001-basic-of-returns.ipynb

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   "source": [
    "2+2"
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  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "764ffc06",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d1d3b8b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "prices_a = np.array([8.70, 8.91, 8.71])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bd7319e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8.7 , 8.91, 8.71])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "69831dd2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.02413793, -0.02244669])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices_a[1:]/prices_a[:-1] - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "04b2e552",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b3dc5c2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "prices = pd.DataFrame({\"BLUE\": [8.70, 8.91, 8.71, 8.43, 8.73],\n",
    "                       \"ORANGE\": [10.66, 11.08, 10.71, 11.59, 12.11]})"
   ]
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       "   BLUE  ORANGE\n",
       "0  8.70   10.66\n",
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    "prices"
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   "execution_count": 9,
   "id": "2512fdf9",
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   ],
   "source": [
    "prices.shift(1)"
   ]
  },
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       "       BLUE    ORANGE\n",
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   ],
   "source": [
    "prices/prices.shift(1) -1"
   ]
  },
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     "metadata": {},
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   "source": [
    "prices.pct_change()"
   ]
  },
  {
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   "id": "91f82a89",
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      "text/plain": [
       "      BLUE   ORANGE\n",
       "0   8.7000  10.6600\n",
       "1   8.9055  11.0828\n",
       "2   8.7113  10.7100\n",
       "3   8.4346  11.5907\n",
       "4   8.7254  12.1070\n",
       "5   9.0551  11.7876\n",
       "6   8.9514  11.2078\n",
       "7   9.2439  12.5192\n",
       "8   9.1276  13.3624\n",
       "9   9.3976  14.4080\n",
       "10  9.4554  11.9837\n",
       "11  9.5704  12.2718\n",
       "12  9.7728  11.5892"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prices = pd.read_csv('data/sample_prices.csv')\n",
    "prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "cc3d7fe2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prices.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fca9e462",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4a0b58fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "returns = prices.pct_change()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "995cec30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "returns.plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "3f4bb51d",
   "metadata": {},
   "outputs": [
    {
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       "       BLUE    ORANGE\n",
       "0       NaN       NaN\n",
       "1  0.023621  0.039662\n",
       "2 -0.021807 -0.033638\n",
       "3 -0.031763  0.082232\n",
       "4  0.034477  0.044544"
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     "metadata": {},
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    "returns.head()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2e10fbad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.023977\n",
       "ORANGE    0.079601\n",
       "dtype: float64"
      ]
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     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
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    "returns.std()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "43d738be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.01\n",
       "ORANGE    0.01\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "628ca6cc",
   "metadata": {},
   "outputs": [
    {
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       "      <th>5</th>\n",
       "      <td>0.037786</td>\n",
       "      <td>-0.026381</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.011452</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.032676</td>\n",
       "      <td>0.117008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.012581</td>\n",
       "      <td>0.067353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.029581</td>\n",
       "      <td>0.078249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.006151</td>\n",
       "      <td>-0.168261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.012162</td>\n",
       "      <td>0.024041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.021149</td>\n",
       "      <td>-0.055623</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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       "        BLUE    ORANGE\n",
       "0        NaN       NaN\n",
       "1   0.023621  0.039662\n",
       "2  -0.021807 -0.033638\n",
       "3  -0.031763  0.082232\n",
       "4   0.034477  0.044544\n",
       "5   0.037786 -0.026381\n",
       "6  -0.011452 -0.049187\n",
       "7   0.032676  0.117008\n",
       "8  -0.012581  0.067353\n",
       "9   0.029581  0.078249\n",
       "10  0.006151 -0.168261\n",
       "11  0.012162  0.024041\n",
       "12  0.021149 -0.055623"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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    "returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "936526ca",
   "metadata": {},
   "outputs": [
    {
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       "      <th>2</th>\n",
       "      <td>0.978193</td>\n",
       "      <td>0.966362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.968237</td>\n",
       "      <td>1.082232</td>\n",
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       "      <th>4</th>\n",
       "      <td>1.034477</td>\n",
       "      <td>1.044544</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.037786</td>\n",
       "      <td>0.973619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.988548</td>\n",
       "      <td>0.950813</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1.032676</td>\n",
       "      <td>1.117008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.987419</td>\n",
       "      <td>1.067353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.029581</td>\n",
       "      <td>1.078249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.006151</td>\n",
       "      <td>0.831739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.012162</td>\n",
       "      <td>1.024041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.021149</td>\n",
       "      <td>0.944377</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        BLUE    ORANGE\n",
       "0        NaN       NaN\n",
       "1   1.023621  1.039662\n",
       "2   0.978193  0.966362\n",
       "3   0.968237  1.082232\n",
       "4   1.034477  1.044544\n",
       "5   1.037786  0.973619\n",
       "6   0.988548  0.950813\n",
       "7   1.032676  1.117008\n",
       "8   0.987419  1.067353\n",
       "9   1.029581  1.078249\n",
       "10  1.006151  0.831739\n",
       "11  1.012162  1.024041\n",
       "12  1.021149  0.944377"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "returns + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "27b1d4d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.123310\n",
       "ORANGE    0.087167\n",
       "dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.prod(returns + 1) - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1450057a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      0.123310\n",
       "ORANGE    0.087167\n",
       "dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(returns + 1).prod() - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e6475cbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      12.331034\n",
       "ORANGE     8.716698\n",
       "dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((returns + 1).prod() - 1) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ae75fdd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BLUE      12.33\n",
       "ORANGE     8.72\n",
       "dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(((returns + 1).prod() - 1) * 100).round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a86c1fd",
   "metadata": {},
   "source": [
    "## Annualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c8f5eb8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "rm = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f621a4bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12682503013196977"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1 + rm) ** 12 - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b98145cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "rq = 0.04"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d0dc0cfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1698585600000002"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1 + rq) ** 4 - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "eb23808a",
   "metadata": {},
   "outputs": [],
   "source": [
    "rd = 0.0001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "9f974883",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.025518911987694626"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1 + rd) ** 252 - 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8def35d2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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