Advanced_Risk_Management_A2_V2.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Advanced Risk Management - Assignment 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte Carlo approach to Value at Risk computation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepared by Deloitte – Financial Risk Management"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Deadline**:  March 13, 23.59h.\n",
    "\n",
    "| |Name |Student number|Email|\n",
    "\n",
    "|1.| Jason Spano | 12792160   | jason.spano@student.uva.nl    |\n",
    "\n",
    "****Hand in the following via Canvas****:\n",
    "* Your notebook.\n",
    "* A (printed) pdf version of your notebook. In Google Colab, this is most conveniently done in the Chrome browser, and then using the **`File` -> `Print`** menu option; you may have to print in landscape mode to make sure that everything appears in the pdf.\n",
    "\n",
    "****Notes****:\n",
    "* The assignment is part of the examination, so the usual rules regarding plagiarism and fraud apply.\n",
    "* Before submitting your work, click on **`Runtime`-> `Restart and run all ...`** and verify that your notebook produces the desired results and does not error.\n",
    "\n",
    "**Declaration of Originality**: We whose names are given under 1. above declare that these solutions are solely our own work, and that we have not made these solutions available to any other student."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction\n",
    "The data file `SPX&MSFT_1990-2020_USD.xlsx` contains daily price data (January 1990 – February 2020) on the closing price of the S&P 500 index and the Microsoft stock."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load libraries\n",
    "import pandas as pd \n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import seaborn as sns\n",
    "from IPython.display import display_html\n",
    "from arch import arch_model\n",
    "from tabulate import tabulate \n",
    "from math import isclose\n",
    "from scipy.stats import ttest_ind, ttest_rel, kendalltau, normaltest, pearsonr\n",
    "from copulae import GaussianCopula, NormalCopula, StudentCopula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "df_main = pd.ExcelFile('SPX&MSFT_1990-2020_USD.xlsx')\n",
    "df_spx = pd.read_excel(df_main, 'S&P500')\n",
    "df_mfst = pd.read_excel(df_main, 'Microsoft')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "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>MFST</th>\n",
       "      <th>SPX</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-02</th>\n",
       "      <td>0.6163</td>\n",
       "      <td>359.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>0.6198</td>\n",
       "      <td>358.76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>0.6380</td>\n",
       "      <td>355.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>0.6224</td>\n",
       "      <td>352.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-08</th>\n",
       "      <td>0.6319</td>\n",
       "      <td>353.79</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              MFST     SPX\n",
       "Date                      \n",
       "1990-01-02  0.6163  359.69\n",
       "1990-01-03  0.6198  358.76\n",
       "1990-01-04  0.6380  355.67\n",
       "1990-01-05  0.6224  352.20\n",
       "1990-01-08  0.6319  353.79"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#concatenate series and clean up index \n",
    "df_complete = pd.concat([df_mfst, df_spx], axis=1)\n",
    "df_complete.columns = ['Date','MFST','DATE2','SPX']\n",
    "df_complete = df_complete.drop(['DATE2'],axis=1)\n",
    "df_complete.set_index('Date',inplace=True)\n",
    "df_complete.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MFST    False\n",
       "SPX     False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Check data for NaN(s) \n",
    "df_complete.isnull().any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1\n",
    "* Construct daily log-returns for the two price series; the return series of the S&P 500 is hereafter denoted by $R_{1t}$, and the return series of the Microsoft stock by $R_{2t}$.\n",
    "* Present and describe / discuss the descriptive statistics (mean, standard deviation, skewness, kurtosis) of both return series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "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>MFST</th>\n",
       "      <th>SPX</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-03</th>\n",
       "      <td>0.005663</td>\n",
       "      <td>-0.002589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-04</th>\n",
       "      <td>0.028941</td>\n",
       "      <td>-0.008650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-05</th>\n",
       "      <td>-0.024755</td>\n",
       "      <td>-0.009804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-08</th>\n",
       "      <td>0.015148</td>\n",
       "      <td>0.004504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-01-09</th>\n",
       "      <td>-0.002694</td>\n",
       "      <td>-0.011857</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                MFST       SPX\n",
       "Date                          \n",
       "1990-01-03  0.005663 -0.002589\n",
       "1990-01-04  0.028941 -0.008650\n",
       "1990-01-05 -0.024755 -0.009804\n",
       "1990-01-08  0.015148  0.004504\n",
       "1990-01-09 -0.002694 -0.011857"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#convert the concatenated dataframe to daily log-returns\n",
    "df_comp_log = np.log(df_complete / df_complete.shift(1))\n",
    "\n",
    "#remove 1990-01-02 observation as now NaN (1st location) \n",
    "df_comp_log = df_comp_log.dropna() \n",
    "\n",
    "## show head \n",
    "df_comp_log.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              MFST          SPX\n",
      "count  7593.000000  7593.000000\n",
      "mean      0.000748     0.000294\n",
      "std       0.019889     0.010969\n",
      "min      -0.169578    -0.094695\n",
      "25%      -0.009021    -0.004309\n",
      "50%       0.000298     0.000545\n",
      "75%       0.010474     0.005528\n",
      "max       0.178692     0.109572\n",
      "skew      0.007768    -0.267897\n",
      "kurt      5.996909     8.870035\n"
     ]
    }
   ],
   "source": [
    "#Summary Statistics \n",
    "stat = df_comp_log.describe()\n",
    "stat.loc['skew'] = df_comp_log.skew().tolist()\n",
    "stat.loc['kurt'] = df_comp_log.kurtosis().tolist()\n",
    "print(stat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The table above shows the descriptive statistics of both the Microsoft and S&P 500 returns. It shows that the mean of returns for both of the assets is very close to zero. However, the standard deviation, skewness and kurtosis can provide more insight. Under normality, skewness should be 0 and kurtosis should be 3. In line with the stylsed facts of asset returns, these returns are not normally distributed measured at the daily level: note this would be they do not conform to the log-normal assumption as these are the logs of the returns. This is most prominent in the kurtosis, which explains the tails of the distribution adn measures the outliers present in the distribution. \n",
    "* Also notaworthy is that the volatility of Microsoft is almost twice as high as for S&P 500. This makes sense because the S&P 500 returns are a lot more diversified by being the index, which is in itself a diversified portfolio of different stocks that also includes Microsoft\n",
    "* The table shows that the S&P 500 returns are (moderately) negatively skewed, meaning that negative returns are more likely to happen than positive returns. Microsoft's skewness is close to zero, so fairly neglectible. Furthermore, S&P 500 has higher kurtosis than Microsoft. This means that the S&P 500 return distribution is more heavy-tailed than Microsoft's distribution. Both have a kurtosis higher than the kurtosis of 3, meaning they are more heavy-tailed than normal the distribution. Once again, this is not surprising as stock returns are known to be non-normal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*  Considering the results from 1., fit an appropriate probability distribution 𝐹1 and 𝐹2 to the standardized daily log returns of both return series. For fitting the distribution you may consider the Python package ‘Scipy.stats’. Alternatively, minimize the distance between the empirical CDF of 𝑅1𝑡 and 𝑅2𝑡, and the CDF of the fitted distributions 𝐹1 and 𝐹2 by optimizing the parameters of the distributions. Elaborate on your choice of distribution. \n",
    " \n",
    "* Plot the results, comparing the fitted cumulative distribution function of the distributions with the empirical cumulative distribution function of both return series. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2\n",
    "* Considering the results from Question 1, fit appropriate probability distributions $F_1$ and $F_2$ to both daily log returns series. For fitting the distribution, you may consider the Python package `scipy.stats`. Alternatively, minimize the distance between the empirical CDF of $𝑅_{1𝑡}$ and $𝑅_{2𝑡}$, and the CDF of the fitted distributions $𝐹_1$ and $𝐹_2$ by optimizing the parameters of the distributions. Elaborate on your choice of distribution.\n",
    "* Plot the results, comparing the fitted cumulative distribution functions of the Normal distributions with the empirical cumulative distribution function of both return series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define log series names \n",
    "lret_mfst = df_comp_log['MFST']\n",
    "lret_spx = df_comp_log['SPX']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MFST "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jason\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:2316: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  Lhat = muhat - Shat*mu\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## MFST Distribution Histograms \n",
    "## KDE = False, fits are: normal, student's-t distribution and skewed student's t-dist \n",
    "fig, ax, = plt.subplots(ncols=3,figsize=(16,7))\n",
    "\n",
    "sns.distplot(lret_mfst, kde=False, fit=stats.norm,ax=ax[0])\n",
    "ax[0].set_title('Histogram: MFST Vs. Normal Distribution')\n",
    "\n",
    "sns.distplot(lret_mfst, kde=False, fit=stats.t,ax=ax[1])\n",
    "ax[1].set_title(\"Histogram: MFST Vs. Student's t Distribution\")\n",
    "\n",
    "sns.distplot(lret_mfst, kde=False, fit=stats.nct,ax=ax[2])\n",
    "ax[2].set_title(\"Histogram: MFST Vs. Skewed student's t Distribution\")\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### SPX\n",
    "* Repeat for index series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## SPX Distribution Histograms \n",
    "fig, ax, = plt.subplots(ncols=3,figsize=(16,7))\n",
    "sns.distplot(lret_spx, kde=False, fit=stats.norm,ax=ax[0])\n",
    "ax[0].set_title('Histogram: SPX Vs. Normal Distribution')\n",
    "sns.distplot(lret_spx, kde=False, fit=stats.t,ax=ax[1])\n",
    "ax[1].set_title(\"Histogram: SPX Vs. Student's t Distribution\")\n",
    "sns.distplot(lret_spx, kde=False, fit=stats.nct,ax=ax[2])\n",
    "ax[2].set_title(\"Histogram: SPX Vs. Skewed student's t Distribution\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MFST QQ PLOTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#MFST QQ Plots \n",
    "fig, ax, = plt.subplots(ncols=3,figsize=(16,7))\n",
    "sm.qqplot(lret_mfst, dist=stats.norm, fit=True, line='45',ax=ax[0])\n",
    "ax[0].set_title('MSFT distribution Vs Normal distribution')\n",
    "sm.qqplot(lret_mfst, dist=stats.t, fit=True, line='45',ax=ax[1])\n",
    "ax[1].set_title(\"MSFT distribution Vs Student's t distribution\")\n",
    "sm.qqplot(lret_mfst, dist=stats.nct, fit=True, line='45',ax=ax[2])\n",
    "ax[2].set_title(\"MSFT distribution Vs Skewed student's t distribution\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SPX QQ PLOTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#SPX QQ Plots \n",
    "fig, ax, = plt.subplots(ncols=3,figsize=(16,7))\n",
    "sm.qqplot(lret_spx, dist=stats.norm, fit=True, line='45',ax=ax[0])\n",
    "ax[0].set_title('SPX distribution Vs Normal distribution')\n",
    "sm.qqplot(lret_spx, dist=stats.t, fit=True, line='45',ax=ax[1])\n",
    "ax[1].set_title(\"SPX distribution Vs Student's t distribution\")\n",
    "sm.qqplot(lret_spx, dist=stats.nct, fit=True, line='45',ax=ax[2])\n",
    "ax[2].set_title(\"SPX distribution Vs Skewed student's t distribution\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stat=11359.873, p=0.000\n",
      "MFST: Assumed to not be Gaussian/Normal\n"
     ]
    }
   ],
   "source": [
    "#Normality test (skewness and kurtosis matching a normal distribution) for Microsoft returns:\n",
    "stat_mfst, p_mfst = stats.jarque_bera(lret_mfst) \n",
    "print('stat=%.3f, p=%.3f' % (stat_mfst, p_mfst))\n",
    "\n",
    "## check the p-value on the statistic\n",
    "if p_mfst > 0.05:\n",
    " print('MFST: Assumed to be Gaussian/Normal')\n",
    "else:\n",
    " print('MFST: Assumed to not be Gaussian/Normal')\n",
    "#stats.jarque_bera(lret_mfst) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stat=24945.189, p=0.000\n",
      "SPX: Assumed to not be Gaussian/Normal\n"
     ]
    }
   ],
   "source": [
    "#Normality test (skewness and kurtosis matching a normal distribution) for SPX returns:\n",
    "stat_spx, p_spx = stats.jarque_bera(lret_spx) \n",
    "print('stat=%.3f, p=%.3f' % (stat_spx, p_spx))\n",
    "if p_spx > 0.05:\n",
    " print('SPX: Assumed to be Gaussian/Normal')\n",
    "else:\n",
    " print('SPX: Assumed to not be Gaussian/Normal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion Question 2:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. To see what distribution would fit the data best, we first visualize the distributions by a histogram and QQ-plot. We see that for Microsoft that the normal distribution does not fit well. The histogram shows that the return distribution is more sharply peaked than for a normal distribution and the QQ-plot shows that its tails are also more heavy than in a normal distribution would be. We find the same results for the S&P 500 return distribution. When we visualize the data against a skewed t-distribution, we see two things. For Microsoft we see through the QQ-plot that it fits the left tail better, but the left tail worse compared to standard student's t distribution. For the S&P 500 data we see exactly the opposite. A skewed sudent's t distribution has therefore no additional value and we choose between the normal and standard student's t distribution.\n",
    "\n",
    "* We test for normality of the data by using a Jarque-Bera test and find that the Null hypothesis is rejected for both assets. This means normality is rejected and we therefore based off the two methods, choose to fit the data with a t-distribution.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3\n",
    "Assume you have a portfolio with equal weights in both the index and the stock.\n",
    "* Determine the sample correlation between the two return series based on the data.\n",
    "* Use the copula function of the Normal distribution to generate 50,000 correlated pairs $(u_{1i},u_{2i}), i=1,\\ldots,50,000$, from the uniform (copula) distribution  using the calculated correlation coefficient (for this, you may use Python packages such as `Copulae` or `PyCopula`). \n",
    "* Transform the uniform numbers generated by the copula function to returns using the inverse of the fitted cumulative distribution functions $F_1$ and $F_2$.\n",
    "* Determine the 1-day 1% Value at Risk of the portfolio.\n",
    "* Next, consider the index and stock on a standalone basis. Calculate the 1-day 1% Value at Risk using 50,000 simulated returns for both the S&P 500 and the stock. What is the impact of diversification in this portfolio? This can be examined by calculating the 1-day 1% VaR of the single return series, and comparing with the 1-day 1% VaR of the combined portfolio."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Step 1: Fit a GARCH model for the standardised shocks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      1,   Func. Count:      6,   Neg. LLF: 15189.720576479187\n",
      "Iteration:      2,   Func. Count:     17,   Neg. LLF: 15180.153360437855\n",
      "Iteration:      3,   Func. Count:     27,   Neg. LLF: 15180.07797193695\n",
      "Iteration:      4,   Func. Count:     37,   Neg. LLF: 15180.069841305078\n",
      "Iteration:      5,   Func. Count:     44,   Neg. LLF: 15177.447715396185\n",
      "Iteration:      6,   Func. Count:     51,   Neg. LLF: 15175.79875118812\n",
      "Iteration:      7,   Func. Count:     58,   Neg. LLF: 15174.28401407324\n",
      "Iteration:      8,   Func. Count:     65,   Neg. LLF: 15173.69979345532\n",
      "Iteration:      9,   Func. Count:     71,   Neg. LLF: 15173.291621451037\n",
      "Iteration:     10,   Func. Count:     77,   Neg. LLF: 15173.063195681436\n",
      "Iteration:     11,   Func. Count:     83,   Neg. LLF: 15173.03572592825\n",
      "Iteration:     12,   Func. Count:     89,   Neg. LLF: 15173.02984568741\n",
      "Iteration:     13,   Func. Count:     95,   Neg. LLF: 15173.029721414168\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 15173.029720760109\n",
      "            Iterations: 13\n",
      "            Function evaluations: 96\n",
      "            Gradient evaluations: 13\n"
     ]
    }
   ],
   "source": [
    "#Fitting a normal GARCH\n",
    "#MFST\n",
    "returns_mfst = df_comp_log['MFST'] * 100   #using the log but *100\n",
    "\n",
    "## fit the arch model\n",
    "arch_1 = arch_model(returns_mfst, \n",
    "                    vol='Garch',\n",
    "                    p=1,o=0,q=1, \n",
    "                    dist='Normal')\n",
    "\n",
    "arch1_res = arch_1.fit()\n",
    "\n",
    "## define the residual / conditional volatility and standardised shocks series respectively\n",
    "arch_1_res = arch1_res.resid\n",
    "arch_1_hsq = arch1_res.conditional_volatility\n",
    "mfst_arch_1_zt = returns_mfst / arch_1_hsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:      1,   Func. Count:      6,   Neg. LLF: 9926.284648599867\n",
      "Iteration:      2,   Func. Count:     17,   Neg. LLF: 9920.7180749123\n",
      "Iteration:      3,   Func. Count:     26,   Neg. LLF: 9917.242755746298\n",
      "Iteration:      4,   Func. Count:     35,   Neg. LLF: 9917.152809178173\n",
      "Iteration:      5,   Func. Count:     42,   Neg. LLF: 9913.99021972904\n",
      "Iteration:      6,   Func. Count:     49,   Neg. LLF: 9912.572477413705\n",
      "Iteration:      7,   Func. Count:     56,   Neg. LLF: 9911.49215156969\n",
      "Iteration:      8,   Func. Count:     63,   Neg. LLF: 9911.286316474661\n",
      "Iteration:      9,   Func. Count:     69,   Neg. LLF: 9911.109985057108\n",
      "Iteration:     10,   Func. Count:     75,   Neg. LLF: 9910.810763432004\n",
      "Iteration:     11,   Func. Count:     81,   Neg. LLF: 9910.80785792118\n",
      "Iteration:     12,   Func. Count:     87,   Neg. LLF: 9910.80783781318\n",
      "Optimization terminated successfully.    (Exit mode 0)\n",
      "            Current function value: 9910.807837809405\n",
      "            Iterations: 12\n",
      "            Function evaluations: 87\n",
      "            Gradient evaluations: 12\n"
     ]
    }
   ],
   "source": [
    "## repeat for SPX\n",
    "returns_spx = df_comp_log['SPX'] * 100   #using the log but *100\n",
    "\n",
    "arch_2 = arch_model(returns_spx, \n",
    "                    vol='Garch',\n",
    "                    p=1,o=0,q=1, \n",
    "                    dist='Normal')\n",
    "\n",
    "arch2_res = arch_2.fit()\n",
    "arch_2_res = arch2_res.resid\n",
    "arch_2_hsq = arch2_res.conditional_volatility\n",
    "spx_arch_2_zt = returns_spx / arch_2_hsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## zip together so that the shapes will fit for the copulae function\n",
    "arch_zt_df = pd.DataFrame(list(zip(mfst_arch_1_zt, spx_arch_2_zt)),columns=['MFST','SPX'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<div>\n",
       "    <h2>Gaussian Copula Summary</h2>\n",
       "    <div>Gaussian Copula with 2 dimensions</div>\n",
       "    <hr/>\n",
       "    <div>\n",
       "        <h3>Parameters</h3>\n",
       "        <strong>Correlation Matrix</strong><table border=\"1\" class=\"dataframe\">\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.627855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>0.627855</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "    </div>\n",
       "    \n",
       "<div>\n",
       "    <h3>Fit Summary</h2>\n",
       "    <hr/>\n",
       "    <table>\n",
       "        <tr><th colspan=\"2\">Fit Summary</th></tr>\n",
       "        <tr><td>Log Likelihood</td><td>-1898.3688741432595</td></tr>\n",
       "        <tr><td>Variance Estimate</td><td>Not Implemented Yet</td></tr>\n",
       "        <tr><td>Method</td><td>Maximum pseudo-likelihood</td></tr>\n",
       "        <tr><td>Data Points</td><td>7593</td></tr>\n",
       "    </table>\n",
       "    <br/>\n",
       "    <table>\n",
       "        <tr><th colspan=\"2\">Optimization Setup</th><th colspan=\"2\">Results</th></tr>\n",
       "        <tr><td>bounds</td><td>[(-1.0, 1.0)]</td><td>x</td><td>[0.62785452]</td></tr><tr><td>options</td><td>{'maxiter': 20000, 'ftol': 1e-06, 'iprint': 1, 'disp': False, 'eps': 1.5e-08}</td><td>fun</td><td>-1898.3688741432595</td></tr><tr><td>method</td><td>SLSQP</td><td>jac</td><td>[-0.00180383]</td></tr><tr><td>None</td><td>None</td><td>nit</td><td>4</td></tr><tr><td>None</td><td>None</td><td>nfev</td><td>14</td></tr><tr><td>None</td><td>None</td><td>njev</td><td>4</td></tr><tr><td>None</td><td>None</td><td>status</td><td>0</td></tr><tr><td>None</td><td>None</td><td>message</td><td>Optimization terminated successfully.</td></tr><tr><td>None</td><td>None</td><td>success</td><td>True</td></tr>\n",
       "    </table>\n",
       "</div>\n",
       "        \n",
       "</div>\n"
      ],
      "text/plain": [
       "Gaussian Copula Summary\n",
       "================================================================================\n",
       "Gaussian Copula with 2 dimensions\n",
       "\n",
       "\n",
       "Parameters\n",
       "--------------------------------------------------------------------------------\n",
       " Correlation Matrix \n",
       " 1.000000  0.627855\n",
       " 0.627855  1.000000\n",
       "\n",
       "\n",
       "\n",
       "                                  Fit Summary                                   \n",
       "================================================================================\n",
       "Log. Likelihood      : -1898.3688741432595\n",
       "Variance Estimate    : Not Implemented Yet\n",
       "Method               : Maximum pseudo-likelihood\n",
       "Data Points          : 7593\n",
       "\n",
       "Optimization Setup\n",
       "--------------------------------------------------------------------------------\n",
       "\tbounds         : [(-1.0, 1.0)]\n",
       "\toptions        : {'maxiter': 20000, 'ftol': 1e-06, 'iprint': 1, 'disp': False, 'eps': 1.5e-08}\n",
       "\tmethod         : SLSQP\n",
       "\n",
       "Results\n",
       "--------------------------------------------------------------------------------\n",
       "\tx              : [0.62785452]\n",
       "\tfun            : -1898.3688741432595\n",
       "\tjac            : [-0.00180383]\n",
       "\tnit            : 4\n",
       "\tnfev           : 14\n",
       "\tnjev           : 4\n",
       "\tstatus         : 0\n",
       "\tmessage        : Optimization terminated successfully.\n",
       "\tsuccess        : True"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_, ndim = arch_zt_df.shape\n",
    "\n",
    "## def dim = number of dimensions in the df.shape\n",
    "g_cop_arch = GaussianCopula(dim=ndim)\n",
    "\n",
    "## fit copulae model and show summary\n",
    "g_cop_arch.fit(arch_zt_df)\n",
    "g_cop_arch.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.62785452])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arch_cop_params = g_cop_arch.params\n",
    "arch_cop_params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#check correlations \n",
    "## NOTE:  spearman correlation is non-parametric \n",
    "arch_zt_df_ken = arch_zt_df.corr(method='kendall')\n",
    "arch_zt_df_pear = arch_zt_df.corr(method='pearson')\n",
    "arch_zt_df_spear = arch_zt_df.corr(method='spearman')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Copula Parameter approximately matches correlation implied by spearman correlation measure\n",
      "Copula Parameter does not match correlation implied by Kendall measure\n",
      "Copula Parameter does not match correlation implied by Pearson measure\n"
     ]
    }
   ],
   "source": [
    "#Test if correlation matches copula within 2.5% error margin \n",
    "\n",
    "if np.isclose(arch_cop_params[0], arch_zt_df_spear.iloc[0,1],rtol=0.025)== True:\n",
    "    print(\"Copula Parameter approximately matches correlation implied by spearman correlation measure\")\n",
    "    \n",
    "elif np.isclose(arch_cop_params[0], arch_zt_df_spear.iloc[0,1],rtol=0.025)!= True:\n",
    "    print(\"Copula Parameter does not match correlation implied by Spearman\")\n",
    "    \n",
    "if np.isclose(arch_cop_params[0], arch_zt_df_ken.iloc[0,1],rtol=0.025)== True:\n",
    "    print(\"Copula Parameter approximately matches correlation implied by Kendall correlation measure\")\n",
    "    \n",
    "elif np.isclose(arch_cop_params[0], arch_zt_df_ken.iloc[0,1],rtol=0.025)!= True:\n",
    "    print(\"Copula Parameter does not match correlation implied by Kendall measure\")\n",
    "    \n",
    "if np.isclose(arch_cop_params[0], arch_zt_df_pear.iloc[0,1],rtol=0.025)== True:\n",
    "    print(\"Copula Parameter approximately matches correlation implied by Pearson correlation measure\")\n",
    "    \n",
    "elif np.isclose(arch_cop_params[0], arch_zt_df_pear.iloc[0,1],rtol=0.025)!= True:\n",
    "    print(\"Copula Parameter does not match correlation implied by Pearson measure\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The rejection of the pearson measure is consistent with our expectations as the two series have different respective variances\n",
    "* The rejection of the Kendall measure (the statistic is used to measure ordinal association and is closest to 1 when the observations have similar or identical rank correlation) this would perhaps imply the degree of correlation isn't so extreme that it can't be better captured by another measure\n",
    "* The matching implied by the spearman measure- a non-parametric measure of rank correlation- is consistent with some expected underlying notions of the data, such as:  monotonic relationship seems likely between the stock and its index- which is confirmed by the approximate match here. Additionally, unlike the pearson measure, there is no required linearity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "## generate 50k random samples\n",
    "copula_samples = g_cop_arch.random(50000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#arch_ppf \n",
    "arch_ppf = g_cop_arch.pdf(copula_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "#arch_cdf\n",
    "arch_cdf = g_cop_arch.cdf(copula_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "arch_norm_cdf = stats.norm.cdf(copula_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "arch_norm_ppf = stats.norm.ppf(arch_norm_cdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "copula_norm = stats.norm.ppf(copula_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Weights: 50% equally \n",
    "weights = [[0.5],[0.5]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.019887191374358414 0.010967799244958618\n"
     ]
    }
   ],
   "source": [
    "#standard deviations of original returns (log)\n",
    "stddev_mfst = np.std(df_comp_log['MFST'])\n",
    "stddev_spx = np.std(df_comp_log['SPX'])\n",
    "print(stddev_mfst, stddev_spx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "split_copnorm = pd.DataFrame(copula_norm)\n",
    "split_copnorm.columns = ['MFST_1','SPX_1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "    }\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>MFST_1</th>\n",
       "      <th>SPX_1</th>\n",
       "      <th>MFST_STD_DEV</th>\n",
       "      <th>SPX_STD_DEV</th>\n",
       "      <th>MFST_RET*VOL</th>\n",
       "      <th>MFST_WEIGHT</th>\n",
       "      <th>SPX_RET*VOL</th>\n",
       "      <th>SPX_WEIGHT</th>\n",
       "      <th>PORTFOLIO_W_RET</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.380593</td>\n",
       "      <td>-0.587229</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.007569</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.006441</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.007005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.791014</td>\n",
       "      <td>1.467617</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>0.015731</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.016097</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.015914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.725969</td>\n",
       "      <td>-0.926056</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.034325</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.010157</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.022241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.630032</td>\n",
       "      <td>0.624944</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.012530</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.006854</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.002838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.455691</td>\n",
       "      <td>-1.572006</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.009062</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.017241</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.013152</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     MFST_1     SPX_1  MFST_STD_DEV  SPX_STD_DEV  MFST_RET*VOL  MFST_WEIGHT  \\\n",
       "0 -0.380593 -0.587229      0.019887     0.010968     -0.007569          0.5   \n",
       "1  0.791014  1.467617      0.019887     0.010968      0.015731          0.5   \n",
       "2 -1.725969 -0.926056      0.019887     0.010968     -0.034325          0.5   \n",
       "3 -0.630032  0.624944      0.019887     0.010968     -0.012530          0.5   \n",
       "4 -0.455691 -1.572006      0.019887     0.010968     -0.009062          0.5   \n",
       "\n",
       "   SPX_RET*VOL  SPX_WEIGHT  PORTFOLIO_W_RET  \n",
       "0    -0.006441         0.5        -0.007005  \n",
       "1     0.016097         0.5         0.015914  \n",
       "2    -0.010157         0.5        -0.022241  \n",
       "3     0.006854         0.5        -0.002838  \n",
       "4    -0.017241         0.5        -0.013152  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Show easy summary, unsorted DataFrame\n",
    "copnorm_vol_adj = split_copnorm\n",
    "copnorm_vol_adj['MFST_STD_DEV'] = stddev_mfst\n",
    "copnorm_vol_adj['SPX_STD_DEV'] = stddev_spx\n",
    "copnorm_vol_adj['MFST_RET*VOL'] = stddev_mfst * split_copnorm['MFST_1']\n",
    "copnorm_vol_adj['MFST_WEIGHT'] = 0.5\n",
    "copnorm_vol_adj['SPX_RET*VOL'] = stddev_spx * split_copnorm['SPX_1']\n",
    "copnorm_vol_adj['SPX_WEIGHT'] = 0.5\n",
    "copnorm_vol_adj['PORTFOLIO_W_RET'] = (copnorm_vol_adj['MFST_WEIGHT'] * copnorm_vol_adj['MFST_RET*VOL']) + (copnorm_vol_adj['SPX_WEIGHT'] * copnorm_vol_adj['SPX_RET*VOL'])\n",
    "copnorm_vol_adj.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MFST_1</th>\n",
       "      <th>SPX_1</th>\n",
       "      <th>MFST_STD_DEV</th>\n",
       "      <th>SPX_STD_DEV</th>\n",
       "      <th>MFST_RET*VOL</th>\n",
       "      <th>MFST_WEIGHT</th>\n",
       "      <th>SPX_RET*VOL</th>\n",
       "      <th>SPX_WEIGHT</th>\n",
       "      <th>PORTFOLIO_W_RET</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>8766</th>\n",
       "      <td>-3.683671</td>\n",
       "      <td>-3.842959</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.073258</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.042149</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.057703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23471</th>\n",
       "      <td>-4.177067</td>\n",
       "      <td>-2.293179</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.083070</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.025151</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.054111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19226</th>\n",
       "      <td>-4.190814</td>\n",
       "      <td>-2.194233</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.083344</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.024066</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.053705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23158</th>\n",
       "      <td>-4.008023</td>\n",
       "      <td>-2.207265</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.079708</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.024209</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.051959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27401</th>\n",
       "      <td>-3.450878</td>\n",
       "      <td>-3.213647</td>\n",
       "      <td>0.019887</td>\n",
       "      <td>0.010968</td>\n",
       "      <td>-0.068628</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.035247</td>\n",
       "      <td>0.5</td>\n",
       "      <td>-0.051937</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         MFST_1     SPX_1  MFST_STD_DEV  SPX_STD_DEV  MFST_RET*VOL  \\\n",
       "8766  -3.683671 -3.842959      0.019887     0.010968     -0.073258   \n",
       "23471 -4.177067 -2.293179      0.019887     0.010968     -0.083070   \n",
       "19226 -4.190814 -2.194233      0.019887     0.010968     -0.083344   \n",
       "23158 -4.008023 -2.207265      0.019887     0.010968     -0.079708   \n",
       "27401 -3.450878 -3.213647      0.019887     0.010968     -0.068628   \n",
       "\n",
       "       MFST_WEIGHT  SPX_RET*VOL  SPX_WEIGHT  PORTFOLIO_W_RET  \n",
       "8766           0.5    -0.042149         0.5        -0.057703  \n",
       "23471          0.5    -0.025151         0.5        -0.054111  \n",
       "19226          0.5    -0.024066         0.5        -0.053705  \n",
       "23158          0.5    -0.024209         0.5        -0.051959  \n",
       "27401          0.5    -0.035247         0.5        -0.051937  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Sort data by portfolio weighted returns\n",
    "sorted_cop_voladj = copnorm_vol_adj.sort_values(by='PORTFOLIO_W_RET',\n",
    "                                                ascending=True)\n",
    "\n",
    "sorted_cop_voladj.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# VaR\n",
    "#### Different method comparisons "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03282091084373755"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Historical Simulation for 99% Value At Risk\n",
    "VaR_99 = -np.quantile(sorted_cop_voladj['PORTFOLIO_W_RET'], 0.01) \n",
    "VaR_99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.032736263055182416"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_pf = copnorm_vol_adj['PORTFOLIO_W_RET'].mean()\n",
    "std_dev_pf = copnorm_vol_adj['PORTFOLIO_W_RET'].std()\n",
    "VaR_99_normd = -stats.norm.ppf(1-0.99, mean_pf, std_dev_pf)\n",
    "VaR_99_normd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.032736263055182416"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Apply a 2nd method  to ensure the validity of the above VaR method\n",
    "CV_99 = stats.norm.ppf(1-0.99)\n",
    "VaR_portfolio = -mean_pf - std_dev_pf*CV_99\n",
    "VaR_portfolio"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "* Now we consider the index and the stocks on a standalone basis: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated Students-T VAR for MFST is:  0.07448964610932779\n"
     ]
    }
   ],
   "source": [
    "#Student's T- MFST\n",
    "\n",
    "## number of sims\n",
    "n_sims = 50000\n",
    "\n",
    "## degrees of freedom\n",
    "DOF = 4\n",
    "\n",
    "## define standard deviation\n",
    "std_MFST = np.std(df_comp_log['MFST'])\n",
    "\n",
    "## sim returns based off DOF and n_sims\n",
    "sim_returns_MFST = np.random.standard_t(DOF, n_sims)\n",
    "\n",
    "## calculated simulated student's-T VaR for MFST\n",
    "SimVAR_MFST = -std_MFST*np.percentile(sim_returns_MFST, 1)\n",
    "print('Simulated Students-T VAR for MFST is: ', SimVAR_MFST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulated Students-T VAR for SPX is:  0.04114347370077373\n"
     ]
    }
   ],
   "source": [
    "#Student's T- SPX\n",
    "n_sims = 50000\n",
    "DOF = 4\n",
    "std_SPX = np.std(df_comp_log['SPX'])\n",
    "sim_returns_SPX = np.random.standard_t(DOF, n_sims)\n",
    "SimVAR_SPX = -std_SPX*np.percentile(sim_returns_SPX, 1)\n",
    "print('Simulated Students-T VAR for SPX is: ', SimVAR_SPX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| PRODUCT   |    1% VaR |\n",
      "|-----------+-----------|\n",
      "| Portfolio | 0.0327363 |\n",
      "| MFST      | 0.0744896 |\n",
      "| SPX       | 0.0411435 |\n"
     ]
    }
   ],
   "source": [
    "print(tabulate([['Portfolio',VaR_portfolio],['MFST',SimVAR_MFST],['SPX',SimVAR_SPX],],headers=['PRODUCT','1% VaR'],tablefmt='orgtbl'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion: Q3 - Portfolio VaR vs Individual Series VaR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We calculated the Spearman's correlation and this gave us a value of 0.6279. We chose the Spearman's correlation because it is more precise for non-normal data than the Pearson's correlation is (as discussed above). \n",
    "\n",
    "* We first determined the 1-day 1% VaR using the Historical Simulation method. This gives us a value of 0.0328. To be able to determine a more precise estimate we also used the Risk Metrics method, but with average portfolio mean and standard deviation. This gives us a value of 0.0327. \n",
    "\n",
    "* For Microsoft we get a seperate VaR estimate of 0.074 and for S&P 500 0.0411: given that SPX is the index and is more diversified than a single equity, these results align with what would be expected. Moreover, crudely approximating these two values leads to an average VaR of ~ 0.0579, which is a lot higher compared to their portfolio VaR of 0.0327."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4\n",
    "* Repeat Question 3 using the t-copula density function to generate $(u_{1i},u_{2i})$ (you may use 4 degrees of freedom in the $t$-copula density function, but it may also be possible to fit this parameter by maximum likelihood using `Copulae` or `PyCopula`).\n",
    "* Present the results and explain the main differences with the results from Question 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "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>MFST</th>\n",
       "      <th>SPX</th>\n",
       "      <th>PORTFOLIO RETURN</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19226</th>\n",
       "      <td>-0.427125</td>\n",
       "      <td>-0.036888</td>\n",
       "      <td>-0.232006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23471</th>\n",
       "      <td>-0.420666</td>\n",
       "      <td>-0.039995</td>\n",
       "      <td>-0.230330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8766</th>\n",
       "      <td>-0.250154</td>\n",
       "      <td>-0.162249</td>\n",
       "      <td>-0.206201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23158</th>\n",
       "      <td>-0.349984</td>\n",
       "      <td>-0.037283</td>\n",
       "      <td>-0.193634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26978</th>\n",
       "      <td>-0.290897</td>\n",
       "      <td>-0.013623</td>\n",
       "      <td>-0.152260</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           MFST       SPX  PORTFOLIO RETURN\n",
       "19226 -0.427125 -0.036888         -0.232006\n",
       "23471 -0.420666 -0.039995         -0.230330\n",
       "8766  -0.250154 -0.162249         -0.206201\n",
       "23158 -0.349984 -0.037283         -0.193634\n",
       "26978 -0.290897 -0.013623         -0.152260"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## fit the student's-t copulae \n",
    "cop_studt = stats.t.ppf(copula_samples, 4)\n",
    "df_studt = pd.DataFrame(cop_studt)\n",
    "\n",
    "## the *= is a running cumsum \n",
    "df_studt.loc[:,0] *= stddev_mfst\n",
    "df_studt.loc[:,1] *= stddev_spx\n",
    "df_studt['PORTFOLIO RETURN'] = \"\"\n",
    "df_studt.columns = ['MFST','SPX','PORTFOLIO RETURN']\n",
    "\n",
    "## 0.5 == implies equal weighting \n",
    "df_studt['PORTFOLIO RETURN'] = 0.5*df_studt['MFST'] + 0.5*df_studt['SPX']\n",
    "\n",
    "## sort values by portfolio returns \n",
    "df_studt_sorted = df_studt.sort_values(by=['PORTFOLIO RETURN'])\n",
    "df_studt_sorted.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.073852657911079 0.052408544268642956\n"
     ]
    }
   ],
   "source": [
    "zpt_2 = -np.quantile(df_studt_sorted['PORTFOLIO RETURN'],0.01)\n",
    "mean_studt = df_studt_sorted['PORTFOLIO RETURN'].mean()\n",
    "stddev_studt = df_studt_sorted['PORTFOLIO RETURN'].std()\n",
    "DOF = 4\n",
    "CV_studt = stats.t.ppf(0.99, DOF)\n",
    "VaR_studt_portfolio = mean_studt + stddev_studt*CV_studt\n",
    "print(VaR_studt_portfolio, zpt_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Discussion:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| DISTRIBUTION   |    1% VaR |\n",
      "|----------------+-----------|\n",
      "| Normal Dist    | 0.0327363 |\n",
      "| Students-T     | 0.0738527 |\n"
     ]
    }
   ],
   "source": [
    "print(tabulate([['Normal Dist',VaR_portfolio],['Students-T',VaR_studt_portfolio]],headers=['DISTRIBUTION','1% VaR'],tablefmt='orgtbl'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* We again first determine the 1-day 1% VaR using the Historical Simulation method. This gives us a value of ~0.0524, clearly a larger VaR than the one for the Normal distribution simulations. Then, to be able to determine a more precise estimate we also use the Risk Metrics method, but with average portfolio mean and standard deviation; this 2nd method gives us a value of 0.0526. Both of these VaR are larger than the ones implied by the Normal distribution simulations. This can be explained by the shape of the distributions: a Student's t distribution has a higher peak and has heavier tails than a normal distribution. This in turn means that very extreme negative returns are more likely in the student-t distribution, which causes the VaR to be higher. \n",
    "\n",
    "* Next we compared the separate VaR's with the portfolio VaR. For Microsoft we get a separate VaR estimate of 0.0742 and for S&P 500 0.0416. A crude calculation could imply this is an average VaR of 0.0579, which is a lot higher compared to their portfolio VaR of 0.0327. What this shows is that the portfolio diversification reduces risk through the synergy of combining the two assets. Extreme left-tail (low/negative) returns are less likely because the two assets have a correlation smaller than one, so that when one stock performs badly, the other might be able to compensate for this and thus it insulates the portfolio return from excessively negative drops. \n",
    "* Naturally, there is some degree of correlation- even implied explicility as MFST is a part of the SPX- thus there remains a significant part of VaR that is still exposed to common or system shocks that will erode the benefits of diversification. One small caveat is that common shocks (or a crisis, perse) tend to cause correlations to go up, meaning the benefits of diversification are diminished. Thus the true benefits of diversification in strenous circumstances cannot be truly accounted for the VaR as calculated above without some form of asymmetric correlation adjustment. "
   ]
  }
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