sqrt(tail(variance_y, 1)) * sqrt(tail(variance_z, 1)))\n",
    "\n",
    "    variance_portfolio = 1/9 * (tail(variance_x, 1) + tail(variance_y, 1) + tail(variance_z, 1))\n",
    "    + 2/9 * (correlation_xy * sqrt(tail(variance_x, 1)) * sqrt(tail(variance_y, 1)) + correlation_xz              *  sqrt(tail(variance_x, 1)) * sqrt(tail(variance_z, 1)) + correlation_yz *\n",
    "    sqrt(tail(variance_y, 1)) * sqrt(tail(variance_z, 1)))\n",
    "    sd_portfolio = sqrt(variance_portfolio)\n",
    "    q = qnorm(1 - a)\n",
    "    value_var = sd_portfolio * q\n",
    "    garch_value_at_risk <- append(garch_value_at_risk, value_var)\n",
    "  }\n",
    "  return(garch_value_at_risk)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "d6d878b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "garch_95_portfolio_var <- garch_var(data7$Return, data8$Return, data9$Return, 0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "bd7c3cdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QIMYQnCEBYwTTQLsIXCOiMsARrCOiqs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\nCcIihJgJwiKEmMn/FyCnf3eLtM0AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data12 <- data.frame(\n",
    "  day = as.Date(data1$Date[251:4028]),\n",
    "  value1 = garch_95_portfolio_var\n",
    ")\n",
    "\n",
    "ggplot(data = data12, aes(x = day, y = value1)) + \n",
    "  geom_line(color = \"darkblue\", size = 0.8) +\n",
    "  ggtitle(\"GARCH simulated portfolio with 95% VaR\") +\n",
    "  ylab('VaR')+xlab('Time')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18ba369b",
   "metadata": {},
   "source": [
    "# 4.4 Comparison of methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "2879c6f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qoqSycgrFNAMjJsg0FYVWXpBIR1CkhG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\nA4QFABgGCAsAMAz/D+0dpgs5RTCZAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "day = as.Date(shanghai$Date)\n",
    "\n",
    "data13 <- data.frame(\n",
    "  day = day[251:4028],\n",
    "  value1 = ewma_95_portfolio_var,\n",
    "  value2 = garch_95_portfolio_var\n",
    ")\n",
    "\n",
    "ggplot(data = data13, aes(x = day, y = value1)) + \n",
    "  geom_line(color = \"darkblue\", size = 1) +\n",
    "  geom_line(aes(x = data13$day, y = data13$value2, color = 'red'), size = 0.5) +\n",
    "  ggtitle(\"Comparison of methods used in portfolios VaR at 95% calculation\") +\n",
    "  ylab('VaR')+xlab('Time') +\n",
    "  scale_colour_manual(name = '',values =c('darkblue'='darkblue', 'red'='red'),\n",
    "                      labels = c('EWMA','GARCH'))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}