05_returns_portfolios.ipynb

{"cells":[{"attachments":{},"cell_type":"markdown","metadata":{},"source":["# Portfolio returns"]},{"cell_type":"code","execution_count":1,"metadata":{"trusted":true},"outputs":[],"source":["# Install and import pandas_datareader\n","import pandas as pd\n","import numpy as np\n","from pandas_datareader import DataReader as pdr\n","import yfinance as yf\n","pd.options.display.float_format = '{:.2f}'.format"]},{"attachments":{},"cell_type":"markdown","metadata":{},"source":["### Portfolio expected return"]},{"cell_type":"code","execution_count":2,"metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Portfolio Expected Return:\t  0.0675\n"]}],"source":["# Expected returns\n","mns = np.array([0.10, 0.05, 0.07])\n","\n","# Portfolio weights\n","wgts = np.array([0.25, 0.5, 0.25])\n","\n","#Portfolio expected return\n","port_expret = wgts @ mns\n","print(f'Portfolio Expected Return:\\t {port_expret: ,.4f}')"]},{"attachments":{},"cell_type":"markdown","metadata":{},"source":["### Portfolio risk (variance and standard deviation)"]},{"cell_type":"code","execution_count":3,"metadata":{},"outputs":[],"source":["##### Inputs\n","# Standard deviations\n","sds = np.array([0.20, 0.12, 0.15])\n","\n","# Correlations\n","corr12 = 0.3\n","corr13 = 0.3\n","corr23 = 0.3\n","\n","# Portfolio weights\n","wgts = np.array([0.25, 0.5, 0.25])"]},{"cell_type":"code","execution_count":4,"metadata":{},"outputs":[{"data":{"text/plain":["array([[0.04  , 0.0072, 0.009 ],\n","       [0.0072, 0.0144, 0.0054],\n","       [0.009 , 0.0054, 0.0225]])"]},"execution_count":4,"metadata":{},"output_type":"execute_result"}],"source":["##### Method 1 to calculate covariance matrix\n","# Covariances\n","cov12 = corr12 * sds[0] * sds[1]\n","cov13 = corr13 * sds[0] * sds[2]\n","cov23 = corr23 * sds[1] * sds[2]\n","# Covariance matrix\n","cov = np.array([[sds[0]**2,  cov12,     cov13], \\\n","                [cov12,      sds[1]**2, cov23], \\\n","                [cov13,      cov23,     sds[2]**2]])\n","cov"]},{"cell_type":"code","execution_count":5,"metadata":{},"outputs":[{"data":{"text/plain":["array([[0.04  , 0.0072, 0.009 ],\n","       [0.0072, 0.0144, 0.0054],\n","       [0.009 , 0.0054, 0.0225]])"]},"execution_count":5,"metadata":{},"output_type":"execute_result"}],"source":["##### Method 2 to calculate covariance matrix\n","# Correlation matrix\n","C  = np.identity(3)\n","C[0, 1] = C[1, 0] = corr12\n","C[0, 2] = C[2, 0] = corr13\n","C[1, 2] = C[2, 1] = corr23\n","# Covariance matrix\n","cov = np.diag(sds) @ C @ np.diag(sds)\n","cov "]},{"cell_type":"code","execution_count":6,"metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Portfolio Variance:\t  0.0118\n"]}],"source":["# Portfolio variance\n","port_var = wgts @ cov @ wgts\n","print(f'Portfolio Variance:\\t {port_var: ,.4f}')"]},{"cell_type":"code","execution_count":7,"metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["Portfolio Standard Deviation:\t  0.1085\n"]}],"source":["# Portfolio standard deviation\n","port_sd  = np.sqrt(port_var)\n","print(f'Portfolio Standard Deviation:\\t {port_sd: ,.4f}')"]},{"cell_type":"markdown","metadata":{},"source":["## Realized portfolio returns (with rebalancing to target weights)"]},{"cell_type":"code","execution_count":8,"metadata":{},"outputs":[{"name":"stderr","output_type":"stream","text":["d:\\bbcx-investments-quarto\\quarto\\venv\\lib\\site-packages\\pandas\\core\\arrays\\datetimes.py:1162: UserWarning: Converting to PeriodArray/Index representation will drop timezone information.\n","  warnings.warn(\n","d:\\bbcx-investments-quarto\\quarto\\venv\\lib\\site-packages\\pandas\\core\\arrays\\datetimes.py:1162: UserWarning: Converting to PeriodArray/Index representation will drop timezone information.\n","  warnings.warn(\n"]}],"source":["# Function to fetch a yahoo time-series\n","def returns(ticker):\n","    ret = yf.download(ticker, start='2000-01-01', end='2020-12-31', progress=False)\n","    ret.index = ret.index.to_period('D')\n","    ret = ret[\"Adj Close\"].resample(\"M\").last()\n","    ret = ret.pct_change()\n","    # ret.index = ret.index.to_period(\"M\")\n","    ret.name = ticker\n","    return ret\n","aapl = returns('AAPL')\n","ibm = returns('IBM')"]},{"cell_type":"code","execution_count":9,"metadata":{"trusted":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>IBM</th>\n","      <th>AAPL</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>2000-01</th>\n","      <td>NaN</td>\n","      <td>NaN</td>\n","    </tr>\n","    <tr>\n","      <th>2000-02</th>\n","      <td>-0.08</td>\n","      <td>0.10</td>\n","    </tr>\n","    <tr>\n","      <th>2000-03</th>\n","      <td>0.15</td>\n","      <td>0.18</td>\n","    </tr>\n","    <tr>\n","      <th>2000-04</th>\n","      <td>-0.06</td>\n","      <td>-0.09</td>\n","    </tr>\n","    <tr>\n","      <th>2000-05</th>\n","      <td>-0.04</td>\n","      <td>-0.32</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>2020-08</th>\n","      <td>0.02</td>\n","      <td>0.22</td>\n","    </tr>\n","    <tr>\n","      <th>2020-09</th>\n","      <td>-0.01</td>\n","      <td>-0.10</td>\n","    </tr>\n","    <tr>\n","      <th>2020-10</th>\n","      <td>-0.08</td>\n","      <td>-0.06</td>\n","    </tr>\n","    <tr>\n","      <th>2020-11</th>\n","      <td>0.12</td>\n","      <td>0.10</td>\n","    </tr>\n","    <tr>\n","      <th>2020-12</th>\n","      <td>0.01</td>\n","      <td>0.12</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>252 rows × 2 columns</p>\n","</div>"],"text/plain":["          IBM  AAPL\n","Date               \n","2000-01   NaN   NaN\n","2000-02 -0.08  0.10\n","2000-03  0.15  0.18\n","2000-04 -0.06 -0.09\n","2000-05 -0.04 -0.32\n","...       ...   ...\n","2020-08  0.02  0.22\n","2020-09 -0.01 -0.10\n","2020-10 -0.08 -0.06\n","2020-11  0.12  0.10\n","2020-12  0.01  0.12\n","\n","[252 rows x 2 columns]"]},"execution_count":9,"metadata":{},"output_type":"execute_result"}],"source":["# Merging time-series\n","df = pd.merge(left=ibm,right=aapl,how='inner',left_index=True,right_index=True)\n","df"]},{"cell_type":"code","execution_count":10,"metadata":{},"outputs":[{"data":{"text/plain":["0.027856068369941766"]},"execution_count":10,"metadata":{},"output_type":"execute_result"}],"source":["df.mean()\n","df.IBM.mean()\n","df.AAPL.mean()"]},{"cell_type":"code","execution_count":11,"metadata":{},"outputs":[{"data":{"text/plain":["0.07273463102565245"]},"execution_count":11,"metadata":{},"output_type":"execute_result"}],"source":["df.IBM.std()"]},{"cell_type":"code","execution_count":12,"metadata":{"trusted":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>IBM</th>\n","      <th>AAPL</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>IBM</th>\n","      <td>1.00</td>\n","      <td>0.45</td>\n","    </tr>\n","    <tr>\n","      <th>AAPL</th>\n","      <td>0.45</td>\n","      <td>1.00</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>"],"text/plain":["      IBM  AAPL\n","IBM  1.00  0.45\n","AAPL 0.45  1.00"]},"execution_count":12,"metadata":{},"output_type":"execute_result"}],"source":["df.corr()"]},{"cell_type":"code","execution_count":13,"metadata":{"trusted":true},"outputs":[{"name":"stdout","output_type":"stream","text":["Mean of  50.00% portfolio is:  1.63% (per month)\n","Mean of  75.00% portfolio is:  2.21% (per month)\n"]},{"data":{"text/plain":["<AxesSubplot:xlabel='Date'>"]},"execution_count":13,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAXAAAAEGCAYAAAB8Ys7jAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAAsTAAALEwEAmpwYAAA2pklEQVR4nO3dd3hc1bX4/e8aadR7sSTLlnuv2MKmx2B6T+gQTBLAPwIkEEgIIclL7k1yQxIgEEijE5pNaDbVgGl2AOMmufcqW713TdnvH3tkuUi2pJmRNPb6PM88Z07fc6IsttfZRYwxKKWUCj2O3i6AUkqp7tEArpRSIUoDuFJKhSgN4EopFaI0gCulVIgK78mbpaWlmcGDB/fkLZVSKuQtX768zBiTfvD2Hg3ggwcPZtmyZT15S6WUCnkisrO97ZpCUUqpEKUBXCmlQpQGcKWUClEawJVSKkRpAFdKqRClAVwppUKUBnCllApRPdoOXCmlVBc018Liv3S4W2vgSinVV9UWw6KHOtytAVwppfqqhvLD7tYArpRSfZUGcKWUClH+BnARGSUieft9akTkThFJEZGPRGSzb5kcsEIrpZSChrLD7j5iADfGbDTGTDbGTAamAg3Am8C9wEJjzAhgoW9dKaVUoDSUQ3hUh7u7mkKZCWw1xuwELgGe921/Hri0O+VTSimFbXGy+rUDtzVUQExah6d0NYBfDbzi+55hjCn0fS8CMrp4LaWUUq3yXoLXb4TGqrZtDeUQk9LhKZ0O4CISAVwM/OfgfcYYA5gOzpstIstEZFlpaWlnb6eUUseW5hq7rN8vTjaUQ0xqh6d0pQZ+HrDCGFPsWy8WkSwA37KkvZOMMU8YY3KNMbnp6YfMCKSUUgqguc4ugxTAr6EtfQIwH7jB9/0GYF4XrqWUUmp/LfV2GegALiKxwFnAG/ttfgA4S0Q2A2f61pVSSnVHS61dtgZwjwuaqiG245eYnRrMyhhTD6QetK0c2ypFKaWUv1pr4HW+AN5QYZeBeImplFIqiA5OobT2wgxQDlwppVSwHPwSUwO4UkqFiJbWAO7rPq8BXCmlQsS+AO5rka0BXCmlQsQhOXDfS8xofYmplFJ9l8cN7iYIi7RNB90tdiTCyEQIj+jwNA3gSinV21rTJ8mD7LKh7IjjoIAGcKWU6n37AvgQu6wrOWIvTNAArpRSva81/5082C7ryzSAK6VUSGhtA54y1C7rin1jgWsAV0qpvq01hZI23C5r9moOXCmlQkJrAI9Js5/yLeBqOOxAVqABXCmlel9rDjwiDhKzoTDfrmsKRSml+rhm31CykXGQOBDKNtp1DeBKKdXH7auBx0JCNhivXdcArpRSfVxrAHfGQuKAtu0awJVSqo9rqbPB2+GwOfBWGsCVUqqPa6mz+W+wOXAAcUBU0mFP0wCulFK9rbnO5r/B5sDBjkLoOHyI7uykxkki8pqIbBCR9SJyooikiMhHIrLZt0z26wcopdSxqqXeNiEEiM8ECTti+gQ6XwN/FPjAGDMamASsB+4FFhpjRgALfetKKaW6qqWuLYA7wiChf6cC+BFnpReRROA04HsAxpgWoEVELgFm+A57HvgM+HmXC66UUse65lqI69e2Pu7SwARwYAhQCjwrIpOA5cAdQIYxptB3TBGQ0d7JIjIbmA2Qk5PTidsppdQxpqkK0ka2rZ/9u06d1pkUSjgwBfiHMeY4oJ6D0iXGGAOY9k42xjxhjMk1xuSmp6d3qlBKKXVMaag84sBV7elMAC8ACowxS3zrr2EDerGIZAH4liVdvrtSSh3rPG5oroborrcDOWIAN8YUAbtFZJRv00xgHTAfuMG37QZgXpfvrpRSx7qmarvsRgDvTA4c4EfASyISAWwDvo8N/q+KyI3ATuDKLt9dKaWOdY2VdhmsAG6MyQNy29k1s8t3VEop1aaxwi6DkUJRSikVRPtq4MF5iamUUipY9gXwpC6fqgFcKaV6kx85cA3gSinVmxoqAIGoxC6fqgFcKaV6U2OlTZ84wrp8qgZwpZTqTY2V3UqfgAZwpZTqXRrAlVIqRDVWaABXSqmQpDVwpZQKUY2V3erEAxrAlVKq93g9djArrYErpVSIaayySw3gSikVYhrK7LIbkzmABnCllOo9tUV2GZ/ZrdM1gCulVG+pK7bLOA3gSikVWvbVwNudE/6INIArpVRvqSsGZwxEJnTrdA3gSinVW2oLIS4DRLp1eqemVBORHUAt4AHcxphcEUkB5gKDgR3AlcaYym6VQimljkW1xd1+gQldq4GfboyZbIxpnRvzXmChMWYEsNC3rpRSqrPqinosgB/sEuB53/fngUv9uJZSSh17aou63QIFOh/ADfChiCwXkdm+bRnGmELf9yKg3deoIjJbRJaJyLLS0tJuF1QppY4qzXXQUtftFijQyRw4cIoxZo+I9AM+EpEN++80xhgRMe2daIx5AngCIDc3t91jlFLqmNPaBjw+q9uX6FQN3Bizx7csAd4EpgHFIpIF4FuWdLsUSil1rKn1JTDiul8DP2IAF5FYEYlv/Q6cDawB5gM3+A67AZjX7VIopdTRrGA5FK87cJuf3eihcymUDOBNse0Uw4GXjTEfiMhS4FURuRHYCVzZ7VIopdTR7M3ZkDQIrn+jbVtrAPejBn7EAG6M2QZMamd7OTCz23dWSqljQUs9lG+FsMgDt5dvgaikbg8lC9oTUymlgqt4HWDaXlq2KtsE6aO73QsTNIArpVRwFa+xy4Zy8LjatpdugPRRfl1aA7hSSgVTawDHQL1vAof6MhvQ00f7dWkN4EopFUzFa9u+t6ZRSn1dadJH+nVpDeBKKRUsxtgAnuVrB1Ln6y5TutEutQaulFJ9VNUuaK6Boafb9X018I0QEQcJ2X5dXgO4UkoFS9lmuxxyml3Wt9bAfS8w/WiBAhrAlVIqeMo22WXWJIhMbEuh1OyBpBy/L68BXCmlgqVsk+2oE5MKcf3aUij1ZRCT5vflNYArpVSwlG+BtJE2VRKXYWvgHhc0VUGsBnCllOq7yjZB2gj7vbUG3lBh12NS/b68BnCllAqGxiobsFP3D+Al0ODrzBOb7vctNIArpVQwlG+xyzRfZ524DNuksHKnXdcUilJK9VGtLVBaA3hrq5O9K+1SX2IqpVQfVbLODiGbPMiutwbwPcvtUmvgSinVRxXmQ8Y4CHPa9SRfIN+7AhC/xgFvpQFcKaUCzRgbwLP2mwsnrh+ER0FjpW2B4gjz+zYawJVSKtCqdkJTNWRNbNsmAokD7fcApE+gCwFcRMJEZKWIvONbHyIiS0Rki4jMFZGIgJRIKaVCXeEqu8w6aDbK1nx4AF5gQtdq4HcA6/db/yPwF2PMcKASuDEgJVJKqVBXmA8SBv3GHbi99UVmrP+deKCTAVxEBgAXAE/51gU4A3jNd8jzwKUBKZFSSoW6wnw71rcz6sDtrQG8h2vgjwD3AF7feipQZYxx+9YLAP8GtlVKqaOBMVCYd2j6BNpaovRUDlxELgRKjDHLu3MDEZktIstEZFlpaWl3LqGUUqGjthDqS6H/5EP37Qvg/nejh87VwE8GLhaRHcAcbOrkUSBJRMJ9xwwA9rR3sjHmCWNMrjEmNz09MIVWSqk+qzDfLturgWeMhdEXwpBvBeRWRwzgxphfGGMGGGMGA1cDnxhjrgM+BS73HXYDMC8gJVJKqVC2Nw8QyJxw6D5nNFz9kt+TGbfypx34z4G7RGQLNif+dEBKpJRSoaww345/EhEb9FuFH/mQNsaYz4DPfN+3AdMCXySllAphhfkw5NQeuZX2xFRKqUCpK4Have3nv4NAA7hSSgXK4V5gBoEGcKWUAijfCm/dBi9eBmVbuneNvXl2mTnxsIcFigZwpZQCyJ8DeS/Clo9h43tdO7fWN9dlYR6kDIOohKAU8WBdeomplFJHrdpCiMsE44WyjV0795Wr7FCx1QUwsOfadmgAV0opsBMQx2dAZAKUdiGAu5rs6IPGY9en3Ryc8rVDUyhKKQVtNfC0kVC6yY5p0hkl69qCN0DW5KAUrz0awJVSCmweOz7TjiLYXG1r5J1RtNouR54LDueBkzgEmaZQlFLK47YDUMVntnVzL91o14+kaBVExMPlz0L5loDMddlZWgNXSqn6UsBAXAakjbLbOpsHL1ptxz2JiOnR2jdoAFdKKagrssv4TPuJTDh8S5RXroEFvwSvB4rWtD9wVQ/QFIpSStX68t1xmXby4bQRNh3SnvKttp141mSo3AGuesgc31MlPYDWwJVSqrbQLuMz7DJpEFTtav/YVa/aZdUuqNhuv6cOD275OqABXCmlWlucxPkCePIgqNptUyT7MwZWzbHfGyug2NcCJXlIz5TzIBrAlVKqtshONBzmtOtJOeB12e37K1ln0ybDZtr17V/YHpidaa0SBBrAlVKqrvjAINw6d2XVzgOP27PCLideZZc7v4LkwTZv3gs0gCuljm3G2BeT7Qbwg/Lge1dAZCIMnWHX3Y29lj4BbYWilDpWuZttOqRim20yeOKtbfuSBtplZTs18P6TIK4fhEfbAJ7SewFca+BKqWPT1/+Av02D12+2tejJ17XtC4+E+KwDa+DuZiheC/2n2JRJUo7dnjy4R4u9vyMGcBGJEpFvRCRfRNaKyP/4tg8RkSUiskVE5opIRPCLq5RS3VS8Dj57oG2Qqj3LISLODkR11v+0vcBslZRzYA68eI19sdn/OLue7Euz9GIKpTM18GbgDGPMJGAycK6InAD8EfiLMWY4UAncGLRSKqWUvxb+L3z2BzvpAtgWJUNnwC/2wNhLDj0+adCBAbxguV1mT/Ht99XA+3IKxVh1vlWn72OAM4DXfNufBy4NRgGVUspv1Xtg8wL7fe1b4Gq0ue+MceDoIAwm5djzPC67vuY1SB0Bib78eP8ptulhayDvBZ3KgYtImIjkASXAR8BWoMoY4/YdUgBkd3DubBFZJiLLSktLA1BkpZTqhMJ8+PxP0FIPK/5tUycZ42Htm1C6wc68029sx+enDrPplapddmCr3UtgyvVtTQYnXwt3b7D58l7SqVYoxhgPMFlEkoA3gdGdvYEx5gngCYDc3NxOjpCulFJ+KFwFz18ETdWw9CnbznvEOTD2Yph3G6x4wR6XMa7ja7R2jy/fAjsWg4TBpGva9oscmjfvYV1qhWKMqQI+BU4EkkSk9T8AA4A9gS2aUkp10/zbwRkL337Cdo8/7Wdw2ZMw5iKIToFlT0NYJKQM7fgarQG8bDNseAeGz7TNB/uQzrRCSffVvBGRaOAsYD02kF/uO+wGYF6QyqiUUp3XUm/H6J5yPUy6Cm5ZBGf8CqIS7ef8P9vj0keBI6zj68Sk2MkZCpbafHnOiT1T/i7oTAolC3heRMKwAf9VY8w7IrIOmCMivwNWAk8HsZxKKdU5hfk2v91/Svv7x18Ge1d2rv126gjY9IH9nj01YEUMlCMGcGPMKuC4drZvA6YFo1BKKdVla9+C/z4Coy6w69kdBHAROOf3nbtm6nAo+AYQ6D/Z/zIGmHalV0odHda8bmvW5dsgYUBg8tWpw+wybYRNv/Qx2pVeKRX6jIFdX9nvzdWQfUjSoHtaX2T2wfQJaABXSoWqkvWw6CEbvCu22YmJW7u5d5T/7qp03wTHfTSAawpFKRVamqptOuODe2HbZ5Cd2zbo1AUPw8oXYMLlh71Ep/UbA1f+G0acHZjrBZgGcKVU6Nj+BbzwbRh9gQ3eAF/9DWJSbZO/rMkdv7zsrvbGSekjNIArpUJDc63tRekIh3XzIDIBpsyCrx63+8df1vG4JiHK5fHyizdWd7hfA7hSKjQsfdqmSr7/AWz9xPaiHHG2bfc9+BQ44dYjXyPELNlWwWvLCzrcrwFcKRUaCpbaViGDTrSfVt97p/fKFECNLR52lNczJith37YFa4uIcnb8r4qj698bSqmjV+EqyJrU26UImme/3M6Fjy1mb1UjAF6v4aN1xXxrZHqH52gAV0r1fQ0VUL0LMif2dkmCJm9XFR6v4d1VhQCs3lNNUU0TZ4/N7PAcDeBKqb6vaJVdHsU18HWFNQC8s2ovAJ9vKkUEzhjdcY9SDeBKqb6vMN8uj9IAXt3goqCykcyEKPILqtlZXk/+7iqGpceRHNvxdMMawJVS3VO5A/Je6Zl7Fa6yU5nFpPTM/XpYa+37xzNHAPDBmiLyC6qZOODw469oAFdKdZ27BV65Ft66BbZ8HOR7NcOORW3d5I9Ca/dWA3DW2AxGZ8YzZ+luyuqamTQg6bDnaQBXSnXOlo9t0G6qhi/+DCVrISoJPvw1eD3Bu++qV+2UaLnfD949etm6whr6xUeSHh/JGaP7sb2sHoBJA5MOe54GcKVU5yx/Dja+C0+cDl/8yc4PedGjULLOBvRg8Hrhy79C5gQYenpw7tEHrCqoZlx/2/575hj70tIZJozJij/sedqRRyl1ZF4PbF8ESYOgYqvttn7xY7Zb+6Rr4LM/2DGzx18W2PuueR3KNsFlT7fNBn+UKa5pYktJHVdMHQDA5IHJJMc4GZAcQ2T4YaZ8QwO4UupwjLGBs2g1NFXZ+SQHToPEnLZxRy76KxSvhS8eDEwAL1gOsWl2gKqF/2Pbfo/7jv/X7aO+3FoGwMnD0wAIcwh/+M5E4iKPHJ6PeISIDAT+DWQABnjCGPOoiKQAc4HBwA7gSmNMZbd+gVKq71nyBCx+GG5fBts/t9uGnAbxB3UsCY+AydfBBz+3M7injYDaImgot+OVOKM7f89tn8G/Dxr979K/H3WDVO1v8eZykmKcjN2vC/254zvuvLO/zjwVN3C3MWYscAJwm4iMBe4FFhpjRgALfetKqaPFyhegthBW/we2LIT00YcG71ZjLrLLdfPA44KnzoJ/nASPTLStSDrDGPjsAYjvDxc8ZGeSv/Lf9j8aRyljDF9uLeOkYak4HF1PEXVmUuNCoND3vVZE1gPZwCXADN9hzwOfAT/vcgmUUn1P5Y623o8L/wcaK+GMX3d8fGI2DDge1r4JCf1tt/cJV9jgv+srGDqj7djyrbZmfnBOe/3b9tjz/gzH3xToX9SrNhbVEuV0MCg19oDta/fWUFjdxO2+9ElXdenfJSIyGDtD/RIgwxfcAYqwKZb2zpktIstEZFlpaWm3CqmU6mHr37bLk++0wTt7Kpx8x+HPOe56KF4D838M6WPgwr+Aw2lr763KNsNjU2HdWweeu+hheHWWPW/KrED+kl7n8nj57tNL+Nlrqw7Z98zi7cREhHHhxP7dunanA7iIxAGvA3caY2r232eMMdj8+CGMMU8YY3KNMbnp6R2PqqWU6mW7l8Lbd8Lub2DZs7bp3ox74dSfwuXPQpjz8OdPmQXn/B8YD5z2U4iMh5wTYOunbcfs+howsOO/bdta6uHzP8HIc+DmheCMCsav6zUfri2mtLaZvF1VNLna2ssXVTcxP38vV+YOJDH6CM+2A51qhSIiTmzwfskY84Zvc7GIZBljCkUkCyjpVgmUUn3Dgl/YMbeXPwsRcXDVC/YF5MzDpE72JwIn3gZTboDIOLtt2Bk2BVNbDPEZsHeF3b5nmZ1hp3CVnYzY3Qgn3g4RsR1fP0S9+PVOwhxCi8fLil2VnDTMpkv++flWvMbwg5OHdPvaR6yBi4gATwPrjTEP77drPnCD7/sNwLxul0Ip1bt2f2OD98l32kB600IbfLujNXgDDJ9pl1s+sss9vgBetAbevRueO98G+Jg0GHRSt4vfV60qqOKrbeXMPm0oDrEz7ABsKanjxa93cvW0HHJSY7p9/c7UwE8GrgdWi0ieb9t9wAPAqyJyI7ATuLLbpVBK9a7/Pmpnej/tZwcGYH9lTrRtxtfNty81i9dC6ggo3wyr5gICFdtg6vfAcfhOK6HG6zX8Zv5a0uIiuXXGMBZtLmXJ9nIAHlywkWhnGHefNdKvexyxBm6MWWyMEWPMRGPMZN/nPWNMuTFmpjFmhDHmTGNMhV8lUUr1jhX/hg3vwIk/CmzwBptWGXsxbPsUdn4JXhdMm922/7Kn7BCxU27o+Boh6q28PazYVcW9540mPsrJ9CGprNhVRWOLh8Vbyrh4cn9S4yL9usfR2zpeqVBjDKx4Af52gu35GGzuFlj8F3j3p7aZ36l3Bec+Yy4GTwss+KVdH3WeHRo2Y7ztufn/voDsKcG5dy+pa3bzh/c3MGlgEt85LhuAE4am0uL28vqKAuqa3RyXk+z3fbQrvVJ9xeKHYeH/2u/5c2wrkGB6725b+x55Hlzyt+ClMAYcDwnZdtCrqd+DxAFwxfO2tn8Ujm/S5PLw27fXUVrbzJOzcvd10Jk2OAUReGrRNgAmDzz8WN+doQFcqb7A3Qxf/wOGzbTN8DZ/BOf8Pnj32/qJDd4n/RjO/m3w7gO2G/yseWC8kD7KbhswNbj37CUV9S1c9Nhi9lQ18oOThzB5v+FgE2OcjM5MYH1hDfGR4QxN8z9dpQFcqb5g7Zu2Od1Jt0PJBtukr3InJA8K/L2MgffugdThcPp9gb9+e9JG9Mx9/LRubw2fbCjmuumDDjuV2cEeXLCR2MhwvMawp6qR575/PDNGHTqX5QlDU1hfWMPEgYnd6jp/MM2BK9WTqnbBo5Ps+Nler93WVAOLHoK0UXbM6xFn2+2bFgSnDDsW2VYgp/2sawNNHeVeX17A+X9dxIMfbuK15QWdPq+gsoG/f7aFPy3YwJOLtnHy8NR2gzfA9CGpAEecaaezNIAr1ZPy59hxRj75Hbz4Hdv7cc61tinduX+wOeHUYbZL+Qf3wtt32Bpzd+3Ns+2ta4vati1/zs6kM/aSDk46Nv1n+W6GpceSnRTNil2dH1j1pSW7AEiPi6SqwcX3Tuq4Y85Jw1PJHZTMeeOz/C4vaApFqZ5jjJ0ebNDJMPEqeP8eePpMkDD7ErG104sIzHoLPv29DbZjLoLhZ3b9fsuegXfuAgxEp8AZv4Q9y+04J7k3au17P9UNLpbuqOSWbw2loLKRr7aWY4xB2nnJureqkZ+/vopJA5K4/YzhzF26m7PGZjD7tGG8v7qQM0a3X/sGSIhy8toPA9dhSQO4Uj2laJVNXZx4G0y9wY4TsutrOwbIwcO0xmfC+Q/B5o9h0V+6HsCr99i5KoecBq5GO8xr/+PsgFHxmXDCDwP3u44Cn20qweM1zByTweqCaubl7WVPVSMDkg/sJVlU3cRFjy2mvL6F/N1VjOufQEV9C9dMy2HqoGSmDvK/aWBXaApFqZ6y9i07BVlr6iJ9lA3kHY2xHR5hX2ruXAwFy7p2rwX3gddt56yceCWUbYQ3b4F+Y2y762C8HO3jSmqbWNlOasQYw7urCkmLi2DygCSm+Npnr9hVdcixD7y/ntpmN3efNZKaJjd/WrCRxGjnvtl0epoGcKV6yvbPITsXYlI6f86UWRAeDXkvdf6cXV/b4VpP+QmkDIHRFwICzTVw8V+7dv8Q5/Uamlwefv3WGk5+4BO+/fcveeUbm7P+cmsZNz2/jDvn5vHhumKuzB2IwyGMzoonyulg+Y4DO5d/s72Ct/L2MvvUofzglCFEhDnYXlbPWWMzcIb1TijVFIpSPaGpGvautEOzdkVkPIy+wDYzPPePtlbekbVv2Zx5zV6Iz4KTfmS3J2TBcd+1Ey30P667vyCkfL6plIc+3Mj6whpSYyMpqmniuuk5FFQ2ct+btpfr459sobS2mRaPl1knDuKnZ9s26s4wBzNG9mPO0t1cPS2HMVkJ7Klq5NaXVjAwJZofzhhGbGQ4Jw5L5fNNpZw/oXPTnwWDBnClesLOr2xHliGndv3ciVfBmtdgy8cw+vy27eVboWqnHTWwaI1NkTjCoaUWLv3ngUOzXvK4/78hRFQ1tHDri8tJi4/k2mk5bCur538vGcfZ4zJpcnn4wXNL+cUbNojPnX0C47MTiT1oAuHfXjqeC/66iNteXsGHd57GXXPzaHZ5eOXm6fuOvW56DrVNrl5Ln4AGcKV6xvYvICwSBkzr+rnDTofYdNsccP182PCuzWUX5tsenD9ZC2/dYkcTvGWRbdUSmxr439DLVhdUc//8NWwvq+eec0dz9fEDAfa1FNlRVs8nG0oorm2ivsXDa9+dypj9JgoGiHKG8eSsXG5/eQVD0uKYPrT955QeH8n9F43jtpdXMGfpbpZsr+Cec0cxIiN+3zFnj8vk7HG9V/sGDeBKBZ8xdjS+gdO6N9tMmBOumQPv3gVrXrcplbItMPhUO872J7+1g19d8DDEddyELZQZY/j/5q9hV3kDg1Jjue/N1TzxxTZKa5v52TmjuPS4bG58filbS+sBOHNMxiHBu1VsZDjPfv/I/yE9c2w/EqLC+b/31gNw4YTuTXsWTBrAlQq2wjw7kNP5D3b/GgNyYfbntmXJ/lOb/eMUyH8FwiJg/Hf8Lmpf9c32ClbuquK3l4zj8qkDufWl5dQ2uclKjOL++Wv53bvrcHsNv7pgDMt2VHL32f6Nsw0QGR7GBROzeOWb3UwckOjXxAvBogFcqWBb/rxtSTLhCv+uI3LovJTjLoHi1XaI1uiebYPcU9weLw99tInU2AiuyB1IlDNsXw3aGMOnG0t4J7+Q43KSuP7EwdzUjdcMHbl0cjavfLObCyYEpudkoGkAVyoY1s2HmFSbq179Goy7FKKTAn+fCVfAl4/D8TcF/tqHsbuigUc+3syWkloev3YKA1OCUzs1xvDbd9bxzfYK/nTZRKKcBw55KyKcMTqDM0ZnBOX+04ak8Oz3jufEYX3znYIGcKUCYeP7tpXJqPNtvvvVWSAOOw62p/nAWWgCKXkw3LszONc+yJdbynhl6W6m5CTx0IebcHm8RIQ7uPyfX/LrC8dyzrjMgLaHbnJ5+OWba3h9RQE3nzqEK30vLXuSiHD6YbrG97YjBnAReQa4ECgxxoz3bUsB5gKDgR3AlcaYzo/+otTRpLkW/vN9O7N6ylCoL7e9LJMH2+aD3309JGacqW1ysam4jgnZiUSEO6iob2FjUS0nDkulyeXhntdXUVDZyNv5exmfncC/rs+lrsnNLS8u5/aXV3L22Az+df3UdscP6QxjDP9ZVsBDH21kcGos28vqKalt5o6ZI7hjZmgMR9vTOlMDfw54HPj3ftvuBRYaYx4QkXt96z8PfPGUCgHr37HB+6QfQ/kWSAfO/A2kjbTN/LrT8qSH7a5o4IZnv2FbaT0JUeHcfsZwXl1WwJaSOn44YxhNLg8FlY08fUMuACcNSyM6wqYzPr7rWzz2yWYe+XgzH60rPmLTuq2ldQxNiz0g0D/+yWZeWrKLwuomJg9MorrRxciMeB675rgOm/opENOJoSpFZDDwzn418I3ADGNMoYhkAZ8ZY0Yd6Tq5ublm2bIujumgVF9RvtVOzBvXD3Z9ZeeUzBwPeS/bcb7vyPd7irDS2mbmLt3FtdMHkdKFCQX8sW5vDd979htbyz53NAvWFrFocxmR4Q5OHZHOx+uLATh/QiZ/v679mXRcHi8X/HURFfUurpuew7urC9lRVs+w9DhevGk66fF28t7VBdVc9PhifnXBGM4dn8mizWUkRju59aUVnDI8jYsn9+fyKQMCMtnB0URElhtjcg/e3t0ceIYxptD3vQgIzhsEpfqKr/4OH//G5rMBHE7b69HdaNdPu8fv4P3pxhLumptHZYOLHeUNPHjFJP/KfLh7bShhXt4e1hfWsr28ntTYCF774UmMzIjnuuk5vLe6iMzEKKbkJPHN9grio5yMyozv8HrOMAePXHUc976xikcXbmZ0Zjw3njKE57/awY9fWckLN04jPMzBnKV2HJK/fbqFOUt3s6WkDoDRmfE8873jiQjX4Zm6wu+XmMYYIyIdVuNFZDYwGyAnJ8ff2ynV8/Ln2CnORp0Pp/8SmqrshMORCbBjsR2qddrNnbrU+sIaZj3zDaMz4/nBKUM4fVQ/mt0eXvx6F//33npGZsQzY1Q/Xl9RwHdPGHTAnIrd5fWaA2q0C9YWccuLy0mNjWTSgEROHp7GTacOoX+SHR9cRLhgYluzuc6mMMb2T2DebSdTVNNERnwUDocwMiOeu/+Tz9OLt3PDSYOZn7+XiQMSWVVQTVWji1+eP4blOyu586wRGry7QVMoSnXE64Xlz8AH99lelNe/eWg77C5webxc8vh/KaxuJDYynILKRk4alsrGolrK61uYMSqdx6+dgtcYTv/zZ5TXt3Di0FT+dPnEbjXT21vVyF8+2sS8/L08ctVkTh/Vj399sZW/f7aVsVkJvHLzCfvy2MF00/PL+HJrGVcfn8Mz/93OyzdNJ7+gmtTYiF5pWRKKOkqhdDeA/xko3+8lZoox5p4jXUcDuAoZ+XPtPJVlG2HoDLj8Wb+HYf3bp1v484KN/Ov6qcwYlc6fP9jIJxtLmJCdyBVTB3Ly8NR9L/Z2VzTw5so9PLloGw4RHr5yEjPH2ExlTZOL+MhwXB5DXbP7kFy512t4bXkBv31nHS0eL6mxETS7vQxMiSFvdxXnjc/kd5eOJzUu0q/f01m7Kxo48+HPaXZ7OWN0P56alas57i7qdgAXkVeAGUAaUAzcD7wFvArkADuxzQgrOrjEPhrAVUj45kl476eQNQlOvN12lvEzv11c08TpD37GKcPTeGLWIf8/7NCu8gZufXk5a/bUcP6ETLxe+GBtEaMz46lsaKGuyc1Hd32L5TsreWeVnUWmrsnNjvIGjh+czENXTKa+xc1Fjy1GBB675jjODdB8jF3x3y1leI3hlOFp3W5meCzzqwYeKBrAVZ+3Zzk8ORNGngtXveBXymR/d83N451VhXx817e6PKZGk8vDgws28lbeXhpa3FwxdQArd1cRHxXO0h2VjMyIY82eGrKTohneLw4DXDYlm4sm9t9X0124vpikGCdTBx07kzkcTQLdCkWp0LbhXdsBZ9hMiEu3TQRjUmDxXyAqAS57MmDBe17eHt5YuYcfnTG8WwMiRTnD+NWFY/nlBWNwe80BvR3/vGADf/vU5rTfuPWkQ7qat2pNv6ijiwZwdezZ8C7MuQ4wgEDiQKjeBTFp0FAOp95tZ8Lpgh1l9TjDHWQnRVNZ38Kv5q2hsr6FtLhIPlxXxPGDk/mxn70JRQRn2IHph1tnDMchwlXHD+wweKujlwZwdWwp2wyv3wz9J9vhXbd9CgXL4fgfQN4rdgb36bd06ZJ7qhq56LHFNLg8nDA0hW2l9ZTXtTA0PZYtJXWcNz6LX5w3OijzJsZGhnP32UdsAKaOUhrA1dGtpcHWuEefb2fEefP/2Xklr37ZzhE5YL+04vRboLHSplTaUVHfwrbSOlwew+ebSmlocZOREMVnG0vwGMN103NYsauS4f3iePzaEZpvVkGnAVwdvXb8F+bfDhXb7LyRcRn2JeXlz9rgfTBntP0cpLbJxU/m5rFwQwmt7/zDHUJMRBg1TW5E4IHvTOCq47WjmupZGsBV8BnTfjO80o1QvAbGXxa4e7mb7czsO7+EdW/ZEQFP+Yl9OYnAt37e6ZlrPF7Dku3l/P7d9WwsquW2GcOZOthOmjAlJ5nEaCcNLW6aXN4eG7dEqf1pAFeBZ4ydv9EZYwd+WvQwXPcf25ux1fYv7IvE5hqb5phyPXjc4GmBiG5MDmCMbUky/0ew60uIy7RtuE+/z87Onj3VvqQcdOIRL7WjrJ773lzN0h0VuDyG5BgnT87KbXdc6JiIcGI0dqteogFcBd6a12HZMwduW/ZMWwCv2WuDd0J/iJ1kg/3G92Bvnp0U4Y78rg3B6mqCFy61IwSGRcBlT8OEyw88ZsxFB6x6vTYXcnCPwJW7KrnuqSWEO4QfnDyEsf0TOGdcprbwUH2SBnAVWLVF8OGvbC/Gix61teJtn8GaN+CCh2xt+P17bE37mlcgKgkW/BL2LIOELJuj3vSBnYKsM7we+ODnNnif+RsY922bNumAx2uYu3Q3j3y8ibpmN6Mz4/d1Mc9IiGJ7WT1pcZHMmX3CvsGdlOqrNICrwHC32Jr3h7+Clnq46iXof5z9JPSHlS/AyhehqQbWvw0z77ez1wB8+x926fXAX8bBqrlHDuDNdTavvfxZ23b7lJ/Yz/6HuD28v7qILzaVckXuQFJiI/j1W2v4ZkcFxw9OZlz/RNYV1vD1tnLG909kQ1EtTS4PL980XYO3CgkawFX3uVtsjbl8C3z+R6jebYdZ/c5T0G9023EDT4B+42zNG2DSNXDSj1m2o4JNxXVcdfxAwhwCjjCb+vj6H1BbDPEd9B5sqICnz7L3HXORrXWPvRSAouom3s7fy47yehasLaKsroWIcAdvrNwDQHxkOH++fCKXTx1wyJgcbo+XRpeH+KjA9MBUKtg0gKvucTfDC9+Gnf+165kT4cJHYPhMGl1eHn1/AwnR4UzJSearreXMuvptUnctgKYamqbcyP1vrmPust0AvLt6L8PT4yira2Fi1EnM5p/IU2fCFc/BgINmgHE1wdzroWo3zJoHQ2fg8nj50/sbWLylnM3Ftbi9hoSocKYNSeH6EweTOyiZpxZtJzxMuHZaDskdtBgJD3MQH4TONkoFiw5mpbqudKNNlWz+EM79o23hkT2VmhYPH6wu4slF29jsm2mlVe6gZF66eTrbSuv51VtrWL6zklu+NYz+SVE88P4Gwh1CcmwEO8sb+OMJLVy1436oL4NrXrbDuZast/n1RQ/BjkWYbz/B+vTzWLqjggVri/hyazmnjkhjQnYi10zL6db42Ur1VToaoeqaiu3w2QOwd6Xtdu512/FBaovsS8bwaBpO+xVfpl1BXbObD9YU8cnGElrcXoakxfKbi8eREhPBtjLbc/Gn/8nHGSa4PIa4yHD+eNnEfbO+GGMQEYwx/GRuHvPz9/L4xf05f8UPoXS97YBTZ+dlxBFO0RkPc0v+cPJ2VwEQ5XTwm4vGcfU07Uijjk4awI9FXg+UbrC54ortkDwIRp5nm+jVFkNknG0V0srdYluMfPWYbacdHgWDToKSDRAeCU3VIA5apt7IO5EX8NtPiqlscAGQFhfBhRP7c+lx2UwakHhIfnnB2iJW7qoiJdbJVbk5JMa0n2eua3Zz43NLWbK9gu9PTeLerDwi93xNado0SmKG83WJkz8tdREbGc6dZ47grLEZ+6bvUupopQH8WOJugd1fw4L7oGj1gfucMZA6HIpW2Y4tJ//YLhc9aLucA574AWzofwlzXDNYWR2NM8xBfbObxGgnToewcnc1jS4PkwYm8fNzRpEQ7WR0ZjzhAcofuz1eHvxwE//6YisxzjASop0UVjft23/RpP78+sIx9IvvQltxpUKYBvBQ5/XCzsW2XXXWROg/5cDu6bVF9oXipgWY9e8grnpqnWm8HH0d2yOGs9WVztSIHcxkKf2bt7LaOZGxzfnk1OUDUBk7jBUJp7O6IZV/lIyj2YSTFhfJuP4JeLyG2MgwKupbaGjxcPzgFM6fkEXuoOSg1nyX76xkXt4eKhtcHD84meH94ugXH8XwfnFBu6dSfVHfCeBLvsZVtBZn6hA7cP5+XK4WWpqbiY3r2ljMRyVjKM17j+qNX+BtaaJfwQcktRTt212VMBJHXAaOpgq8UcnE7f0KBx7qJJZ3PSfwqXsCXzKRkQOzcIgQFxVOUXUTW0vraHZ76Z8YRVldM6meMrKknHwzjLjoKHJSYjh9dD/OGpPB+OwEnf5KqT6gTwTwccMHmEWznKR47fSZa+JPpWrwOTj3fIPxuBla/TWCl8LL5jNxwqQeK1dv8noNtc1uqhtcVDe6qKuuoGXbIrJXPc5w10YAPEb40kxkadI5VCVPILZwCec3vYMDQ7lJIEsq+MQ7hRXxM2hKGcOwzGRGZ8Zzyoi0QzqkGGNodnuJcoZR0+Ri1e5qSuuamJqT0q3ZYpRSwReUAC4i5wKPAmHAU8aYBw53/KjB/c1zN42lPOccIqu3c3LZa8RIMzXE4sLJ3piRDGpYR6lJ4KOMm4kZdByJGTk4w8PZ+s0HIA6i4xNxlG3CUb6JhvAkmqIziGgqw5U0DGdiJpFxycSmD6K0pJDywh14q/eS5C4lyVOBiYjDE5WEs7mKiMhoYuPiiUjKwjFwGukZ/YlyhhMR7iA5xsnm4lrK6ppxOBykxUUiYoOtxxg8XvspLSulvnQXxtWEcTXidTXhbWnEuOwnWlxESQviasK4mxBPEw53E2GeJuLC3ESYZuK91QyWImJoJgI3TvEAUCTprBs2m4zTvk90pJOctIR9OWav1/D19nIaWzxEO8OobHAxbUgK6fE9M8u4UqpnBTyAi0gYsAk4CygAlgLXGGPWdXTO1Nxcs2zp0n3/LK8v30Nt0XYyRp+AhNk+RdXrP8X52vXEeGr3nddsnESK64BruQknHHeny+vFgQNvh/sbTCQuwnDiIRw3Eb5A6jWCBwdeBK9v6cGBQUiUhi7cX3BLBG5HJG5HJC1il+6IBOrihiBR8TgjogmPTSI8YzRZU85HwjUgK6WCM6nxNGCLMWab7wZzgEuADgO42OP2rcemZhObmn3AMYljTof7tsOeFbSUbKK2ZCfu+gpSx59JeGSsHWcjfRThSYPs7Cn1pXbI0rLN0FiJu66c+rKdxCX3IywxG+KzID4LR1w/O4ltcw1Ep4DXBS0NNJfvoGbrEprKdmE8blyEU+8WEuNjiI+MwOv10NTSAsaLA4MDD2IMDrzUJGcRnzkcccbYpnnh0b6l7+OM3rd0hEUQIYKOPKqUChR/Ang2sHu/9QJg+sEHichsYDZATk4nO1qEOSFnOhE500k93HFx6W3TX8WmAfYHJXZ0fHSS/exbTyYyMZv0oSd3rlxKKdWHBH3gB2PME8aYXGNMbnp6+3MNKqWU6jp/AvgeYOB+6wN825RSSvUAfwL4UmCEiAwRkQjgamB+YIqllFLqSLqdAzfGuEXkdmABthnhM8aYtQErmVJKqcPyazxwY8x7wHsBKotSSqku0NHrlVIqRGkAV0qpEKUBXCmlQlSPDmYlItXAZj8ukQhUh/D5aUBZL94/1M/X56fP71h9foOMMYd2pDHG9NgHeOIYP39ZiJe/t8/X56fP75h9fu19ejqF8vYxfr6/erv8vX2+v3q7/L19vr96u/y9fb6/An7/Hk2hHOtEZJlpZ0Qx1Tn6/Pyjz88/ffH56UvMnvVEbxcgxOnz848+P//0ueenNXCllApRWgNXSqkQpQFcKaVClAZwP4jIQBH5VETWichaEbnDtz1FRD4Skc2+ZbJvu4jIX0Vki4isEpEpB10vQUQKROTx3vg9PS2Qz09E/igia3yfq3rrN/Wkbjy/0SLylYg0i8hP27lemIisFJF3evq39IZAPj8RucP3t7dWRO7sqd+gAdw/buBuY8xY4ATgNhEZC9wLLDTGjAAW+tYBzgNG+D6zgX8cdL3fAl/0RMH7iIA8PxG5AJgCTMbOCvVTEUnowd/RW7r6/CqAHwMPdnC9O4D1wS1ynxKQ5yci44GbsdNMTgIuFJHhPfEDNID7wRhTaIxZ4ftei/3jz8bODfq877DngUt93y8B/m2sr4EkEckCEJGpQAbwYc/9gt4VwOc3FvjCGOM2xtQDq4Bze+6X9I6uPj9jTIkxZingOvhaIjIAuAB4Kvgl7xsC+PzGAEuMMQ3GGDfwOfCd4P8CDeABIyKDgeOAJUCGMabQt6sIG5ih/XlEs0XEATwEHPLP2mOFP88PyAfOFZEYEUkDTufA2aKOep18fofzCHAP4A1G+fo6P5/fGuBUEUkVkRjgfHro78+v8cCVJSJxwOvAncaYGhHZt88YY0TkSG01bwXeM8YU7H/uscLf52eM+VBEjge+BEqBrwBPEIvcp/j7/ETkQqDEGLNcRGYEs6x9UQD+/taLyB+x/3quB/Loob8/rYH7SUSc2P/xXzLGvOHbXLxfaiQLKPFt72ge0ROB20VkBza/NktEHuiB4ve6AD0/jDG/N8ZMNsacBQiwqSfK39u6+Pw6cjJwse/vbw5whoi8GKQi9ykBen4YY542xkw1xpwGVNJDf38awP0g9j/VTwPrjTEP77drPnCD7/sNwLz9ts/ytaY4Aaj25eGuM8bkGGMGY9Mo/zbG3MtRLlDPz9d6ItV3zYnARI6BdwndeH7tMsb8whgzwPf3dzXwiTHmu0Eocp8SqOfnu1Y/3zIHm/9+ObCl7UCgR8c6lj7AKYDBvjTL833OB1Kxb683Ax8DKb7jBfgbsBVYDeS2c83vAY/39m8LpecHRAHrfJ+vgcm9/dv66PPLxL43qAGqfN8TDrrmDOCd3v5tofb8gEW+v798YGZP/QbtSq+UUiFKUyhKKRWiNIArpVSI0gCulFIhSgO4UkqFKA3gSikVojSAq6OWiHhEJM83Qly+iNztG7bgcOcMFpFre6qMSvlDA7g6mjUa2ztzHHAWdjTD+49wzmBAA7gKCdoOXB21RKTOGBO33/pQYCmQBgwCXgBifbtvN8Z8KSJfY0eX244die6vwAPYDi6RwN+MMf/qsR+h1GFoAFdHrYMDuG9bFTAKqAW8xpgmERkBvGKMyfUN5vRTY8yFvuNnA/2MMb8TkUjgv8AVxpjtPfhTlGqXjkaojlVO4HERmYwdOW5kB8edDUwUkct964nYCSU0gKtepwFcHTN8KRQPdnS5+4Fi7AwqDqCpo9OAHxljFvRIIZXqAn2JqY4JIpIO/BM7UJjB1qQLjTFe4HogzHdoLRC/36kLgB/6hh1FREaKSCxK9QFaA1dHs2gRycOmS9zYl5atw4b+HXhdRGYBH2AH4gc7Mp1HRPKB54BHsS1TVviGHy2lbYo3pXqVvsRUSqkQpSkUpZQKURrAlVIqRGkAV0qpEKUBXCmlQpQGcKWUClEawJVSKkRpAFdKqRD1/wMIu+vdVRr9SAAAAABJRU5ErkJggg==","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":["# How would different portfolios of AAPL and IBM have fared?\n","\n","wgt = 0.5\n","df['retp'] = wgt*df.AAPL + (1-wgt)*df.IBM\n","df['cumretp'] = (1+df['retp']).cumprod()\n","print(f'Mean of {wgt: .2%} portfolio is: {df.retp.mean(): .2%} (per month)')\n","df.cumretp.plot()\n","\n","\n","wgt = 0.75\n","df['retp'] = wgt*df.AAPL + (1-wgt)*df.IBM\n","df['cumretp'] = (1+df['retp']).cumprod()\n","print(f'Mean of {wgt: .2%} portfolio is: {df.retp.mean(): .2%} (per month)')\n","df.cumretp.plot()\n"]}],"metadata":{"kernelspec":{"display_name":"Python 3.10.6 ('venv': venv)","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.10.6"},"vscode":{"interpreter":{"hash":"cc788b38d8cb434c82f45ef9d481d0310e17b79321e4c8cbfbfe90f656a3f023"}}},"nbformat":4,"nbformat_minor":4}