Value-at-Risk (VaR) Calculator Class in Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intro"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As part of my self-development, I wanted to rework a script, which are typically one-offs, and turn it into a reusable component, although there are existing packages for VaR. For those unfamiliar with VaR, it is an acronym for value at risk, the worst case loss in a period for a particular probability. This is currently a work in progress, a reworking of prior work with scripted VaR calculations, https://dataanalyticsworkouts.blogspot.com/2017/07/calculating-value-at-risk-var-with.html, implementing various high-level good practices, e.g., hiding/encapsulation, do-not-repeat-yourself (DRY), dependency injection, etc.\n",
    "\n",
    "Features:\n",
    "\n",
    "- Requires a data frame of stock returns, factor returns, and stock weights\n",
    "- Exposes a method for calculating and returning VaR, for different variance types\n",
    "- Exposes a method for calculating and returning an array of VaR values by confidence level\n",
    "- Exposes a method for calculating and plotting an array of VaR values by confidence level\n",
    "\n",
    "Still to do:\n",
    "\n",
    "- Dynamic factor usage\n",
    "\n",
    "Note: Data to validate this class is available from my Google Drive Public folder: https://drive.google.com/folderview?id=0B5Mi6_CV6da5aFc2Q0g3cHowVms&usp=sharing.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from  enum import Enum\n",
    "class VaRType(Enum):\n",
    "    Historical = 1\n",
    "    Factor = 2\n",
    "    Scenario = 3\n",
    "\n",
    "class RiskCalculator(object):\n",
    "\n",
    "    #################################\n",
    "    # Class back-of-the-napkin\n",
    "    # \n",
    "    # - Provide dataframe of stocks prices\n",
    "    #\n",
    "    # - Provide weights of stocks\n",
    "    # -- Alt: Calculate weights\n",
    "    #\n",
    "    # - Provide dataframe of factor prices\n",
    "    #\n",
    "    # - Extracts stock names into data frame \n",
    "    # - Extract stock returns\n",
    "    #\n",
    "    # - Extracts factor names into data frame \n",
    "    # - Extract factor returns\n",
    "    #\n",
    "    # Historical\n",
    "    # - Use weights and stock returns (no dates)\n",
    "    #\n",
    "    # Factor Model\n",
    "    # - Use factors, stock names, returns\n",
    "    # - create matrix of scenarios\n",
    "    #\n",
    "    # VaR\n",
    "    # - for different risk types and confidence levels calculate VaR\n",
    "    # - for different risk types and confidence levels calculate a range ofVaR\n",
    "    # - for different risk types and confidence levels plot a range ofVaR\n",
    "    #\n",
    "    # To do\n",
    "    # - dynamically build factor matrix\n",
    "    # - Compare dates between stocks and factors\n",
    "    # - Validate data\n",
    "    # - Allow date range\n",
    "    # - Auto-limit date range, with warning\n",
    "    ###################################\n",
    "\n",
    "    \n",
    "    # Hidden Attributes\n",
    "    __stockNames = []\n",
    "    __factorNames = []\n",
    "    __historicalRisk = 0\n",
    "    __systemicVariance = 0\n",
    "    __idiosyncraticVariance = 0\n",
    "    __factorBasedVariance = 0\n",
    "    __scenarioTotalVariance = 0\n",
    "    __modelCoeffs = []\n",
    "\n",
    "    \n",
    "    #################################\n",
    "    # Constructor\n",
    "    #################################\n",
    "    def __init__(self, stockReturns, factorReturns, weights):\n",
    "        self.ChangeData(stockReturns, factorReturns, weights)\n",
    "\n",
    "        \n",
    "    #################################\n",
    "    # Load data, sets and (re)calculates\n",
    "    #################################\n",
    "    def ChangeData(self, stockReturns, factorReturns, weights):        \n",
    "        self.stockReturns = stockReturns\n",
    "        self.factorReturns = factorReturns\n",
    "        self.weights = weights\n",
    "        RiskCalculator.__run()\n",
    "\n",
    "        \n",
    "    #################################\n",
    "    # Run interrnal code\n",
    "    #################################\n",
    "    def __run():\n",
    "        \n",
    "        RiskCalculator.__extractNames()\n",
    "        RiskCalculator.__calculateHistoricalVariance()\n",
    "        RiskCalculator.__calculateHistoricalVariance()\n",
    "        RiskCalculator.__buildFactorModel()\n",
    "        RiskCalculator.__calculateFactorVariance()\n",
    "        RiskCalculator.__calculateScenarioVariance()\n",
    "\n",
    "        \n",
    "    #################################\n",
    "    # Extract names\n",
    "    #################################\n",
    "    def __extractNames():\n",
    "        RiskCalculator.__stockNames = stockReturns.columns\n",
    "        RiskCalculator.__factorNames = factorReturns.columns\n",
    "    \n",
    "    \n",
    "    #################################\n",
    "    # Estimating Historical Risk\n",
    "    # cacluate portfolio variance\n",
    "    # Var(p) = W * COV(Y) * W_transposed\n",
    "    # matrix multiplication is done via np.dot\n",
    "    # first is transpose of weights\n",
    "    # second is the covariance of the returns\n",
    "    # third is the matrix of weights\n",
    "    #################################\n",
    "    def __calculateHistoricalVariance():\n",
    "        RiskCalculator.__historicalRisk = np.dot(np.dot(weights, stockReturns.cov()), weights.T)\n",
    "\n",
    "\n",
    "    #################################\n",
    "    # Building Factor Models\n",
    "    # - Calculate lm (regression) for FVX, SP500, and the each stock\n",
    "    #################################\n",
    "    def __buildFactorModel():\n",
    "\n",
    "        import statsmodels.api as sm\n",
    "\n",
    "        # loops for each stock to create\n",
    "        RiskCalculator.__modelCoeffs = []\n",
    "        for stockName in RiskCalculator.__stockNames:\n",
    "            stockReturn = returns[stockName]\n",
    "            model = sm.OLS(stockReturn, factorReturns)\n",
    "            result = model.fit()\n",
    "            modelCoeffRow = list(result.params)\n",
    "            modelCoeffRow.append(np.std(result.resid,ddof=1))\n",
    "            RiskCalculator.__modelCoeffs.append(modelCoeffRow)\n",
    "    \n",
    "        # convert and cleanup data frame\n",
    "        RiskCalculator.__modelCoeffs = pd.DataFrame(RiskCalculator.__modelCoeffs)\n",
    "        RiskCalculator.__modelCoeffs.columns = [\"B_FVX\", \"B_SP500\",  \"Alpha\", \"ResidualVol\"]\n",
    "        RiskCalculator.__modelCoeffs[\"Names\"] = RiskCalculator.__stockNames\n",
    "\n",
    "        \n",
    "    #################################\n",
    "    # Factor Analysis - Idiosyncratic and Systemic Risk\n",
    "    # TotalVaR(P) = SystemicVaR(P) + IdisyncraticVaR(P)\n",
    "    # SystemicVaR(P) = weights * betas * Cov(Factors) * betas_transposed * weights_transposed\n",
    "    # idosyncraticVariance(P) = weights * var(residuals) * weight_transposed\n",
    "    # totalVariance = systemicVariance + idiosyncraticVariance\n",
    "    #################################\n",
    "    def __calculateFactorVariance():\n",
    "\n",
    "        # inner terms\n",
    "        factorCovariance = factorReturns[[\"SP500\",\"FVX\"]].cov()\n",
    "        reconstructedCov = (np.dot(np.dot(RiskCalculator.__modelCoeffs[[\"B_SP500\", \"B_FVX\"]]\n",
    "                                          ,factorCovariance),RiskCalculator.__modelCoeffs[[\"B_SP500\", \"B_FVX\"]].T))\n",
    "        # include outer terms\n",
    "        RiskCalculator.__systemicVariance = np.dot(np.dot(weights, reconstructedCov), weights.T)\n",
    "\n",
    "        RiskCalculator.__idiosyncraticVariance = sum(weights * RiskCalculator.__modelCoeffs[\"ResidualVol\"] * weights * RiskCalculator.__modelCoeffs[\"ResidualVol\"])\n",
    "\n",
    "        RiskCalculator.__factorBasedVariance =  RiskCalculator.__systemicVariance +  RiskCalculator.__idiosyncraticVariance\n",
    "\n",
    "        \n",
    "    #################################\n",
    "    # Scenario-based Stress Testing\n",
    "    # create a range of scenarios, stepping from min to max for factors, FVX and S&P500\n",
    "    # build scenarios from fvxScenarios by sp500Scenarios\n",
    "    # set column names\n",
    "    # totalVariance(P) = weights * cov(scenarios) * weight_transposed\n",
    "    #################################\n",
    "    def __calculateScenarioVariance():\n",
    "\n",
    "        fvxScenarios = np.arange(min(returns[\"FVX\"]), max(returns[\"FVX\"]), .05)\n",
    "        sp500Scenarios = np.arange(min(returns[\"SP500\"]), max(returns[\"SP500\"]), .02)\n",
    "\n",
    "        scenarios = []\n",
    "        for fvxValue in fvxScenarios:\n",
    "            for sp500value in sp500Scenarios:\n",
    "                scenario = [fvxValue, sp500value]\n",
    "                for stockName in RiskCalculator.__stockNames:\n",
    "                    alpha = float( RiskCalculator.__modelCoeffs[ RiskCalculator.__modelCoeffs[\"Names\"] == stockName][\"Alpha\"])\n",
    "                    beta_sp = float( RiskCalculator.__modelCoeffs[ RiskCalculator.__modelCoeffs[\"Names\"] == stockName][\"B_SP500\"])\n",
    "                    beta_fvx = float( RiskCalculator.__modelCoeffs[ RiskCalculator.__modelCoeffs[\"Names\"] == stockName][\"B_FVX\"])\n",
    "                    scenarioPredictedReturn = alpha + (beta_sp * sp500value) + (beta_fvx * fvxValue)\n",
    "                    scenario.append(scenarioPredictedReturn)\n",
    "                scenarios.append(scenario)\n",
    "\n",
    "        scenarios = pd.DataFrame(scenarios)\n",
    "\n",
    "        scenarios.columns = [\"FVX\",\"SP500\",\"AAPL\",\"ADBE\",\"CVX\",\"GOOG\",\"IBM\",\"MDLZ\",\"MSFT\",\"NFLX\",\"ORCL\",\"SBUX\"]\n",
    "\n",
    "        scenariosCov = scenarios[RiskCalculator.__stockNames].cov()\n",
    "        RiskCalculator.__scenarioTotalVariance = np.dot(np.dot(weights, scenariosCov), weights.T)\n",
    "\n",
    "\n",
    "    #################################\n",
    "    # Simple VaR calculator\n",
    "    # VaR = P x Z_alpha x stdDev\n",
    "    #################################\n",
    "    def __calculateVaR(risk, percentile, principal = 1, numMonths = 1):\n",
    "\n",
    "        import math\n",
    "        import scipy.stats as st\n",
    "\n",
    "        vol = math.sqrt(risk)\n",
    "        return abs(principal * st.norm.ppf(1-percentile, 0, 1) * vol * math.sqrt(numMonths))\n",
    "    \n",
    "    \n",
    "    #################################\n",
    "    # Returns the instance value of the risk type\n",
    "    #################################\n",
    "    def __getRiskByType(varType):\n",
    "                \n",
    "        if varType == VaRType.Historical:\n",
    "            varianceType = RiskCalculator.__historicalRisk\n",
    "        elif varType == VaRType.Factor:\n",
    "            varianceType = RiskCalculator.__factorBasedVariance\n",
    "        elif varType == VaRType.Scenario:\n",
    "            varianceType = RiskCalculator.__scenarioTotalVariance\n",
    "\n",
    "        return varianceType\n",
    "        \n",
    "        \n",
    "    #################################\n",
    "    # Exposed calculator\n",
    "    #################################\n",
    "    def GetVaR(self, varType = VaRType.Historical, percentile = 0.99):\n",
    "\n",
    "        # Type checking\n",
    "        if not isinstance(varType, VaRType):\n",
    "            raise TypeError('vaRType must be an instance of VaRType Enum')\n",
    "        \n",
    "        varianceType = RiskCalculator.__getRiskByType(varType)\n",
    "\n",
    "        return RiskCalculator.__calculateVaR(varianceType, percentile)\n",
    "        \n",
    "        \n",
    "    #################################\n",
    "    # Exposed range calcualtor\n",
    "    #################################\n",
    "    def GetVaRRange(self, varType = VaRType.Historical, minPercentile = 0.90, maxPercentile = 0.995, step = 0.01):\n",
    "\n",
    "        return RiskCalculator.__getVaRRange(varType, minPercentile, maxPercentile, step)\n",
    "        \n",
    "\n",
    "    #################################\n",
    "    # Range calcualtor\n",
    "    #################################\n",
    "    def __getVaRRange(varType = VaRType.Historical, minPercentile = 0.90, maxPercentile = 0.995, step = 0.01):\n",
    "\n",
    "        # Type checking\n",
    "        if not isinstance(varType, VaRType):\n",
    "            raise TypeError('varType must be an instance of VaRType Enum')\n",
    "        \n",
    "        varianceType = RiskCalculator.__getRiskByType(varType)\n",
    "\n",
    "        import numpy as np\n",
    "        stepValues = np.arange(minPercentile, maxPercentile, step) \n",
    "        \n",
    "        # loops for each stock to create\n",
    "        riskArray = []\n",
    "        for stepValue in range(0, len(stepValues), 1):\n",
    "            percentile = stepValues[stepValue]\n",
    "            riskVal = RiskCalculator.__calculateVaR(varianceType, percentile)\n",
    "            riskRow = [percentile, riskVal]\n",
    "            riskArray.append(riskRow)\n",
    "            \n",
    "        import pandas as pd\n",
    "        riskArray = pd.DataFrame(riskArray)\n",
    "        riskArray.columns = [\"Confidence\",\"VaR\"]\n",
    "\n",
    "        return riskArray\n",
    "\n",
    "    \n",
    "    #################################\n",
    "    # Exposed range calcualtor\n",
    "    #################################\n",
    "    def PlotVaRRange(self, varType = VaRType.Historical, minPercentile = 0.90, maxPercentile = 0.995, step = 0.01):\n",
    "\n",
    "        varArray = RiskCalculator.__getVaRRange(varType, minPercentile, maxPercentile, step)\n",
    "\n",
    "        import matplotlib.pyplot as plt\n",
    "        plt.plot(varArray[\"Confidence\"],varArray[\"VaR\"])\n",
    "        plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Use Class"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import and Clean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "import pandas as pd\n",
    "\n",
    "# Get data\n",
    "portfolios = pd.read_csv(\"Portfolios.csv\", sep=\",\")\n",
    "\n",
    "# format date\n",
    "portfolios['AsOfDate'] = pd.to_datetime(portfolios['AsOfDate'], format='%m/%d/%Y', yearfirst = True)\n",
    "\n",
    "# sort by date\n",
    "portfolios = portfolios.sort_values(['AsOfDate'] , ascending=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Data Frames for Class Initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "import numpy as np\n",
    "\n",
    "# calculate returns\n",
    "returns = portfolios[[ key for key in dict(portfolios.dtypes) if dict(portfolios.dtypes)[key] in [ 'float64', 'int64']]].pct_change()\n",
    "returns = returns[1:]\n",
    "\n",
    "# add intercept column\n",
    "returns['Intercept'] = 1\n",
    "\n",
    "# create lists of names to easily filter returns\n",
    "stockNames = list(returns)[0:10]\n",
    "factorNames = list(returns)[10:13]\n",
    "\n",
    "# set values for returns and weights\n",
    "stockReturns = returns[stockNames]\n",
    "factorReturns = returns[factorNames]\n",
    "weights = np.array([1.0/len(stockNames)]*len(stockNames))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Display VaR Measures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create and Run Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "test = RiskCalculator(stockReturns, factorReturns, weights)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Display Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get VaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.11978443009308773"
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "\n",
    "test.GetVaR(VaRType.Historical, 0.99)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.11676976342787508"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "\n",
    "test.GetVaR(VaRType.Factor, 0.99)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "0.1842391287037653"
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "\n",
    "test.GetVaR(VaRType.Scenario, 0.99)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get a Range of VaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   Confidence       VaR\n0        0.90  0.065988\n1        0.91  0.069036\n2        0.92  0.072348\n3        0.93  0.075989\n4        0.94  0.080056\n5        0.95  0.084694\n6        0.96  0.090143\n7        0.97  0.096843\n8        0.98  0.105748\n9        0.99  0.119784",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Confidence</th>\n      <th>VaR</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.90</td>\n      <td>0.065988</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.91</td>\n      <td>0.069036</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.92</td>\n      <td>0.072348</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.93</td>\n      <td>0.075989</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.94</td>\n      <td>0.080056</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>0.95</td>\n      <td>0.084694</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>0.96</td>\n      <td>0.090143</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>0.97</td>\n      <td>0.096843</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>0.98</td>\n      <td>0.105748</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>0.99</td>\n      <td>0.119784</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "\n",
    "test.GetVaRRange(VaRType.Historical, 0.90, 0.995, 0.01)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   Confidence       VaR\n0        0.90  0.064327\n1        0.91  0.067298\n2        0.92  0.070527\n3        0.93  0.074077\n4        0.94  0.078041\n5        0.95  0.082563\n6        0.96  0.087875\n7        0.97  0.094405\n8        0.98  0.103087\n9        0.99  0.116770",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Confidence</th>\n      <th>VaR</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.90</td>\n      <td>0.064327</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.91</td>\n      <td>0.067298</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.92</td>\n      <td>0.070527</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.93</td>\n      <td>0.074077</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.94</td>\n      <td>0.078041</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>0.95</td>\n      <td>0.082563</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>0.96</td>\n      <td>0.087875</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>0.97</td>\n      <td>0.094405</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>0.98</td>\n      <td>0.103087</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>0.99</td>\n      <td>0.116770</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "\n",
    "test.GetVaRRange(VaRType.Factor, 0.90, 0.995, 0.01)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "   Confidence       VaR\n0        0.90  0.101495\n1        0.91  0.106183\n2        0.92  0.111277\n3        0.93  0.116878\n4        0.94  0.123133\n5        0.95  0.130267\n6        0.96  0.138649\n7        0.97  0.148953\n8        0.98  0.162650\n9        0.99  0.184239",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Confidence</th>\n      <th>VaR</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0.90</td>\n      <td>0.101495</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0.91</td>\n      <td>0.106183</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0.92</td>\n      <td>0.111277</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0.93</td>\n      <td>0.116878</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0.94</td>\n      <td>0.123133</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>0.95</td>\n      <td>0.130267</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>0.96</td>\n      <td>0.138649</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>0.97</td>\n      <td>0.148953</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>0.98</td>\n      <td>0.162650</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>0.99</td>\n      <td>0.184239</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "\n",
    "test.GetVaRRange(VaRType.Scenario, 0.90, 0.995, 0.01)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot VaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "\n",
    "test.PlotVaRRange(VaRType.Historical, 0.90, 0.991, 0.01)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "\n",
    "test.PlotVaRRange(VaRType.Factor, 0.75, 0.991, 0.005)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "\n",
    "test.PlotVaRRange(VaRType.Scenario, 0.5, 0.995, 0.003)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.7.6 64-bit ('base': conda)",
   "language": "python",
   "name": "python_defaultSpec_1595392818537"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}