Markowitz portfolio of PG and GSPC.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Henry Markowitz=Investor should not put all eggs in single basket. \n",
    "#He proved existence of an efficient set of portfolios that optimize returns for amount of risk that investors willing to accept.\n",
    "#Investors invest in those securities that have low correlations between them.\n",
    "#He assumes investors are rational(expecting high returns) and risk averse(low risk).\n",
    "#"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from pandas_datareader import data as wb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "assets = ['PG', '^GSPC']\n",
    "pf_data = pd.DataFrame()\n",
    "\n",
    "for a in assets:\n",
    "    pf_data[a]= wb.DataReader(a, data_source='yahoo', start ='2010-1-1')['Adj Close']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PG</th>\n",
       "      <th>^GSPC</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>2009-12-31</th>\n",
       "      <td>43.701378</td>\n",
       "      <td>1115.099976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-04</th>\n",
       "      <td>44.054558</td>\n",
       "      <td>1132.989990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-05</th>\n",
       "      <td>44.068977</td>\n",
       "      <td>1136.520020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-06</th>\n",
       "      <td>43.859955</td>\n",
       "      <td>1137.140015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-07</th>\n",
       "      <td>43.622089</td>\n",
       "      <td>1141.689941</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   PG        ^GSPC\n",
       "Date                              \n",
       "2009-12-31  43.701378  1115.099976\n",
       "2010-01-04  44.054558  1132.989990\n",
       "2010-01-05  44.068977  1136.520020\n",
       "2010-01-06  43.859955  1137.140015\n",
       "2010-01-07  43.622089  1141.689941"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pf_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PG</th>\n",
       "      <th>^GSPC</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>2020-06-03</th>\n",
       "      <td>118.529999</td>\n",
       "      <td>3122.870117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-04</th>\n",
       "      <td>116.050003</td>\n",
       "      <td>3112.350098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-05</th>\n",
       "      <td>118.330002</td>\n",
       "      <td>3193.929932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-08</th>\n",
       "      <td>119.050003</td>\n",
       "      <td>3232.389893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-09</th>\n",
       "      <td>118.339996</td>\n",
       "      <td>3207.179932</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    PG        ^GSPC\n",
       "Date                               \n",
       "2020-06-03  118.529999  3122.870117\n",
       "2020-06-04  116.050003  3112.350098\n",
       "2020-06-05  118.330002  3193.929932\n",
       "2020-06-08  119.050003  3232.389893\n",
       "2020-06-09  118.339996  3207.179932"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pf_data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11e2d0e90>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#normalization to 100 and plotting how two assets are performing\n",
    "norm=pf_data/pf_data.iloc[0]*100\n",
    "\n",
    "(pf_data/pf_data.iloc[0]*100).plot(figsize=(10,5))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>PG</th>\n",
       "      <th>^GSPC</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>2009-12-31</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-04</th>\n",
       "      <td>100.808167</td>\n",
       "      <td>101.604342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-05</th>\n",
       "      <td>100.841162</td>\n",
       "      <td>101.920908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-06</th>\n",
       "      <td>100.362865</td>\n",
       "      <td>101.976508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-07</th>\n",
       "      <td>99.818568</td>\n",
       "      <td>102.384536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    PG       ^GSPC\n",
       "Date                              \n",
       "2009-12-31  100.000000  100.000000\n",
       "2010-01-04  100.808167  101.604342\n",
       "2010-01-05  100.841162  101.920908\n",
       "2010-01-06  100.362865  101.976508\n",
       "2010-01-07   99.818568  102.384536"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\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>PG</th>\n",
       "      <th>^GSPC</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>2009-12-31</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-04</th>\n",
       "      <td>0.008049</td>\n",
       "      <td>0.015916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-05</th>\n",
       "      <td>0.000327</td>\n",
       "      <td>0.003111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-06</th>\n",
       "      <td>-0.004754</td>\n",
       "      <td>0.000545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-07</th>\n",
       "      <td>-0.005438</td>\n",
       "      <td>0.003993</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  PG     ^GSPC\n",
       "Date                          \n",
       "2009-12-31       NaN       NaN\n",
       "2010-01-04  0.008049  0.015916\n",
       "2010-01-05  0.000327  0.003111\n",
       "2010-01-06 -0.004754  0.000545\n",
       "2010-01-07 -0.005438  0.003993"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#log returns\n",
    "log_returns=np.log(pf_data/pf_data.shift(1))\n",
    "log_returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PG       0.094838\n",
       "^GSPC    0.100576\n",
       "dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#annualized average log returns\n",
    "log_returns_a=log_returns.mean()*250\n",
    "log_returns_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "        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>PG</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PG</th>\n",
       "      <td>0.029531</td>\n",
       "      <td>0.017881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>^GSPC</th>\n",
       "      <td>0.017881</td>\n",
       "      <td>0.030334</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             PG     ^GSPC\n",
       "PG     0.029531  0.017881\n",
       "^GSPC  0.017881  0.030334"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#annualized covariance between log returns of assets \n",
    "cov_a=log_returns.cov()*250\n",
    "cov_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
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       "        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>PG</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PG</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.597445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>^GSPC</th>\n",
       "      <td>0.597445</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             PG     ^GSPC\n",
       "PG     1.000000  0.597445\n",
       "^GSPC  0.597445  1.000000"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_returns.corr()#correlation between log returns of PG and GSPC. HIgh correlation between PG and GSPC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#what would be weights of assets?.  We wants sum of weights =1 \n",
    "#lets do experiment\n",
    "num_assets = len(assets)\n",
    "num_assets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.09279021, 0.34772529])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#if we randomly selected weigths, then\n",
    "arr = np.random.random(2)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.44051550525683836"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[0] + arr[1]#sum not equal to 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.47574884, 0.52425116])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#so we will find sum of weights equal to 1 by using following method\n",
    "weights = np.random.random(num_assets)\n",
    "weights /=np.sum(weights)#/= is a incremental operation. #weights=(w1/w1+w2)+(w2/w1+w2)=1\n",
    "weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights[0]+weights[1]#got sum is equal to 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Expected portfolio return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09926051817603876"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sum(weights*annualized average log return\n",
    "np.sum(weights* log_returns_a)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Expected portfolio variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "#(w1*sd1+w2*sd2)^2=w1^2*sd1^2+2w1*sd1*sd2*cov()+w2^2*sd2^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0258913011627511"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#W^T*Cov*W\n",
    "exp_port_var= np.dot(weights.T, np.dot(log_returns.cov()*250, weights))\n",
    "exp_port_var"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Expced portfolio volatility\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16090774115234824"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sd of expected portfolio variance\n",
    "exp_port_vol= np.sqrt(exp_port_var)\n",
    "exp_port_vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "#consider 1000 different combinations fof the smae assets\n",
    " #simulate 1000 combinations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "#we want to pfolio_returns and pfolio_vol for efficient frontier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
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       "  0.16451373064313848,\n",
       "  0.1630885794111183])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#define those objects\n",
    "pfolio_returns = []\n",
    "pfolio_volatilities = []\n",
    "\n",
    "for x in range(1000):\n",
    "    weights = np.random.random(num_assets)\n",
    "    weights /=np.sum(weights)#(w1/w1+w2)+(w2/w1+w2)=1#got two weights whose sum is 1\n",
    "    pfolio_returns.append(np.sum(weights* log_returns_a))\n",
    "    pfolio_volatilities.append(np.sqrt(np.dot(weights.T, np.dot(log_returns.cov()*250, weights))))\n",
    "    \n",
    "pfolio_returns, pfolio_volatilities#gives list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "        0.10033267, 0.09678632, 0.09740081, 0.09871451, 0.09804952,\n",
       "        0.09952491, 0.09931569, 0.09860975, 0.09671624, 0.09718775,\n",
       "        0.09732287, 0.09681087, 0.09936735, 0.09861321, 0.09749498,\n",
       "        0.09806664, 0.09938893, 0.0956642 , 0.09589555, 0.09629439,\n",
       "        0.09732446, 0.09878426, 0.09870232, 0.097676  , 0.09887013,\n",
       "        0.09530427, 0.09867148, 0.09822502, 0.0959862 , 0.09668438,\n",
       "        0.0983629 , 0.09871874, 0.09576573, 0.09979843, 0.0960076 ,\n",
       "        0.09803008, 0.09968673, 0.10043488, 0.09962186, 0.09606665,\n",
       "        0.09766152, 0.09566375, 0.09664821, 0.09736542, 0.09776934,\n",
       "        0.09773887, 0.09770004, 0.09785083, 0.09945611, 0.09829063,\n",
       "        0.09851797, 0.09915994, 0.09630524, 0.09650457, 0.09552072,\n",
       "        0.09637655, 0.09637837, 0.09976482, 0.09692611, 0.09594566,\n",
       "        0.09502073, 0.09672774, 0.09522964, 0.09651759, 0.09617533,\n",
       "        0.09948628, 0.09906891, 0.09929021, 0.09650757, 0.0965313 ,\n",
       "        0.09514309, 0.09864226, 0.09834765, 0.09928452, 0.09986613,\n",
       "        0.09899652, 0.09635283, 0.09745352, 0.09579782, 0.09509901,\n",
       "        0.09655973, 0.09965066, 0.0978728 , 0.09588234, 0.09630825,\n",
       "        0.09949019, 0.0973771 , 0.09932152, 0.09660357, 0.09870299,\n",
       "        0.09634649, 0.09975477, 0.09550429, 0.09762711, 0.09710048,\n",
       "        0.09495691, 0.09840954, 0.09986044, 0.09841318, 0.09823225,\n",
       "        0.09577935, 0.09774044, 0.09988324, 0.09946988, 0.09657618,\n",
       "        0.09790986, 0.09655567, 0.09715739, 0.09959663, 0.10049992,\n",
       "        0.09763298, 0.09800171, 0.09875953, 0.09902862, 0.09759426,\n",
       "        0.09783461, 0.09585413, 0.09848982, 0.09739065, 0.0972814 ,\n",
       "        0.09841716, 0.09850338, 0.09920757, 0.09768009, 0.09585262,\n",
       "        0.09785216, 0.0998128 , 0.0970412 , 0.09703973, 0.09757664,\n",
       "        0.0989317 , 0.09787353, 0.097278  , 0.09765467, 0.1001231 ,\n",
       "        0.09961035, 0.0986642 , 0.09824412, 0.09990384, 0.10023329,\n",
       "        0.09719932, 0.10002536, 0.09658538, 0.09819809, 0.09881988,\n",
       "        0.09825312, 0.0968696 , 0.09951925, 0.09919944, 0.09721141,\n",
       "        0.09621184, 0.09738529, 0.09852628, 0.09521471, 0.09940996,\n",
       "        0.09767581, 0.09844023, 0.10001075, 0.09747402, 0.09962168,\n",
       "        0.09823678, 0.0987281 , 0.0967658 , 0.09621765, 0.09696188,\n",
       "        0.10033416, 0.09623524, 0.09785242, 0.10012543, 0.09893838,\n",
       "        0.097597  , 0.09698426, 0.09789336, 0.09735624, 0.09685677,\n",
       "        0.09989966, 0.0979446 , 0.09939575, 0.09916101, 0.09893686,\n",
       "        0.0990466 , 0.09705699, 0.09808403, 0.09633915, 0.09741469,\n",
       "        0.0965165 , 0.09761808, 0.09828106, 0.09912202, 0.09853439,\n",
       "        0.10052211, 0.09969747, 0.09714278, 0.0976205 , 0.1004386 ,\n",
       "        0.09789979, 0.09881864, 0.09498408, 0.09502777, 0.09888213,\n",
       "        0.09726888, 0.09516055, 0.09888118, 0.09687778, 0.09786934,\n",
       "        0.09861664, 0.09646688, 0.09772946, 0.09540853, 0.09891562,\n",
       "        0.09759098, 0.09725348, 0.09861317, 0.09810612, 0.09652496,\n",
       "        0.09855861, 0.09754568, 0.09911241, 0.09737218, 0.09802781,\n",
       "        0.09664778, 0.09722718, 0.0967675 , 0.09822955, 0.09746298,\n",
       "        0.09507874, 0.09791909, 0.09809468, 0.09630366, 0.09613839,\n",
       "        0.09741084, 0.09725422, 0.0960466 , 0.10027001, 0.09677169,\n",
       "        0.0950561 , 0.0964905 , 0.09783027, 0.09841055, 0.09837551,\n",
       "        0.09681113, 0.09895752, 0.09909963, 0.09780997, 0.0989473 ,\n",
       "        0.09924331, 0.0975053 , 0.09743009, 0.09954101, 0.09873972,\n",
       "        0.09883401, 0.09794245, 0.09768713, 0.10004889, 0.09703253,\n",
       "        0.09570683, 0.09712451, 0.09492606, 0.0958044 , 0.09594556,\n",
       "        0.09581109, 0.09795747, 0.0969718 , 0.0965885 , 0.09885558,\n",
       "        0.09913663, 0.09766796, 0.09799918, 0.09659995, 0.10025046,\n",
       "        0.09841225, 0.09736693, 0.09779987, 0.09600422, 0.09983088,\n",
       "        0.09979744, 0.09485707, 0.09821765, 0.09738504, 0.0982462 ,\n",
       "        0.09517316, 0.09715508, 0.09819518, 0.09893355, 0.0954663 ,\n",
       "        0.09696494, 0.09497494, 0.09877912, 0.09708497, 0.10007334,\n",
       "        0.09941929, 0.09885577, 0.09614336, 0.09975502, 0.0975151 ,\n",
       "        0.09978986, 0.09978954, 0.09909108, 0.09501949, 0.09716748,\n",
       "        0.09773251, 0.09611781, 0.0969939 , 0.09827832, 0.0968449 ,\n",
       "        0.09584445, 0.09700823, 0.09789922, 0.09787993, 0.09932825,\n",
       "        0.09745941, 0.09634063, 0.0994256 , 0.09862325, 0.09543341,\n",
       "        0.09780043, 0.09914025, 0.09495775, 0.09582407, 0.09487354,\n",
       "        0.09576508, 0.09498468, 0.09756637, 0.09743333, 0.09820333,\n",
       "        0.09824599, 0.09774579, 0.09757394, 0.09906651, 0.09706535,\n",
       "        0.09509227, 0.09769815, 0.09948172, 0.09710198, 0.09610828,\n",
       "        0.09492071, 0.09780227, 0.09866381, 0.09808255, 0.09852195,\n",
       "        0.09823781, 0.09571531, 0.09706256, 0.10052851, 0.09726963,\n",
       "        0.09908336, 0.09837867, 0.09782257, 0.09645686, 0.09523291,\n",
       "        0.09770151, 0.0984492 , 0.09855491, 0.09565405, 0.09644584,\n",
       "        0.0970634 , 0.09683885, 0.09729537, 0.09614949, 0.09843433,\n",
       "        0.099573  , 0.09732577, 0.09947499, 0.09978249, 0.09580565,\n",
       "        0.0972851 , 0.0984105 , 0.0965318 , 0.09802667, 0.09837972,\n",
       "        0.0981405 , 0.09572028, 0.09856878, 0.0975189 , 0.09590115,\n",
       "        0.09726569, 0.09743674, 0.09854437, 0.09688668, 0.09916267,\n",
       "        0.09686574, 0.09599008, 0.09624491, 0.09759165, 0.09849749,\n",
       "        0.09892612, 0.09771505, 0.09721972, 0.09491179, 0.09689292,\n",
       "        0.09651868, 0.09804517, 0.09698131, 0.09946085, 0.09771255,\n",
       "        0.09620583, 0.09787507, 0.09903856, 0.09951982, 0.09929648,\n",
       "        0.09907841, 0.09855323, 0.09790137, 0.09982678, 0.09878711,\n",
       "        0.09755392, 0.09742585, 0.09778066, 0.09741274, 0.09899964,\n",
       "        0.09769799, 0.09687551, 0.09777193, 0.09731797, 0.09639963,\n",
       "        0.09813467, 0.09685794, 0.0990083 , 0.09686683, 0.09709453,\n",
       "        0.09926698, 0.09891317, 0.09710561, 0.0969742 , 0.09744893,\n",
       "        0.09860246, 0.09915615, 0.09650773, 0.09658482, 0.09763237,\n",
       "        0.09827252, 0.09517703, 0.09856759, 0.09755135, 0.09675312,\n",
       "        0.09691624, 0.09645273, 0.10029008, 0.09536719, 0.10031568,\n",
       "        0.09491103, 0.09764361, 0.09950289, 0.10023041, 0.09636097,\n",
       "        0.09525431, 0.09773615, 0.09607945, 0.09522307, 0.09926952,\n",
       "        0.09526012, 0.09843266, 0.09668911, 0.0973208 , 0.10003781,\n",
       "        0.0953982 , 0.09586452, 0.09512738, 0.09908693, 0.09758149,\n",
       "        0.09711969, 0.09991335, 0.09775295, 0.0964104 , 0.09892491,\n",
       "        0.09799856, 0.09830813, 0.09587642, 0.09867331, 0.0972295 ,\n",
       "        0.10013132, 0.09817846, 0.09818369, 0.09872995, 0.09541417,\n",
       "        0.09764092, 0.09997701, 0.09937268, 0.09811047, 0.09789737,\n",
       "        0.09720875, 0.10013335, 0.09592737, 0.09996699, 0.09784337,\n",
       "        0.09603394, 0.09871928, 0.09904335, 0.09713226, 0.09705478,\n",
       "        0.09587896, 0.09677807, 0.09958807, 0.09636278, 0.09547972,\n",
       "        0.09781353, 0.09808957, 0.09755405, 0.09645578, 0.0979463 ,\n",
       "        0.09742665, 0.09865367, 0.09716366, 0.09713639, 0.09834247,\n",
       "        0.09857009, 0.09780972, 0.09609944, 0.09868803, 0.09747232,\n",
       "        0.09873815, 0.09967292, 0.09560194, 0.09910229, 0.09819337,\n",
       "        0.09849956, 0.09521085, 0.09930595, 0.09599562, 0.0958957 ,\n",
       "        0.09719941, 0.09812907, 0.09544647, 0.09614129, 0.09978261,\n",
       "        0.09571689, 0.09834394, 0.0990351 , 0.09949672, 0.09752217,\n",
       "        0.09957264, 0.09865925, 0.10049049, 0.09773292, 0.09771422,\n",
       "        0.09637101, 0.09801246, 0.09935864, 0.10035638, 0.09981892,\n",
       "        0.09711564, 0.09791701, 0.09795689, 0.09878227, 0.0995606 ,\n",
       "        0.10024583, 0.09832083, 0.09671451, 0.09921695, 0.0963744 ,\n",
       "        0.09780053, 0.09626134, 0.10027315, 0.09815432, 0.0989821 ,\n",
       "        0.09770854, 0.09805659, 0.09928556, 0.09633665, 0.09967023,\n",
       "        0.09534614, 0.09684698, 0.0961531 , 0.09981553, 0.09811008,\n",
       "        0.09765346, 0.09996878, 0.09726106, 0.09702815, 0.09750532,\n",
       "        0.09677118, 0.09529454, 0.09988107, 0.09917553, 0.09949112,\n",
       "        0.09983152, 0.09991873, 0.09896787, 0.0967646 , 0.09585811,\n",
       "        0.09950267, 0.09844025, 0.09964163, 0.09621222, 0.09673932,\n",
       "        0.09869341, 0.09949676, 0.09692968, 0.09778636, 0.09716791,\n",
       "        0.09807859, 0.09818325, 0.09593119, 0.09785802, 0.09815201,\n",
       "        0.09811674, 0.09937905, 0.09824246, 0.09571569, 0.10012227,\n",
       "        0.0977547 , 0.09762579, 0.09825246, 0.09973335, 0.09704329,\n",
       "        0.09960665, 0.09608872, 0.09771483, 0.09626078, 0.09927234,\n",
       "        0.09714786, 0.09679744, 0.09700743, 0.09819205, 0.09971857,\n",
       "        0.09749058, 0.09825282, 0.09749947, 0.09702138, 0.0959187 ,\n",
       "        0.09823262, 0.09719893, 0.09690059, 0.09958933, 0.09760108,\n",
       "        0.09727289, 0.09727796, 0.09844588, 0.09619843, 0.09799509,\n",
       "        0.09743546, 0.09601602, 0.0979073 , 0.09765954, 0.09697396,\n",
       "        0.09843617, 0.09621222, 0.09830678, 0.09795736, 0.09764652,\n",
       "        0.09839527, 0.09786488, 0.09976987, 0.09640402, 0.09922398,\n",
       "        0.09922512, 0.09700606, 0.09570178, 0.09939313, 0.09828844,\n",
       "        0.09663669, 0.09845294, 0.09525679, 0.09924878, 0.09713701,\n",
       "        0.09681165, 0.09756499, 0.09928217, 0.09692286, 0.09828616,\n",
       "        0.09944969, 0.0966823 , 0.09874929, 0.09882498, 0.0978492 ,\n",
       "        0.09884236, 0.09735885, 0.09748496, 0.0977715 , 0.09509113,\n",
       "        0.09989322, 0.09816232, 0.09620436, 0.09911743, 0.10013976,\n",
       "        0.09606712, 0.09891782, 0.09845042, 0.0973096 , 0.09999037,\n",
       "        0.09564274, 0.09756686, 0.09657328, 0.09921391, 0.09938034,\n",
       "        0.09776609, 0.09965902, 0.09894844, 0.09638479, 0.09767433,\n",
       "        0.09883809, 0.09655699, 0.10034381, 0.09643616, 0.09585387,\n",
       "        0.09988951, 0.09808093, 0.09501172, 0.09978186, 0.09964405,\n",
       "        0.09685694, 0.099343  , 0.09511819, 0.09843298, 0.0987069 ,\n",
       "        0.09574906, 0.09801783, 0.09935094, 0.09679259, 0.0999677 ,\n",
       "        0.09601287, 0.09815805, 0.09981638, 0.09665983, 0.09759096,\n",
       "        0.0954684 , 0.09793429, 0.0966188 , 0.09505038, 0.09559908,\n",
       "        0.09853496, 0.09810364, 0.09702917, 0.09960998, 0.0961949 ,\n",
       "        0.09543439, 0.09755256, 0.09599063, 0.09806641, 0.10039032,\n",
       "        0.09850006, 0.09778799, 0.09833051, 0.09501594, 0.09728813,\n",
       "        0.09972424, 0.09731829, 0.09862185, 0.09802166, 0.09639254,\n",
       "        0.09854813, 0.0984958 , 0.100403  , 0.09968087, 0.09918337,\n",
       "        0.09933625, 0.09658831, 0.09775706, 0.09618731, 0.09662451,\n",
       "        0.09897565, 0.09715118, 0.09827272, 0.09809164, 0.09660339,\n",
       "        0.09967752, 0.09699006, 0.09690601, 0.09589964, 0.09974218,\n",
       "        0.09703431, 0.0971325 , 0.09698275, 0.0980057 , 0.096717  ,\n",
       "        0.09674107, 0.09851404, 0.09646012, 0.09595666, 0.09781316,\n",
       "        0.09546012, 0.10017913, 0.09612607, 0.0993058 , 0.0982932 ,\n",
       "        0.09527528, 0.09825212, 0.09880515, 0.09604128, 0.0965179 ]),\n",
       " array([0.16828376, 0.15842544, 0.16159158, 0.15521772, 0.15627592,\n",
       "        0.1577084 , 0.15461915, 0.17251448, 0.1547707 , 0.15864089,\n",
       "        0.16075724, 0.15486052, 0.15461054, 0.15460138, 0.16540453,\n",
       "        0.15705374, 0.1708537 , 0.17295829, 0.15472773, 0.15630792,\n",
       "        0.15992456, 0.15726035, 0.15509827, 0.15724438, 0.15467485,\n",
       "        0.15527287, 0.16066792, 0.15459753, 0.15563475, 0.17412218,\n",
       "        0.15938217, 0.1647701 , 0.16469014, 0.15462214, 0.16514279,\n",
       "        0.15487187, 0.15468356, 0.15511385, 0.17099343, 0.1547595 ,\n",
       "        0.17106567, 0.16920367, 0.16344116, 0.16243403, 0.16866017,\n",
       "        0.16017624, 0.15476542, 0.16199809, 0.15459777, 0.16082341,\n",
       "        0.16581835, 0.15675493, 0.15849829, 0.15465205, 0.15460392,\n",
       "        0.16788157, 0.15537592, 0.15533651, 0.15497897, 0.16044182,\n",
       "        0.15497464, 0.15491723, 0.15624372, 0.15466811, 0.1582841 ,\n",
       "        0.15504123, 0.15616095, 0.15554469, 0.15516832, 0.15542786,\n",
       "        0.15462691, 0.15949123, 0.15508297, 0.16300368, 0.15512116,\n",
       "        0.1545992 , 0.15544772, 0.15946643, 0.15481702, 0.15522835,\n",
       "        0.16327553, 0.15478437, 0.16626758, 0.15481216, 0.16025416,\n",
       "        0.15507666, 0.16906719, 0.16481908, 0.15818379, 0.15978919,\n",
       "        0.15516867, 0.15888936, 0.15476252, 0.15463069, 0.16204746,\n",
       "        0.15809698, 0.15568582, 0.15569886, 0.16051715, 0.15629357,\n",
       "        0.15652213, 0.16000888, 0.16050799, 0.15461103, 0.15461019,\n",
       "        0.15506362, 0.15539047, 0.15562064, 0.16719105, 0.15832764,\n",
       "        0.15936418, 0.16012802, 0.1665387 , 0.15527394, 0.16652541,\n",
       "        0.15470204, 0.15809752, 0.1546488 , 0.16990415, 0.16610163,\n",
       "        0.15504815, 0.155077  , 0.15548203, 0.1574648 , 0.15562505,\n",
       "        0.15469697, 0.15479454, 0.15538644, 0.16322574, 0.15887552,\n",
       "        0.16267655, 0.16602432, 0.16990714, 0.15508771, 0.15630286,\n",
       "        0.15475522, 0.16269181, 0.15817557, 0.15461942, 0.15604826,\n",
       "        0.15974232, 0.17104875, 0.16508508, 0.15613772, 0.16438659,\n",
       "        0.15700137, 0.15620888, 0.16932062, 0.15485821, 0.15648204,\n",
       "        0.15519244, 0.15468587, 0.15624505, 0.16148204, 0.15476561,\n",
       "        0.15479768, 0.1546034 , 0.1546455 , 0.15583184, 0.1560919 ,\n",
       "        0.1546954 , 0.16265334, 0.15466942, 0.15461595, 0.16284238,\n",
       "        0.15937626, 0.15945081, 0.15519226, 0.15468381, 0.15525506,\n",
       "        0.15505197, 0.15855377, 0.16682369, 0.16030783, 0.16509265,\n",
       "        0.15942421, 0.16418291, 0.16739431, 0.154699  , 0.15463142,\n",
       "        0.16617596, 0.15463039, 0.1546937 , 0.17150734, 0.16340562,\n",
       "        0.16257041, 0.15463918, 0.15591862, 0.15914574, 0.16159817,\n",
       "        0.16715084, 0.15459755, 0.15854275, 0.15460736, 0.16101164,\n",
       "        0.16515903, 0.16068304, 0.15579544, 0.15867744, 0.15485962,\n",
       "        0.15908017, 0.15514469, 0.15467109, 0.15917042, 0.16927973,\n",
       "        0.15464971, 0.1559924 , 0.15461154, 0.15465087, 0.15478441,\n",
       "        0.15591202, 0.15781323, 0.15511587, 0.15466165, 0.15469329,\n",
       "        0.15578256, 0.16695067, 0.1546543 , 0.15477593, 0.15642674,\n",
       "        0.17123667, 0.15620134, 0.15470228, 0.15745188, 0.15505085,\n",
       "        0.16303661, 0.16132814, 0.15693923, 0.15648368, 0.15502184,\n",
       "        0.15479435, 0.15610779, 0.16173321, 0.15695534, 0.15462934,\n",
       "        0.15508695, 0.16190568, 0.16333019, 0.16141939, 0.15865214,\n",
       "        0.15479218, 0.15782053, 0.15738966, 0.15460704, 0.15830412,\n",
       "        0.16672732, 0.15723532, 0.15548599, 0.16073103, 0.15661947,\n",
       "        0.15592844, 0.15747361, 0.16246472, 0.1655358 , 0.16057356,\n",
       "        0.15501153, 0.16447957, 0.17244398, 0.16388854, 0.16014906,\n",
       "        0.15460311, 0.16333415, 0.15677918, 0.15474053, 0.15465617,\n",
       "        0.1546356 , 0.15461575, 0.15473277, 0.16245498, 0.15568554,\n",
       "        0.15653088, 0.16017438, 0.15858644, 0.15747208, 0.16462379,\n",
       "        0.15816752, 0.15815711, 0.1652129 , 0.15570565, 0.16103462,\n",
       "        0.16974938, 0.1564358 , 0.16749393, 0.15740543, 0.15940676,\n",
       "        0.1627077 , 0.15954775, 0.16113236, 0.15745663, 0.15733609,\n",
       "        0.16840897, 0.15709299, 0.15587517, 0.16108903, 0.16619946,\n",
       "        0.1590749 , 0.15830435, 0.15465629, 0.16219989, 0.16888562,\n",
       "        0.15719498, 0.16414889, 0.15475879, 0.16152257, 0.15856828,\n",
       "        0.16274072, 0.15472725, 0.16137329, 0.15698456, 0.1573931 ,\n",
       "        0.15834139, 0.16511714, 0.16477711, 0.15459777, 0.15521436,\n",
       "        0.17046985, 0.15609804, 0.16614303, 0.15611167, 0.15550698,\n",
       "        0.16235181, 0.15463655, 0.16637003, 0.16256987, 0.15711502,\n",
       "        0.15480784, 0.15721489, 0.15508477, 0.16366329, 0.17323087,\n",
       "        0.15459828, 0.15495734, 0.15768734, 0.15928179, 0.15459789,\n",
       "        0.15471502, 0.1617454 , 0.15641333, 0.15471265, 0.15485502,\n",
       "        0.15612671, 0.1564695 , 0.16051635, 0.15460833, 0.16175737,\n",
       "        0.15473428, 0.16567523, 0.15536549, 0.15536944, 0.15460007,\n",
       "        0.15867085, 0.15475968, 0.15486036, 0.1546016 , 0.16887578,\n",
       "        0.16378543, 0.1571995 , 0.15554201, 0.16657679, 0.17009758,\n",
       "        0.15499899, 0.16782897, 0.15707079, 0.15540986, 0.15801713,\n",
       "        0.15556899, 0.15589518, 0.16298801, 0.16045725, 0.1549758 ,\n",
       "        0.15916881, 0.15471832, 0.15656628, 0.16764976, 0.16207569,\n",
       "        0.15460698, 0.15621507, 0.16767549, 0.15464195, 0.163887  ,\n",
       "        0.15552027, 0.15752196, 0.15628167, 0.15913145, 0.15559334,\n",
       "        0.17125392, 0.1590193 , 0.15473458, 0.16890116, 0.15871164,\n",
       "        0.15459769, 0.15552609, 0.1547852 , 0.15475142, 0.15594026,\n",
       "        0.1665347 , 0.1548597 , 0.16196067, 0.16018197, 0.15870236,\n",
       "        0.15939963, 0.15532363, 0.15512503, 0.15838445, 0.1546889 ,\n",
       "        0.15741095, 0.15459729, 0.15565519, 0.15990905, 0.15660111,\n",
       "        0.17350264, 0.16457896, 0.15511658, 0.15459738, 0.17248854,\n",
       "        0.15479387, 0.15801022, 0.17016134, 0.16967073, 0.15837428,\n",
       "        0.15487493, 0.16822215, 0.15836867, 0.15586682, 0.15475453,\n",
       "        0.1569714 , 0.15766922, 0.15463013, 0.16569155, 0.15857347,\n",
       "        0.15459819, 0.15490043, 0.15695514, 0.15517543, 0.15736803,\n",
       "        0.15670697, 0.15460745, 0.15984274, 0.15473277, 0.15500706,\n",
       "        0.15678112, 0.15494656, 0.15627495, 0.15549912, 0.15464942,\n",
       "        0.16910713, 0.15482107, 0.15514906, 0.15859595, 0.15965339,\n",
       "        0.15469251, 0.15489918, 0.16029155, 0.17051447, 0.15625842,\n",
       "        0.16935631, 0.15754492, 0.15471048, 0.15610181, 0.15597331,\n",
       "        0.15610679, 0.15882961, 0.15975527, 0.15469044, 0.15876643,\n",
       "        0.16077922, 0.1546239 , 0.15467511, 0.16317551, 0.1575826 ,\n",
       "        0.15809672, 0.15485633, 0.15461073, 0.16807777, 0.15538896,\n",
       "        0.16296172, 0.15515779, 0.17082324, 0.16214612, 0.16103542,\n",
       "        0.1620916 , 0.15488037, 0.15556324, 0.15705591, 0.15821983,\n",
       "        0.16001057, 0.15460474, 0.15495268, 0.15700157, 0.17029193,\n",
       "        0.15610821, 0.15473877, 0.15468119, 0.16059832, 0.16585172,\n",
       "        0.16552628, 0.17162563, 0.15546482, 0.15471859, 0.15554822,\n",
       "        0.16808795, 0.15508972, 0.15540183, 0.15868212, 0.16513564,\n",
       "        0.155584  , 0.17026478, 0.15779261, 0.15525233, 0.16833841,\n",
       "        0.16215164, 0.15822093, 0.15961986, 0.16511951, 0.1546192 ,\n",
       "        0.16545306, 0.16544998, 0.1596971 , 0.16976322, 0.15506336,\n",
       "        0.15463186, 0.15979332, 0.15549783, 0.15564656, 0.15598266,\n",
       "        0.16182255, 0.15545663, 0.15479309, 0.15476772, 0.16142557,\n",
       "        0.15465196, 0.1583757 , 0.16220322, 0.15700249, 0.1654505 ,\n",
       "        0.15468169, 0.16003583, 0.17046026, 0.16198642, 0.17143262,\n",
       "        0.16247012, 0.17015456, 0.15460201, 0.15467235, 0.1554244 ,\n",
       "        0.15554757, 0.15463988, 0.15460053, 0.15953176, 0.15530195,\n",
       "        0.16895908, 0.15461497, 0.16266923, 0.15521075, 0.15985875,\n",
       "        0.17088483, 0.15468334, 0.1571976 , 0.15512174, 0.15654779,\n",
       "        0.1555233 , 0.16288935, 0.15530915, 0.17358125, 0.15487372,\n",
       "        0.15964486, 0.15598468, 0.15470265, 0.15772271, 0.16745988,\n",
       "        0.15461637, 0.15625009, 0.15669062, 0.16341905, 0.15778206,\n",
       "        0.15530696, 0.15600451, 0.15483367, 0.15957866, 0.15619226,\n",
       "        0.16345453, 0.15479041, 0.16261271, 0.16538215, 0.16213591,\n",
       "        0.15484928, 0.15610164, 0.15733359, 0.15500482, 0.15598847,\n",
       "        0.15525846, 0.16284697, 0.15675219, 0.15461749, 0.16137588,\n",
       "        0.15488012, 0.1546695 , 0.15664441, 0.15583634, 0.16019373,\n",
       "        0.15590867, 0.16070231, 0.15895823, 0.15459812, 0.15644502,\n",
       "        0.15863695, 0.15462258, 0.15496025, 0.17098781, 0.15581517,\n",
       "        0.1573999 , 0.15504191, 0.1555348 , 0.16249447, 0.15462136,\n",
       "        0.15920754, 0.15476161, 0.15934677, 0.16299295, 0.1611803 ,\n",
       "        0.15961152, 0.15668322, 0.15479604, 0.16581161, 0.15783604,\n",
       "        0.15460504, 0.15467879, 0.15466493, 0.15469072, 0.15909486,\n",
       "        0.1546149 , 0.15587465, 0.15465813, 0.15480109, 0.15803676,\n",
       "        0.15524399, 0.15593611, 0.15915033, 0.15590486, 0.1552288 ,\n",
       "        0.16095634, 0.15855871, 0.15520206, 0.15555602, 0.15465976,\n",
       "        0.15690536, 0.16014761, 0.15745581, 0.15707351, 0.15459822,\n",
       "        0.15562845, 0.16804682, 0.15674691, 0.15460576, 0.15633232,\n",
       "        0.1557377 , 0.15774487, 0.17074419, 0.1660973 , 0.17103947,\n",
       "        0.17099666, 0.15459963, 0.16284839, 0.1700651 , 0.15825714,\n",
       "        0.16723819, 0.15463398, 0.16005898, 0.16756243, 0.16097543,\n",
       "        0.16717834, 0.15618582, 0.15659901, 0.15479719, 0.16796038,\n",
       "        0.16579231, 0.16166291, 0.16857801, 0.15966897, 0.15459932,\n",
       "        0.15516893, 0.16667274, 0.15464456, 0.15797656, 0.15862957,\n",
       "        0.15495155, 0.15574214, 0.16156911, 0.15724437, 0.15494236,\n",
       "        0.16896547, 0.1553565 , 0.15537056, 0.15753161, 0.16563667,\n",
       "        0.15459924, 0.16732412, 0.16177564, 0.15518563, 0.15479058,\n",
       "        0.15498085, 0.16898762, 0.16117389, 0.16722062, 0.15472444,\n",
       "        0.16038234, 0.1574764 , 0.15937822, 0.15514013, 0.15532942,\n",
       "        0.16154915, 0.15623343, 0.16358741, 0.15824667, 0.1650083 ,\n",
       "        0.15469381, 0.15513745, 0.15460501, 0.15772852, 0.1548624 ,\n",
       "        0.15467809, 0.15714812, 0.15507142, 0.15513083, 0.15585732,\n",
       "        0.15675805, 0.1546902 , 0.1599198 , 0.15731763, 0.15464306,\n",
       "        0.15757438, 0.16435239, 0.16388145, 0.15977341, 0.15539688,\n",
       "        0.1564536 , 0.16769021, 0.16125295, 0.16066149, 0.16141828,\n",
       "        0.15499882, 0.15523024, 0.16532501, 0.15963377, 0.16538329,\n",
       "        0.16287587, 0.1558624 , 0.15932407, 0.16279598, 0.15461609,\n",
       "        0.16345134, 0.15717529, 0.17311592, 0.15463209, 0.15462217,\n",
       "        0.15819925, 0.15497743, 0.16166417, 0.17151352, 0.16573483,\n",
       "        0.15517837, 0.15481805, 0.15487942, 0.1578097 , 0.16334582,\n",
       "        0.17023941, 0.15578412, 0.15649092, 0.16058482, 0.15817981,\n",
       "        0.15468178, 0.15885538, 0.17055033, 0.15529337, 0.15898342,\n",
       "        0.15461949, 0.15506559, 0.16109698, 0.15839915, 0.16432769,\n",
       "        0.16630639, 0.15597517, 0.15955446, 0.16570181, 0.15518472,\n",
       "        0.15460136, 0.16723905, 0.15488775, 0.15540097, 0.15462389,\n",
       "        0.15626046, 0.16682604, 0.1663483 , 0.16028525, 0.16274853,\n",
       "        0.16585801, 0.16672719, 0.15889405, 0.15628644, 0.16171375,\n",
       "        0.16284645, 0.15621515, 0.16406695, 0.15916636, 0.15638822,\n",
       "        0.15734464, 0.1627963 , 0.15569417, 0.15466958, 0.15506247,\n",
       "        0.15511296, 0.15536936, 0.16114468, 0.15474103, 0.15528747,\n",
       "        0.15520048, 0.16182649, 0.15553708, 0.16288603, 0.16886675,\n",
       "        0.15464574, 0.15459767, 0.15556702, 0.16491445, 0.15535987,\n",
       "        0.16375244, 0.15999422, 0.15462247, 0.15885887, 0.16099675,\n",
       "        0.1551054 , 0.15615863, 0.15545891, 0.15539326, 0.16477563,\n",
       "        0.15463181, 0.15556809, 0.15462691, 0.15541966, 0.16124036,\n",
       "        0.15550807, 0.15499975, 0.15578941, 0.1635985 , 0.15459745,\n",
       "        0.15486848, 0.15486042, 0.15623711, 0.15925548, 0.15494523,\n",
       "        0.15467056, 0.16051209, 0.15480425, 0.15460265, 0.15555675,\n",
       "        0.15619934, 0.15916633, 0.15573771, 0.15488019, 0.15460009,\n",
       "        0.1560451 , 0.15474914, 0.1652611 , 0.15801216, 0.16063635,\n",
       "        0.16064476, 0.15546281, 0.16300504, 0.16193948, 0.15567856,\n",
       "        0.15683135, 0.15626483, 0.16721262, 0.16081997, 0.15512942,\n",
       "        0.15610484, 0.15460231, 0.16107118, 0.15571615, 0.15567132,\n",
       "        0.16240168, 0.15662849, 0.15763299, 0.15804577, 0.15473092,\n",
       "        0.15814415, 0.15474828, 0.15463511, 0.15465779, 0.16897159,\n",
       "        0.16646999, 0.15531399, 0.15921704, 0.15987735, 0.16905776,\n",
       "        0.16014575, 0.15858672, 0.15625489, 0.15481288, 0.16746273,\n",
       "        0.16351847, 0.15460191, 0.15712902, 0.16056258, 0.16183685,\n",
       "        0.15465377, 0.1642251 , 0.15877345, 0.15812057, 0.15460654,\n",
       "        0.15811981, 0.15720843, 0.17136641, 0.15783463, 0.16174748,\n",
       "        0.16643276, 0.15511813, 0.16985018, 0.16537607, 0.16408888,\n",
       "        0.15593967, 0.1615409 , 0.1686774 , 0.15618703, 0.15741298,\n",
       "        0.16260399, 0.15498766, 0.16160332, 0.15617719, 0.16722788,\n",
       "        0.16053504, 0.15530294, 0.16571003, 0.15672723, 0.15459819,\n",
       "        0.16511568, 0.15484372, 0.15691347, 0.16941957, 0.16390719,\n",
       "        0.1566036 , 0.15516967, 0.15539816, 0.16378217, 0.1592785 ,\n",
       "        0.16544111, 0.15460542, 0.16069829, 0.15508647, 0.17191316,\n",
       "        0.15645567, 0.15467093, 0.15581658, 0.16980298, 0.15484462,\n",
       "        0.16482879, 0.15480065, 0.15699588, 0.15499505, 0.15807671,\n",
       "        0.15666083, 0.15643801, 0.17206358, 0.16442549, 0.1603414 ,\n",
       "        0.16148804, 0.15705679, 0.15464736, 0.15932805, 0.1568871 ,\n",
       "        0.15894283, 0.15509817, 0.15562906, 0.15514214, 0.15698539,\n",
       "        0.16439467, 0.15550904, 0.15577135, 0.16138764, 0.16499785,\n",
       "        0.15538411, 0.15513958, 0.15553054, 0.15496472, 0.1564805 ,\n",
       "        0.15638109, 0.15651425, 0.15770528, 0.16095153, 0.15469346,\n",
       "        0.16519447, 0.16949167, 0.15973695, 0.16125185, 0.15569376,\n",
       "        0.16702266, 0.15556598, 0.15793514, 0.1603296 , 0.15740385]))"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pfolio_returns = []\n",
    "pfolio_volatilities = []\n",
    "\n",
    "for x in range(1000):\n",
    "    weights = np.random.random(num_assets)\n",
    "    weights /=np.sum(weights)#(w1/w1+w2)+(w2/w1+w2)=1#got two weights whose sum is 1\n",
    "    pfolio_returns.append(np.sum(weights* log_returns_a))\n",
    "    pfolio_volatilities.append(np.sqrt(np.dot(weights.T, np.dot(log_returns.cov()*250, weights))))\n",
    "    \n",
    "pfolio_returns = np.array(pfolio_returns)\n",
    "\n",
    "pfolio_volatilities=np.array(pfolio_volatilities)\n",
    "\n",
    "pfolio_returns, pfolio_volatilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "portfolio = pd.DataFrame({'Returns':pfolio_returns, 'Volatility':pfolio_volatilities})#dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "        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>Returns</th>\n",
       "      <th>Volatility</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.095155</td>\n",
       "      <td>0.168284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.096332</td>\n",
       "      <td>0.158425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.099349</td>\n",
       "      <td>0.161592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.098124</td>\n",
       "      <td>0.155218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.096767</td>\n",
       "      <td>0.156276</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Returns  Volatility\n",
       "0  0.095155    0.168284\n",
       "1  0.096332    0.158425\n",
       "2  0.099349    0.161592\n",
       "3  0.098124    0.155218\n",
       "4  0.096767    0.156276"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "portfolio.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>Returns</th>\n",
       "      <th>Volatility</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>0.095275</td>\n",
       "      <td>0.167023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>0.098252</td>\n",
       "      <td>0.155566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>0.098805</td>\n",
       "      <td>0.157935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>0.096041</td>\n",
       "      <td>0.160330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>0.096518</td>\n",
       "      <td>0.157404</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Returns  Volatility\n",
       "995  0.095275    0.167023\n",
       "996  0.098252    0.155566\n",
       "997  0.098805    0.157935\n",
       "998  0.096041    0.160330\n",
       "999  0.096518    0.157404"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "portfolio.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Expected Returns')"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#scatterplot of returns v/s volatility=Markowitz Effiecient Frontier \n",
    "portfolio.plot(x='Volatility', y='Returns', kind='scatter', figsize=(10,6));\n",
    "plt.xlabel('Expected Volatility')\n",
    "plt.ylabel('Expected Returns')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}