{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sharpe Ratio - Introduction\n",
    "\n",
    "\n",
    "Sharpe Ratio is the most common metric used to measure risk in finance.\n",
    "\n",
    "The formula is \n",
    "\n",
    "> (return on portfolio - risk free rate)/standard deviation of the excess return on the portfolio\n",
    "\n",
    "There are tons of resources on the internet about sharpe ratio.\n",
    "\n",
    "[This investopedia page](https://www.investopedia.com/terms/s/sharperatio.asp) is a good introduction.\n",
    "\n",
    "In this series of articles, we take a deep dive into the sharpe ratio and its variations and usage.\n",
    "\n",
    "We assume the risk free rate to be zero, then the formula simply becomes mean returns divided by the standard deviation of returns. The following terms are used interchangebly throughout this article\n",
    "\n",
    " * mean returns/average returns/mu\n",
    " * standard deviation of returns/deviation/sigma\n",
    "\n",
    "We would be working on the NSE Nifty 50 index data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import empyrical as ep\n",
    "from typing import Tuple\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "parameters"
    ]
   },
   "outputs": [],
   "source": [
    "# Parameters \n",
    "# useful when running as a papermill notebook\n",
    "\n",
    "filename:str = '/tmp/nifty.csv'\n",
    "periods:Tuple[str] = ('W','M','Y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>open</th>\n",
       "      <th>high</th>\n",
       "      <th>low</th>\n",
       "      <th>close</th>\n",
       "      <th>daily_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-03</th>\n",
       "      <td>1482.15</td>\n",
       "      <td>1592.90</td>\n",
       "      <td>1482.15</td>\n",
       "      <td>1592.2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-04</th>\n",
       "      <td>1594.40</td>\n",
       "      <td>1641.95</td>\n",
       "      <td>1594.40</td>\n",
       "      <td>1638.7</td>\n",
       "      <td>0.029205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>1634.55</td>\n",
       "      <td>1635.50</td>\n",
       "      <td>1555.05</td>\n",
       "      <td>1595.8</td>\n",
       "      <td>-0.026179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>1595.80</td>\n",
       "      <td>1639.00</td>\n",
       "      <td>1595.80</td>\n",
       "      <td>1617.6</td>\n",
       "      <td>0.013661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>1616.60</td>\n",
       "      <td>1628.25</td>\n",
       "      <td>1597.20</td>\n",
       "      <td>1613.3</td>\n",
       "      <td>-0.002658</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               open     high      low   close  daily_return\n",
       "date                                                       \n",
       "2000-01-03  1482.15  1592.90  1482.15  1592.2           NaN\n",
       "2000-01-04  1594.40  1641.95  1594.40  1638.7      0.029205\n",
       "2000-01-05  1634.55  1635.50  1555.05  1595.8     -0.026179\n",
       "2000-01-06  1595.80  1639.00  1595.80  1617.6      0.013661\n",
       "2000-01-07  1616.60  1628.25  1597.20  1613.3     -0.002658"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(filename, index_col=['date'], parse_dates=['date'])\n",
    "df['daily_return'] = df.close.pct_change()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Daily mean return = 0.0005\n",
      "Deviation of daily returns = 0.0144\n",
      "Sharpe ratio = 0.0381\n"
     ]
    }
   ],
   "source": [
    "mu,sigma = df.daily_return.mean(), df.daily_return.std()\n",
    "print(f\"Daily mean return = {mu :.4f}\")\n",
    "print(f\"Deviation of daily returns = {sigma :.4f}\")\n",
    "print(f\"Sharpe ratio = {mu/sigma :.4f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sharpe ratio - converting to various periods\n",
    "\n",
    "The sharpe ratio calculated here is based on daily return. To calculate it for other periods, multiply this by the square root of the period.\n",
    "\n",
    "`sharpe ratio * √n`\n",
    "\n",
    "To get the weekly sharpe ratio, multiply by √5 since there are 5 trading days in a week, √20 for a month and so on. Most of the literature and news display the annualized sharpe ratio, sharpe ratio per annum\n",
    "\n",
    "<!-- TEASER_END -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sharpe ratio for the period weekly is 0.0851\n",
      "Sharpe ratio for the period monthly is 0.1703\n",
      "Sharpe ratio for the period yearly is 0.6044\n",
      "Sharpe ratio annualized calculated using empyrical is 0.6044\n"
     ]
    }
   ],
   "source": [
    "def sharpe_period(sr:float, n:int)->float:\n",
    "    sr_p = sr*np.sqrt(n)\n",
    "    return sr_p\n",
    "\n",
    "for p,n in zip(('weekly','monthly','yearly'),(5,20,252)):\n",
    "    print(f\"Sharpe ratio for the period {p} is {sharpe_period(mu/sigma, n):.4f}\")\n",
    "    \n",
    "print(f\"Sharpe ratio annualized calculated using empyrical is {ep.sharpe_ratio(df.daily_return):.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate sharpe ratio by resampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sharpe ratio for the period weekly is 0.0852\n",
      "Sharpe ratio for the period monthly is 0.1752\n",
      "Sharpe ratio for the period yearly is 0.5821\n"
     ]
    }
   ],
   "source": [
    "def resampled_sharpe(dataframe:pd.DataFrame, freq:str)->float:\n",
    "    resampled = dataframe.resample(freq).close.last().pct_change()\n",
    "    sharpe = resampled.mean()/resampled.std()\n",
    "    return sharpe\n",
    "\n",
    "for p,n in zip(('weekly','monthly','yearly'),periods):\n",
    "    print(f\"Sharpe ratio for the period {p} is {resampled_sharpe(df, n):.4f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sharpe ratio by both the methods match though not exact and bigger the timeframe, the bigger is the difference between the methods. This may be due to the fact that the daily returns have more data compared to the resampled series which has got less data when we increase the time period.\n",
    "\n",
    "The sharpe ratio calculated thus far is the *ex-post* sharpe ratio since it is calculated after the event has occured. In practice, we use this ratio on a *ex-ante* basis, as a predictor for the future. *ex-ante* is the the expected sharpe ratio while the *ex-post* is the actual/realised sharpe ratio\n",
    "\n",
    "This excellent [article](https://corporatefinanceinstitute.com/resources/knowledge/trading-investing/ex-ante-vs-ex-post/) shows how ex-post and ex-ante are calculated in general"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A note on the risk free rate\n",
    "\n",
    "All the calculations are done assuming 0 is the risk-free rate. Let us see a simulation with different risk free rates\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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gUql4qWk1mta1Zf0vF9h+8ArR8UmM7eNC3WqV9R2eEEKUGBlRPKfKFc14vX8z3hzkxoOMLBZ8E8OW/RfJys7Vd2hCCFEiZERRQjwa2dO4lg2b919iV9Q1Yi8kMbq3C41rV9F3aEII8VxkRFGCLC1MGd3bhenDWqBRFD5cf5zvdp+XJoNCiHJNCoUOuNa1JXisFz1b1+LAiZsErY4i7lKyvsMSQohikUKhI+Zmxgzr3oh3X2tFBXMTlm2J46udZ0hLz9J3aEII8UykUOhYgxrWzBvdmn7t6xJ9Tk3Q6iiiziZKk0EhRLkhhaIUmJoYMaBjfeaNbo1dZQu+3HGGz7ed4m5apr5DE0KIQkmhKEU1HayY7d+KV7o25MzVVIJWH+HXEzdldCGEKNOkUJQyYyMjennVJnhcG2o7VOKb8PN8tOE46rvp+g5NCCGeSgqFnjhWsWT6cA/8ezXmj8Q05q45yu6j14rdo0oIIXRFfnCnR0YqFV1aOOFe347vdp9n076LHD2nZoyvCzXtn+/hS0IIUVJkRFEG2Fa2YMpgdyb0a0LSvQzmr40m7HdpMiiEKBtkRFFGqFQq2japRpO6tmz8JYGw368Qc17NWF9X6lWXJoNCCP2REUUZU9nSjAn9mjJlsDvpj3JY+G0Mm/YlkClNBoUQeiIjijKqRcOqONe0YeuBi+w+ep3jF5IZ3dsFlzrSZFAIUbpkRFGGWVqY4N/LhXde9QBg8YbjfBMeT/ojaTIohCg9UijKAZc6VZg/rg29vGrz28lbBK0+wokEaTIohCgdUijKCXNTY17p2pAgf0+sKpjy2bY4vtxxhj+lyaAQQsekUJQz9apXZu7o1gzoUI+YeDVBq6I4cuaOtAERQuiMFIpyyMTYiH4d6vHemNY4VKnAVzvP8tnWOFL/fKTv0IQQLyApFOWYk70V745sxbDujTh37S5Bq6M4cPwmGhldCCFKkBSKcs7ISEXP1rUIHudFveqV+Xb3eT7ecJxEaTIohCghOi0UO3fuxNfXF29vb0JCQp5Yvnz5crp27Ur//v3p37+/dp385ov8OdhUYNqwFozu7cIfiQ+Yu+Yo4VHXyNVIGxAhxPPR2Q/uEhMTWbp0KT/88ANmZmYMGzYMLy8vGjZsqF3n9OnTLFmyBA8Pjzzb5jdfFEylUtGpeQ3c6tvxfcR5Nu+/yNFziYzxdaWWgzQZFEIUj85GFJGRkbRt2xYbGxssLS3x8fEhPDw8zzqnT59m1apV+Pn5ERwcTGZmZoHzRdFUqWTOGwPdeL1/U1L+fETwumi2/3aZ7BwZXQghnp3ORhRqtRp7e3vttIODA3Fxcdrphw8f4urqyowZM3BycmLmzJmsWLGCCRMmPHV+YGBgkY9tZ/d8357t7Ss91/ZlRR+HynRsVZtVYafYGXmVE5dSmDK0BS51bPOs96Lk+ywkZ8MgOZcMlaKjG/D/+9//kpGRof2A37JlC6dOnSI4OPip6589e5Z3332X0NDQIs0vSErKg2I/AMjevhJJSWnF2rYsi7uUzDfh57mXlkkPz1oM7FQfczPjFzbfgkjOhkFyLjojI1WBX7B1durJ0dGR5OT/bzOhVqtxcHDQTt+6dYutW7dqpxVFwcTEJN/54vm4N6jKwvFedGnpxJ6Y68xZE8XZq6n6DksIUQ7orFC0a9eOw4cPk5qaSkZGBhEREXTq1Em73MLCgo8++ojr16+jKAohISF4e3vnO188vwrmJrzWszEzhntgbKTi440n+GzTcdIfZes7NCFEGaazr+qOjo4EBgbi7+9PdnY2gwcPxt3dnYCAAKZMmYKbmxvBwcFMmjSJ7OxsWrZsyZgxYzAzM3vqfFFyGteuwvyxbQg7dIXdR69z9Owd/Hs2xsPZvvCNhRAGR2fXKPRJrlEU3f1HuSxZf4zr6ge0dnFguLcz1hXN9B2WThnaewySs6Eod9coRPnQsJYNc0Z58nKn+hxPSCJo1REiT9+WJoNCCC0pFAITYyP82tXlvTFtqGZnyeofz7FsSxwp96XJoBBCCoX4mxpVKzJrRCuG92jEhev3CFoTxb7YG9JkUAgDJ4VC5GFkpKKHZy0WjGtDwxqV+T7iAotDYrmTKk0GhTBUUijEU1W1qcDUoS0Y6+vKjaSHzF1zlJ+P/CFNBoUwQPJLNpEvlUpFB/fqNKtvS0jEBbYeuET0OTVjfF2o7Wh4rRGEMFQyohCFsrEyZ/JAN/41oBl3H2Sy4JsYfvjtEtk5ufoOTQhRCmREIYrM08UBlzpV2LQ3gR8j/+DY+STG9HalYU1rfYcmhNAhGVGIZ2JVwZRxfZswdWhzsrI1/Of7Y4TsucCjrBx9hyaE0BEpFKJYmtWzY8H4NnRrVZN9x24wZ/VRTl9J0XdYQggdkEIhis3CzIQR3s7MGNESUxMjlmw6yZqfzvIgQ5oMCvEikUIhnptzLRvmj21Nn5fqcPh0IkGro4iJV+s7LCFECZFCIUqEqYkxgzo3YM4oT2yszFgRepovtp/i/gN5jK0Q5Z0UClGi6lSrRJC/J4M61+fkxRSCVkfxe5w0GRSiPJNCIUqcibERfV6qy/yxralRtSJf/3yOJZtPknwvQ9+hCSGKQQqF0JnqdhWZMaIlI3s6c/HmfeasOcovMdelyaAQ5YwUCqFTRioV3VrWZMG4NjSqac36XxJYFBLL7ZSH+g5NCFFEUihEqahqXYHAV5ozro8rt5MfMu/ro/wYeZWcXGkyKERZJy08RKlRqVS0d6tOs/p2hESc54ffLhMdr2asryt1qkmTQSHKKhlRiFJnXdGMf73sxuSX3fjzYRYLvolh64FLZGVLk0EhyiIZUQi9adXYHpc6Nmzad5Gfj/zBsQtJjOntgnMtG32HJoT4GxlRCL2qaGHKWF9X/j2sBbm5GhaFxPJ9xHkyMqXJoBBlhRQKUSY0rWtL8Lg29PCsyf7Ym8xZE8Wpy9JkUIiyoEiF4tGjR5w/fx5FUXj06JGuYxIGysLMhOE9nJn1WivMTY1Zuvkkq3+UJoNC6FuhheLEiRP06NGDiRMnkpiYSOfOnYmNjS3Sznfu3Imvry/e3t6EhIQ8sXz58uV07dqV/v37079/f+06586dY9CgQfj4+DB79mxycuQ0hCFp6GTNe2Pa4NeuLlFnEwladYSYeLW0ARFCTwotFIsXL2bdunXY2NhQrVo1Fi9ezPvvv1/ojhMTE1m6dCnr168nLCyMTZs2cfHixTzrnD59miVLlhAWFkZYWBgjRowAYPr06cyZM4fdu3ejKAqbN28uZnqivDI1MeLlTvWZM8qTKpUt/tdk8DT3pMmgEKWu0ELx6NEjGjZsqJ3u3LkzubmF38YYGRlJ27ZtsbGxwdLSEh8fH8LDw/Osc/r0aVatWoWfnx/BwcFkZmZy8+ZNHj16RIsWLQAYOHDgE9sJw1HbsRJB/q0Y0rUBpy6nMHtVFAdP3pLRhRClqNDbY01MTLh//z4qlQqAy5cvF2nHarUae3t77bSDgwNxcXHa6YcPH+Lq6sqMGTNwcnJi5syZrFixgi5duuTZzt7ensTExCInBGBnZ/VM6/+Tvb1h/firPOTr39eaHl51+WzzCdbuiuf4xRQmD2lONbuKxdpfeci5pEnOhkEXORdaKF5//XVGjhxJcnIyU6dO5dChQwQHBxe646d94/ur2ABUrFiRVatWaafHjh3Lu+++S+fOnQvcrihSUh6g0RTvG6e9fSWSktKKtW15VJ7yNQUCh7jz64lbbNl/kckf7WNQpwZ0b1UTI6Oi/xspTzmXFMnZMBQ3ZyMjVYFfsAstFN26daNBgwYcOnQIjUbDv/71rzynovLj6OhITEyMdlqtVuPg4KCdvnXrFpGRkQwePBh4XFhMTExwdHQkOTlZu15SUlKe7YRhM1Kp6OrhRPMGdny7+zwb9iZwND6R0b1dcapavNGFEKJghV6jePfdd6lTpw7Dhw9n5MiRNGzYkDfffLPQHbdr147Dhw+TmppKRkYGERERdOrUSbvcwsKCjz76iOvXr6MoCiEhIXh7e+Pk5IS5uTnHjh0DIDQ0NM92QgDYVrbgrcHuBPg1ITE1g/lrj7Lz0BVpMiiEDuQ7opg3bx6JiYkcO3aM1NRU7fycnJwiXadwdHQkMDAQf39/srOzGTx4MO7u7gQEBDBlyhTc3NwIDg5m0qRJZGdn07JlS8aMGQPAxx9/TFBQEA8fPqRJkyb4+/uXQKriRaNSqXipaTWa1rVl/S8X2H7wCtHxSYzxdaFe9cr6Dk+IF4ZKyef2kVOnTpGQkMDnn3/OlClTtPONjY3x8PCgVq1apRbks5JrFEX3IuV7PCGJ73af5/7DLHza1GZAh3qYmRo/sd6LlHNRSc6GodSvUbi5ueHm5ka7du2oVq3aMx9YiNLm0ciexrVs2Lz/EuFR14j9X5PBxrWr6Ds0Icq1Qi9m3759m/nz55Oeno6iKGg0Gm7cuMGBAwdKITwhno2lhSmje7vg5erAuvB4Plx/nC4eTgzp0oAK5tIsWYjiKPRidlBQEB4eHjx48AA/Pz+srKzo2bNnacQmRLG51rUleJwXPm1q8euJmwStjuLkxeTCNxRCPKHQQqFSqZgwYQJt2rShfv36fPrpp3luexWirDI3NWZot0a8+1orLM1N+HRrHF/tPMN9aQMixDMptFBUrPj43vTatWuTkJCAubl5kVp4CFFWNKhhzbwxrenXvi7R59T8a/E+os4mShsQIYqo0JO2bm5uvP3227z11ltMnDiRq1evYmz85J0kQpRlJsZGDOhYH8/GDny35wJf7jhD1NlEXvNpTJVK5voOT4gyLd/bY/+SlZXF2bNnadGiBQcOHCAyMpJhw4ZRv3790orxmcntsUVnaPkC2NpZsf7ns4QevIyxsYpXujakU/Maz9wqpjwxxPdZci66wm6PLbRQDBgwgNDQ0Gc+sD5JoSg6Q8sX/j/nxLvpfLMrnvhr93CpbcPo3i44VLHUd3g6YcjvsyHRVaEo9BqFhYUFd+7ceeYDC1HWOVaxZNqrHvj3aswfiWnMXXOU3UevFftLhhAvqkKvUWRkZNC9e3eqVauGpeX/f9vauXOnTgMTojQYqVR0aeGEe307vtt9nk37LnL0nJoxvi7UtH++dvVCvCgKLRSzZ88ujTiE0CvbyhZMGezO0XNqQvZcYP7aaPq2q0ufl+pgYlykR8sL8cIqtFC0adOmNOIQQu9UKhVeTRxpUrcKG35JIOz3K8ScVzOmtyv1a0iTQWG45KuSEP9QydKMCf2aMmWwO+mPcnj/uxg27k0gM1t+PyQMkzS/ESIfLRpWxbmmDVt/vURE9HWOJyQxurcrrnWkyaAwLEUeUfz555+6jEOIMsnSwgR/n8bMGO6BSqXiow3HWbcrnvRHOfoOTYhSU2ihuHz5Mn369KFPnz4kJibSu3dvLl26VBqxCVFmNK5dhflj29DLqzYH424RtPoIJxKkyaAwDIUWioULF/Luu+9iZ2eHo6MjI0eOZO7cuaURmxBlirmpMa90bUiQvydWFUz5bFsc/w07zZ8Ps/QdmhA6VWihuHfvHu3bt9dOjxgxggcPHug0KCHKsnrVKzN3dGte7liP2AtJBK2O4vCZO9JkULywinSNIjMzU9sHJykpCY1GHmAvDJuJsRF+7esxb0wbHKtUYNXOs3y6NY7UPx/pOzQhSlyhhWL48OGMGzeOlJQUPvnkE4YOHcqrr75aGrEJUeY5Va3IrJGteLV7I+Kv3SVodRT7j99EI6ML8QIp9PbYwYMHU6dOHQ4cOEBOTg7BwcF06NChNGITolwwMlLh3boWLRpV5ZvweL7bfZ6jZxMZ3dsFR9sXs8mgMCxFOvVUq1Yt2rRpw7///W8aNGig65iEKJfsbSrw76EtGNPbhWvqB8z9+ii7ov4gV07VinKu0EJx4MABhg0bxvz580lNTcXX15dffvmlNGITotxRqVR0bF6DheO9aFbPli37L/H+t8e4rpYbQET5VWihWL58OZs3b6Zy5co4ODiwfv16PvvssyLtfOfOnfj6+uLt7U1ISEi+6x04cIBu3bppp6Ojo/Hy8qJ///7079+fWbNmFel4QpQVVSqZ88ZANyYNaEbqn48IXhfN9t8uk50jowtR/hR6jUKj0eDg4KCddnV1LdKTwBITE1m6dCk//PADZmZmDBs2DC8vLxo2bJhnveTkZD788MM8806dOsXYsWOZOHFiUfMQosxRqVS0dnHAtU4VNu5NYGfkVY5dSGJMbxcaOFnrOzwhiqzQEUWFChW4deuWtjjExMRgbl74M4YjIyNp27YtNjY2WFpa4uPjQ3h4+BPrBQUF8cYbb+SZd+rUKQ4dOsSAAQN4/fXXuX37dlHzEaLMsapgyvi+TXh7SHMeZeXwwXfH2PBLAplZ0mRQlA+FFop///vfjB07lmvXrjF06FAmT57MtGnTCt2xWq3G3t5eO+3g4EBiYmKedb799luaNGlC8+bN88yvVKkS/v7+hIaG0rlzZwIDA4uajxBllnsDOxaM86JrSyf2xFxnzpoozlxN1XdYQhSq0FNPtWvXZvPmzRw/fhyNRkPz5s2xtbUtdMdP+5Xq309ZXbhwgYiICNatW/fEo1aDg4O1f3/11Vf55JNPSEtLo1KlSoUeFyjw2a9FYW9ftOO8KAwtX9BvzoEjPOn5Uj0+23ScTzaewLtNbcb2a4ZVBVOdHlfeZ8Ogi5wLLRQjR44kPDyczp07P9OOHR0diYmJ0U6r1eo81zrCw8NJSkpi0KBBZGdno1arGT58ON9//z1ffvklEyZMwNjY+P8DNSl6R/SUlAfFfu6xoT2Q3dDyhbKRs0MlM+aO8mTHoauER13j6Nk7vNazMS2d7QvfuBjKQs6lTXIuOiMjVYFfsAs99eTk5ERsbOwzt+1o164dhw8fJjU1lYyMDCIiIujUqZN2+ZQpU9i9ezdhYWF89dVX2juqjIyM2LNnD7t37wYgNDSU5s2bU6FChWc6vhBlnZmpMYO7NGDOKE+sLc1Y/sMpVoSe5r40GRRlTKFf0y9dusTw4cMxMTHBzMwMRVFQqVTExsYWuJ2joyOBgYH4+/uTnZ3N4MGDcXd3JyAggClTpuDm5pbvth9++CFz5szhiy++wNbWlsWLFz97ZkKUE3WqVSJolCfhUdfYcegK566m8mqPRrzUtFqR7jAUQtdUSj4tL/fs2YO3tzeXLl3CwsLiieVOTk46D6645NRT0RlavlC2c76d8pC1P8dz8eZ9mtW3ZZSPC3bWT/7/e1ZlOWddkZyLrtinnv76Ud20adNwcnJ64o8QouRVt6vIzJEtGd6jEQnX7xO0Joq9x25Ik0GhV/meeqpYsSI+Pj4kJibi5+f3xPKdO3fqNDAhDJWRSkUPz1q0aPi4yWDIngscPfe4yWB1u4r6Dk8YoHwLxerVqzl37hyzZ89mzpw5pRmTEAKoalOBqUNbEHn6Dhv3JjDv62j6d6hLL6/aGBsV+XH3Qjy3fAuFlZUVrVu35ssvv6RevXqlGZMQ4n9UKhXt3arTrJ4t3++5wLZfLxMTn8QYXxdqOxrebwSEfhT6tUSKhBD6Z21lzuSX3fjXgGbcfZBJ8LoYtv16iewcaQMidK/ov2ITQuidp4sDLnWqsGlfAj8d/oNj5x+PLhrVtNF3aOIFVqwTnWlphnXLmRBliVUFU8b1acLUoc3JztGw6PtYQiIukJGZo+/QxAuq0ELxySef5Jk+dOjQU++CEkKUrmb17Fgwvg3dWtVkX+wN5q6J4vSVFH2HJV5AhRaK48ePs2bNGrKysli4cCEzZsxg9uzZpRGbEKIQFmYmjPB2ZubIlpiZGrNk00nW/HSWBxnZ+g5NvEAKLRRfffUVe/bsoVevXiQnJ7Njxw68vb1LIzYhRBE1qmnDe2Na07ddHQ6fTiRodRQx8Wp9hyVeEPkWijNnznDmzBmuXLnCW2+9RXZ2Nl5eXty+fZszZ86UZoxCiCIwNTFmYKcGzB3tiY2VGStCT/PF9lPcf5Cp79BEOZdvr6e/P8P6iY1UKvbu3auzoJ6X9HoqOkPLFwwj51yNht1HrxN68ArmpkaM7++Ge10bg2oyaAjv8z/pqtdTvrfH7tu375kPJoQoG4yNjPBtWwePRlVZtyueTzcdp2ndKozq5UJVG2nZL55NodcoLl26xJYtW1AUhcmTJ9O9e3eOHDlSGrEJIZ5TdbuKzBjRktcHunPx1p/MWXOUX2KuF3vELQxToYVi3rx5mJubs3//flJTU/nggw9YunRpacQmhCgBRioVfdrXY+E4LxrVsmb9LwksConlVvJDfYcmyolCC0VmZib9+vXj0KFD9O7dGy8vL7Kz5dY7IcobO2sLAoc0Z3xfV26nPOS9tUfZGXmVnNxne3qlMDyFFoqsrCySk5M5cOAA7dq1Izk5mcxMuYtCiPJIpVLRrll1Fga0xaORPdt/u8yCb2L4445hXfQVz6bQQjF06FC6du1Kq1ataNiwIYMHD2bUqFGlEZsQQkesK5oxaUAz3hjoxp8Ps1jwTQxbDlwkK1uaDIon5Xt77N9pNBqM/tf//u7du1SpUkXngT0PuT226AwtX5Cc/+nho2w277vIwbjbONpaMqa3C861bEo3QB2Q97noin177KpVqwgICGDhwoVPXR4UFPTMwQghyp6KFqaM8XWlTRNHvtkVz6KQWLq2dGJw5wZUMJcG06KAQlGp0uOHotjY2JRWLEIIPWpa15YF47z44bfL/BJznZMXk/H3ccG9gZ2+QxN6VqRTT/906NAh2rdvr4t4SoSceio6Q8sXJOeiuHTzPmt3xXMr+SEvNa3Gqz0aYVXBVIcRljx5n4uusFNPBfZ6GjZsGK+//jqpqakA3Lp1i8mTJzNp0qRnDkQIUX40cLJm3ujW+LWry9FzicxedYSj5xIpxvdK8QLIt1C899579OzZk5o1a7Jy5Up+/vln+vTpw6NHjwgLCyvNGIUQemBqYsTLneozd3Rr7Cpb8N+wMyz/4RR30+T2eEOTb6FIS0tj7NixzJo1i/379/PBBx+wcOFC1qxZU+TnaO/cuRNfX1+8vb0JCQnJd70DBw7kaUL4559/MmHCBHr37s2IESNISkp6hpSEECWploMVs/1b8UrXhpy+kkrQ6ih+O3lLRhcGJN9CUaHC48ZhxsbGZGZmsmrVKvr06VPkHScmJrJ06VLWr19PWFgYmzZt4uLFi0+sl5yczIcffphn3rJly/D09GTXrl0MGTKE999/v8jHFUKUPGMjI3p51SZ4XBtqO1ixblc8H288gfpehr5DE6Ug30Lx928Ltra2uLq6PtOOIyMjadu2LTY2NlhaWuLj40N4ePgT6wUFBfHGG2/kmXfgwAHt41b79u3Lb7/9Jm1DhCgDHKtYMn24B/4+jbly+0/mrokiIlqaDL7o8i0UGo2G+/fvc+/ePRRF0f79rz+FUavV2Nvba6cdHBxITEzMs863335LkyZNaN68eb7bmpiYYGVlpb2gLoTQLyOVii4eTiwc74VL7Sps3JvAf74/xk1pMvjCyvd3FBcuXKBt27bakYWXl5d2mUql4ty5cwXu+GnnL//+0JQLFy4QERHBunXruHPnTqGB/vXL8KIo6DavorC3r/Rc25c3hpYvSM4ltb+Fk6ry6/GbfLX9FPPXHmWod2MGdW2EqUnR/7/qkrzPJSPfQhEfH/9cO3Z0dCQmJkY7rVarcXBw0E6Hh4eTlJTEoEGDyM7ORq1WM3z4cNavX4+DgwPJyclUq1aNnJwcHjx48Ew//JPfURSdoeULknNJa1rLmgXj27B+zwVCwuP59dh1xvi6Uq96ZZ0cr6jkfS66Yv+O4nm1a9eOw4cPk5qaSkZGBhEREXTq1Em7fMqUKezevZuwsDC++uorHBwcWL9+PQCdO3cmNDQUgJ9//hlPT09MTcvXj32EMCSVLc14vX8z3hzkxoOMbBZ+G8PmfRfJlCaDLwSdNXJxdHQkMDAQf39/srOzGTx4MO7u7gQEBDBlyhTc3Nzy3fatt95i5syZ9OnTh0qVKvHxxx/rKkwhRAnyaGRP41pV2Lz/IuFHrxGbkMToXi641CnbjURFwYrVwqOsk1NPRWdo+YLkXFrOXU1lXXg8Sfce0aVFDQZ3aYilRek1GZT3uej0dupJCGHYXOvaEjzOi56ta/HryVvMWRPFyYvJ+g5LFIMUCiGEzpibGjOseyPefa0VluYmfLo1jq92nOHP9Cx9hyaegRQKIYTONahhzbwxrenXvi7R8WqCVkURdVaaDJYXUiiEEKXCxNiIAR3rM29Ma+xtKvDljjN8vk2aDJYHUiiEEKWqpr0Vs19rxdBuDTl7NZWg1Uf49cRNGV2UYVIohBClzshIhU+bx00G6zhW4pvw83y04Tjqu+n6Dk08hRQKIYTeOFSxZPqrHozq1Zg/EtOYu+Yo4VHXpMlgGSNPThdC6JVKpaJzCyfcG1Tlu93n2bz/ItHxiYzxdaWm/fP1bRMlQ0YUQogyoUolc94c5Mbr/ZuSfP8R89dGE3rwMtk5Gn2HZvBkRCGEKDNUKhVtXB1xrVOFDXsT2HHoKsfOJzHa14UGNaz1HZ7BkhGFEKLMqWRpxgS/prw12J30zBw++PYYG/cmkJklTQb1QUYUQogyq3nDqiysZcPWA5eIiL7O8f81GXSta6vv0AyKjCiEEGVaBXMTXvNpzIzhHqhUKj7aeIJ1u+JJf5Sj79AMhhQKIUS50Lh2FYLHtqG3V20Oxt0iaPURjick6TssgyCFQghRbpiZGjOka0OC/D2xqmDG59tO8d+w09JkUMekUAghyp161Sszd7QnL3esR+yFJIJWRXHkzB1pA6IjUiiEEOWSibERfu3rMW9MGxyrVOCrnWf5dGscqX8+0ndoLxwpFEKIcs2pakVmjWzFq90bEX/tLkGro9h//Ka0ASlBcnusEKLcMzJS4d26Fi0aVWXdrni+232e4xeTGdG9EY62lvoOr9yTEYUQ4oVhb1OBacNaMKa3C1du3mfu10fZFfUHuRppA/I8pFAIIV4oKpWKjs1r8MU73WhWz5Yt+y+x8NtjXEtM03do5ZYUCiHEC8nOugJvDHRj0oBm3P3zEQu+ieGH36TJYHHINQohxAtLpVLR2sXhcZPBXxL4MfIqx86rGePrSkMnaTJYVDKiEEK88KwqmBLg14S3hzQnMzuX/3x3jPW/XJAmg0Wk00Kxc+dOfH198fb2JiQk5Inle/bswc/Pjz59+jBz5kyysh7/ujI0NJQOHTrQv39/+vfvz9KlS3UZphDCQLg3sGPBOC+6tnTil5gbzFkTxZmrqfoOq8zT2amnxMREli5dyg8//ICZmRnDhg3Dy8uLhg0bApCenk5wcDDbt2+natWqBAYGsn37doYOHcqpU6eYOXMmffv21VV4QggDVcHchJE9G9PG1ZG1u+L5ZOMJOrhXZ2i3hlS0MNV3eGWSzkYUkZGRtG3bFhsbGywtLfHx8SE8PFy73NLSkn379lG1alXS09NJSUmhcuXKAJw6dYrQ0FD69evHtGnTuH//vq7CFEIYKOdaNgSPbY1v2zpEnrpD0OooYi9Ik8Gn0dmIQq1WY29vr512cHAgLi4uzzqmpqb8+uuvvPPOOzg4ONChQwcA7O3tmTBhAu7u7ixZsoTg4GA++eSTIh/bzu75nrNrb1/pubYvbwwtX5CcDUVRcp40pAXeL9Xl800nWP7DKdo3r8HEl92oUsmiFCIsebp4n1WKjrpo/fe//yUjI4PAwEAAtmzZwqlTpwgODn7q+kuWLOHmzZtPFIT79+/To0cPoqOji3zslJQHxf75vr19JZKSDOd+a0PLFyRnQ/GsOefkath99Bphv1/F3NSIYd0b0a5ZNVQqlQ6jLFnFfZ+NjFQFfsHW2aknR0dHkpOTtdNqtRoHBwft9L179/j999+1035+fpw/f560tDTWrVunna8oCiYmchevEEK3TIyN6PNSXeaPbU11u4qs+ekcSzefJPl+hr5D0zudFYp27dpx+PBhUlNTycjIICIigk6dOmmXK4rC9OnTuXXrFgC7du2iZcuWWFpasnr1ak6ePAnA999/j7e3t67CFEKIPKrbVWTmyJaM8HYm4cZ95qw5yt5jN9AYcAtznX1Vd3R0JDAwEH9/f7Kzsxk8eDDu7u4EBAQwZcoU3NzcWLBgARMnTkSlUtGwYUPmz5+PsbExy5Yt47333uPRo0fUrVuXxYsX6ypMIYR4gpFKRfdWNWnewI5vdp8nZM8Fjp5LZHRvF6rbVdR3eKVOZ9co9EmuURSdoeULkrOhKKmcFUUh8vQdNu5NIDNbQ/8OdfFpUxsT47L3e2VdXaOQk/9CCFEAlUpFe7fqNKtny/d7LrDt18tEx6sZ6+tKbUfDuJOs7JVEIYQog6ytzJn8shv/GtCMew+yCF4Xw7ZfL5Gd8+K3AZERhRBCPANPFwdc6lRh074Efjr8B8fOJzHG14VGNW30HZrOyIhCCCGekVUFU8b1acLUoc3JztGw6PtYQvZc4FFWjr5D0wkpFEIIUUzN6tmxYHwbureqyb5jN5iz+iinr6ToO6wSJ4VCCCGeg4WZCcO9nZk1shVmpkYs2XSSNT+d5UFGtr5DKzFSKIQQogQ0rGnNe2Na07ddHQ6fTiRodRQx8Wp9h1UipFAIIUQJMTUxZmCnBswd7YmNlRkrQk/zxQ+nuPcgU9+hPRcpFEIIUcJqO1ZizihPBndpwMlLKQStiuJg3C3K6++bpVAIIYQOGBsZ4du2DvPHtsbJviJrf45nyaYTJN8rf00GpVAIIYQOVberyIwRLRnZ05mLt/5kzpqj7Im5Xuw2Q/oghUIIIXTMSKWiW8uaLBznRaNa1mz4JYFFIbHcSn6o79CKRAqFEEKUEjtrCwKHNCegbxNupzzkvbVH2Rl5lZxcjb5DK5C08BBCiFKkUql4qVk1mtazJWTPBbb/dpnoc2rG9nGhbrXK+g7vqWREIYQQelC5ohmTBjTjjYFupGVksfCbY2w5cJGs7LLXZFBGFEIIoUctne1xqW3Dpn0X2XXkGrHnkxjd24XGtavoOzQtGVEIIYSeWVqYMsbXlWnDWpCrUfhw/XG+izhPRmbZaDIohUIIIcqIJnVtWTDOC2/PWhyIvcmcNVHEXdJ/k0EpFEIIUYaYmxnzao9GvPtaKyzMTFi25SSrduq3yaAUCiGEKIMaOFkzb3Rr+rWvy9FzicxedYSj5xL10gZECoUQQpRRpiZGDOhYn7mjW2NX2YL/hp1h+Q+nuJtWuk0GpVAIIUQZV8vBitn+rXila0NOX0klaHUUv50svSaDUiiEEKIcMDYyopdXbYLHtaG2gxXrdsXz8cYTqEuhyaBOC8XOnTvx9fXF29ubkJCQJ5bv2bMHPz8/+vTpw8yZM8nKygLg1q1bjBgxgl69ejFp0iQePiwf/VCEEELXHKtYMn24B/4+jbly+0/mrokiIlq3TQZ1VigSExNZunQp69evJywsjE2bNnHx4kXt8vT0dIKDg1m7di0//fQTmZmZbN++HYD58+czfPhwwsPDadasGStWrNBVmEIIUe4YqVR08XBi4XgvXGpXYePeBD74/hh3UnTzpVpnhSIyMpK2bdtiY2ODpaUlPj4+hIeHa5dbWlqyb98+qlatSnp6OikpKVSuXJns7Gyio6Px8fEBYODAgXm2E0II8ZhtZQveGuzOBL8mqO9msC/muk6Oo7MWHmq1Gnt7e+20g4MDcXFxedYxNTXl119/5Z133sHBwYEOHTpw9+5drKysMDF5HJq9vT2JiYm6ClMIIco1lUpF26bVaNPEkapVK5Ga8qDEj6GzQvG0q/EqleqJeZ07dyYqKoolS5bw3nvv8c477xRpu4LY2Vk90/r/ZG9f6bm2L28MLV+QnA2F5FwydFYoHB0diYmJ0U6r1WocHBy00/fu3eP06dN06NABAD8/PwIDA7G1teXBgwfk5uZibGxMUlJSnu2KIiXlQbEv7NjbVyIpKa1Y25ZHhpYvSM6GQnIuOiMjVYFfsHV2jaJdu3YcPnyY1NRUMjIyiIiIoFOnTtrliqIwffp0bt26BcCuXbto2bIlpqameHp68vPPPwMQGhqaZzshhBClS2eFwtHRkcDAQPz9/RkwYAB9+/bF3d2dgIAATp06RZUqVViwYAETJ06kX79+XL16lenTpwMwb948Nm/ejK+vLzExMbz99tu6ClMIIUQhVIo+GofomJx6KjpDyxckZ0MhORed3k49CSGEeDFIoRBCCFGgF/JRqEZGz3Y7bUlvX94YWr4gORsKyblktnkhr1EIIYQoOXLqSQghRIGkUAghhCiQFAohhBAFkkIhhBCiQFIohBBCFEgKhRBCiAJJoRBCCFEgKRRCCCEKJIVCCCFEgQymUOzcuRNfX1+8vb0JCQl5Yvm5c+cYNGgQPj4+zJ49m5ycHABu3brFiBEj6NWrF5MmTeLhQ908vFwXipvzsWPHGDRoEP3792fUqFHcvHmztEMvtuLm/JezZ8/SrFmz0gq3RBQ3Z7VazYQJExgwYADDhg3jxo0bpR16sRU35xs3bjBixAj69+/Pa6+99kL92/7LjBkz+OGHH7TTJfIZphiAO3fuKF27dlXu3r2rPHz4UPHz81MSEhLyrNOnTx/l+PHjiqIoyqxZs5SQkBBFURRlwoQJyo8//qgoiqIsX75cWbx4canGXlzPk3PXrl2Vc+fOKYqiKFu2bFFef/31Uo29uJ4nZ0VRlPT0dGXo0KGKs7NzaYb9XJ4n51GjRinr169XFEVR1q9fr7z11lulGXqxPU/O06ZN0/7922+/Vf7973+XauzFVZSc79y5o0ycOFFxd3dXtm3bpp1fEp9hBjGiiIyMpG3bttjY2GBpaYmPjw/h4eHa5Tdv3uTRo0e0aNECgIEDBxIeHk52djbR0dH4+PjkmV8eFDfnrKws3nrrLVxcXABo3Lgxt2/f1kcKz6y4Of9l0aJFjB49upSjfj7FzTk1NZX4+HiGDRsGwKBBg8rNA8Ke533WaDQ8ePAAgIyMDCwsLEo9/uIoLGd4POLo3r07vXv31s4rqc8wgygUarUae3t77bSDgwOJiYn5Lre3tycxMZG7d+9iZWWFiYlJnvnlQXFzNjMzo3///sDj/1TLly+nR48epRf4cyhuzgB79+7l0aNH9OrVq/QCLgHFzfn69evUqFGDDz74gH79+jFlyhRMTU1LNfbiep73+a233mLdunV07NiRr7/+moCAgNIL/DkUljPA+PHjGTJkSJ55JfUZZhCFQnlKg1yVSlXo8sK2K8uKm/NfsrKymDZtGjk5OUycOFE3QZaw4uaclJTEypUrmTNnjk7j04Xi5pyTk8PZs2dp164dO3bsoHv37sycOVOnsZaU5/m3PWPGDIKDgzl48CDz58/njTfeeOr6ZU1xP4tK6jPMIAqFo6MjycnJ2mm1Wo2Dg0O+y5OSknBwcMDW1pYHDx6Qm5ubZ355UNycAR4+fMj48ePJyclh5cqV5eabZnFzPnDgAPfu3dNe5ATo37+/9hRFWVbcnO3t7alYsSJdu3YFoG/fvsTFxZVe4M+huDmnpqZy+fJl7QjZx8eHpKQk7t69W3rBF1NhOeenpD7DDKJQtGvXjsOHD5OamkpGRgYRERF06tRJu9zJyQlzc3OOHTsGQGhoKJ06dcLU1BRPT09+/vnnPPPLg+LmDDB9+nTq1KnDp59+ipmZmV7iL47i5jxkyBB++eUXwsLCCAsLAyAsLAwrq/yfIVxWFDfn2rVr4+joyK+//grA/v37adq0qV5yeFbFzblKlSqYm5sTExMDPL67r2LFitja2uolj2dRWM75KbHPsGe+/F1O7dixQ+nTp4/Ss2dP5auvvlIURVHGjx+vxMXFKYqiKOfOnVMGDRqk9OrVS5k6daqSmZmpKIqi3LhxQxk5cqTSu3dvZezYscq9e/f0lsOzKk7OZ86cUZydnRVfX1+lX79+Sr9+/ZTx48frM41nUtz3+e/K011PilL8nC9duqSMHDlS6dOnjzJ06FDlypUr+krhmRU355MnTyqDBw9W+vbtqwwdOlQ5c+aM3nJ4VoXl/JcZM2bkueupJD7D5Al3QgghCmQQp56EEEIUnxQKIYQQBZJCIYQQokBSKIQQQhRICoUQQogCmeg7ACFKw4kTJ/jkk0+4d+8eiqJQrVo1ZsyYQaNGjYiKimLBggX8+OOP+g6Txo0b4+zsjJGRESqVioyMDKysrHjvvfdwc3MrcNstW7aQlZXFiBEj2LBhA2lpaUyYMKGUIhcvMikU4oWXlZXFxIkT+frrr7U/KgsLCyMgIIC9e/fqObonffPNN3l+BLZmzRoWLlzIpk2bCtzu2LFjNGrUCIBXX31VpzEKwyKFQrzwMjIySEtLIz09XTuvX79+WFlZaVsbpKenExgYyOXLl8nMzGThwoV4enpy5coVgoODSU9PR61W4+LiwrJlyzA3N6dZs2Z0796d+Ph4Pv74Y4YOHcqoUaOIiooiPT2dqVOn0rNnT+Dxt/0NGzag0WiwsbFhzpw5NGjQoNDYc3JyuH37NtbW1gAkJyczd+5cUlJSSEpKwsnJiWXLlhEbG8u+ffs4dOgQFhYWpKamcvfuXebOnUtCQgLBwcHcu3cPlUrF2LFjGTBgQMm/0OLF9Rw/FBSi3Pj6668Vd3d3pVu3bsq0adOULVu2KOnp6YqiKMqRI0cUV1dX5cSJE4qiKMratWsVf39/RVEUZdGiRUpoaKiiKIqSlZWl9O3bVwkPD1cU5fEvuLdv3649hrOzs7Jy5UpFUR7/MrhVq1ZKSkqKEhUVpQwfPlx7vIMHDyq9e/d+apzOzs5K3759FT8/P6V9+/ZKt27dlAULFijJycmKoijKunXrlC+//FJRFEXRaDTK+PHjlTVr1iiK8vgXuatXr1YURVE+++wzZf78+Up2drbSvXt3Zffu3YqiPH5mQceOHZXY2NgSeFWFoZARhTAIY8aMYciQIURHRxMdHc2qVatYtWoVW7duBaBWrVo0b94cABcXF7Zt2wY87nt16NAhVq1axdWrV1Gr1XlGJp6ennmOM3LkSO0+nJ2diY6O5uTJk/zxxx/aZz8A3L9/n3v37mFjY/NErH+dejp79iwBAQF4eHhgZ2cHwKhRo4iJiWHt2rVcvXqVhIQEbdxPc/XqVTIzM7UjG0dHR3r27MnBgwfx8PB41pdRGCgpFOKFd+zYMY4fP8748ePp2rUrXbt2ZerUqfj5+XHo0CGqVKmSp0Pu31vMT506ldzcXHr37k2XLl24fft2ntbNlpaWeY5lbGys/btGo8HY2BiNRkP//v2ZPn26dr5ardaeTspPkyZNmDVrFkFBQTRv3pyaNWvy0UcfERcXx6BBg/Dy8iInJ6fANtkajeaJeYqiPPEIWCEKIrfHiheera0tK1eu1HYNhcftljMyMnB2di5w299//53Jkyfj6+uLSqXi5MmT2usaTxMaGgrAmTNnuHLlCq1bt6Z9+/b89NNPqNVqADZs2MCoUaOKFHvfvn1p0aIFH3zwgTaeUaNGMWDAAOzs7IiMjNTGY2xs/EQBqFevHqampkRERACQmJjI7t27adeuXZGOLwTIiEIYgHr16vHFF1+wdOlS7ty5g7m5OZUqVSI4OJj69euTlJSU77aBgYFMnjwZa2trKlSoQOvWrbl27Vq+68fGxrJ582Y0Gg1Lly7F2tqajh07EhAQwNixY1GpVFhZWbF8+fIiP0Bmzpw59OvXj4MHDzJ58mQWL17MihUrMDY2pmXLltp4OnXqxIIFC/Jsa2pqyooVK1i4cCGff/45ubm5TJ48mbZt2xbp2EIASPdYIUpI48aNOXz4cLl4voEQz0JOPQkhhCiQjCiEEEIUSEYUQgghCiSFQgghRIGkUAghhCiQFAohhBAFkkIhhBCiQFIohBBCFOj/AMUguKkmC6lqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rates = np.linspace(0,0.1,50)\n",
    "sharpe_ratios = {}\n",
    "for r in rates:\n",
    "    sharpe_ratios[r] = ep.sharpe_ratio(df.daily_return,risk_free=r/365)\n",
    "ax = pd.Series(sharpe_ratios).plot(title='Sharpe ratio versus risk free rate')\n",
    "ax.set_xlabel('Sharpe Ratio')\n",
    "ax.set_ylabel('Risk free rate');\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.2"
  },
  "nikola": {
   "category": "risk management",
   "date": "2021-11-04 06:52:05 UTC",
   "slug": "sharpe-ratio",
   "tags": "sharpe,risk",
   "title": "Sharpe ratio"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}