Multi-Asset Efficient frontier & Global Sharpe Ratio.ipynb

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   "source": [
    "### Part I. Use the Fama-French “48 Industry Portfolios,” which are available on Ken French’s data library. Use the set of monthly returns for value weighted portfolios in the past 20 years, that is since January 2002. \n",
    "\n",
    "Pick your favorite ten industries and plot the efficient frontier using those industries as the universe of risky assets and do a mMlti-Asset Efficient Frontier Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "62f677bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "# Import libraries for data manipulation\n",
    "# these two lines of code usually help to get the code running again. its called a magic function.\n",
    "# use this when your code downloads external packages\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fdd97030",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the data\n",
    "ret = pd.read_csv(\"Average Value Weighted Returns -- Monthly.csv\", \n",
    "                  header=0, index_col=0)/100\n",
    "\n",
    "# Convert index from Year-month period (this is how the data is imported) to monthly returns \n",
    "# Q: What if we don't do this? isn't the data in yearly period already? \n",
    "ret.index = pd.to_datetime(ret.index, format=\"%Y%m\").to_period(\"M\")\n",
    "# file has header in row 1 \n",
    "\n",
    "# remove spaces in column name (we know this because it is the same data)\n",
    "ret.columns = ret.columns.str.strip()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9dfeb17c",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Agric</th>\n",
       "      <th>Food</th>\n",
       "      <th>Soda</th>\n",
       "      <th>Beer</th>\n",
       "      <th>Smoke</th>\n",
       "      <th>Toys</th>\n",
       "      <th>Fun</th>\n",
       "      <th>Books</th>\n",
       "      <th>Hshld</th>\n",
       "      <th>Clths</th>\n",
       "      <th>...</th>\n",
       "      <th>Boxes</th>\n",
       "      <th>Trans</th>\n",
       "      <th>Whlsl</th>\n",
       "      <th>Rtail</th>\n",
       "      <th>Meals</th>\n",
       "      <th>Banks</th>\n",
       "      <th>Insur</th>\n",
       "      <th>RlEst</th>\n",
       "      <th>Fin</th>\n",
       "      <th>Other</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1926-07</th>\n",
       "      <td>0.0237</td>\n",
       "      <td>0.0012</td>\n",
       "      <td>-0.9999</td>\n",
       "      <td>-0.0519</td>\n",
       "      <td>0.0129</td>\n",
       "      <td>0.0865</td>\n",
       "      <td>0.0250</td>\n",
       "      <td>0.5021</td>\n",
       "      <td>-0.0048</td>\n",
       "      <td>0.0808</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0770</td>\n",
       "      <td>0.0192</td>\n",
       "      <td>-0.2379</td>\n",
       "      <td>0.0007</td>\n",
       "      <td>0.0187</td>\n",
       "      <td>0.0461</td>\n",
       "      <td>-0.0054</td>\n",
       "      <td>0.0289</td>\n",
       "      <td>-0.0577</td>\n",
       "      <td>0.0520</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-08</th>\n",
       "      <td>0.0223</td>\n",
       "      <td>0.0268</td>\n",
       "      <td>-0.9999</td>\n",
       "      <td>0.2703</td>\n",
       "      <td>0.0650</td>\n",
       "      <td>0.1681</td>\n",
       "      <td>-0.0076</td>\n",
       "      <td>0.4298</td>\n",
       "      <td>-0.0358</td>\n",
       "      <td>-0.0251</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.0238</td>\n",
       "      <td>0.0485</td>\n",
       "      <td>0.0539</td>\n",
       "      <td>-0.0075</td>\n",
       "      <td>-0.0013</td>\n",
       "      <td>0.1183</td>\n",
       "      <td>0.0257</td>\n",
       "      <td>0.0530</td>\n",
       "      <td>0.0032</td>\n",
       "      <td>0.0676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-09</th>\n",
       "      <td>-0.0057</td>\n",
       "      <td>0.0158</td>\n",
       "      <td>-0.9999</td>\n",
       "      <td>0.0402</td>\n",
       "      <td>0.0126</td>\n",
       "      <td>0.0833</td>\n",
       "      <td>0.0642</td>\n",
       "      <td>-0.0491</td>\n",
       "      <td>0.0073</td>\n",
       "      <td>-0.0051</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.0554</td>\n",
       "      <td>0.0008</td>\n",
       "      <td>-0.0787</td>\n",
       "      <td>0.0025</td>\n",
       "      <td>-0.0056</td>\n",
       "      <td>-0.0175</td>\n",
       "      <td>0.0072</td>\n",
       "      <td>-0.0306</td>\n",
       "      <td>-0.0481</td>\n",
       "      <td>-0.0386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-10</th>\n",
       "      <td>-0.0046</td>\n",
       "      <td>-0.0368</td>\n",
       "      <td>-0.9999</td>\n",
       "      <td>-0.0331</td>\n",
       "      <td>0.0106</td>\n",
       "      <td>-0.0140</td>\n",
       "      <td>-0.0509</td>\n",
       "      <td>0.0537</td>\n",
       "      <td>-0.0468</td>\n",
       "      <td>0.0012</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.0508</td>\n",
       "      <td>-0.0262</td>\n",
       "      <td>-0.1538</td>\n",
       "      <td>-0.0220</td>\n",
       "      <td>-0.0411</td>\n",
       "      <td>-0.1182</td>\n",
       "      <td>-0.0428</td>\n",
       "      <td>-0.0574</td>\n",
       "      <td>-0.0094</td>\n",
       "      <td>-0.0849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1926-11</th>\n",
       "      <td>0.0675</td>\n",
       "      <td>0.0626</td>\n",
       "      <td>-0.9999</td>\n",
       "      <td>0.0729</td>\n",
       "      <td>0.0455</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0182</td>\n",
       "      <td>-0.0640</td>\n",
       "      <td>-0.0054</td>\n",
       "      <td>0.0187</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0384</td>\n",
       "      <td>0.0161</td>\n",
       "      <td>0.0467</td>\n",
       "      <td>0.0652</td>\n",
       "      <td>0.0433</td>\n",
       "      <td>-0.0297</td>\n",
       "      <td>0.0358</td>\n",
       "      <td>0.0221</td>\n",
       "      <td>0.0513</td>\n",
       "      <td>0.0400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 48 columns</p>\n",
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      "text/plain": [
       "          Agric    Food    Soda    Beer   Smoke    Toys     Fun   Books  \\\n",
       "1926-07  0.0237  0.0012 -0.9999 -0.0519  0.0129  0.0865  0.0250  0.5021   \n",
       "1926-08  0.0223  0.0268 -0.9999  0.2703  0.0650  0.1681 -0.0076  0.4298   \n",
       "1926-09 -0.0057  0.0158 -0.9999  0.0402  0.0126  0.0833  0.0642 -0.0491   \n",
       "1926-10 -0.0046 -0.0368 -0.9999 -0.0331  0.0106 -0.0140 -0.0509  0.0537   \n",
       "1926-11  0.0675  0.0626 -0.9999  0.0729  0.0455  0.0000  0.0182 -0.0640   \n",
       "\n",
       "          Hshld   Clths  ...   Boxes   Trans   Whlsl   Rtail   Meals   Banks  \\\n",
       "1926-07 -0.0048  0.0808  ...  0.0770  0.0192 -0.2379  0.0007  0.0187  0.0461   \n",
       "1926-08 -0.0358 -0.0251  ... -0.0238  0.0485  0.0539 -0.0075 -0.0013  0.1183   \n",
       "1926-09  0.0073 -0.0051  ... -0.0554  0.0008 -0.0787  0.0025 -0.0056 -0.0175   \n",
       "1926-10 -0.0468  0.0012  ... -0.0508 -0.0262 -0.1538 -0.0220 -0.0411 -0.1182   \n",
       "1926-11 -0.0054  0.0187  ...  0.0384  0.0161  0.0467  0.0652  0.0433 -0.0297   \n",
       "\n",
       "          Insur   RlEst     Fin   Other  \n",
       "1926-07 -0.0054  0.0289 -0.0577  0.0520  \n",
       "1926-08  0.0257  0.0530  0.0032  0.0676  \n",
       "1926-09  0.0072 -0.0306 -0.0481 -0.0386  \n",
       "1926-10 -0.0428 -0.0574 -0.0094 -0.0849  \n",
       "1926-11  0.0358  0.0221  0.0513  0.0400  \n",
       "\n",
       "[5 rows x 48 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Inspect the head and tail of the data, \"mydata.head() or mydata.tail()\"\n",
    "# pd.read_csv(\"path or dataname\", header=0, index_col=0)\n",
    "\n",
    "ret.tail()\n",
    "ret.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1087d7f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "384"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We want to build assets for a whole potfolio,find the efficient frontier, using\n",
    "# we need vector of expected returmns, covariance matrix \n",
    "# this calculates the number of rows only\n",
    "ret[\"1992\":].shape[0]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92afac8e",
   "metadata": {},
   "source": [
    "# Calculate the expected annual return and volatility of the portfolio  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "16df63e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# mydata[\"1992\":].shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7a85beca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "48"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ret[\"1992\":].shape\n",
    "ret[\"1992\":].shape[1]"
   ]
  },
  {
   "cell_type": "raw",
   "id": "424161bf",
   "metadata": {},
   "source": [
    "Notes: \n",
    "\n",
    "- mydata[\"1992\":].shape[0] returns the length of the matrix or counts the number of rows and mydata[\"1992\":].shape[1] counts the number of columns while  \"mydata[\"1992\":].shape\" returns the dim. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f617d5e5",
   "metadata": {},
   "source": [
    "## Calulate and visualize returns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "69352002",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calulate the number of years from 1992. The data starts from 1926, we filter the most recent 20 years of returns\n",
    "n_years=ret[\"1992\":].shape[0]/12 \n",
    "\n",
    "# Cal the E(R) using the formula  \" (1+R)^1/n_years -1 \"\n",
    "eret=((1+ret[\"1992\":]).prod())**(1/n_years)-1\n",
    "\n",
    "# Look at the top returns for the first 5 industries \n",
    "eret.head()\n",
    "\n",
    "# Sort and plot returns\n",
    " # eret.sort_values() ~ this sorts the returns \n",
    "eret.sort_values().plot.bar(figsize=(10,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa3e6dbd",
   "metadata": {},
   "source": [
    "## Calculate the volatility of the portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "daed0071",
   "metadata": {},
   "outputs": [],
   "source": [
    "# The diagonal of the covariance matrix is the SD or the average volatility of each industry\n",
    "cov=ret[\"1992\":].cov()*12\n",
    "# cov\n",
    "\n",
    "# cov.shape - dim of the covariance matrix "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "b259f569",
   "metadata": {},
   "source": [
    "## Part II.\tMulti-Asset Efficient Frontier Analysis: (15%) Pick your favorite ten industries and plot the efficient frontier using those industries as the universe of risky assets. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "2e459ae8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Agric    0.097653\n",
       "Food     0.080716\n",
       "Soda     0.115073\n",
       "Beer     0.099680\n",
       "Smoke    0.103592\n",
       "Toys     0.030835\n",
       "Fun      0.111984\n",
       "Books    0.068876\n",
       "Hshld    0.093361\n",
       "Clths    0.090767\n",
       "dtype: float64"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l= [\"Agric\", \"Food\", \"Soda\", \"Beer\", \"Smoke\", \"Toys\", \"Fun\", \"Books\", \"Hshld\", \"Clths\"]\n",
    "\n",
    "# Calculate the E(R)\n",
    "eret[l]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "1d64fe9d",
   "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>Agric</th>\n",
       "      <th>Food</th>\n",
       "      <th>Soda</th>\n",
       "      <th>Beer</th>\n",
       "      <th>Smoke</th>\n",
       "      <th>Toys</th>\n",
       "      <th>Fun</th>\n",
       "      <th>Books</th>\n",
       "      <th>Hshld</th>\n",
       "      <th>Clths</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Agric</th>\n",
       "      <td>0.046055</td>\n",
       "      <td>0.009700</td>\n",
       "      <td>0.009953</td>\n",
       "      <td>0.008375</td>\n",
       "      <td>0.010668</td>\n",
       "      <td>0.017564</td>\n",
       "      <td>0.022171</td>\n",
       "      <td>0.019004</td>\n",
       "      <td>0.008521</td>\n",
       "      <td>0.016928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Food</th>\n",
       "      <td>0.009700</td>\n",
       "      <td>0.018775</td>\n",
       "      <td>0.014645</td>\n",
       "      <td>0.013834</td>\n",
       "      <td>0.016591</td>\n",
       "      <td>0.013491</td>\n",
       "      <td>0.013809</td>\n",
       "      <td>0.013156</td>\n",
       "      <td>0.012084</td>\n",
       "      <td>0.014434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Soda</th>\n",
       "      <td>0.009953</td>\n",
       "      <td>0.014645</td>\n",
       "      <td>0.053101</td>\n",
       "      <td>0.020730</td>\n",
       "      <td>0.015570</td>\n",
       "      <td>0.019399</td>\n",
       "      <td>0.024218</td>\n",
       "      <td>0.019795</td>\n",
       "      <td>0.017288</td>\n",
       "      <td>0.021368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Beer</th>\n",
       "      <td>0.008375</td>\n",
       "      <td>0.013834</td>\n",
       "      <td>0.020730</td>\n",
       "      <td>0.025130</td>\n",
       "      <td>0.013791</td>\n",
       "      <td>0.012605</td>\n",
       "      <td>0.013570</td>\n",
       "      <td>0.011413</td>\n",
       "      <td>0.015548</td>\n",
       "      <td>0.013191</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Smoke</th>\n",
       "      <td>0.010668</td>\n",
       "      <td>0.016591</td>\n",
       "      <td>0.015570</td>\n",
       "      <td>0.013791</td>\n",
       "      <td>0.052970</td>\n",
       "      <td>0.015245</td>\n",
       "      <td>0.013988</td>\n",
       "      <td>0.012561</td>\n",
       "      <td>0.013106</td>\n",
       "      <td>0.013067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Toys</th>\n",
       "      <td>0.017564</td>\n",
       "      <td>0.013491</td>\n",
       "      <td>0.019399</td>\n",
       "      <td>0.012605</td>\n",
       "      <td>0.015245</td>\n",
       "      <td>0.057136</td>\n",
       "      <td>0.038807</td>\n",
       "      <td>0.027877</td>\n",
       "      <td>0.016100</td>\n",
       "      <td>0.033053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fun</th>\n",
       "      <td>0.022171</td>\n",
       "      <td>0.013809</td>\n",
       "      <td>0.024218</td>\n",
       "      <td>0.013570</td>\n",
       "      <td>0.013988</td>\n",
       "      <td>0.038807</td>\n",
       "      <td>0.073651</td>\n",
       "      <td>0.037793</td>\n",
       "      <td>0.017378</td>\n",
       "      <td>0.039036</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Books</th>\n",
       "      <td>0.019004</td>\n",
       "      <td>0.013156</td>\n",
       "      <td>0.019795</td>\n",
       "      <td>0.011413</td>\n",
       "      <td>0.012561</td>\n",
       "      <td>0.027877</td>\n",
       "      <td>0.037793</td>\n",
       "      <td>0.041734</td>\n",
       "      <td>0.014832</td>\n",
       "      <td>0.029643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hshld</th>\n",
       "      <td>0.008521</td>\n",
       "      <td>0.012084</td>\n",
       "      <td>0.017288</td>\n",
       "      <td>0.015548</td>\n",
       "      <td>0.013106</td>\n",
       "      <td>0.016100</td>\n",
       "      <td>0.017378</td>\n",
       "      <td>0.014832</td>\n",
       "      <td>0.020957</td>\n",
       "      <td>0.016138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Clths</th>\n",
       "      <td>0.016928</td>\n",
       "      <td>0.014434</td>\n",
       "      <td>0.021368</td>\n",
       "      <td>0.013191</td>\n",
       "      <td>0.013067</td>\n",
       "      <td>0.033053</td>\n",
       "      <td>0.039036</td>\n",
       "      <td>0.029643</td>\n",
       "      <td>0.016138</td>\n",
       "      <td>0.047917</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Agric      Food      Soda      Beer     Smoke      Toys       Fun  \\\n",
       "Agric  0.046055  0.009700  0.009953  0.008375  0.010668  0.017564  0.022171   \n",
       "Food   0.009700  0.018775  0.014645  0.013834  0.016591  0.013491  0.013809   \n",
       "Soda   0.009953  0.014645  0.053101  0.020730  0.015570  0.019399  0.024218   \n",
       "Beer   0.008375  0.013834  0.020730  0.025130  0.013791  0.012605  0.013570   \n",
       "Smoke  0.010668  0.016591  0.015570  0.013791  0.052970  0.015245  0.013988   \n",
       "Toys   0.017564  0.013491  0.019399  0.012605  0.015245  0.057136  0.038807   \n",
       "Fun    0.022171  0.013809  0.024218  0.013570  0.013988  0.038807  0.073651   \n",
       "Books  0.019004  0.013156  0.019795  0.011413  0.012561  0.027877  0.037793   \n",
       "Hshld  0.008521  0.012084  0.017288  0.015548  0.013106  0.016100  0.017378   \n",
       "Clths  0.016928  0.014434  0.021368  0.013191  0.013067  0.033053  0.039036   \n",
       "\n",
       "          Books     Hshld     Clths  \n",
       "Agric  0.019004  0.008521  0.016928  \n",
       "Food   0.013156  0.012084  0.014434  \n",
       "Soda   0.019795  0.017288  0.021368  \n",
       "Beer   0.011413  0.015548  0.013191  \n",
       "Smoke  0.012561  0.013106  0.013067  \n",
       "Toys   0.027877  0.016100  0.033053  \n",
       "Fun    0.037793  0.017378  0.039036  \n",
       "Books  0.041734  0.014832  0.029643  \n",
       "Hshld  0.014832  0.020957  0.016138  \n",
       "Clths  0.029643  0.016138  0.047917  "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the covariance matrix where the leading doagonal is the SD of the industry. \n",
    "cov.loc[l,l]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "d9975608",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define portfolio returns\n",
    "def portfolio_ret(weights, returns):\n",
    "    \"\"\"\n",
    "    weights + asset returns --> portfolio return \n",
    "    \"\"\"\n",
    "    return weights.T @ returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "6c463146",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define portfolio variance \n",
    "def portfolio_vol(weights, covmat): \n",
    "    \"\"\"\n",
    "    weights + covariance matrix --> portfolio volatility \n",
    "    \"\"\"\n",
    "    return (weights.T @ covmat @ weights)**0.5 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a0ec80c",
   "metadata": {},
   "source": [
    "# Multi-Asset Efficient Frontier\n",
    "\n",
    "In order to plot the frontier for portfolios with more than 2 assets, we need to find the weights of the portfolios on the efficient frontier. To find the optimal weights, we need a function that will **minimize the volatility for a given level of return**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "b64b7238",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "raw",
   "id": "76306959",
   "metadata": {},
   "source": [
    "The minimize_vol() aims to find the weights of assets in a minimum-variance portfolio that generates a target return. We specify the target return in the beginning of the problem. This is the ***Global minimum variance portfolio***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "04a50dd8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# variance-covariance matrix (covmat), \n",
    "def minimize_vol(target_return, ereturns, covmat): #ereturns represents the dotted lines\n",
    "    \"\"\"\n",
    "    target return --> weights in a minimum-variance portfolio that generates the target return\n",
    "    \n",
    "    \"\"\"\n",
    "    n = ereturns.shape[0] # this is the number of assets in our universe. we use E(R) because this is what we have for each asset plotted on our efficient frontier\n",
    "    \n",
    "                \n",
    "                # here, we tryna get the minimum weight. We make an initial guess, we give it a range and then it \n",
    "                # iterates and then finds the try different values. This will be out init_value || init_guess\n",
    "                # we create an array of size 1/n,n. We need a range (bounds) from 0-1 representing the weights\n",
    "                # the shape of our initial guess should be the same as the number of assets in our portfolio. \n",
    "                # The initial guess will be 1/n, n=number of assets in our portfolio. if n=10, init_guess = 1/10\n",
    "                # using numpy, create an array of size 10 with 10 initial weights (1/10, 1/10, ... 1/10) 10 times\n",
    "                # the range of the weights MUST lie between [0,1]\n",
    "    \n",
    "    init_values = np.repeat(1/n,n)\n",
    "    bounds = ((0,1),)*n # create an array from 0 - 1 . The weights must be between [0,1]\n",
    "                \n",
    "    # constraints ( these are from slide 3) of our \n",
    "    weights_sum_to_1 = {'type': 'eq', # Weight transpose x Returns = Ro. the type is equality 'eq' we use\n",
    "                        'fun': lambda weights: np.sum(weights) -1} # lambda fxn allows you to define a fxn and use it immediately. we give the fxn an input, which is weights, such that the sum (weights)=1 but here, we write it as np.sum(weights)-1=0 which is the same thing but written in a different way. \n",
    "   \n",
    "    return_is_target = {'type': 'eq',\n",
    "                        'args': (ereturns,), # the argument here is ereturns because Weight.T * R = target return\n",
    "                        'fun': lambda weights, ereturns: portfolio_ret(weights, ereturns)-target_return} \n",
    "    # this says that portfolio_ret(weights, ereturns)-target_return (what you give to the fxn at the beginning) should be zero to ensure you get the same output\n",
    "    # if a client says INVEST IN EVERY STOCK EXECEPT TESLA, GOOGLE, then you need to add contraints \"weight.Tesla=0\" and so on. \n",
    "                        \n",
    "                \n",
    "    # how does the optimization work? we want to minimize portfolio volatility # read the minimize documentation \n",
    "    results = minimize(portfolio_vol, \n",
    "                      init_values, # give the function the initial weights (1/n)\n",
    "                      args = (covmat,), # what will be the variance given the weights\n",
    "                      method = 'SLSQP', # we do this minimization using the sequencial least square programming\n",
    "                      bounds = bounds, # we also tell the function that the weights lie between [0,1]\n",
    "                      constraints = (weights_sum_to_1, return_is_target), # these weights should abide by this\n",
    "                      options = {'disp': False}) # this prevents the fxn from writing a bunch of stuff\n",
    "    weights = results.x \n",
    "    return weights # we write this function to give us the optimum weights for our portfolio for any level of return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "55a5c487",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7.29607637e-02, 0.00000000e+00, 4.71849658e-01, 6.79704549e-02,\n",
       "       1.85828430e-01, 5.55382563e-17, 2.01390693e-01, 0.00000000e+00,\n",
       "       3.03576608e-17, 0.00000000e+00])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For the above defined 10 industries \"l\", we define the weights \n",
    "w11 = minimize_vol(0.11, eret[l], cov.loc[l,l])\n",
    "w11\n",
    "\n",
    "### Observation, we don't have the desired return here even though we previously defined our target return. \n",
    "### To get the effiient frontier, here are the weights that we need or this is the % of investment of our capital\n",
    "### we need to make "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "48dce3ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11000000000058519"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "portfolio_ret(w11, eret[l])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "2aa916ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.170701287293143"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "portfolio_vol(w11, cov.loc[l,l])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55b2c491",
   "metadata": {},
   "source": [
    "### NOte\n",
    "Now that we can find the weights to minimize the vol given a target return, we can plot the efficient frontier by dividing up the range from the highest to the lowest possible return into a grid, and finding the portfolio that targets the minimum volatility given a particular targeted rate of return."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "8d754589",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This fxn takes the number of points (the grids in btw the Max and Min. returns) and the find the optimal weights\n",
    "def optimal_weights(n_points, ereturns, covmat):\n",
    "    \"\"\"\n",
    "    Takes expected returns and vols + number of grid points --> weights of efficient frontier portfolios\n",
    "    \"\"\"\n",
    "    target_returns = np.linspace(ereturns.min(), ereturns.max(), n_points) # we plot the min, max and grid points in between\n",
    "    opt_weights = [minimize_vol(tr, ereturns, covmat) for tr in target_returns] # for the first line, find the optimum weights for any \"tr\" target return\n",
    "    \n",
    "    return opt_weights"
   ]
  },
  {
   "cell_type": "raw",
   "id": "03605b27",
   "metadata": {},
   "source": [
    "Now, plot the efficient frontier for any number of assets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "cf75244c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Volatility'>"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TbunTE/F9vDGyrw/6+bnjs+M5LCcmIrITDCxkc0RRRGZJNY5eKkbStds8xZX6++y4y2W4ObwxoMRHeCM60NPg9g7LiYmI7AcDC1mcsVLjy1erG9egXCrB0UslyC+v1XuNwkmC4b174pY+3hgZ4Y2Bwcp2lRWznJiIyD4wsJBFNS81FgAMC+uB/Ipa5Fyp0WvnLJVgSC8vxEd4Y2SEDwaFKiGXcQNAIiJHxcBCFiGKIn4+X6RXaiwC+C3rKgBAKhEwKESpCyhDe/XgDsVERKTDwEJmo9GK+D37Kn48nY8fU/MNZlGaPDU1EnPje8Ndzj+ORERkHH9DUJeqV2tx9FIxfjxTgD2p+XqLZY3tXCwVBMwYEsywQkREbeJvCeq0qjo1Dpwrwo9n8vHT2UJUNHsmiqdChluj/TFlgD/G9vfFtyfzWGpMREQmY2ChDrlSVY+9aQXYfSYfP18oRr36+pNlfT3kmBzjj6mxAbiljzecmlXzsNSYiIg6goGF2tS8BFkUgR/P5OPHM/k4lnEF2mZ3d3p7u2LKgABMHhCAIaFekLTxyHuWGhMRkakYWKhVzUuQjYkJ9MSUAQGYEuuPSH8PCAL35SEiIvNgYCEDVXVqfPRLFtZ+f9bg3OAQL/xpUCCmDAhAaE9XK/SOiIgcEQML6ZzOLcO2Y9n45kSewWaCTZ6aFoX4CG8L94yIiBwdA4uDq6xT49uTedh2LBt/XC7THQ/xUiC3tBbN7wZJBQG9fTirQkRElsfA4qBOXS7DJ8eyseNELqrqNQAaH4c/JTYAf705FPF9vLnbMRER2QwGFgdSUduAHddmU07nluuO9/Fxw19v7oW7hwbD212uO84SZCIishUMLHaqqRy5t7criirqse1YNnaczEN1s9mUaQMD8Nebe2FEeM9WK3xYgkxERLaAgcUOtVWOHOHbOJsyc2gIerg5W75zREREHcDAYmdyrlTp7YjcZOqAACwYE45hYT34vBQiIup2GFjshCiK2JtWiFXfnDYIKwDwwMjeGN67p8X7RURE1BUkN25iaP369QgPD4dCoUBcXBwOHTrUaluVSoV77rkHkZGRkEgkWLx4sdF227dvR0xMDORyOWJiYvDVV191pGsO6WROKea88wsWfnAceWW1BudZjkxERN2dyYElMTERixcvxooVK5CSkoIxY8Zg2rRpyM7ONtq+rq4Ovr6+WLFiBQYNGmS0TVJSEmbPno25c+fi5MmTmDt3LmbNmoVff/3V1O45lJwr1XhiWwrufOsIfs24ArlMgkfGR+C5O2IgvXbbh+XIRERkDwRRFFvZKca4ESNGYOjQodiwYYPuWHR0NGbMmIG1a9e2+drx48dj8ODBeP311/WOz549G+Xl5fj+++91x6ZOnYoePXpg27Zt7epXeXk5lEolysrK4Onp2f4L6obKqhvw5k8X8P7RLNRrtBAE4K7BwfjnlEgEezUGE1VZDcuRiYjI5rX397dJa1jq6+uRnJyMZcuW6R2fPHkyjh492rGeonGGZcmSJXrHpkyZYhBsmqurq0NdXZ3u+/Ly8lbb2gNVWQ3OF1QgOfMq3k/KQllNAwBgVF9vLJ8WjdhgpV57liMTEZE9MSmwFBcXQ6PRwN/fX++4v78/8vPzO9yJ/Px8k99z7dq1eP755zv8M7uTT481lik3nwqL9PfAstuiML6/L6t+iIjI7nVo0W3LX5CiKHb6l6ap77l8+XKUlZXpvnJycjr1823VufxyLGsRVgQB2DxvGBIi/RhWiIjIIZg0w+Lj4wOpVGow81FYWGgwQ2KKgIAAk99TLpdDLpe3et4eHL5QjL9v+93guCgCOVdqENKDlT9EROQYTJphcXZ2RlxcHPbs2aN3fM+ePRg5cmSHOxEfH2/wnrt37+7Ue3ZntQ0arNmZivs2/4qr1Q0G51mmTEREjsbkB8ctXboUc+fOxbBhwxAfH4933nkH2dnZWLRoEYDGWzW5ubn44IMPdK85ceIEAKCyshJFRUU4ceIEnJ2dERMTAwD4xz/+gbFjx+Lll1/GnXfeiW+++QZ79+7F4cOHu+ASu5fUvHIsSTyBcwUVAID7bumFSH8PPLcjlbsmExGRwzI5sMyePRslJSVYvXo1VCoVYmNjsWvXLoSFhQFofFBcy2eyDBkyRPfvycnJ+OSTTxAWFobMzEwAwMiRI/Hpp5/imWeewcqVKxEREYHExESMGDGiE5fWPTRtUhjW0xXfnVLhPz+eR71GCx93Z7zy55swIarxttjEGH+WKRMRkcMy+Tkstqo7PoeltU0KJ8X446W7B8Lb3b7X6BAREZnlOSzUdVRlNUbDyvKpUXh4XB9W/xARETXTobJm6rz0wiqDsAIAN4V6MawQERG1wMBiBVV1arxz6JLBcVb/EBERGcdbQhaWW1qDh94/jjRVOaSCAC1EiCI3KSQiImoLA4sFJWddxd8+TEZxZR183J3x9txhCPJSsPqHiIjoBhhYzKypbPmsqhwvfX8O9RotogM9sen+ON2TahlUiIiI2sbAYkbGypYnx/jjv7MHw03OoSciImovLro1E2NlywKAVdNjGFaIiIhMxMBiJhcKKg3KlkUA2VdqrNIfIiKi7oyBxQzUGi22HMkwOM6yZSIioo5hYOliGq2If35+EgfOFUEqCJBcewYcy5aJiIg6jospupBWK2L5l3/gmxN5kEkEbLgvDrHBnixbJiIi6iQGli6gKqtBRlEVPk/OwVcpeZAIwP/mDMGkmMadlhlUiIiIOoeBpZOMlS6/OmsQbr8p0HqdIiIisjNcw9IJRkuXBeCWPt7W6xQREZEdYmDphIxiwx2XRRHILK62ToeIiIjsFANLJ/R0dTY4xtJlIiKirsfA0kGiKOK1Pef1jrF0mYiIyDy46LaDPjmWjd2pBXCSCth0/zDIZVKWLhMREZkJA4uJVGU1OHyhGKu/PQMAeGpqFMZH+lm5V0RERPaNgcUELUuY+/m5Y/6ocOt2ioiIyAFwDUs7GSthvlRUiYKKWut1ioiIyEEwsLSTsRJmLUuYiYiILIKBpZ3CfdwgtDjGEmYiIiLLYGBpJ283OTwU15f8sISZiIjIcrjotp12/pGH8lo1vN2c8frswejr786wQkREZCEMLO2QV1qN1/deAADMHx2OMf19rdwjIiIix8LAcgOJv2Vj2ZenIF5bcOvqLLVuh4iIiBwQ17C0oamUWWxWHfTvnWlQldVYr1NEREQOiIGlDcZKmTWiyFJmIiIiC2NgaUO4jxskLWqZWcpMRERkeQwsbQhUuuCJW/vpvmcpMxERkXVw0e0NRAV4AAAifNzw0cIRDCtERERWwBmWG/jjchkAIMKPz10hIiKyFgaWNiT+lo31By4BAPakFiDxt2wr94iIiMgxMbC0oqmkuYkI4OkvT7OkmYiIyAoYWFrBkmYiIiLbwcDSCpY0ExER2Q4GllYEKl2w9u6BaMosAsCSZiIiIithYGnD7OG98PDYcADA7TcFYPbwXlbuERERkWNiYLmBMG93AEBeaS0X3BIREVkJA8sNpKkan8Pye3YpRr20n6XNREREVsDA0gZVWQ0++vV6QNGKLG0mIiKyBgaWNmQUV0FkaTMREZHVMbC0gaXNREREtoGBpQ1Npc1NBIGlzURERNbAwHIDs4f3wsIxjaXNw8N6YGx/Xyv3iIiIyPEwsLRDg0YLADiWeZWVQkRERFbAwHIDqrIafJCUpfuelUJERESWx8ByA9wEkYiIyPoYWG6AlUJERETWx8ByA02VQs1Dywt3sVKIiIjIkhhY2mH28F7Y/8/xcJY2DldssNLKPSIiInIsDCzt1NvHDROi/AAAmw+nc9EtERGRBTGwmMDTRQYA+Colj+XNREREFsTA0k6qshp8kXxZ9z3Lm4mIiCyHgaWdWN5MRERkPQws7WSsvFkigOXNREREFsDA0k7GypvvHhrC8mYiIiILYGAxwezhvXBk2QT89eZQAMCZvHKIoniDVxEREVFnMbCYKFDpgqemRkHhJEGaqhxbjmRw4S0REZGZMbB0gJerMwaFeAEA1uxMY4kzERGRmTGwdICqrAa/ZV7Rfc8SZyIiIvNiYOkAljgTERFZFgNLB7DEmYiIyLIYWDqgqcRZKlxPLX183RHgqbBir4iIiOwXA0sHzR7eC4eXJeCNOYPhJBFwsbASB88XWbtbREREdomBpRMClS64Y3AwHhjZGwCw+ttUHL5QzMW3REREXYyBpQs8PqEvFDIJ0ourcN/mX1nmTERE1MU6FFjWr1+P8PBwKBQKxMXF4dChQ222P3jwIOLi4qBQKNCnTx9s3LjRoM3rr7+OyMhIuLi4IDQ0FEuWLEFtbW1HumdxNQ0a1Km1uu9Z5kxERNS1TA4siYmJWLx4MVasWIGUlBSMGTMG06ZNQ3a28RmFjIwM3HbbbRgzZgxSUlLw9NNP44knnsD27dt1bT7++GMsW7YMq1atQlpaGjZv3ozExEQsX76841dmQRnFVWj5gH6WORMREXUdQTRxM5wRI0Zg6NCh2LBhg+5YdHQ0ZsyYgbVr1xq0f+qpp7Bjxw6kpaXpji1atAgnT55EUlISAODxxx9HWloa9u3bp2vzz3/+E8eOHbvh7E2T8vJyKJVKlJWVwdPT05RL6jRVWQ1GvbRf79ksEgE4smwCN0ckIiJqQ3t/f5s0w1JfX4/k5GRMnjxZ7/jkyZNx9OhRo69JSkoyaD9lyhQcP34cDQ0NAIDRo0cjOTkZx44dAwCkp6dj165duP3221vtS11dHcrLy/W+rMVYmbPSxQmeCier9YmIiMiemBRYiouLodFo4O/vr3fc398f+fn5Rl+Tn59vtL1arUZxcTEAYM6cOVizZg1Gjx4NJycnREREICEhAcuWLWu1L2vXroVSqdR9hYaGmnIpXa6pzHnLvOEI8FTganUDXvnhrFX7REREZC86tOhWEPQf8yqKosGxG7VvfvzAgQN44YUXsH79evz+++/48ssvsXPnTqxZs6bV91y+fDnKysp0Xzk5OR25lC4VqHTBhCg/rPvLTQCA95Oy8N0feTh6iaXOREREnSEzpbGPjw+kUqnBbEphYaHBLEqTgIAAo+1lMhm8vb0BACtXrsTcuXPx0EMPAQAGDhyIqqoqPPzww1ixYgUkEsNcJZfLIZfLTem+xYzp54u/3hyKbcdy8NgnKQAa17SsvXsgZg/vZeXeERERdT8mzbA4OzsjLi4Oe/bs0Tu+Z88ejBw50uhr4uPjDdrv3r0bw4YNg5NT4xqP6upqg1AilUohiiJMXBNsMx4cFa73PUudiYiIOs7kW0JLly7Fu+++iy1btiAtLQ1LlixBdnY2Fi1aBKDxVs3999+va79o0SJkZWVh6dKlSEtLw5YtW7B582Y8+eSTujbTp0/Hhg0b8OmnnyIjIwN79uzBypUrcccdd0AqlXbBZVpecWWdwTGWOhMREXWMSbeEAGD27NkoKSnB6tWroVKpEBsbi127diEsLAwAoFKp9J7JEh4ejl27dmHJkiV46623EBQUhDfeeAMzZ87UtXnmmWcgCAKeeeYZ5ObmwtfXF9OnT8cLL7zQBZdoHU07OrcsdeaOzkRERKYz+Tkstsqaz2FpTeJv2Vj+5SldaPFxd8b+J8ez3JmIiOgaszyHhUwze3gvHFk2Ae/MjYO/hxzFlfX4f5+f7LbrcoiIiKyFgcXMApUumDwgAG/fPwxOUgE/ninAq7vPsdSZiIjIBLwlZEEf/pKFlV+f1n3PUmciInJ0vCVkg26N8tX7nqXORERE7cPAYkGZJYYlzSx1JiIiujEGFgtqKnVuKVCpsHxniIiIuhEGFgsytqszAKz9Pg0arV0sJSIiIjILLrq1AlVZDTKLq3G1qg6LE0+iXqPFvJG9sWp6TJubSBIREdmb9v7+NvlJt9R5gUoXBCpdAAAaEfj7thS8dzQTngoZbonwRriPm+48ERERcYbFJmz6OR0v7ErTfc9yZyIichQsa+5Gbr8pAM1vBLHcmYiISB8Diw3ILKlGy2kuljsTERFdx8BiA1ord87jDAsREREABhab0Fq58/IvT+Hg+SIr9YqIiMh2cNGtDWkqdw7uocC/d6Zhd2oBnGUSvHv/MPTzd0dGcRUriIiIyK609/c3A4uNqldr8ejHv2NvWgFkEgEaUYQosoKIiIjsC6uEujlnmQTr7x2K0X29odY2hhWAFUREROSYGFhsmLNMgoVj+xgcZwURERE5GgYWG9ff38OggkgQgN4+rtbpEBERkRUwsNi4pgqi5qFFFIHPj1+GnSw/IiIiuiHuJdQNzB7eC2P7+yKzuAq7zxRg69FMvLbnPIor67Bq+gBIjT3EhYiIyI4wsHQTTRsmxkf4IMzbFc/vTMUHSVkoqarHv6ZEIre0hiXPRERkt1jW3E19ezIPSz87gQbN9f98LHkmIqLuhmXNdm76oCD85y+D9I6x5JmIiOwVA0s35ushNzjGkmciIrJHDCzdWGubJmYUV1q+M0RERGbEwNKNtbZp4tNfncYb+y6w7JmIiOwGF93agaZNE0N6KLDlSCa2HskE0LjOZd2fb4LCSWrdDhIREbWCmx86sG3HsrHy69NQa0UMClHinfuHQSuK3O2ZiIhsDgOLg0u6VIJHPk5GaXUDPBUyVNSpudszERHZHJY1O7j4CG9889go9PZ2RXmtmrs9ExFRt8bAYsfCvN3wzJ9iDI6z9JmIiLobBhY7NyDI02jps1zG/YeIiKj7YGCxc62VPs9//zh+OldopV4RERGZhotuHURT6bOzTMDz36bij8tlEATg7wl98Y+J/bnjMxERWQWrhKhVdWoNVn+bio9/zQYAjOnng+XTolBa08CyZyIisigGFrqhr1Iu4+kvT6OmQaM7xrJnIiKyJJY10w3dNSQE7z4wTO9YY9nzKZY9ExGRTWFgcXCCkaUrGhFIyS61eF+IiIhaw8Di4Frb8Xn59j+w+0y+5TtERERkBAOLg2tZ9iwRgCClAmW1ajz8YTJWfHUKNfWaG7wLERGReXHRLQG4Xvbc28cVPd2c8eru83jn53QAQF8/d7wxZwhigjiuRETUtVglRJ126EIR/vnZSRRW1MFZKsG/pkZiWmwAsq5Us/yZiIi6BAMLdYmSyjo8tf0P7E3Tfyouy5+JiKgrsKyZuoS3uxyb7h+GJ6dE6h3nrs9ERGRJDCx0Q4IgYGgvL4PjGlHE6ctllu8QERE5HAYWapfWyp//tf0U9qQWWL5DRETkUBhYqF2MlT/7echxtboeCz84jqWJJ1BW3WDlXhIRkb3iolsySfPy5x6uzvjvnvN451A6RBHw95TjpZk3ISHSz9rdJCKiboJVQmQxyVlX8OTnfyCjuAoAMHtYKB4aE46iyjqWPxMRUZsYWMiiauo1WPfjOWw9moHmf6JY/kxERG1hWTNZlIuzFM9Oj8Fbfx2id1wrAsu5+zMREXUSAwt1KS83Z4NjWhH45Nds2MlkHhERWQEDC3Wp1sqf/2//RSx4/zhySznTQkREpmNgoS5lrPx5YrQfnKUS7D9biEmvHcTWIxnQaDnbQkRE7cdFt2QWzcufA5UuuFhYgWXbT+F41lUAwOBQL7w0cyCiAvjfiojIkbFKiGyOVivik2PZePn7s6ioU0MmEfC3cX3wl7hQ5JXVsASaiMgBMbCQzcovq8WqHafx4xn9R/qzBJqIyPGwrJlsVoBSgbfnDsPauwbqHWcJNBERtYaBhawmzMfV4JhWBF7fewF1ao0VekRERLaKgYWsprUS6MTfcjD5vz9jXxp3gSYiokYMLGQ1LUugpQIwZ3go/D3lyCqpxoL3j+PBrcd0exQREZHj4qJbsrqWJdCVdWq8uf8iNh9OR4NGhLNUggVjwvF4Ql+4yWVQldUgo7iKVUVERHaAVULU7aUXVWL1zlQcOFcEAAjwVGB8pC8+O54DrciqIiIie8DAQnZBFEXsSyvE6p2pyL5SbXBeKgg4vCyBMy1ERN0Uy5rJLgiCgIkx/ti9ZCxmDQsxOK8RRWQWGwYZIiKyLwws1C0onKRYMqm/0aqiz4/noLCi1vKdIiIii2FgoW6jZVVRky9TcjHulQN4dfc5VNQ2WKl3RERkTlzDQt1O86qirJJqvPT9WZzIKQUA9HB1wuMT+uG+W3pBLpNat6NERHRDZl3Dsn79eoSHh0OhUCAuLg6HDh1qs/3BgwcRFxcHhUKBPn36YOPGjQZtSktL8dhjjyEwMBAKhQLR0dHYtWtXR7pHdi5Q6YL4CG8EKl1wSx9vfPXoSGy8Lw59fN1wtboBa3amYsJ/DmJ78mVotCJUZTU4eqmYj/wnIurGZKa+IDExEYsXL8b69esxatQovP3225g2bRpSU1PRq5dheWlGRgZuu+02LFy4EB999BGOHDmCRx99FL6+vpg5cyYAoL6+HpMmTYKfnx+++OILhISEICcnBx4eHp2/QrJ7giBgamwAJkb74Yvky3h97wXkltbgn5+fxCs/nkVhRR1ElkETEXVrJt8SGjFiBIYOHYoNGzbojkVHR2PGjBlYu3atQfunnnoKO3bsQFpamu7YokWLcPLkSSQlJQEANm7ciHXr1uHs2bNwcnLq0IXwlhA1qW3Q4L2jmXhz/wVU1unvScQyaCIi22KWW0L19fVITk7G5MmT9Y5PnjwZR48eNfqapKQkg/ZTpkzB8ePH0dDQuEByx44diI+Px2OPPQZ/f3/ExsbixRdfhEbT+gZ4dXV1KC8v1/siAhorihaNi8B/Zw0xOKcRRew8qYKdLN0iInIYJgWW4uJiaDQa+Pv76x339/dHfn6+0dfk5+cbba9Wq1FcXAwASE9PxxdffAGNRoNdu3bhmWeewauvvooXXnih1b6sXbsWSqVS9xUaGmrKpZADiA3xNFoG/cKuNPxlYxJ+Pl/E4EJE1E10aNGt0KKsVBRFg2M3at/8uFarhZ+fH9555x3ExcVhzpw5WLFihd5tp5aWL1+OsrIy3VdOTk5HLoXsWMsyaIkAjIzwhrNMguNZV3H/lmO4e8NR/HSukMGFiMjGmbTo1sfHB1Kp1GA2pbCw0GAWpUlAQIDR9jKZDN7e3gCAwMBAODk5QSq9XoYaHR2N/Px81NfXw9nZ2eB95XI55HK5Kd0nBzR7eC+M7e+rt7liYXktNh5Mx8e/ZiEluxQPbv0Ng0KUeOLWfpgQ5ddm+CYiIuswaYbF2dkZcXFx2LNnj97xPXv2YOTIkUZfEx8fb9B+9+7dGDZsmG6B7ahRo3Dx4kVotVpdm/PnzyMwMNBoWCEyRfMyaADw81Tg2ekxOPRUAhaOCYeLkxQnL5dhwfvHMf3Nw9h9Jh+iyHJoIiJbYnKVUGJiIubOnYuNGzciPj4e77zzDjZt2oQzZ84gLCwMy5cvR25uLj744AMAjWXNsbGx+Nvf/oaFCxciKSkJixYtwrZt23RlzTk5OYiJicG8efPw97//HRcuXMD8+fPxxBNPYMWKFe3qF6uEqKOKK+uw6VA6PkzKQnV940LvQKUC+WW1EMFyaCIiczLrbs3r16/HK6+8ApVKhdjYWPz3v//F2LFjAQDz5s1DZmYmDhw4oGt/8OBBLFmyBGfOnEFQUBCeeuopLFq0SO89k5KSsGTJEpw4cQLBwcFYsGABnnrqKb3bRF1xwUStuVJVj3cPpWPrkQzUNGj1zkkE4MiyCSyHJiLqYmYNLLaIgYW6yp4z+Vj4YbLB8bm3hGHZtCi4yU1+3iIREbXCrI/mJ7JnsSFKo+XQH/6Shfi1+7Dux7MoqqizfMeIiBwYAwtRC8bKoe8eGow+Pm4or1XjrZ8uYdTL+7H8y1NIL6q0cm+JiBwDbwkRtaL5rtCBShdotCL2pBbg7Z8vISW7FAAgCMDkGH/8bVwEhvbqYd0OExF1Q1zDQmQmoijieNZVvH3wEvamFeqO39y7J/42rg8SIv1QUFGLjOIqhPu4caEuEVEbGFiILOBCQQU2HUrHVym5aNA0/lXy85CjqKKOJdFERO3AwEJkQflltdh6NAMfJWWhql5/006WRBMRtY5VQkQWFKBUYPm0aPzvr4Y7RGtFYNn2P5Caxx3FiYg6ig+UIOpCA4Iad4jWtpi3PHi+GAfPH8KI8J54cFRvTIoJgNRY7TQRERnFGRaiLtSyJFoqAI+Mj8CfbgqEVCLg14wrWPTR7xj7yk945+dLKKtusHKPiYi6B65hITKDliXRTcc++iULn/yajavXgoqLkxQz44Ixb2Rv9PXzsGaXiYisgotuiWxUbYMG35zIxdYjmTibX6E7PqafD+aPCse4/r4siyYih8HAQmTjRFFEUnoJth7JxN60AjT9TfRxd0ZJZT3LoonIITCwEHUj2SXV+CApE9t+y0ZVHcuiichxsKyZqBvp5e2KZ/4Ug/9rpSz6gS3H8HVKLurUGiOvJiKyfwwsRDYkOtDT6E7R5wsqsTjxBOLX7sfa79OQXVJt+c4REVkRAwuRDTEsixaw4rZoLJnYHwGeClypqsfbB9Mx7j8/4YEtx7AntQCalg99ISKyQ1zDQmSDjJVFqzVa7D9biI9+zcbP54t0bYOUCsy5uRfmDA+Fn6fCWl0mIuoQLrolsmNZJVX45NdsfHY8R/dMF5lEwOQB/rhvRBjiI7yRX87SaCKyfQwsRA6gtkGD70+r8NEv2UjOuqo7ztJoIuouGFiIHEyaqhwf/5qF7cmXUdOg1TsnEYBD/0pAcA9XK/WOiMg4ljUTOZjoQE/8e8ZAvHXvUINzWhG4a/1RvPXTReSX1Vqhd0REncPAQmRnWiuNLqyow7ofz2HkS/uw4L3fsPtMPho0WsOGREQ2iLeEiOxQ4m/ZePrL09CIIqSCgOfuGABXZykSf8vBscwrunY+7nL8OS4Es4eHItzHzYo9JiJHxTUsRA7OWGk0AFwqqsRnx3OwPfkyiivrdcdvDu+JOcNDMS02EC7OUmt0mYgcEAMLEbWpQaPFvrRCfHY8BwfOFaLp+XMeChnuHByEOcN7wdvdmaXRRGRWDCxE1G6qshp8cfwyPkvOQc6VGoPzLI0mInNhYCEik2m1IpLSS7D1SCb2phUYnF/355swY0gwnKRcr09EXYNlzURkMolEwKi+Ppg/urfR8//viz8Qv3Yf1uxMRZqq3LKdIyKHJrN2B4jI9oT7uEEiAM33VRQAeLk6obiyHpsPZ2Dz4QzEBHpiZlwI7hwcBB93udX6S0T2j7eEiMiolqXRL94di7uHhuDguSJs//0y9qUVov7ac1xkEgHjI/3w57hgTIjyh7OMk7dE1D5cw0JEndZaaTQAXK2qx7d/5GF78mWcvFymO97D1Ql3DArCzLgQDAxWQhAE3Xux4oiIWmJgISKLuVBQgS9+v4yvU3JRUF6nO97Pzx1/jguBRBCw9vs0aEVWHBGRPgYWIrI4jVbE4YvF+CL5MnafyUed2vij/6WCgMPLEjjTQkTt/v3NRbdE1GWkEgHj+vtiXH9flNc24Ls/VNh6JAPnCyr12mlEETtO5GHB6HDIWCJNRO3AGRYiMitVWQ1GvbRfr+Koia+HHNNvCsJdQ4IRG+ypW+9CRI6Dt4SIyGY0rziSCI37Fp3Lr8DV6gZdmwhfN8wYHIwZQ4IR2tPVir0lIktiYCEim9Ky4qhercXP54vw9Ylc7Ekt0FvvEhfWAzOGBONPAwPRw83Zir0mInNjYCGibqOitgE/ninA1ym5OHKpGE2fSo3Pd/HFjCHBmBjtD4VT4y7SLJEmsh8MLETULRWU1+Lbk3n4KiUXZ/KuP/7fXS7D1NgAeLk4YcuRDJZIE9kJBhYi6vYuFFTg6xO5+DolD7mlhrtIA4BUAA4vm8CZFqJuioGFiOyGVisiOfsqNh64hH1nCw3OzxgchEcT+qK/v4cVekdEncHAQkR2p60SaQCICvDA9EFBmH5TEHp5s9KIqDtgYCEiu9SyRHrWsFAUV9bj4PlCNGiuf5wNCvXC9JsCMX1QEPw9FVbsMRG1hYGFiOyWsU0Zy6ob8OOZfOw4mYejl4p1szCCAIwI74npg4IwLTYQPVkmTWRTGFiIyGEVVdRh1ykVvj2Zh+NZV3XHZRIBo/v54I5BQZgU4w8PhRMAlkkTWRMDCxERgMtXq/HdHyrsOJmnVyYtl0kwIcoPPd2cse1YNsukiayEgYWIqIVLRZX49mQedpzMQ3pRldE2EgE4wjJpIothYCEiaoUoikhVlWPjgXR8+0eewfnRfX0wb2RvjOnvA7lMaoUeEjkOBhYiohu4UZm0h1yGSQP8cfvAQIzux/BCZA4MLERE7dC8TFoqAA+P7YNatRa7TqlQUF6na+ehkGFyTABuvykAo/v6wlkmsWKviewHAwsRUTsZK5Nuerrud3+osOuUCoUV18OLp0KGyQMCcPtNgRgV4cPwQtQJDCxERF1EqxVxPOsqvvsjD7tO56OoRXiZ0hRe+vrASSphmTSRCRhYiIjMQKMVcTzzCr47pcKuU/korrweXrxcndDX1x3J2VchskyaqF0YWIiIzEyjFXEs4wp2nVLh+9MqFFfWG7SRCMBPT45HmLebFXpIZPsYWIiILEijFbHlSDpe+O6swTkXJwmmxgZiamwAxvX3hcKJ1UZETRhYiIgs7EZl0gDg6ixFQpQfpsUGICHSD25ymeU6SGSDGFiIiKxAv0xawL/vikU/P3d8fzof359SIa+sVtdWLpNgXH9f3DYwEBOi/eB5bW8jIkfCwEJEZCXGyqSBxifs/nG5DLtOq/DD6XxklVTrzjlLJRjdzwdTYwMwOcYfXq7cVZocAwMLEZENa9oe4IfT+dh1SoVLzfY2kkkExEd4Y2psAKYMCICPu5yl0mS3GFiIiLqRCwUV+P5aeDmbX6E7LhGAMG83ZBZXQQRLpcn+MLAQEXVTGcVV+P7abaM/LpcZnBcAJP7tFtwc7m35zhF1MQYWIiI78E1KLv6ReMLouUh/D0wZ4I8psQGICfSEIAiW7RxRF2jv72/W0xER2bCb+/SERIBBqbRUAM4VVOBcQQXe2H8RIT1cMGVAAKbGBmBorx6QShheyL5whoWIyMa1LJV+8e5YTB0QiH1nC/DD6Xz8fKEItQ1aXXsfd2dMignAlAH+GMnNGcnG8ZYQEZEdaa1UGgCq69X4+XwRfjxTgL1pBaioVevOechlmBDthykDGp+yywfVka1hYCEickD1ai1+SS/Bj2fysTu1QG9nablMgjH9fDFlgD8mRvujh5szy6XJ6hhYiIgcnFYrIiXnKn4803jrKPvK9QfVSSUCenu7Ir2I5dJkXQwsRESkI4oizuZX4Mcz+fjhdL7es16aCAA+XDACo/p6s+KILIaBhYiIWvVVymUsSTxp9FyYtysmRftj8oAAxIWx4ojMq72/vzu0dHz9+vUIDw+HQqFAXFwcDh061Gb7gwcPIi4uDgqFAn369MHGjRtbbfvpp59CEATMmDGjI10jIqJ2uKWPN4zlECepgKySarx7OAOz3k7C8Bf24v99fhJ7UgtQ26CxfEeJrjE5sCQmJmLx4sVYsWIFUlJSMGbMGEybNg3Z2dlG22dkZOC2227DmDFjkJKSgqeffhpPPPEEtm/fbtA2KysLTz75JMaMGWP6lRARUbsFKl2w9u6BkF679SMVBLw8cyBOPDsZG+4diruGBEPp4oQrVfX4PPkyFn5wHINX78bDHxzHF8mXcaWq3spXQI7G5FtCI0aMwNChQ7FhwwbdsejoaMyYMQNr1641aP/UU09hx44dSEtL0x1btGgRTp48iaSkJN0xjUaDcePG4cEHH8ShQ4dQWlqKr7/+utV+1NXVoa7u+ur38vJyhIaG8pYQEZEJ2iqXbtBo8VvGFexOLcCe1ALkltbozkkEYHjvnpgU44/JMQHo5e1q6a6TnTDLLaH6+nokJydj8uTJescnT56Mo0ePGn1NUlKSQfspU6bg+PHjaGho0B1bvXo1fH19sWDBgnb1Ze3atVAqlbqv0NBQUy6FiIjQONMSH+FttKTZSSrByL4+eO6OATj8VAJ2/n00/nFrP0QHekIrAr9mXMG/v0vD2HU/YerrP+O13edwOrcMoihCVVaDo5eKoSqrMfJTiUxn0hOEiouLodFo4O/vr3fc398f+fn5Rl+Tn59vtL1arUZxcTECAwNx5MgRbN68GSdOnGh3X5YvX46lS5fqvm+aYSEioq4nCAJig5WIDVZiyaT+yLlSjT2pBdidmo/fMq/ibH4FzuY3bhOgdJGhvEbNcmnqUh165GHLcjdRFNssgTPWvul4RUUF7rvvPmzatAk+Pj7t7oNcLodcLjeh10RE1FVCe7pi/uhwzB8djqtV9dh/thB7Ugtw4FwhymquP2lXKwLLtp9CbYMGMwaHQOnqZMVeU3dmUmDx8fGBVCo1mE0pLCw0mEVpEhAQYLS9TCaDt7c3zpw5g8zMTEyfPl13Xqtt3BNDJpPh3LlziIiIMKWbRERkQT3cnDEzLgQz40Jw4Fwh5m39Te+8CGDVjlSs2ZmG4b17YmKMPyZF+3PdC5nEpMDi7OyMuLg47NmzB3fddZfu+J49e3DnnXcafU18fDy+/fZbvWO7d+/GsGHD4OTkhKioKJw6dUrv/DPPPIOKigr873//420eIqJuJDLAw2B3aQFAbx9XZBRXIym9BEnpJVizMxX9/d0xMdofE2P8MTjECxI+74XaYPItoaVLl2Lu3LkYNmwY4uPj8c477yA7OxuLFi0C0Li2JDc3Fx988AGAxoqgN998E0uXLsXChQuRlJSEzZs3Y9u2bQAAhUKB2NhYvZ/h5eUFAAbHiYjItjWVS7fcXXr28F7IKqnC3rRC7E0twLHMKzhfUInzBZVYf+ASfNzluDXKDxNj/DG6rw9cnKXWvhSyMSYHltmzZ6OkpASrV6+GSqVCbGwsdu3ahbCwMACASqXSeyZLeHg4du3ahSVLluCtt95CUFAQ3njjDcycObPrroKIiGzG7OG9MLa/r0G5dJi3GxaMDseC0eEoq27AgfON614OnitCcWUdEo/nIPF4zrVNGn0wMdofE6L94Oeh0L03N2t0XHw0PxERWVW9WotjGVewN83weS8AMDjUC5Ni/KHWavG/vRegFVl9ZE+4lxAREXU7TZs07k0twN60Apy8XNZqW4kAHFk2gTMt3RwDCxERdXv5ZbXYd7YAnx/PwYkcw/ByS3hPzBoeioRIP/Rwc7ZCD6mzGFiIiMhuqMpqMOql/XrVR81JBGBorx64NdofE6P90NfPvc3ng5HtYGAhIiK7kvhbdrPqI2DRuAgIgoC9aQU4m1+h1za0pwtujfLHrdF+GBHuDWeZyXv9koUwsBARkd1pbbPG3NIa7E8rwL6zhTh6qQT1aq3unLtchrH9fTAhyh8Jkb7wdudT0m0JAwsRETmkqjo1Dl8sxv60Quw7W4jiyjrdOUEAhoR6Xbt15I/+/tdvHbFk2joYWIiIyOFptSJO5ZZh37XZlzN55XrnQ3q44NYoP8ikEmw9ksGSaStgYCEiImpBVVaDfWmF2H+2EEcuFqOu2a2j5lgybTkMLERERG2orlfjyMUSbDuWhf1niwzO9/Fxw/RBQbg12g+xQUrudWQmDCxERETtcKOSaQDwcZcjIdIXt0b7YXQ/X7jLTd7ZhlrBwEJERNRO+iXTApbdFgWlixP2pxXi0IUiVNVrdG2dpAJGhHsjIcoPE6L8EO7jZsWed38MLERERCZorWS6aa+j/WcL8dO5QmQUV+m9ro+PGxKi/HBrlB+G9e7JZ76YiIGFiIjIDNKLKnXh5df0K1A3u5fkLpdhTD8fTIjyw/hIP/h6XH/mC8umjWNgISIiMrOK2gYcvlCsCzDFlfV65weFKDEhqnGn6bd+usiyaSMYWIiIiCxI98yXs4X46WwhTuVyp+n2YGAhIiKyosLyWvx0rhCfJ1/G8cyrBudjAj0xY0gQJkT5IcLXcTdrZGAhIiKyAe0pmw7p4YKESD8kRPkivo8PXJylluuglTGwEBER2YiWZdNLJ/eHq7MUP50rwi/p+ps1ymUSxEd4NwaYSD/08na1Ys/Nj4GFiIjIhrRWNl1dr0bSpRLsP1uIA+eKkFtao/e6CF+3a7Mvfhhuh2XTDCxERETdjCiKuFBYiZ/ONu53dDzrKjTN7iW5OUsxup8PEiIby6YDlAoA3btkmoGFiIiomyuracCRi8W62Zfiyjq989GBngjwlOPA+SKI3bRkmoGFiIjIjmi1Is7kleOnc42zLycvl8LYb3BBAL59fDRig5WW72QHMLAQERHZsZLKOmw+nIH1By4ZPT8wWInxkb4YH+mHwaFekNrobtMMLERERHauPSXTAODl6oQx/Xwxvr8vxkX6wsdd3vYLLIiBhYiIyAG0LJl+8e5YJET54eC5Ihw4X4RD54tQXqvWe81NIUqM7++L8VF+GBRi3dkXBhYiIiIH0VrJNACoNVqk5JTiwLnGhbtn8sr1zvdomn2J9MXY/paffWFgISIiIgOF5bU4cL4IB88V4ecLRahoNvsiCMBNwUqMi/TD+Ehf3eyLOcumGViIiIioTWqNFr9nX599SVUZzr6EebviZE4ZRJinbJqBhYiIiExSUF57be1LIQ5dKNabfWkiFQQcXpbQZTMt7f39LeuSn0ZERETdnr+nArOGh2LW8FA0aLT4ICkTa3am6bXRiCIyi6st/kRd+9qQgIiIiLqEk1SC2wYGomUBkVQQ0NvH8hsyMrAQERGRUYFKF6y9eyCkQmNqaSqbtsZ+RbwlRERERK2aPbwXxvb3bbVs2lIYWIiIiKhNgUoXq+8CzVtCREREZPMYWIiIiMjmMbAQERGRzWNgISIiIpvHwEJEREQ2j4GFiIiIbB4DCxEREdk8BhYiIiKyeQwsREREZPMYWIiIiMjmMbAQERGRzbObvYREUQQAlJeXW7knRERE1F5Nv7ebfo+3xm4CS0VFBQAgNDTUyj0hIiIiU1VUVECpVLZ6XhBvFGm6Ca1Wi7y8PHh4eEAQhA69R3l5OUJDQ5GTkwNPT88u7qF94piZhuNlOo6Z6ThmpuF4ma4rx0wURVRUVCAoKAgSSesrVexmhkUikSAkJKRL3svT05N/aE3EMTMNx8t0HDPTccxMw/EyXVeNWVszK0246JaIiIhsHgMLERER2TwGlmbkcjlWrVoFuVxu7a50Gxwz03C8TMcxMx3HzDQcL9NZY8zsZtEtERER2S/OsBAREZHNY2AhIiIim8fAQkRERDaPgYWIiIhsnl0HlvXr1yM8PBwKhQJxcXE4dOhQq21VKhXuueceREZGQiKRYPHixQZtNm3ahDFjxqBHjx7o0aMHJk6ciGPHjpnxCiyvq8esuU8//RSCIGDGjBld22krM8eYlZaW4rHHHkNgYCAUCgWio6Oxa9cuM12BZZljvF5//XVERkbCxcUFoaGhWLJkCWpra810BZZnyph9+eWXmDRpEnx9feHp6Yn4+Hj8+OOPBu22b9+OmJgYyOVyxMTE4KuvvjLnJVhcV4+ZvX/+m+PPWJOu+uy328CSmJiIxYsXY8WKFUhJScGYMWMwbdo0ZGdnG21fV1cHX19frFixAoMGDTLa5sCBA/jrX/+Kn376CUlJSejVqxcmT56M3Nxcc16KxZhjzJpkZWXhySefxJgxY8zRdasxx5jV19dj0qRJyMzMxBdffIFz585h06ZNCA4ONuelWIQ5xuvjjz/GsmXLsGrVKqSlpWHz5s1ITEzE8uXLzXkpFmPqmP3888+YNGkSdu3aheTkZCQkJGD69OlISUnRtUlKSsLs2bMxd+5cnDx5EnPnzsWsWbPw66+/WuqyzMocY2bPn//mGK8mXfrZL9qpm2++WVy0aJHesaioKHHZsmU3fO24cePEf/zjHzdsp1arRQ8PD/H999/vaDdtirnGTK1Wi6NGjRLfffdd8YEHHhDvvPPOLuitbTDHmG3YsEHs06ePWF9f31XdtBnmGK/HHntMnDBhgt6xpUuXiqNHj+5UX21FZ8asSUxMjPj888/rvp81a5Y4depUvTZTpkwR58yZ07nO2ghzjFlL9vT5b67x6urPfrucYamvr0dycjImT56sd3zy5Mk4evRol/2c6upqNDQ0oGfPnl32ntZizjFbvXo1fH19sWDBgk69j60x15jt2LED8fHxeOyxx+Dv74/Y2Fi8+OKL0Gg0ne2yVZlrvEaPHo3k5GTd9Hx6ejp27dqF22+/vVP9tQVdMWZarRYVFRV6n1NJSUkG7zllypQu/Xy0FnONWUv28vlvzvHq6s9+u9n8sLni4mJoNBr4+/vrHff390d+fn6X/Zxly5YhODgYEydO7LL3tBZzjdmRI0ewefNmnDhxopM9tD3mGrP09HTs378f9957L3bt2oULFy7gscceg1qtxrPPPtvZbluNucZrzpw5KCoqwujRoyGKItRqNR555BEsW7ass122uq4Ys1dffRVVVVWYNWuW7lh+fr7ZPx+txVxj1pK9fP6ba7zM8dlvl4GliSAIet+LomhwrKNeeeUVbNu2DQcOHIBCoeiS97QFXTlmFRUVuO+++7Bp0yb4+Ph0RfdsUlf/OdNqtfDz88M777wDqVSKuLg45OXlYd26dd06sDTp6vE6cOAAXnjhBaxfvx4jRozAxYsX8Y9//AOBgYFYuXJlZ7trEzo6Ztu2bcNzzz2Hb775Bn5+fl3ynt2FOcasiT1+/nfleJnrs98uA4uPjw+kUqlBOiwsLDRIkR3xn//8By+++CL27t2Lm266qdPvZwvMMWaXLl1CZmYmpk+frjum1WoBADKZDOfOnUNERETHO21l5vpzFhgYCCcnJ0ilUt2x6Oho5Ofno76+Hs7Ozh1+b2sy13itXLkSc+fOxUMPPQQAGDhwIKqqqvDwww9jxYoVkEi6753vzoxZYmIiFixYgM8//9xgFiAgIMBsn4/WZq4xa2Jvn//mGC9zffZ337/JbXB2dkZcXBz27Nmjd3zPnj0YOXJkp9573bp1WLNmDX744QcMGzasU+9lS8wxZlFRUTh16hROnDih+7rjjjuQkJCAEydOIDQ0tCu6bjXm+nM2atQoXLx4UfcXHADOnz+PwMDAbhtWAPONV3V1tUEokUqlEEURYjffKq2jY7Zt2zbMmzcPn3zyidG1PPHx8QbvuXv37k5/PtoCc40ZYJ+f/+YYL7N99ndqya4N+/TTT0UnJydx8+bNYmpqqrh48WLRzc1NzMzMFEVRFJctWybOnTtX7zUpKSliSkqKGBcXJ95zzz1iSkqKeObMGd35l19+WXR2dha/+OILUaVS6b4qKiosem3mYo4xa8neqoTMMWbZ2dmiu7u7+Pjjj4vnzp0Td+7cKfr5+Yn//ve/LXpt5mCO8Vq1apXo4eEhbtu2TUxPTxd3794tRkREiLNmzbLotZmLqWP2ySefiDKZTHzrrbf0PqdKS0t1bY4cOSJKpVLxpZdeEtPS0sSXXnpJlMlk4i+//GLx6zMHc4yZPX/+m2O8WuqKz367DSyiKIpvvfWWGBYWJjo7O4tDhw4VDx48qDv3wAMPiOPGjdNrD8DgKywsTHc+LCzMaJtVq1ZZ5oIsoKvHrCV7CyyiaJ4xO3r0qDhixAhRLpeLffr0EV944QVRrVZb4GrMr6vHq6GhQXzuuefEiIgIUaFQiKGhoeKjjz4qXr161TIXZAGmjNm4ceOMjtkDDzyg956ff/65GBkZKTo5OYlRUVHi9u3bLXQ1ltHVY2bvn//m+DPWXFd89gui2M3nTImIiMju2eUaFiIiIrIvDCxERERk8xhYiIiIyOYxsBAREZHNY2AhIiIim8fAQkRERDaPgYWIiIhsHgMLERER2TwGFiKyuN69e+P111/v8vcRBAFff/01ACAzMxOCIHTp9vZEZD0MLERkkunTp7e6k21SUhIEQcDvv//epT/zvffeg5eXl8Hx3377DQ8//LDR14SGhkKlUiE2NhYAcODAAQiCgNLS0i7tGxFZBgMLEZlkwYIF2L9/P7KysgzObdmyBYMHD8bQoUMt0hdfX1+4uroaPSeVShEQEACZTGaRvhCReTGwEJFJ/vSnP8HPzw/vvfee3vHq6mokJiZiwYIF2L59OwYMGAC5XI7evXvj1VdfbfM9X3vtNQwcOBBubm4IDQ3Fo48+isrKSgCNMyMPPvggysrKIAgCBEHAc889B6DtW0vNbwllZmYiISEBANCjRw8IgoB58+bhgw8+gLe3N+rq6vReO3PmTNx///2mDw4RmQ0DCxGZRCaT4f7778d7772H5nunfv7556ivr0d8fDxmzZqFOXPm4NSpU3juueewcuVKg4DTnEQiwRtvvIHTp0/j/fffx/79+/Gvf/0LADBy5Ei8/vrr8PT0hEqlgkqlwpNPPmlSn0NDQ7F9+3YAwLlz56BSqfC///0Pf/nLX6DRaLBjxw5d2+LiYuzcuRMPPvigST+DiMyLgYWITDZ//nxkZmbiwIEDumNbtmzB3Xffjddeew233norVq5cif79+2PevHl4/PHHsW7dulbfb/HixUhISEB4eDgmTJiANWvW4LPPPgMAODs7Q6lUQhAEBAQEICAgAO7u7ib1VyqVomfPngAAPz8/BAQEQKlUwsXFBffccw+2bt2qa/vxxx8jJCQE48ePN+lnEJF5MbAQkcmioqIwcuRIbNmyBQBw6dIlHDp0CPPnz0daWhpGjRql137UqFG4cOECNBqN0ff76aefMGnSJAQHB8PDwwP3338/SkpKUFVVZfZrWbhwIXbv3o3c3FwAwNatWzFv3jwIgmD2n01E7cfAQkQd0rRWpby8HFu3bkVYWBhuvfVWiKJo8Mu++a2jlrKysnDbbbchNjYW27dvR3JyMt566y0AQENDg1mvAQCGDBmCQYMG4YMPPsDvv/+OU6dOYd68eWb/uURkGgYWIuqQWbNmQSqV4pNPPsH777+PBx98EIIgICYmBocPH9Zre/ToUfTv3x9SqdTgfY4fPw61Wo1XX30Vt9xyC/r374+8vDy9Ns7Ozq3OzrSXs7MzABh9n4ceeghbt27Fli1bMHHiRISGhnbqZxFR12NgIaIOcXd3x+zZs/H0008jLy9PNyvxz3/+E/v27cOaNWtw/vx5vP/++3jzzTdbXSgbEREBtVqN//u//0N6ejo+/PBDbNy4Ua9N7969UVlZiX379qG4uBjV1dUm9zcsLAyCIGDnzp0oKirSVSEBwL333ovc3Fxs2rQJ8+fPN/m9icj8GFiIqMMWLFiAq1evYuLEiejVqxcAYOjQofjss8/w6aefIjY2Fs8++yxWr17d6m2WwYMH47XXXsPLL7+M2NhYfPzxx1i7dq1em5EjR2LRokWYPXs2fH198corr5jc1+DgYDz//PNYtmwZ/P398fjjj+vOeXp6YubMmXB3d8eMGTNMfm8iMj9BbOvmMhGRg5g0aRKio6PxxhtvWLsrRGQEAwsRObQrV65g9+7duPfee5GamorIyEhrd4mIjOAzq4nIoQ0dOhRXr17Fyy+/zLBCZMM4w0JEREQ2j4tuiYiIyOYxsBAREZHNY2AhIiIim8fAQkRERDaPgYWIiIhsHgMLERER2TwGFiIiIrJ5DCxERERk8/4/8vJq+WmTipoAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# efweights = efficient frontier weight. This is a list that gives us all the points associated with the portfolios \n",
    "# of these 4 assets defined above on the ef. Look at the 50 portfolios on the ef line\n",
    "efweights = optimal_weights(50, eret[l], cov.loc[l,l])\n",
    "\n",
    "# Calculate the portfolio return and vol \n",
    "pret = [portfolio_ret(w, eret[l]) for w in efweights]\n",
    "pvol= [portfolio_vol(w, cov.loc[l,l]) for w in efweights]\n",
    "\n",
    "# Put the above returns and volatilities in a data frame then visuslize then \n",
    "ef = pd.DataFrame({\"Return\": pret, \n",
    "                   \"Volatility\": pvol})\n",
    "ef\n",
    "ef.plot.line(x=\"Volatility\", y=\"Return\", style=\".-\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "fed63cc9",
   "metadata": {},
   "source": [
    "### Part A.\tGlobal Minimum Variance Portfolio: (25%) \n",
    "1.\ta)  Modify the optimization function that we developed in class (“minimize_vol()”) so that it generates the weights for the Global Minimum Variance portfolio and name it gmv(). \n",
    "2.\tb)  Use the function that you developed on the set of your favorite ten industries and characterize the Global Minimum Variance portfolio—that is, find the asset weights, expected return, and volatility for this portfolio. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "92f93a5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gmv(target_return, ereturns, covmat):\n",
    "    \"\"\"\n",
    "    target return --> weights in a minimum-variance portfolio that generates target return\n",
    "    \"\"\"\n",
    "    n=ereturns.shape[0]\n",
    "    init_values=np.repeat(1/n, n)\n",
    "    \n",
    "    bounds=((0,1),)*n \n",
    "    \n",
    "    #Constraints:\n",
    "    weights_sum_to_1={'type':'eq',\n",
    "                     'fun': lambda weights: np.sum(weights)-1}\n",
    "    \n",
    "    return_is_target={'type':'eq',\n",
    "                     'args':(ereturns,),\n",
    "                     'fun': lambda weights, ereturns: portfolio_ret(weights, ereturns)-target_return}\n",
    "    \n",
    "    results=minimize(portfolio_vol,\n",
    "                    init_values,\n",
    "                    args=(covmat,),\n",
    "                    method='SLSQP',\n",
    "                    bounds=bounds,\n",
    "                    constraints=(weights_sum_to_1, return_is_target),\n",
    "                    options={'disp':False})\n",
    "    \n",
    "    weights=results.x\n",
    "    return weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "1e430e46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7.29607637e-02, 0.00000000e+00, 4.71849658e-01, 6.79704549e-02,\n",
       "       1.85828430e-01, 5.55382563e-17, 2.01390693e-01, 0.00000000e+00,\n",
       "       3.03576608e-17, 0.00000000e+00])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Asset weights og the global minimum variance portfolio\n",
    "w11=gmv(0.11, eret[l], cov.loc[l,l])\n",
    "w11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "99f1bde4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11000000000058519"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Porfolio return \n",
    "portfolio_ret(w11,eret[l])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "68d91713",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.170701287293143"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Porfolio variance \n",
    "portfolio_vol(w11, cov.loc[l,l])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "0a3f7c17",
   "metadata": {},
   "source": [
    "### Part B.\tMaximum Sharpe Ratio Portfolio: (45%) \n",
    "1.\ta)  Modify the optimization function that we developed in class (“minimize_vol()”) so that it generates the weights for the Maximum Sharpe Ratio portfolio and name it msr().        Hint: maximizing f(x) is the same as minimizing -f(x). \n",
    "\n",
    "2.\tb)  Use the function that you developed on the set of your favorite ten industries and characterize the Maximum Sharpe Ratio portfolio—that is, find the asset weights, expected return, and volatility for this portfolio. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "b5901a5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def msr(returns):\n",
    "    \"\"\"\n",
    "    Computes the weights of the Maximum Sharpe Ratio portfolio.\n",
    "\n",
    "    Parameters:\n",
    "    returns (pd.DataFrame): A pandas dataframe of asset returns.\n",
    "\n",
    "    Returns:\n",
    "    weights (np.array): An array of floats representing the weights of each asset in the portfolio.\n",
    "    \"\"\"\n",
    "    n = returns.shape[1]\n",
    "    initial_weights = np.array([1/n]*n)\n",
    "\n",
    "    # Define the objective function to be minimized\n",
    "    def negative_sharpe_ratio(weights, returns):\n",
    "        port_return = np.dot(returns.mean(), weights)\n",
    "        port_volatility = np.sqrt(np.dot(weights.T, np.dot(returns.cov(), weights)))\n",
    "        return -port_return/port_volatility\n",
    "\n",
    "    # Define the weight constraints\n",
    "    bounds = ((0,1),)*n\n",
    "    weight_constraint = {'type': 'eq', 'fun': lambda x: np.sum(x) - 1}\n",
    "\n",
    "    # Use scipy.optimize.minimize to minimize the objective function\n",
    "    result = minimize(negative_sharpe_ratio, \n",
    "                      initial_weights, \n",
    "                      args=returns, \n",
    "                      method='SLSQP', \n",
    "                      bounds=bounds, \n",
    "                      constraints=weight_constraint)\n",
    "\n",
    "    return result.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "6c5b1559",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.21908365e-02, 3.54922438e-01, 5.41000551e-11, 1.51114096e-01,\n",
       "       3.90206809e-01, 3.98781159e-10, 3.23071392e-10, 1.38303233e-10,\n",
       "       1.55209318e-10, 9.15658190e-02])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Weights for the Maximum Sharpe Ratio portfolio\n",
    "w11=msr(ret[l])\n",
    "w11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "605527ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09363485780253815"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Porfolio return \n",
    "portfolio_ret(w11,eret[l])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "3deb8d72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.14700292802768974"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Porfolio variance\n",
    "portfolio_vol(w11, cov.loc[l,l])"
   ]
  }
 ],
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