JannesKlaas/Corp_Fin.ipynb

## Corp_Fin.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('Book1.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>NetInflows</th>\n",
       "      <th>NegativeCosts</th>\n",
       "      <th>Return</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>76.8</td>\n",
       "      <td>28.2</td>\n",
       "      <td>1.72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>56.8</td>\n",
       "      <td>25.4</td>\n",
       "      <td>1.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>47.3</td>\n",
       "      <td>22.6</td>\n",
       "      <td>1.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>47.0</td>\n",
       "      <td>21.2</td>\n",
       "      <td>1.22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>44.4</td>\n",
       "      <td>35.3</td>\n",
       "      <td>0.26</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   NetInflows  NegativeCosts  Return\n",
       "0        76.8           28.2    1.72\n",
       "1        56.8           25.4    1.24\n",
       "2        47.3           22.6    1.10\n",
       "3        47.0           21.2    1.22\n",
       "4        44.4           35.3    0.26"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a226f1ac8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.Return.plot.hist(bins=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df.Return.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.08242424242424241"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.206635769660599"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_d = np.linspace(np.min(x)-1, np.max(x)+1, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KernelDensity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KernelDensity(algorithm='auto', atol=0, bandwidth=0.5, breadth_first=True,\n",
       "       kernel='gaussian', leaf_size=40, metric='euclidean',\n",
       "       metric_params=None, rtol=0)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kde = KernelDensity(bandwidth=0.5, kernel='gaussian')\n",
    "kde.fit(x[:, None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# score_samples returns the log of the probability density\n",
    "logprob = kde.score_samples(x_d[:, None])\n",
    "plt.fill_between(x_d, np.exp(logprob), alpha=0.5)\n",
    "plt.plot(x, np.full_like(x, 0), '|k', markeredgewidth=1)\n",
    "plt.xlabel('Return')\n",
    "plt.ylabel('Probability');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "returns = kde.sample(10000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "returns[returns > 1.5] = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#returns = returns[(returns >= -1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_cash = (returns+1) * 22.6/1.0532 - 22.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6092907657051607"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(r_cash.clip(min=0))/1.0532**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2050020., 1310934., 1209468.,  972388.,  715374.,  520643.,\n",
       "         406135.,  348829.,  311597.,  267591.]),\n",
       " array([-1.00000000e+00, -7.50000085e-01, -5.00000169e-01, -2.50000254e-01,\n",
       "        -3.38036657e-07,  2.49999577e-01,  4.99999493e-01,  7.49999408e-01,\n",
       "         9.99999324e-01,  1.24999924e+00,  1.49999915e+00]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(returns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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