Monte Carlo Value at risk https://nbviewer.jupyter.org/gist/DBremen/8aef035c038cd14b120c19391c429c2b

Monte Carlo Value at risk.ipynb

Monte+Carlo+Value+at+risk.ipynb

{
  "cells": [
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "# Monte Carlo Value at risk\nWhat is worth expected loss we might see?"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "<h1 id=\"tocheading\">Table of Contents</h1>\n<div id=\"toc\"></div>"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "%%javascript\n$.getScript('https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js')",
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<IPython.core.display.Javascript object>",
            "application/javascript": "$.getScript('https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js')\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "import numpy as np\nimport pandas as pd\nimport numpy.random as npr\nimport pandas_datareader as pdr\nimport matplotlib.pyplot as plt\nimport matplotlib.ticker as mtick\nfrom pandas.plotting import register_matplotlib_converters\nregister_matplotlib_converters()\n#ax.yaxis.set_major_formatter(mtick.PercentFormatter())\npd.options.display.float_format = '${:,.2f}'.format\n%matplotlib inline\nimport seaborn\nseaborn.set()\n#format DataFrame example\n#formatted = df.style.format({'EPS': '${:,.2f}', 'PE':'{:,.2f}', 'Exp_Ret': '{:,.2%}', 'Price': '${:,.2f}'})",
      "execution_count": 2,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "https://github.com/PacktPublishing/Hands-on-Python-for-Finance-V/blob/master/Section+6/VaR.ipynb"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Deterministic value at risk calculation"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# for short time horizons expecected retur will be small, and therefore VaR estimations\n# will not be much influenced by it\nfrom scipy.stats import norm\nconfidenceLevels = [0.95,.99]\nvolatility = 0.307\nTRADING_DAYS_PA= 252\nTRADING_DAYS_PM = 21\nquantity = 5000\naapl_price = pdr.get_quote_yahoo('AAPL')['price']\nportfolio_value = quantity * aapl_price\nportfolio_value = aapl_value.at['AAPL']\nt = TRADING_DAYS_PM/TRADING_DAYS_PA\nfor cl in confidenceLevels:\n    cutoff = norm.ppf(cl)\n    VaR = portfolio_value * volatility * np.sqrt(t) * cutoff\n    text = \"At {:.0%} CL, loss will not exceed ${:,.2f} ({:.2f} StdDev below the average return)\"\n    print(text.format(cl, VaR,cutoff))",
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": "At 95% CL, loss will not exceed $211,304.24 (1.64 StdDev below the average return)\nAt 99% CL, loss will not exceed $298,851.62 (2.33 StdDev below the average return)\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Probabilistic model"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "er = .19\niterations = 50000",
      "execution_count": 43,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "aapl_value",
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 44,
          "data": {
            "text/plain": "AAPL   $1,449,550.00\nName: price, dtype: float64"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "def VaR(pv, er, vol, T, iterations):\n    end = pv * np.exp((er - .5 * vol ** 2) * T + \n                     vol * np.sqrt(T) * np.random.standard_normal(iterations))\n    return (end - pv)",
      "execution_count": 45,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "at_risk = VaR(portfolio_value,er,volatility, t, iterations)",
      "execution_count": 46,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "plt.figure(figsize=(12,8))\nplt.xlim(at_risk.min(), at_risk.max() );\nplt.hist(at_risk, bins=100, edgecolor='k');\nplt.axvline(np.median(at_risk), color='r');",
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 864x576 with 1 Axes>",
            "image/png": 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bb0ry0uH1FcN6hu2XVFWt8PgAbCZbtqWqxi5z8wuzbh3AVLZOu2Nr7VBV/WqSB5P8vyR/lOQTSb7SWntyqHYwyY7h9Y4kB4Z9n6yqx5M8PcmXp20DAJvMsaM5f++tYzc9cN3la9wYgNWxkiEl52TUa31Bkm9P8s1JLhtTtR3fZYlti9/3qqraV1X7jhw5Mm3zAABgXVjJkJIfTPKF1tqR1trRJB9M8q+TnD0MMUmS+SQPDa8PJjkvSYbt35bk0RPftLV2fWttd2tt9/bt21fQPAAAmL2VBO4Hk1xUVd80jMW+JMnnkvxJkpcNdfYk+dDw+pZhPcP2P26tndTDDQAAm8nUgbu1dndGNz9+Mslnhve6PsneJG+oqv0ZjdG+YdjlhiRPH8rfkOTqFbQbAAA2hKlvmkyS1tq1Sa49ofj+JBeOqfu3SV6+kuMBAMBG40mTAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA1raG5+IVU1dgEANqcVPdodOD2HDx3I+XtvHbvtgesuX+PWAABrQQ83AAB0JHADsDFs2TZxSNbc/MKsWwcwkSElAGwMx44akgVsSHq4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAHY+LZsS1WdtMzNL8y6ZQDZOusGAMCKHTua8/feelLxA9ddPoPGAPx9ergBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbOpibXxg7RRkAcOYxLSB0cPjQAVOUAQBJ9HADAEBXAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AAB0JHADAEBHAjcAAHQkcAMAQEcCN0xp0uPbPcIdAFhsRY92r6qzk7wzyfOStCSvTnJfkvcl2Znki0l+pLX2WI1SyFuTvDjJV5P8RGvtkys5PszSpMe3Jx7hDgB8w0p7uN+a5H+21v5Jkn+e5N4kVyf5cGttV5IPD+tJclmSXcNyVZJ3rPDYALC0Ldsm/iVqbn5h1q0DzhBT93BX1bcm+YEkP5EkrbUnkjxRVVckuXiodlOSO5PsTXJFkne31lqSu6rq7Kqaa609PHXrAWApx476SxQwcyvp4X52kiNJfruq/qyq3llV35zkmcdD9PDzGUP9HUkOLNr/4FAGAACb1koC99Ykz0/yjtba9yT5v/nG8JFxxt1J1k6qVHVVVe2rqn1HjhxZQfMAAGD2VhK4DyY52Fq7e1j/QEYB/EtVNZckw89HFtU/b9H+80keOvFNW2vXt9Z2t9Z2b9++fQXNAwCA2Zs6cLfWDic5UFXPGYouSfK5JLck2TOU7UnyoeH1LUleWSMXJXnc+G0AADa7FU0LmOT1Sd5TVWcluT/JqzIK8e+vqtckeTDJy4e6t2U0JeD+jKYFfNUKjw0AAOveigJ3a+3Pk+wes+mSMXVbkteu5HgAALDReNIkAAB0JHADAEBHAjcAAHQkcAMAQEcCNwAAdCRwAwBARwI3AGemLdtSVWOXufmFWbcO2ERW+uAbANiYjh3N+XtvHbvpgesuX+PGAJuZHm4AAOhI4AYAgI4EbgAA6EjgBgCAjgRuWMLc/MLEWQwAAE6FWUpgCYcPHTCLAQCwInq4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwBOtGVbquqkZW5+YdYtAzagrbNuAACsO8eO5vy9t55U/MB1l8+gMcBGp4cbAAA6ErgBAKAjgRsAADoSuAEAoCOBGwAAOhK4AQCgI4EbAAA6ErgBAKAjgRsAADoSuDnjzc0vjH2Ec1XNumkAwCbg0e6c8Q4fOjD2Ec6JxzgDACunhxsATtWWbRP/IjY3vzDr1gHrlB5uADhVx476ixhw2vRwAwBARwI3AAB0tOLAXVVbqurPqurWYf2Cqrq7qj5fVe+rqrOG8qcM6/uH7TtXemwAAFjvVqOH+2eS3Lto/bokb2mt7UryWJLXDOWvSfJYa+07krxlqAdrZtL0fwAAPa3opsmqmk/yw0nelOQNNUovL0jyo0OVm5L8tyTvSHLF8DpJPpDkN6qqWmttJW2AUzVp+j83OgEAPa20h/vXk/x8kq8N609P8pXW2pPD+sEkO4bXO5IcSJJh++NDfQAA2LSmDtxVdXmSR1prn1hcPKZqO4Vti9/3qqraV1X7jhw5Mm3zAABgXVhJD/f3J3lJVX0xyc0ZDSX59SRnV9XxoSrzSR4aXh9Mcl6SDNu/LcmjJ75pa+361tru1tru7du3r6B5ALCGPBQHmGDqMdyttWuSXJMkVXVxkp9rrf1YVf1ukpdlFML3JPnQsMstw/pHh+1/bPw2AJuGh+IAE/SYh3tvRjdQ7s9ojPYNQ/kNSZ4+lL8hydUdjg0AAOvKqjzavbV2Z5I7h9f3J7lwTJ2/TfLy1TgeAABsFJ40CQAAHQncAADQkcANAAAdCdwAANCRwA0AvU2Yo9v83HBmWJVZSgCAJUyYo9v83HBm0MMNAAAdCdwAANCRwA0AAB0J3AAwKxNupnRDJWwubpoEgFmZcDNl4oZK2Ez0cAMAQEcCNwAAdCRws6nMzS9MHA8JADALxnCzqRw+dMB4SABgXdHDDQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQDr0ZZtqaqxy9z8wqxbB5yGrbNuAJyuufmFHD50YNbNAOjr2NGcv/fWsZseuO7yNW4MsBICNxvO4UMHfAkBZ7ah9/tEz9pxXh4++OAMGgQsReAGgI1mQu+3TgdYn4zhBgCAjgRuAADoSOBm3ZqbXxh7dz4AwEZiDDfr1qSbI41RBAA2Ej3cAADQkcANAJuFh+XAujT1kJKqOi/Ju5M8K8nXklzfWntrVT0tyfuS7EzyxSQ/0lp7rEaDb9+a5MVJvprkJ1prn1xZ8wGAr/OwHFiXVtLD/WSS/9Ja+6dJLkry2qp6bpKrk3y4tbYryYeH9SS5LMmuYbkqyTtWcGwAANgQpg7crbWHj/dQt9b+Jsm9SXYkuSLJTUO1m5K8dHh9RZJ3t5G7kpxdVXNTtxwAADaAVRnDXVU7k3xPkruTPLO19nAyCuVJnjFU25HkwKLdDg5lJ77XVVW1r6r2HTlyZDWaBwAAM7PiwF1V35Lk95L8bGvtr5eqOqasnVTQ2vWttd2ttd3bt29fafMAgMQNlTBDK5qHu6q2ZRS239Na++BQ/KWqmmutPTwMGXlkKD+Y5LxFu88neWglxwcATpEbKmFmpu7hHmYduSHJva21X1u06ZYke4bXe5J8aFH5K2vkoiSPHx96AgAAm9VKeri/P8mPJ/lMVf35UPYLSd6c5P1V9ZokDyZ5+bDttoymBNyf0bSAr1rBsQEAYEOYOnC31v53xo/LTpJLxtRvSV477fEAAGAj8qRJAADoSOCmu7n5BXfGAwBnrBXNUgKn4vChA+6MBwDOWHq4AQCgI4EbAJho0rBAQwLh1BlSAgBMNGlYoCGBcOoEbmZreNQwAMBmJXAzWx41DABscsZwA8CZbvhr47hlmn2M74a/Tw83AJzppvlro79QwinTww0AAB0J3AAA0JHADQAAHQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHAzaqZm184vaeUAQCcATxpklVz+NCBsU8d88QxAOBMpocbAAA6Erg5LZOGjRg6AgAwniElnJZJw0YSQ0cAGGzZNrEj5lk7zsvDBx9c4wbBbAncAMDqOnZU5wwsYkgJAAB0JHADAGtnGG5y4jI3vzDrlkE3hpRwkrn5hRw+dGDWzQBgM5ow3MRQEzYzgfsMtVyoNvYOAGB1CNxnKLONALCumNmETUzgBgBmb6mZTX713wvjbGgC9yZnPDYAG55pBtngBO5NbtLQERcoAIC1YVpAAADoSOAGADYu83qzARhSAgBsXJPm9XajJeuIwA0AbD5utGQdMaRkE5ibXxj757RJ/7IHgDPahGEoyw1FmfR9a/gKy9HDvQl4iA0AnIYp5/xOxj+J2XctyxG4AQCOMxSFDgwpAQCAjgTuDcI4bQBYp6YcE86Zw5CSDcI4bQBYp6YcE256wjPHmgfuqro0yVuTbEnyztbam9e6DWthbn4hhw8dGLttqf/BltoPANhgpgjjgvjms6aBu6q2JHl7kh9KcjDJx6vqltba59ayHatpqYDsDmgAYKJVfmjPpEyy5ayn5tgTf3va7zeNaTscN7u17uG+MMn+1tr9SVJVNye5IsmGDdyThnosGZDdAQ0ATNJh2sK1GvJiCOx4ax24dyRZ/M+eg0m+d1LlT33602s27mmpf5Et9S9DAIA1s9qddlOE+x65aLV75ye936x62au1tnYHq3p5khe11n5yWP/xJBe21l6/qM5VSa4aVp+T5L5VOPS5Sb68Cu/DxuY8IHEeMOI8IHEeMHL8PDi/tba9xwHWuof7YJLzFq3PJ3locYXW2vVJrl/Ng1bVvtba7tV8TzYe5wGJ84AR5wGJ84CRtTgP1noe7o8n2VVVF1TVWUmuTHLLGrcBAADWzJr2cLfWnqyq1yW5PaNpAW9srd2zlm0AAIC1tObzcLfWbkty2xofdlWHqLBhOQ9InAeMOA9InAeMdD8P1vSmSQAAONOs9RhuAAA4o2y4wF1VP1dVrarOHdarqt5WVfur6tNV9fxFdfdU1eeHZc+i8n9ZVZ8Z9nlbDZNMVtXTquqOof4dVXXOcsdgbVXVr1TVXwyfw+9X1dmLtl0zfEb3VdWLFpVfOpTtr6qrF5VfUFV3D5/3+4YbeVNVTxnW9w/bdy53DNa/SecBG0tVnVdVf1JV91bVPVX1M0P5aV+/V+s7gtmoqi1V9WdVdeuwvmrX9NP93mB2qursqvrAkA3urarvW5fXg9bahlkymlLw9iQPJDl3KHtxkj9MUkkuSnL3UP60JPcPP88ZXp8zbPtYku8b9vnDJJcN5b+c5Orh9dVJrlvqGJaZnAMvTLJ1eH3dos/ouUk+leQpSS5I8lcZ3Zi7ZXj97CRnDXWeO+zz/iRXDq9/K8lPDa9/OslvDa+vTPK+pY4x6/8mllM6byaeB5aNtSSZS/L84fU/SvKXw/+bp3X9Xs3vCMvMzoU3JPmdJLcO66tyTZ/me8My0/PgpiQ/Obw+K8nZ6/F6sNF6uN+S5OeTLB54fkWSd7eRu5KcXVVzSV6U5I7W2qOttceS3JHk0mHbt7bWPtpG/5XeneSli97rpuH1TSeUjzsGa6y19kettSeH1bsymss9GX1GN7fW/q619oUk+5NcOCz7W2v3t9aeSHJzkiuGf6G+IMkHhv1P/LyPnwcfSHLJUH/SMVj/xp4HM24TU2itPdxa++Tw+m+S3JvRU4xP9/q9mt8RrLGqmk/yw0neOayv5jV9mu8NZqCqvjXJDyS5IUlaa0+01r6SdXg92DCBu6pekuRQa+1TJ2wa97j4HcuUHxxTniTPbK09nIwu6kmescwxmK1XZ/SvzeT0z4OnJ/nKovC++DP9+j7D9seH+s6DjctntwkNQwO+J8ndOf3r92p+R7D2fj2jDrivDeureU2f5nuD2Xh2kiNJfnsYXvTOqvrmrMPrwZpPC7iUqvpfSZ41ZtMbk/xCRsMJTtptTFmbonzJpk2xD1Na6jxorX1oqPPGJE8mec/x3cbUbxn/j8rlzoPVPHdYH3x2m0xVfUuS30vys621vx6GVY6tOqZstb8jWENVdXmSR1prn6iqi48Xj6k67TV9mu8NZmNrkucneX1r7e6qemtGwzsmmdn1YF0F7tbaD44rr6p/ltH4qk8NF9X5JJ+sqgsz+XHxB5NcfEL5nUP5/Jj6SfKlqpprrT08/BnhkaF82UfSs3omnQfHDTczXJ7kkuFPPMnSn9G48i9n9KekrUNvxeL6x9/rYFVtTfJtSR5d5hisbz67TaSqtmUUtt/TWvvgUHy61+/V/I5gbX1/kpdU1YuTPDXJt2bU472a1/TT/cyacrgAAAHXSURBVN5gNg4mOdhau3tY/0BGgXvdXQ82xJCS1tpnWmvPaK3tbK3tzOg/wPNba4czejT8K4c7Ty9K8vjQtX97khdW1TnDnaMvTHL7sO1vquqiYTzWK5N8aDjULUmO35m654TyccdgjVXVpUn2JnlJa+2rizbdkuTK4W70C5LsyuhGh48n2TXcWX5WRjfM3DIE9T9J8rJh/xM/7+PnwcuS/PFQf9IxWP/GngczbhNTGK7bNyS5t7X2a4s2ne71ezW/I1hDrbVrWmvzQx64MqNr9I9l9a7p03xvMANDDjxQVc8Zii5J8rmsx+vBUndUrtclyRfzjVlKKsnbM7qj+DNJdi+q9+qMboLYn+RVi8p3J/nssM9v5BsPAHp6kg8n+fzw82nLHcOy5p/9/ozGWf35sPzWom1vHD6j+zLcRTyUvzijmQz+KqNhKcfLn53RxXV/kt9N8pSh/KnD+v5h+7OXO4Zl/S+TzgPLxlqS/JuM/qT76UXXgRdPc/1ere8Iy0zPh4vzjVlKVu2afrrfG5aZngP/Ism+4ZrwBxnNMrLurgeeNAkAAB1tiCElAACwUQncAADQkcANAAAdCdwAANCRwA0AAB0J3AAA0JHADQAAHQncAADQ0f8H+b1w/BRkQ18AAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "percentiles = [1] + list(range(5,55,5))\nvalues = np.percentile(at_risk, percentiles)\ni = 0\nfor percentile in percentiles:\n    print(('There is a {:,.0%} chance that the end balance will be ${:,.2f}').format((100-percentile)/100,values[i]))\n    i = i + 1",
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "text": "There is a 99% chance that the end balance will be $-255,227.81\nThere is a 95% chance that the end balance will be $-180,322.94\nThere is a 90% chance that the end balance will be $-139,725.19\nThere is a 85% chance that the end balance will be $-111,959.73\nThere is a 80% chance that the end balance will be $-88,859.28\nThere is a 75% chance that the end balance will be $-69,002.56\nThere is a 70% chance that the end balance will be $-49,940.08\nThere is a 65% chance that the end balance will be $-32,613.31\nThere is a 60% chance that the end balance will be $-15,754.47\nThere is a 55% chance that the end balance will be $398.81\nThere is a 50% chance that the end balance will be $16,650.14\n",
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
  ],
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3",
      "language": "python"
    },
    "language_info": {
      "name": "python",
      "version": "3.7.3",
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      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
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    "toc": {
      "nav_menu": {},
      "number_sections": true,
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      "base_numbering": 1,
      "title_cell": "Table of Contents",
      "title_sidebar": "Contents",
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      "toc_position": {},
      "toc_section_display": true,
      "toc_window_display": false
    },
    "gist": {
      "id": "8aef035c038cd14b120c19391c429c2b",
      "data": {
        "description": "Monte Carlo Value at risk https://nbviewer.jupyter.org/gist/DBremen/8aef035c038cd14b120c19391c429c2b",
        "public": true
      }
    },
    "_draft": {
      "nbviewer_url": "https://gist.github.com/8aef035c038cd14b120c19391c429c2b"
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  "nbformat": 4,
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}