Practical_Position_Sizing_Pt3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd, numpy as np\n",
    "import matplotlib.pyplot as plt, matplotlib as mpl, matplotlib.ticker as ticker\n",
    "import seaborn as sns\n",
    "import pystore\n",
    "import time\n",
    "import cma\n",
    "import itertools\n",
    "\n",
    "sns.set_style('white')\n",
    "mpl.rcParams['savefig.dpi'] = 300\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_weighted_returns(returns, weights):\n",
    "    weighted_returns = returns.multiply(weights).sum(axis=1)\n",
    "    return weighted_returns\n",
    "\n",
    "def calc_ghpr(returns):\n",
    "    returns_array = np.array(returns)\n",
    "    twr = np.product(1 + returns_array)\n",
    "    ghpr = twr ** (1 / len(returns_array)) - 1\n",
    "    return ghpr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Two Uncorrelated Coins"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_weighted_returns(returns, weights):\n",
    "    weighted_returns = returns.multiply(weights).sum(axis=1)\n",
    "    return weighted_returns\n",
    "\n",
    "def calc_ghpr(returns):\n",
    "    returns_array = np.array(returns)\n",
    "    twr = np.product(1 + returns_array)\n",
    "    ghpr = twr ** (1 / len(returns_array)) - 1\n",
    "    return ghpr\n",
    "\n",
    "def get_worst_losses(returns):\n",
    "    worst_losses = np.min(returns, axis=0)\n",
    "    abs_worst = np.abs(worst_losses)\n",
    "    return np.array(abs_worst)\n",
    "\n",
    "def weight_combinations(returns, steps=100, bound_factor=1):\n",
    "    num_components = returns.shape[1]\n",
    "    worst_losses = get_worst_losses(returns)\n",
    "    potential_weights = np.linspace(0, 1, steps+1)[:-1]\n",
    "    weights_list = [list(potential_weights)] * num_components\n",
    "    combos = list(itertools.product(*weights_list))\n",
    "    combos_array = np.array(combos)\n",
    "    loss_bound = np.multiply(worst_losses, bound_factor)\n",
    "    norm_combos = np.divide(combos_array, loss_bound)\n",
    "    return norm_combos\n",
    "\n",
    "def f_multiple_returns(returns):\n",
    "    strategies = returns.columns\n",
    "    potential_weights = weight_combinations(returns)\n",
    "    f_curve = pd.DataFrame()\n",
    "    for i in range(len(potential_weights)):\n",
    "        weights = potential_weights[i]\n",
    "        weighted_returns = calc_weighted_returns(returns, weights)\n",
    "        ghpr = calc_ghpr(weighted_returns)\n",
    "        for j in range(len(strategies)):\n",
    "            f_curve.loc[i, strategies[j]] = weights[j]        \n",
    "        f_curve.loc[i, 'ghpr'] = ghpr\n",
    "    optimal_f = f_curve.loc[f_curve['ghpr'].idxmax()]\n",
    "    return {'f_curve':f_curve, 'optimal_f':optimal_f}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-Correlated Coins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>coin 1</th>\n",
       "      <th>coin 2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Scenario</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          coin 1  coin 2\n",
       "Scenario                \n",
       "1              2       2\n",
       "2              2      -1\n",
       "3             -1       2\n",
       "4             -1      -1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_coins = pd.DataFrame({'coin 1':np.array([2,2,-1,-1]), 'coin 2':np.array([2,-1,2,-1])})\n",
    "two_coins.index = np.arange(1,5)\n",
    "two_coins.index.name = 'Scenario'\n",
    "two_coins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/bblandin/anaconda3/envs/crypto/lib/python3.6/site-packages/ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "coin 1    0.230000\n",
       "coin 2    0.230000\n",
       "ghpr      0.119119\n",
       "Name: 2323, dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_two_coins = f_multiple_returns(two_coins)\n",
    "f_two_coins['optimal_f']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c23696208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "optimal_idx = f_two_coins['f_curve']['ghpr'].idxmax()\n",
    "optimal_weights = f_two_coins['f_curve'].loc[optimal_idx, ['coin 1', 'coin 2']]\n",
    "pivoted = pd.pivot_table(f_two_coins['f_curve'], values='ghpr', index='coin 1', columns='coin 2')\n",
    "pivoted.sort_index(ascending=False, inplace=True)\n",
    "pivoted.index = np.round(pivoted.index, 2)\n",
    "pivoted.columns = np.round(pivoted.columns, 2)\n",
    "sns.heatmap(pivoted, cmap='RdYlGn', center=0, ax=ax, cbar_kws={'label':'GHPR'})\n",
    "\n",
    "# xvals = ax.get_xticklabels()\n",
    "# ax.set_xticklabels(['{:,.2f}'.format(float(x)) for x in xvals])\n",
    "# yvals = ax.get_yticklabels()\n",
    "# ax.set_yticklabels(['{:,.2f}'.format(float(x)) for x in yvals])\n",
    "\n",
    "# ax.imshow(pivoted)\n",
    "# ax.scatter(optimal_weights[0], optimal_weights[1], marker='x', c='r')\n",
    "ax.scatter(optimal_weights[0]*100, (1 - optimal_weights[1])*100, marker='x', c='b', s=100)\n",
    "fig.tight_layout()\n",
    "fig.savefig('Two Coins Heatmap')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                \n",
      "coin 1  0.230000\n",
      "coin 2  0.230000\n",
      "ghpr    0.119119\n"
     ]
    }
   ],
   "source": [
    "results = f_two_coins['optimal_f'].to_frame()\n",
    "results.columns = ['']\n",
    "print(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Positively Correlated Coins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>Coin 1</th>\n",
       "      <th>Coin 2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Scenario</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Coin 1  Coin 2\n",
       "Scenario                \n",
       "1              2       2\n",
       "2             -1      -1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_coins_corr = pd.DataFrame([[2,2], [-1,-1]], columns=['Coin 1', 'Coin 2'])\n",
    "two_coins_corr.index = np.arange(1,3)\n",
    "two_coins_corr.index.name = 'Scenario'\n",
    "two_coins_corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/bblandin/anaconda3/envs/crypto/lib/python3.6/site-packages/ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  \n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "               \n",
      "Coin 1  0.00000\n",
      "Coin 2  0.25000\n",
      "ghpr    0.06066\n"
     ]
    }
   ],
   "source": [
    "f_two_coins_corr = f_multiple_returns(two_coins_corr)\n",
    "results_corr = f_two_coins_corr['optimal_f'].to_frame()\n",
    "results_corr.columns = ['']\n",
    "print(results_corr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2370f048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "optimal_idx = f_two_coins_corr['f_curve']['ghpr'].idxmax()\n",
    "optimal_weights = f_two_coins_corr['f_curve'].loc[optimal_idx, ['Coin 1', 'Coin 2']]\n",
    "pivoted = pd.pivot_table(f_two_coins_corr['f_curve'], values='ghpr', index='Coin 1', columns='Coin 2')\n",
    "pivoted.sort_index(ascending=False, inplace=True)\n",
    "pivoted.index = np.round(pivoted.index, 2)\n",
    "pivoted.columns = np.round(pivoted.columns, 2)\n",
    "sns.heatmap(pivoted, cmap='RdYlGn', center=0, ax=ax, cbar_kws={'label':'GHPR'})\n",
    "\n",
    "# xvals = ax.get_xticklabels()\n",
    "# ax.set_xticklabels(['{:,.2f}'.format(float(x)) for x in xvals])\n",
    "# yvals = ax.get_yticklabels()\n",
    "# ax.set_yticklabels(['{:,.2f}'.format(float(x)) for x in yvals])\n",
    "\n",
    "# ax.imshow(pivoted)\n",
    "# ax.scatter(optimal_weights[0], optimal_weights[1], marker='x', c='r')\n",
    "ax.scatter(optimal_weights[0]*100, (1 - optimal_weights[1])*100, marker='x', c='b', s=100)\n",
    "fig.tight_layout()\n",
    "fig.savefig('Two Correlated Coins Heatmap')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative Correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>Coin 1</th>\n",
       "      <th>Coin 2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Scenario</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Coin 1  Coin 2\n",
       "Scenario                \n",
       "1              2    -1.0\n",
       "2             -1     0.6"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_coins_neg_corr = pd.DataFrame([[2,-1.0], [-1,0.6]], columns=['Coin 1', 'Coin 2'])\n",
    "two_coins_neg_corr.index = np.arange(1,3)\n",
    "two_coins_neg_corr.index.name = 'Scenario'\n",
    "two_coins_neg_corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                \n",
      "Coin 1  0.790000\n",
      "Coin 2  0.990000\n",
      "ghpr    0.130646\n"
     ]
    }
   ],
   "source": [
    "f_two_coins_neg_corr = f_multiple_returns(two_coins_neg_corr)\n",
    "results_corr = f_two_coins_neg_corr['optimal_f'].to_frame()\n",
    "results_corr.columns = ['']\n",
    "print(results_corr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119d4f940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "optimal_idx = f_two_coins_neg_corr['f_curve']['ghpr'].idxmax()\n",
    "optimal_weights = f_two_coins_neg_corr['f_curve'].loc[optimal_idx, ['Coin 1', 'Coin 2']]\n",
    "pivoted = pd.pivot_table(f_two_coins_neg_corr['f_curve'], values='ghpr', index='Coin 1', columns='Coin 2')\n",
    "pivoted.sort_index(ascending=False, inplace=True)\n",
    "pivoted.index = np.round(pivoted.index, 2)\n",
    "pivoted.columns = np.round(pivoted.columns, 2)\n",
    "sns.heatmap(pivoted, cmap='RdYlGn', center=0, ax=ax, cbar_kws={'label':'GHPR'})\n",
    "\n",
    "# xvals = ax.get_xticklabels()\n",
    "# ax.set_xticklabels(['{:,.2f}'.format(float(x)) for x in xvals])\n",
    "# yvals = ax.get_yticklabels()\n",
    "# ax.set_yticklabels(['{:,.2f}'.format(float(x)) for x in yvals])\n",
    "\n",
    "# ax.imshow(pivoted)\n",
    "# ax.scatter(optimal_weights[0], optimal_weights[1], marker='x', c='r')\n",
    "ax.scatter(optimal_weights[1]*100, (1 - optimal_weights[0])*100, marker='x', c='b', s=100)\n",
    "fig.tight_layout()\n",
    "fig.savefig('Neg Correlated Coins Heatmap')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Drawdown Constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_equity_curve(returns):\n",
    "    equity_curve = (1 + returns).cumprod(axis=0)\n",
    "    # Set the starting value of every curve to 1\n",
    "    # normalized_eq = raw_eq / raw_eq[0]\n",
    "    return equity_curve\n",
    "\n",
    "def calc_twr(equity_curve, start_at_1=True):\n",
    "    eq_arr = np.array(equity_curve)\n",
    "    if start_at_1 == True:\n",
    "        twr = eq_arr[-1] \n",
    "    else:\n",
    "        twr = eq_arr[-1] / eq_arr[0]\n",
    "    return twr\n",
    "\n",
    "def calc_ghpr_eq(equity_curve):\n",
    "    twr = calc_twr(equity_curve)\n",
    "    ghpr_eq = twr ** (1 / len(equity_curve)) - 1\n",
    "    return ghpr_eq\n",
    "\n",
    "def calc_drawdown(equity_curve):\n",
    "    eq_series = pd.DataFrame(equity_curve)\n",
    "    drawdown = eq_series / eq_series.cummax() - 1\n",
    "    return drawdown\n",
    "\n",
    "def calc_max_drawdown(equity_curve, percent=True):\n",
    "    abs_drawdown = np.abs(calc_drawdown(equity_curve)).values\n",
    "    max_drawdown = np.max(abs_drawdown)\n",
    "    if percent == True:\n",
    "        return max_drawdown * 100\n",
    "    else:\n",
    "        return max_drawdown\n",
    "    \n",
    "def calc_ulcer_index(equity_curve):\n",
    "    drawdown = calc_drawdown(equity_curve)\n",
    "    ulcer_index = np.sqrt(np.mean(drawdown**2)) * 100\n",
    "    return ulcer_index\n",
    "\n",
    "def ideal_f_multiple(returns, time_horizon=250, n_curves=1000, \n",
    "                     drawdown_limit=20, certainty_level=95, steps=100, \n",
    "                     bound_factor=1):\n",
    "    start = time.time()\n",
    "    strategies = returns.columns\n",
    "    potential_weights = weight_combinations(returns, steps, bound_factor)\n",
    "    f_curve = pd.DataFrame()\n",
    "    for i in range(len(potential_weights)):\n",
    "        # Record weights\n",
    "        weights = potential_weights[i]\n",
    "        for j in range(len(strategies)):\n",
    "            f_curve.loc[i, strategies[j]] = weights[j]\n",
    "        weighted_returns = calc_weighted_returns(returns, weights)\n",
    "            \n",
    "        # Generate n random equity curves\n",
    "        reordered_returns = np.random.choice(weighted_returns, size=(time_horizon, n_curves))\n",
    "        curves = get_equity_curve(reordered_returns)\n",
    "        curves_df = pd.DataFrame(curves)\n",
    "        \n",
    "        # Calculate GHPR and Maximum Drawdown for each equity curve\n",
    "        curves_drawdown = calc_max_drawdown(curves_df)\n",
    "        curves_ghpr = calc_ghpr_eq(curves_df)\n",
    "        \n",
    "        # Calculate drawdown at our certainty level\n",
    "        drawdown_percentile = np.percentile(curves_drawdown, certainty_level)\n",
    "        \n",
    "        # Calculate median ghpr value\n",
    "        ghpr_median = np.median(curves_ghpr)\n",
    "        if drawdown_percentile <= drawdown_limit:\n",
    "            ghpr = ghpr_median\n",
    "        else:\n",
    "            ghpr = 0\n",
    "        f_curve.loc[i, 'ghpr'] = ghpr * 100\n",
    "        f_curve.loc[i, 'drawdown'] = drawdown_percentile\n",
    "    optimal_f = f_curve.loc[f_curve['ghpr'].idxmax()]\n",
    "    elapsed = time.time() - start\n",
    "    print('Ideal f calculated in {}s'.format(elapsed))\n",
    "    \n",
    "    return {'f_curve':f_curve, 'optimal_f':optimal_f}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 downloaded\n",
      "[*********************100%***********************]  1 of 1 downloaded\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1c25b9ed30>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD5CAYAAAAHtt/AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzsnXd4U9X7wD9N23TTwYbSMsveG2TIEBTrAJEtX0ERFFFE/TkAAUFQ3CiiiKggS0RlCCJDQPbeSyiVVWihdKdNk/z+uElubkablqRtyvk8T5+ce86595ykyXvPfc87vAwGgwGBQCAQeAyq4p6AQCAQCAqGENwCgUDgYQjBLRAIBB6GENwCgUDgYQjBLRAIBB6GENwCgUDgYfjk1ajVannrrbe4evUqOTk5jBkzhu7du5vb165dyw8//IC3tzcxMTFMmTIFlUrcCwQCgcCd5CllV69eTVhYGEuWLGH+/Pm8++675jaNRsOnn37Kjz/+yLJly0hPT2fr1q1un7BAIBDc6+S54u7duze9evUyH3t7e5vLarWaZcuWERAQAEBubi5+fn4219BoNJw4cYLy5csrzhcIBAKBY3Q6HQBVq1bFx0cpqvMU3EFBQQCkp6czbtw4Xn75ZXObSqWiXLlyACxatIjMzEw6duxoc40TJ04wZMiQu3sHAoFAcI+yefNmIiMjFXV5Cm6A69ev88ILLzB48GBiY2MVbXq9ntmzZxMXF8ecOXPw8vKyOb98+fIA/PTTT1SqVOlu5i8QCAT3DAkJCQ4XvXkK7qSkJEaMGMHkyZNp3769TfvkyZNRq9XMnTvX4aakST1SqVIlm7uGQCAQCApOnoJ73rx5pKamMnfuXObOnQtA//79ycrKolGjRqxcuZJWrVoxfPhwAJ566il69uzp/lkLBALBPUyegnvixIlMnDjRYfuZM2dcPiGBQCAQ5I0wuhYIBAIPQwhugUAg8DCE4BYIBAIPQwhugUAgcAMJKRpOX091y7XzteMWCAQCQcFpN3MzAJdm9XH5te9pwf3NN9+wa9cuVCoVXl5ejB8/nsWLF3Py5EnCwsIAye106tSp7Nmzh23btvHtt9+az3/xxRfp0KEDgwYNKq63IBAIShhanZ4ryVluHeOeFdz//vsvW7ZsYenSpXh5eXH69Gn+7//+jwYNGvDaa6/RuXNnALZt28Znn33GnDlz2LJlCz///DP9+/dn3bp1aLVaIbQFAoGZMwmp9P50BzN95vOFbyZjtS+5ZZwSIbh/OXiFFQcuu/SaT7aqRr+Wjj01IyIiuHbtGitXrqRz587Ur1+flStXMnnyZEW/lJQUAgMD8fLyYubMmQwePJjmzZszb948fvjhB5fOWSAQeDa9P90BwCAfKVLqWC3o9QZUKttwIHdDiRDcxUFERARfffUVixcv5ssvv8Tf35/x48cDMHv2bObPn49KpaJChQq89tprgOS2P27cOAYMGMDHH39MREREcb4FgUBQwulRXe2W65YIwd2vZWSeq2N3EB8fT3BwMDNnzgTg+PHjjBo1iqZNmypUJdY89thjzJ49my5duhTldAUCQQknMycXgEA05rpvE54ArzsuH+ueNQc8e/YsU6ZMITs7G4AaNWoQEhIiYoYLBIJCsXhPPACNK/gqG+xETb1bSsSKuzh44IEHuHDhAv379ycwMBCDwcDrr7/Opk2bintqAoHAA3nvDyl207guUbDGvWPds4IbYMyYMYwZM0ZR16NHj3zP27lzp7umJBAIPBCtTg/A8PbRRJYxyA2BZd0y3j2rKhEIBAJXsffibQCqRQQSoEuTG0KruWU8IbgFAkHBWPsKzLuvuGdRrOTq9Mxaf4aEFGkj8sWlhwBI0+Tir02RO1Zu6pbxheAWCAQF48ACSDhe3LMoNo5fSaH22+uZt+0Cr/9yDIAuMVKKxue61CRQJwnu97SD4MEP3DKHfAW3VqvltddeY/DgwTzxxBNs3rxZ0b5lyxb69evHgAEDWLFihVsmKRAIBCWB7FwdsV/8Yz7efi4RAJ0BapYLItBHhc++rwFYqesCvv5umUe+m5OrV68mLCyM2bNnk5yczOOPP0737t0BSajPnDmTlStXEhAQwKBBg7j//vvNCYIFAkEpIO0GBFdwi1mbp/HppvO2lV+0pmFCDGtyB8Pp3+GapDZJIcht88h3xd27d29eekn2t7e0c75w4QJRUVGEhoaiVqtp2bIlBw4ccM9MBQJB0XP7InwUA7u/kI4TTsht8buLZ05FyO2MHE5fT2XskkPM336RLadv2nZKOsdon7VSWSsHl9LhPp+QfFfcQUHSXSM9PZ1x48bx8ssvm9vS09MJCQlR9E1PT3fDNF3PrFmzOHnyJImJiWg0GqpVq0Z4eDgJCQkKlc/t27fNN67Tp09TvXp1AgICeOSRR+jfv39xTV8gKBo0xo22I0ugw4swr6PctrA3TEmxf14p4aVlh9lxPgmAtceu06thRXL1ejaO70Ktt/4AZNO/nvXKQc418/Hfr3Z127ycsuO+fv06L7zwAoMHDyY2NtZcHxwcTEZGhvk4IyNDIchLMm+88QYAq1at4uLFi7z66qtcuXKFV155RdEvIiKCRYsWATBs2DCmTJlCrVq1iny+AkGxoDKKiLSE4p1HMbEv7rbi+PB/d6hbKQRvlReVQ/25nSInSrh4+SrUkN3bq5dzn6okX8GdlJTEiBEjmDx5Mu3bt1e01apVi/j4eO7cuUNgYCAHDhxg5MiRBZ/FkaVweHHBz8uL5kOhmQi5KhDcFTqtsWAAg0HZ1nQQpCdC4hmo0anIp+Zutp65SXauXlF3My2bzkYLkmWj2jHsw+Xmtuebq+GqUVU8fK1b55av4J43bx6pqanMnTuXuXPnAtC/f3+ysrIYMGAAb7zxBiNHjsRgMNCvXz8qVqzo1gkLBIIiRK+TXg0GWW1y3yvwz8dwdCn4+MPBhfDMZohsJZ+XnQZ750GHl8DHPRHy3Ileb+Dp7/fbbzPewEIDfKnlJatG+h0YIhWCK7n9Rpav4J44cSITJ0502N6tWze6det2d7NoNkisjgWCkojeuOLW3IEEyWaZSo3BLxT0uZB0Tqq7HacU3P98Ajs+gqAK0HJ40c7ZBQz8Zo+5vOTZtvh6q+g/T9qM7VSnHCAJ7v7e22xPTne/Wkk44AgEAseYVSXAD8b9rcCy0HSAtJL2Nq6mtRnK864dkV7XjIMpoaDLdW48rQb2fAW5OXc377tk3yVJt12nQjAdapXDz0cWlVpNJuTm4OXlxUPe+2xPruH+kM9CcFtx/vx5+vbta/7bt8/OP0YguFfQ2xG46iDIugNZyXBRyvRCbrayj85K8F5x8nd0ZDFseAP2zy/4XN1AzwaS6tdS1/3kn63hqw4KnX9dzfdSwT8UBrvfEfGejg4I0LdvX3M5MjKSw4cPO+xrsi4RCO4Z7Alu/zCI266sO7oU1r8Oz++BCvUhV6Ns3/ExRHfIe6zsdFg3QS4XE6euyZYiL3arA0C9SlbWcrfOQ9p182E2ajLevEWQX9GIVLHiFggEjrFUlZgIi4JHv1TWXTMueOa2g5QrksrDkjJVIOWq43Eu7YSZVeVjtftM6fLDlP/2z5c7E6CWnGhC/KXkCAO9t8gdvZTi08e76DxLheAWCASOsV5xD/hJ0m3X7u74nE8awY3jUmS8vt9KdYd+gE8aOD5nndJ/gpBKhZuvC/h+1yUA6lqtspc/24ZZvt/KFcZAW5t1zQHw8ym67FlCcAsEAvtk3YG/Z0nlug/Bm1eh/sPScZ5xS4y639wcaPyEc2OFRSmP7aloioA9F28B0LaGbSLwttUClRXbPwSgqleS2+dljRDcAoHAPqd+g8TTUrnXDPALtt+vWjv79YmnbQW8Xm+/b3AF5bE20/l53iWXb8tjmcwAu9WrYNsxx8py5rLUd63Owft3I0JwCwQC+1iuelV5bLoFlcv7OuE15HJ2qv0+1tdfOz7va7qIXReS6PTBVtYdu857f5w212u0VjeY9ET4vLnda3yhe8ydU7TLPW9VIhDcM+Rmg8oXVE6u10xekwABtqoDMyGV7dc//In06m2R9Tw7FQLC7HQu2pCxt9KzWX30GrczJLPFF5YcUrSnaaw2ZT+sLZfbPAeHF1k8FXjRsEoZN87WFiG4BYJ7hekVoH4sDHAyLpApROnDnzhWk4BkMWKPViOkV43FKvvTxlCjMwy3SoNuUqk8OBuSzsKJVc7NsZB8tvk8P+6Od9g+qnNN+eDWBWVjSCXpKeLmSQAOTOyBr3fRKi+EqkQgKE1cPQjv14CMW8p60+r59BrbcxyRlSyt0Fv8L49OXqAyWlO0sggwN2aXXB6wSLlij9su2WnfOAUXjA48uhwIqQJtR0nxT7Ju274HF3L8qv1wtBVC/LgwrTsVfOW42iwdqOzU7nnMG7APfUi5YD9CA3wpSoTgFghKE1tmSEIvfqdcl3iucGFZ065LahBHqpVXz8PrF+VNu6By0PUtyXuwYkO5X7U2MHSl8tz0G/BVe1j0mLSiPbwY0owBm9TG1f23dxkDyQG5Oj2H/7tjU/9486rse7sH3iuHw/vV5YYGj8rl+o9I6chunpKOrT1EiwihKhEISgtx2+GCMSesyTkkLQG+bA3RFlnZU65KK/MGj+R9vczbEFTWcbvJEiTTuDIOLAttn4Ou/2fb19tPeWwp8PbOU7aZbLiTL+U9Pye5kJiOt5cXfr4qKocGcOmWfYuV9rXKSje5cxukiixjYK3ts6XjNs9Bj3ekcpUWUooyC+/JokQIboGgtBC3Qy6b1Bcm/XK8nODW7AjT/wdpNenIJjsrGQLC8x/XUnA7wtou21Jw7/tG2aZynSOLXm+g+0dyBL9fxrSn31dyyjU/H5U5DkkZfx/pJmfiwhZY+bR8/OD78mc1eDmseArajnbZXAuCUJUIBKUFhcAzChiDA7tpgJ+HS8LJEc4K7uw06TUwD8uT0Ejptc0o6fW3F+TIgiZGbjIWLG4kd/7Lf/w82H4+UXH80cZz5vLxKQ9wZPIDZouQsljpvf/5RHlseYMLrgAjNsjvq4hxSnAfPXqUYcOG2dSvXr2axx9/nH79+rFkyRKXT04gEBQAy9gZphVtbpb9viYyb9uv12bB7Qu2waTs8dCH0PJpqJ5H8oCgclJ+yt7vS8c3jtvqh03xvC29LdPtJOctAAfjkxXHuXo5ol+Ivy8Bam+up0hxVVqvbKs82RR/HKDfgruah6vJV3DPnz+fiRMnkp2dbdP2wQcfsHDhQpYuXcrChQtJSSndiUMFghKNpeA2ReezDvbkLP8aV7/OxMWOqAGxnyrttR2Rlw25aUXrGwCxn0nlb7tLQasKifUmZFKaJMf+GCffZN56qD7hgfnM3ZknjyIkX8EdFRXFnDlz7LbVrVuXtLQ0cnJyMBgMeOUZv0AgELgVP4ugSLka+OdT+Gty3ud4+8DPT8vR/QCS/oXlQ6Xy6B32z3M1bccoj6u2lMvxuygM11Oy+OffJOpVCuH9fo0BSEyXBHe5YFlN80TLSA5PfiDvi1WoX6g5uIt8BXevXr3w8bG/h1mnTh369etHnz596Nq1K2XKFK33kEAgsMA/VC5rNbDpnfwTGPzxGpxcBd90lRMDLB0gt4dHu3yaNDWmKXzYQodsnbrQ8r3kd/OxIlenp/ob62g/U9LfX03OYkDrKALV3qRppE3SMpZ215oUKUuPJUN/kcshlR07GRUThbYqOXPmDH///TebN28mMDCQ1157jfXr1/Pggw+6cn4CgcBZLDf78tNtm8iw2LxLOA63/pX+3Mnj86Q/kMwSU69JIWAtUVt4aqZdl24qTj7RT1t7SnE8tpvkrp6ZIzkhVS8biL+vxUbu1pnKC/RbALV7SDr5EkqhrUpCQkLw9/fHz88Pb29vIiIiSE11EEBGIBC4H0sLEq0DwT3sN6WHoyU6rdL8rSh49EsY9qttfUA4VGwkH19znJnKGmtX9qR05f6cxf6kxOW9cnn0P86Hoi1GCrziXrNmDZmZmQwYMIABAwYwePBgfH19iYqK4vHHH3fHHAUCgTNYBoVyZC1S634pyNMBO1YScRYZy9uPhQemu3Z+BcHLSzK3m2k0tzOZHBaCvXHKz8Iy8S/fdJVvCk0HSxnsPQCnBHdkZCQrVkgJMGNjY831gwYNYtCgQY5OEwgERYnBQnCn37Bt9zdG5Stfz/75x5bL5SrNnVZNuA3LzVZ7KdTssOqQbIEys29j3lx1nO/+JznVvNitNmu27kDtVVPyivTyUq7kH//KJdMuCoQDjkBQWrBccSedU7ZNugWvGXXXvgHQ/3sIr27RwUty4zbFxa5iP/Z0kTPK+BSgszVHtmbvxVu8suIoAM2jwhjUJoq4mQ9RLlhyt+9VTc/ffhMYofkB3o+GWVF5Xa5EI1zeBYLSgmnF7VdGDoIE0qalt9VPveHjUsCkpPOQchn+eNUYDdBHymhTtlbRzTsvfIwxTi79A3V62b4PC9Ydl+OGTHtE0o9bmigHZUvOPE21x7ChyQDbuhKMWHELBKUF04rbOsvMhLP2+6u8oUI9qNNTCt96br1k/60OtN+/ODBZyuyZC4e+z7Or5aZksL+tgA/QS1EMw7wybNpKmoNNfgjBLRCUFuzFJek2Me8YIiYsvR59/F03p7vFxyKq4M0zcH6T3W6WGWuGt48mOsL25lNpi5QOLcJPZ9NGQ88yrBCqEoGgtJBrx709r1yRCiw2Ii3N44oby3Cw++dLf6/H2dyMbmfkcMl/sHTQMw5UdjZW06WY5KpMq6zsE87KoWQ9BLHiFghKA4nnYONEqfzQh3K9ysnMLJZC355FSnHho7ats5jf6euprD12jYxsi1X06hedv36PKR4ntEEIboGgdGAZR7rNs3LZ2RX3bYu8io6S/xYHPgG2davk99d37i4mLNlLpsbC6uSSnfgqegfhbSNb268v4QhViUBQGgmLhjvxhUtK4EyUv6LC3oo74Tjs+Bg6vUKONocL/v/j8NIWcrvGjqt6cpz02nyodDPr+JK08VlM8bTvFrHiFghKIzW7Sq/Orrgt+90/0dWzuTtej7Ot2zwVgDJIFiLNtYeU7VlWOSWXDZFe/UKlkLERNT1WaIMQ3AJB6cRkGuis4O5mFNbD10LTEmbT7MgqZkoozVUOAmK9bxXVMPG09Nq9YJEGSypCVSIQeDqn18jlGGN0TlN2Gev0YI7oMA6qtYXoDq6dm6to9zxL919mkG6Novo79YcOTgAOfCd5h1rmwvQtQaaOd4EQ3AKBJ5ORJCc9uG+8ZCUBcjzrgDDnrqPyLrlCG9D2nMGbf69H75PJEJ/NNu27dQ1o731KSqF2cKFUuXa8stP9bxfBTIsGoSoRFC/arLvOK3hPk5Muly3VIj2mSGaBdfLJ7OIhmFKQvZ07kkNR/7Npf1b7Cm9qR0JUO8cX8WCdtjVCcAuKj/jdMKMSfFhHSpclKDiWOSEtbbb9giWzwOKO8FdIvtl+gfnbL5qPr6dI8cVXjm6Pl2XUQCPpBLJU1z1vixh7DkoeilCVCIqPmyfl8p14KFe7+ObiqZywSLFVGNO/Esp7f5wBoH2tsjSqGsrtDOkGVbN8MP/ZiSsyomMN2tSIgBhboW6mxXC3zLU4EIJbUHwEVZDL6qDim4cns22WXL6wBTq/WnxzcRFnEuQgWQ/P+QeABxpUROUFoQG+BJetanPO5NgGFge34eZpyZ47IBy+ag/d3ylVNzanBPfRo0f58MMPWbRokaL+2LFjzJo1C4PBQPny5Zk9ezZ+fn4OriIQWKGzeMzHMx/pSxTxO4t7Bi4hV2edWww2nrpBRJAab5UXteo1hq0WjSM2KjurvKGSRdqzEpw7srDkK7jnz5/P6tWrCQhQup4aDAYmTZrE559/TnR0ND///DNXr16lZs2abpusoJRhmdWkFOkfBXfH+Zv205TFVJQSCHtVbAjAktz7qfH0AtpHlbXbvzST7+ZkVFQUc+bMsamPi4sjLCyMH374gaFDh3Lnzh0htAUFwzKriWL1LbiXGb/8qN36muXlzO+5k5Lp/voy2te694Q2OCG4e/XqhY+P7cI8OTmZw4cPM3jwYBYuXMiePXvYvXu3WyYpKKUoVtz5p6YSWGGwUim8ebV45uEmusSUVxxbRmr18VZRsUzpcKYpDIU2BwwLCyM6OpratWvj6+tLp06dOHHihCvnJijtWK6yhaqk4Fh+Zu3HSiaAHk6aRovaW8X/OlS3yWLTpsa9ubq2R6EFd7Vq1cjIyCA+XkoXdODAAerUqeOyiQnuAXKFquSu2L9ALrd9rvjm4UIS07LJ0elpVi2M6Y82on9L2WkmtkkJCjdbzBTYHHDNmjVkZmYyYMAAZsyYwYQJEzAYDDRv3pyuXbu6YYqCUoulquS3MaDPhRZPFd98PI3jK+Syl+ebuu04n8gvB68AkJ2rIzxIzXNdavKzsc7LQ52J3IFTgjsyMpIVK6QvSWxsrLm+ffv2rFy50j0zE5R+rFfZG97ybMG96HFIuQpj9xXNeNosuRxcwXE/D2HYAvlzS86UburVywr7fnsIBxxB8aHLkXIKmqxL7CW79RQMBskBpijJyZTLJSn5QSHIyVX+7zvXkTYmfbxFVA57CMEtKD50OVJGcZPg1mYU73zuhoTjclmvKxovPa1RcJer6/6x3IjBYKD3Z9vNx4PaRNGgShnz8crR7fEVAlyBENyC4kOX4/ErRTOWca9zs6UbksrNwsa0R1C3t3vHcSPXU7JoP1P5pFI2SBlDvFV1B4kU7mHEbUxQfGSnlZ4YJec2yOWTv8K0cJgS6t4x246SXju85N5x3Ei/ubts6mpX8HyzRncjBLegeNCkwvGfwU9+JMbbg+PcnP1DLv/+vFy2tJxxNT5GBxRnkyWUQK6l2NrvhwWWkqcwNyIEt6B4+KK19HrjODw6F4Irgd6NQs7dpF23X3/tsPvG1OUAXh4b9c5gMBCk9ibA15vZTzRh7Yv30bBKGaEacQIhuAXFQ3qC9Np7FjQfAq1HSlYlpiS3nsad/+zX33CjN7FO63xOyRLG7YwcBs3fQ0aOjpd71KF/q2o0qhrKunGdCPYTW2/5IT4hQfFiUpWYNil1OaAKcNzf08hOz79PYdHneuzm7gOfbCcpXbImqhJWiv7fRYRYcQuKF1PWbdPK0VODTfmHQsv/2dbnuNHEUZejzDPpIWw/l2gW2gDNqnmujr64EIJbUDyYktjW7SO9mly2N3pgJm6DQbKQCbKIZhcaJb1um+W+ZMjaLHmD0kPI1el56julZ+m9HOWvsAjBLSgetFkQ1UFecWMMUXp4cbFNqVCkXofMW5J+3i9EzmsYUlHu82EdpZejq7gTD2HVXH9dN7Lj3ySbOrWPEEMFRXxiguIhJ90qDKmHBRC6fhQW9YWP68HCB6U6/zCI6SWVa3ZV9j/y092Nl3IVbl2Qyno97PoCrh6G0Mi8zythHL18p7inUCrwPAWZoHSQkwHh1eVjR444f74trSwHlLCV+Ned5XLSOenVPxTqPgSPfwON+sL22XKf7FTuik8skuGGVJbND308a2Nv9dFrdKxdlp+eacf+S7fJzPFQK6JiRqy4BcVDdrpSWFduKpdPrJLLu7+A02uKbl53g38oeHlB0wGStcfT6+W2bR+4bhxLm3EPsirZf+k2FxMzaFxV2oxsXT3CJsuNwDmE4BYUDzkZoLZQlVRuIpdXPg1pCe71OnQHAeHK4+gOctnHD26egaxCqAq+us9xmzutVlxITq6e/vOk1IY96nt+CNrixinBffToUYYNG+awfdKkSXz44Ycum5SglGMwSDruvOKUfFQXPmlUdHMqCI6chCo1sa17fq/0qkmBuW1hyZMFH+/GccdtJSDl27kbaTz59W4O/5fMiv2X2WlnA3Lz6RvmsvCMvHvy1XHPnz+f1atXExBgX5e2bNkyzp07R+vWrV0+OUEpRZsFBp1yxW0Pk3clwPKhJUfPfeo3+/X2ogGWi1EeXy5gkoX38tl8rP9Iwa7nBlYdusq+uNs8bhEw6tKsPuZyQoqGedukjdUxXWsV+fxKI/muuKOiopgzZ47dtsOHD3P06FEGDBjg8okJSjGmzbzAAiR/Pb0GLm5zz3yc5dYF2DQVVo6wbRuWhzCv3kk+9g10fjy9DnLSpHJoNXjltGxuCPDaRUmfXsyUCch7/ddu5maOXkkB4MFGlYpiSqWefAV3r1698PGx/cfcvHmTL774gsmTJ7tlYoJSzDddpNfAAj4yrx3v+rk4i1YDc1rAPx/LdU+thqc3wJQUqHW/43Mv7bC4TobzNt2aFLn80IdQpgo0eFSuCyoZWc/XHLUNsJWrs5/NKFDtmQGxShqF3pzcsGEDycnJjBo1im+++Ya1a9eyatWq/E8UCExYrz6757MIKKhJXW4O3DhVsHMckZVsW1e1JUS3z/9c6ycLrZOC2zIVWu3u0mv1TvDADHjljHPXcDMGg4HT123/L7XfXs+O84k2AjxALSyQXUGhBfdTTz3FqlWrWLRoEaNGjeLhhx+mb9++rpyboLRj7a5do6v9foOWSa+Ztwt2/Y0T4av2ELcj/755odcrEyWY8HMy4H+Dx5TH2ixpBW9NTiZ80Qbid0lqkl9GSvXjjshmfz5q6DAWylR2fv5uwmAwkKWVN2rXvqi0fhm2YB+1316vqLPObiMoHAUW3GvWrGH58uXumIvAzRgMBoePsMWCteCObAnv3IEXD0HtnnJ9XaNnokEnCVFnOfmr9PrDw3c3zz1fwtqXlXWW88sPa5XQkSUwo6LsCWki8QwknZU8Mfd8JddH1CjYfIuICT8fpcHkPwGY9HADGlUNZd9b3fM8x99XqEpcgVPPLZGRkaxYsQKA2NhYm3ax0vYMarwpZWn5d8aDJSN7ti7Hts7LC8rWgqErpdRf5etJ9eoQaaNOmyHFBHGGDBcFd0o6b1s35GfnzzfN1ycAcrPg7/ek442TYNASqWwKVGWiGIJtbT1zkxeWHGLti/dRs3zeTxPp2bmsOnTVfGzSXUfYWVGX8ffh+ftrs/fiLddO+B6mBPx6BUVBSqbszHL0yh002hLgapxfnI3n98jehw9Mk16diW+wA2HTAAAgAElEQVSt1Uj6bX8X5Xy09k5s2Fe6wTiLKQJipcbK+rPrpCBVALu/hB/tmPZNtqNbdwPXU7J4+vv9ZObo+GjjOdYeu8a2c4kO+y/bp0wc0SJKcj7y8VZxaVYfosvK+xfbX7+f0V1qsfDpNu6Z/D2I2CkoRRgMBppN+wuNVsfZ6Q8q2nZdkJ0i+n21mxB/H45P6VXUU5SI6iAlAcgvsl2F+nJZbVy1ZqcC+eh3Z1SUVuomtYpfqKSWKFsL/tsjCcknvnPeXdzS3vyZzUr3fGcoV1uyPNHrYJqV2uTjejBkJRxYYP9cd2eKN/LSsiPmcq5ez9glUso1S3tsS/48mUDlUH++f7oNKi+oU1H5FJSYJsXb7tWwImGBQq/tasSK28PJztVxIVFahd5MyyYlS0t2rp5bFoHqDQYDY346pDgvTZNbpPNUYNBbhHN1EpO64cs2sPfr/PsnnpFtoLNTJFM+gO96wenVkHKl4GMDVGxY+PggjnJD/vSEMvVZuFGn7aonBifYFydv/P558kYePWH5/v/YfymZ0ABf6lYKsRHagDl4lJ+P0Gm7AyG4PZyus/+m+0fbqP7GOmLn/GOu339JfsT+dkec3XMNBgPnb6Tx+5GrdttdRk4GXDloMbBOTpzgLJYWHOtfl8vJ8XDoR/l460zH15hnYfVgz7zPEZZZZnzdFI1Pb3Ejjf1Ueg0qWTE9LiVl8MGGM/zfL5IL/tU7WQ77vtS9DgDeKg8L1+shCMHtwfx6+ArXU2Szsptp9tN+LfjHvuA+k5BGz0+2Kx6T3cK6V+HbbpBmXMnlZktBlwpC+fr26z9rAqtfhKvGJ4pts5TtNbvK5QSLmB+aAgR7sreJerdMSYHKzey3VWgIZWtD90muH9cOKw5cBqBfC9s9B0srpJeXH2Hu37IlTEa246e2ciHS/9dPJElwC+JT9VBycvWMX37UYbvl5uPgtlIarZ+eaavok6szmMvPLTrAzTQXByzS62HFU3DUaDmRclmq0+UUPDt5fl6CR5fZ1vn4Q7Mh9vvfOOn82KZATjXz8I50lpdPSOaOAM9tg7ajle1NBkBweXjxoNJL0k3cTNXw+spjAOjsmFr+dUq62e78N4kjVkkQlj/n2PmoU+1yAAxo7VkZejwFIbg9lJiJ6/NsX3/iuln3bTDK57Y1lBtjlvtef568wd9nHFsRFIrE03Dqd/n42+6SmVuuxjW5Eg0GCDPmdryyT5ncACTHncb9QWVHJ71xovNelTs+kl6fchCPpCCEVZM2SU2c/0suvx4Hfb+5+zEKQJv3NpvLsU2rmL8jXw9rCcDxq5Lb/ZBv99qc2zqPKH/VywVxaVYfmkeFO+wjKDxCcHsgO87LArZqmFLnuu21roAkiLt/tI21x67xySYpqJOPt4q1L97H+/0ks7RP/jqnOFdnMOBSUuzozvfMlUz1fO7S0kCvlywxTJt61w5L6cRMjNktqUm8vOB/a+X6ihahYr8yrhi3zZZsxn98FBJOQNx2yd1cr3d/1vmmg+RyQWO33CWL9sQrjkP8fZk/vBWrnu9Ar4aVqF0h2HzzF5QshOD2MAwGA8MWyKFBlz7bTtEebuUAYTLrMtGoaijVIiQb202nlQ4qV5MdbzYViiX97denXQPvAuq4AR6dC17Gr+zB7+yrRwDajoGKDWRb66h28PYNyZTvue3Q8n9y34wk2DpdKl/8G+Z1hB9iYdHjcOh7ZbwQd9D5Vem16WCbpuSMHFbsv4xO7+IbKpKqbdJvJxR1Fcv4Ucbf12yTHRURyKH/7vDFFlsHpGfuK5nenPcKwo7bw0hIlfXQS55pS1TZQH57oSOhAb6cuJpCsIMgPpab+47cjo9eKcJErqnXCn5O8yFSxLw/34R1Exz3sxesytcfIltJ5XoPw8HvpbKlKsea2xfliIS18nblLjReXtJGpR0+33KehTsv8fovxxT21EO+3cOxKylsHN+ZyqGFs3Kx3M/Y8fr9JKVnE11WmdgiKiKQLWdu8uFG5ZPZnje7UynUBaouQaERK24Pw2TmN6pzTToYN4CaVQujRrkgYptWQeXA/Gp8Dzmgf4ADwX02Ic1uPRe3SeqNgpCRj3tzpUJmtwkql3+f/Ez26vSUrVTWveK436WdcvmxufmP62KuWDwBPfDJNr7fGYfBYGDnv7dI0+TSfuYWktILp8pZuPMSAPOGtqRaRKBdXXSFMrZPRffXLS+EdglACO4SjF5vYMOJ62YvNID/bkk5BscZ7WSdpUW0/MMsE2DfgSRVYyfH441Tkiu2ReyMO5k5jPrxAOduOBD0AKn5OLg4G2/EmrJOZFBxxh29jlWQqJgHbftcs3BaCnFfAoDEtGzGLjlESpb0+Wu0OtYfv2626AA4dyOdKWtOccbq5ro/roARE4HLtzPNJqKhDr4LADqdrYpmcmzDAo8ncD1CcJdQtDo9nT7YyujFh3hxqSRADAaD+bE12M95LdfI+2rQsba8Uq1cRrliOju9N2O61pLMA5POK+OB5BjL+76BZUO4k3ybZtP+YuOpG6w9ZhtA38xf7+Qzq0I6ZoRamZdVbGy/X34EWWUXH7hELg+3yir/hjIuh6sZvfgga49dp+nUjWRk51Jv0gYbT1cTJuFuwtKO31lMliIAVcIcr57vWI0VN/MhapTLI0+ooMgQgrsEYjAYeHHJYbNn2p6Lt8nIzmXS7yfyOVNi3tAWimNbM0AvRnSUN5f8fLzx81FRw3AZvmgFHzeQO2+3SAJ9Zi0rPhprPryUlMGpa3aSG2Snw8WtyrrR/yiFbKunnXovNlirQfzLSLE+TDQZ6Nx16luFelWpoMdUKFdXSlYQ3dFiDPe5nuv1Bg7Gy16cXWYrP7evhij/l9ZOL5k5BQ9dEJckPbX9PLq9jV7bkipWFkteBQmsJXArQnCXMDRaHd0/3saGkwmK+rFLDrF4j7TyWzk676wrvRtV5rFmVQBJt/1AQ9vH/J4NKiqOfb1V/OVndCXPToGjxpjrVw8o+mmR9eOrj17joc+NSQpWjpTyMQLMrCq9RraG/4uH0TulyHg9je0j/yq8qsTa/rtRP0nt0e55ePxrePRL564TUVPaFHzyR8l0EOC+l2HsPknV8rQUAldhPugGDl9Wut4npSv3EsoE+LLq+Q6A5D6ekaOM6mh9nB8Gg4HZf54FoHHVvG9I/+tQnSmxDfLsIygehOAuIWw7l0j1N9bR9r3NXEzMMNeb7LRTLYJCtcrD8cGEKd52pVD7Zndta0TwiGoX/b3/BqBFFauV7K+j4HYcZCo3GZt5WQX/B8kR5sRKKR+jZQyQAYshIEzeiKzdXTLLq3YX4T29faHFU/JxK2Pi3t4zoelA8C6goVSDRyXTQXtMOAcjNxZunk7y3T+X8mwPUHvTIiqcUZ1r4qPy4vfDkm38A8Ybb5q9fQlApzdw6L9kDFa2+Yf+ky2H8ktq4K3y4qHGUiTGgcIDskThlOA+evQow4YNs6lfu3Yt/fv3Z+DAgUyePBl9QbKTCMykZGkZ/t0+c9nEgFbVGNouGoD/bkt5Cq3VII4Y2i4alRd0ibEfqEil8uJz9RfM9v0Gjq+k3rYxtp0+t4il0U8KO9rR+yTr1G9S3ysef4ybpt90lfsttXAosbehV9CogPaI/Vwuu/PxPaQiqN2n001I0bDuuLRP8Hrvuoq2E1N78emAZjSvFgZAZHgA2bl6Np+RbO8/fLIpDauU4cx1+xvEvx+5St+5uxi79LBCeL+2UnJS+jmfpzYTFcr4s+uNbkx5RGxKliTyFdzz589n4sSJZGcrzY40Gg2ffvopP/74I8uWLSM9PZ2tW7c6uIrAETfTNHT/aJtN/elpvZnZtzG/HJKsMxLTsqkc6k/vRs7lGmxWLYyLM/s4Z7q17xvCbjuOewLwY3orc7mhKp71fm+ywNeo/75uEaTqv91Oze+uKAW61hupGtrNlN3Nn+9aW7HvEOznw2PNq5r1ytXClYmVg9Q+NK0WxsWkDOxx1mjxs+7YdXZfuEVKlpZNp26Yn+bycle3pkpYgEg5VsLI97kyKiqKOXPm8Prrryvq1Wo1y5YtIyBAesTOzc3Fz68Q3nD3MHq9gTYz5B/v9McaodHqiC4bRIAxFdS/N2ULD0fR/wqFzmJT6/Jes43H/3Je43v1bOU8ozow+feT/OY1hVV+U8z1Hb1P0iLX6JxRLgaSLBw1nreNbeFS2o6G8OruHcONfL7Z1hsxtmllvtsZR0U79tPtaiqDbHmrvPD38SYn1/5TboiF1dGoRQdJzyOSn8DzyHfF3atXL3x8bOW7SqWiXDnJxGzRokVkZmbSsWNHm34C+ySmZfOn1Qbk0HbRPNOppmLj0FI14lLXZztZyw9Ej+RvfXNG5ygT415rOg6A44aaNueYBXmMVTadCvVcMk2HPPg+tLOj3vEA9HoDP+2VTQwfaiyplExJB4LsmHqabuQg67fVPiqHgnvnv/LehLXQrl3Byez0ghLLXbm86/V6Zs+eTVxcHHPmzBHmQgWg9YxNiuOudcvb7dfBwv56w8udXDeBK/ttqrIDJDXMQb3SuafTz7mACi0+jIzawIJ6ByEjEXZ+KneKbC2lC0s849CFWyBxzMKOeucb3ahgjF1tujH7O8gac2hST+KS0mkZLak51D4qcnR6DAaDzW9vdx6JeX9/QSywPJ27EtyTJ09GrVYzd+5cVEWUG680cNEq4trEPvV5rHlVu33L+PvSo34FHm5ShXqVyrhmAgaDUuga8TZG7LuFbCb2Qs44DBYPZulaoMNYKaKeJTW6FEn8aE/ndkYOj30pudJveLmTIrpjjfJBBPv52GxUmogIUhMRJOum1d6SsNbqDKh9nFs0dY4pb3dFL/AsCvwfXLNmDZmZmTRq1IiVK1fSqlUrhg8fDsBTTz1Fz54987mCoJvFZuTgtlE808lWBWHJt8Nbu27w3BxYZhGJrmZXKSoeUEZ7A6iNHhUxmh/wJZcMlGaCXUxPBh3HSVls/pKytOy6mkuH2q6bZmll/yXJRb1qWIDNjTjYz4cTU51P4Kw2ZpfJ0enNZZBuDo7QFNDuW1AycUpwR0ZGsmLFCgBiY2PN9WfOnHHPrEoxJywek+cMak7nGPsqEpeRmw1/TZb0weHVpWS7ycZUZg99KNk+L+oLV/ZxK7InHJXMDgMDA3msWVW+33XJfKnPBjajj9GuFx8/6DiOrfqmvLLuGjk/HuDktN7k6vTM3niWoW2jqRzqb7YnF0i65ucWSbk3/3jp7tVeauNnm5OrZ+ulm1QO9SfYz4f/LbRVg5nYd6ngsU0EJQ/xzFTEvGZME/XBE02IbVrF/QPG7YC986S/KSmy0AZoNVJy9X5GysIS/F8ysItKZfzZ81Z3Np++oRDcsU1sow/e36kLyevW8ZzR3nzHv0l8ve0iX2+7CKAIR3qvYtJBH/5Pck5S+6jyDO7kLGqjLvz41RSediCs+7eM5OeDBchoL/AIhOAuQi4mpnP6uhTb48lWReSJlmjxVPS9RXyOfguUucuQkiwA9G4kWTlYhn99qHElhyFjfb29zHFVXl2Rtz34vYZWp6fJlI10q1fBHAP7r/Gd8znLOXyNOu4JK+wne+5RvyJd61YwC+53H21Iw3zc3AWegRDcRYTBYDDrtltXL8I8fOlyaFAuGeOKdJsEjZ+w6errreLE1F5mgW25ifVS9xib/ia0OgNrj13n5LW/uWWlX42/lZFnIKPSTnJGDllaHeuOX6dN9Qh8vb1c9nmY/j/W8U0aVinDyWupfDKgqSL07rD21V0yrqD4EQrIuyAxLZvqb6xjxf7LefbL1ekZ+YMcrGnRSGW2dfZ/C0sHy1l9LclOk/IhTg0veDIDgwF2fW5bn0e0u2A/H7yNK2tTijMAH+/8rRbi7Hjxvbv2tBMTLblcTExn2ppTZOcWblMvOVMOYbDv0m0613Hdnka5YPsOb6kaLW1rRBDi70towF3m9hSUSITgLgQ3UjX8ezPdbIv9+i/HHPa9lJTB6MUH2WKMMTGhZ4zSfVivl9JwnV0HW6bbXsBkAWLQw3cWFgcpV+Cmg83hnAzYN1/6s4d1LGoHhAdKetggtTc18lgl9m8Z6bBt0+kbbsmZWBSkabR0+2gb3+2M4921TmaEt+JOpvJmq3dhQmZLSxJLLt/OIjxQEth+DvoIPJvSpyrZ85UUGGj1i/DEd1LYTxO/PAtVmkP75wt16YPxyfT7apdNfdNIxyvYt349zq4LsjPEC/db2MwZDPDbaPl4x4cQWFYKU1rO6ARTvr6UdRykjCzZabDwQUg4LtVNumUbEe+35+HUb/Jxk4FwbBk0GwoNH4Oa9zv1fr28vJzaXOxev4LNBtiWCV3MqqFdF5Lo5MKVZlFxwSJK4+I9/zH9sYIlbdDpDbyz+qSibuvZRJfMDfIWysnGG4apj/CNK12UrtvxsRWw4Q1JaAOsHKFsP75CSjTrBAaDQRFVLf5WBl9u/ddu36NXUoi/lWET1P5WerY58H2dCsHM7Vsd1eZ34PoxuHIApobBseXKi/35ppTMQK+D9ETY97VUf/9E6XVmpCy0QbIWscZSaAP0+RC6vwOPfC7dFAoa+jQfejZQRgFsGhmK5SLbMiu9J/HMDwfy75QHtd76wybVWLd69qM1FgZHK26AvcaUZmWD/WgZHc57jxcyU5CgRFK6Vtwb7AjltBtSeM6rB+W6s+uhrp0cgyZunmbgorPMzXiFm90+ZvyBCJsfIEj64LqVQjgYn0yX2X/TMjqcOYOa89rKo7zRuz6xX/wDQKvocFaO6SCt+I+vgJ2fwX3j5Qs1GwJd34RPLYL2//iovJkI0PlV2GpHlbLxbSmJgMlCJFvplUmnV6WkBZ3ySIp7l3irvCgf4mfOjTnlkYZElw3M56ySTXauziYRr05vMOv/8yNXJ8cQWT6qHfG3MmlXsyzVIgqXld0e6jxs5F+4X8rN6a3y4pcxHVw2pqBkULpW3H52gud8FCMJyvnd5LqlA+Gyg1VgWgLMbcfytOGU1d+i/qbhJCVcYZ36Te5TSSvdE1N7UTnUn6+GtuD5rnLy2oPxyQxdsJed/94yC22AA6bUVGkWORqvGFdz3mp4ZA6EVYPndkAVY1ApS6E9apv0rPvmVbluUhKojPfdaeGg00p//3xs8Wa8oNtE++/TxUQbNzI/G9iM5lHh+HqrGGa07fZE6k6UgnANaFWN+4zxYv4vj70MayzTzDWtFsaTrasRVTbQpfF8/HyVP993H5Nv/A2rCLO/0kzpEdz/boLkS/JxlEWg+L8m2/Zf0FOxOk3J1HL1ThYz5sy16XrAfwwNVfEsVs+kRVQYwX4+7H6zO53qlLdxL7a3CvpxhDHji84iW4lJML9yBlTGzcrKTWDUVqjVXe4X2QaqGBMa+AVLGWTeui5lghlr8Sgftx3eLQc7PpKO306AKXeKTLlpsjqxtHSICJItGiw9Rks6P+2NN5efv78W3etL6o2VTjqypGRqWbpPsjQ6P+NBt8Wy9vNWXjfdIkuS2JQs3XjOf/fYz/ImnT0WGzcha3SR1APD10JZZZQ7XjykDIQ0syqc+AWAh95byawPpvN2zmcAnNXbt5RY/IzSlK9tDWWcZGuVyqVZfejsf0Ey6bu8R5kwN6oDBCnPB+CJBeAbBDG9zV6NZnz9QW1UQ0TUgIFLpfLJVVb9XPdI7gxjukqbrg0qy/E3VBY3DU8S3F9ukfYy/q93PaLLBhVY8DadJqc783Wjy7+1jrt/K/k7KxIflG48Q3Dr9bDqGfgh1rZNq4ElA+Tj4auh+yRpA+6FvZIQN1G2lpTJu2FfuW7lCHJOrGGnz2jmqL8wV/fK+YBZ9X6RpxAh3QQC3ysLy+U0blFlA4mpmEd8Y22WpK82UacnhBlVCC3/Z/+cgHCYcBr6/+D4uiYijQGoDi+W6yxzMhYRXWLKc2lWH8ItVtm9GslxxUP8797F2x2MXXKI6m+sM3s1GgwGbmXkUMbfhzFGNZi/r/M/E+scj+7EUnB//3RrygX70a6m85ltBJ6LZ2xOWsbXyLilXKV+2x1uGPWJPaYqz1N5o+n8FrfuZFGlViO8gATvylR84ju8ImqY1QrqlUMVpz2d8xrlgv14Y2APNNrbpGq0VIhfJ1upnF4t3UyMG4Ibx3ch/lYGXWb/DUCbGhHsi7vNC01V8HEDyNVAnV7ShmizwdDjnfzfcx5OMgoC7azYH7YN2VocVC4jr/oD1SVvBfjvzTTWHpP2HdYevc6I+2qw+ug1snP1THjAvqdoSpbWJs7I8O/2sTfuFiem9FI4Ie18o5v16S7FW+XFiam98PdRmYN5mZIxaLQiCmBpxjME9514i/IlWXDfuiALbYB6D2NNvUkbgI6UO+3H8qrp5vyOh94cT8SFLXDtsM05n7/1Et5qSej4+3pLj50NHgevZyRHGADNHQiUVzdhRoeH8iF+LH22HUev3KH52ocgyxiNbciKwr33/LCMN9JhHHSfLOvMixsL9Xq2g0wtxYllFppyxmQGplRxQ9rKG6vZWnnutzNy0OkN5Or1VAjxR683sO2cZJt97kY6uy4kAdKmpmWsbXcRbBVbu2+Lqmw7lyiy3JRySr6qRKeFRY/LxwsfggPfSeUjS+T67u9IqhALen8q68ST0rMVSXlbzNzOifu/Uw41KRmmpBASHEKg2uqeplLBO8mSUw/AmnGK5jKks676Cn55PARvL2ix/lG8bhbO267AhBhDrT7wrrRpWUKwNJ0bvfhgHj2Lno0nE1i485L52BSn+lZGDqEBvoo4LTkWpn1ZOTpavPsXbWZsRqc3MM3CozJVo+XzzeepFhHA+080cf+bsMOjzapyfsaD93R8mHuBki+4rWNt5GpgrdEGeocxy/gzWyQ7ZeNmWKpGS2Jatl3ba0sOJ6n4rOIMALb3XIe3MxtJJq/D02sUsUW89syjYcJvRMX9DNtnw3VjlLxWI+Gp3/O/7t0wdj+8dtG9YxSCYD8fJvR0HJyqqNHrDdxM03AlOZNRi5Q3koycXPbF3WbJ3v9obBVBr0Y5WQg+9LlsppmapVWEvZ2//SKpmlwu385yzxtwEnduiApKBk79h48ePcqwYcNs6rds2UK/fv0YMGCAOdGCS9Fq4O/3pXKlJhjK15fbFj4klyNbmos30zQ0mbLRHEekX4tIDk2yn5UnVZPLQb821M1dRueO9zk3p8AI8DE+Ak8Ng9RrEL8Lts2S6s6sg60zjH3LwsMfS1lm3IlfiH3rlBLAE60cxzEpan7YfYk2MzZz3/tbzXWLRkqmmlPXnOLJr3cDkKtXqnU61SnPu482tLneayuVIWw3G+PROOukIxAUlnwF9/z585k4cSLZ2UovMq1Wy8yZM/nuu+9YtGgRy5cvJzHRdXEYALh9AXTZ0PVNNnb6mRqXJ5JhMNoJx0t5+6gmm+d9uukcbWZsVlzinUcaEBGkZuoj0g9vYp/6LBjeCoDZf55l+7lExYrKKTpaqEl+eVaKHWIi7Zr0WrExTDhXsOuWQvLy7isKDAYD7649RVxSBlPXKFVX4YG+dKxVzuacER1r2NQ1qGKb73PT6Zt2x1w+ql0hZysQOEe+v6qoqCjmzJljU3/hwgWioqIIDQ1FrVbTsmVLDhy4u9gONhjttuPDOxgfbb14RvuqokvqAMlkb/PpG3y66bzNJYKNuurhHapz8b2HeKZTTbrXr6joY+ko4hSdX5c8HgHiZQ9Joixci2M/dXlMEE+kuFOXrThwmQX/xHH/h3/btP0ypoNNcoheDSvyQMNKNn0zsp230qhZXmwMCtxLvr+qXr164eNjK4DS09MJCQkxHwcFBZGenm7T726I27WSOH1F7l8qO2/s1jdkovZpAOblPkyT6ZJwn/GHHPd5Yh9JpfLVkBaKH6ZluU0N2SLEWpDni7cPTLJ6uuj5LgxfAz2nwbBfIbJVwa5ZSiluDz5raxa1t4ptr3XlxNReZgFr+V14pGlVu9epUMZ+7GsT84a2MJcDhPOLwM0UekkYHBxMRoZss5qRkaEQ5K7gq1vNuW3ogt7i/hIVEchPyT35SdMdg7G+96fbuZiYociSnV/m9BmPNaLnJ9t5omUkIzpWL9wEp6TA/gWQelVWn3R8qXDXKqX4+3pTLSKgyFUmt9KzeX/DGbOdtonfx3a0sbgY07UW+4zR9Bw5sNSrVIbxPWL4ZJOk/vJWeZnjjB+e1NOcug0K5rAjEBSGQgvuWrVqER8fz507dwgMDOTAgQOMHDnSlXOjctdRrNgsqT/aVI9g8TNt8fKCn/bEM8VCX2myHknPzrV7HXvUqRjimkS2rV37nksjTaqGcSYhtUjHbDl9k936yqH+NnX315VDrealNnupRx2z4A5Ue5OmyeWDJ5oQHqTG2yJDkCsDSQkE9iiw4F6zZg2ZmZkMGDCAN954g5EjR2IwGOjXrx8VKxZQ5ZAP43vG0CI6nOHf7WPEfTXMLr4DWkdx5PIdziSkKUz+WkSFuXR8gWsIUHuTlVO0nnwVQvy4aQwzq/LCHB+8jAPX+z/GdeLU9dR8he7aF+/jRqqGCT9LFiWmmCBl/H3ZPKFLsauGBPcGTgnuyMhIs7lfbKwcL6Rbt2506+Zet94uMeU5Na2XwiEmQO3NpwOb8+rPR82C+77a5fh8UHO3zkVQOALV3mQWoQu2Tm8wZ4ABiAjyM8fWdpSpvkGVMnYtR6xpVDWURlVDzU6h/haCupbYlBQUER6xPLDxYjTS22L3f1a/xgW3DhEUCQG+3mQW4Yr72JU7aHWyc9Rjzaq4fIwKIZLKpXpBTUkFAhfg0fZqPRpU5Jcx7alVPtgcK0RQ8ghQe5OTqy9QBpnC8tmm82Y9dEzFYM7dSCe6bCAvdqtdcOuhPPh0YDMOxicTU9G1G/ICgTN4tOAGaBktwliWdEyRAbO0OpugSK7EYDDw7T+y6/+Mxxszfe0pHm5SRRFu1ruDlZQAABYUSURBVBXUr1yG+pXzV60IBO7A4wW3oORjip2hzdVD3ubQd0WNN/9QHLeuHsHvY50MZSAQeBAeoeMWeDYm70mt3n2hXbecueG2awsEJQ0huAVux9eo19594ZbbxjgUf0dxLDaqBaUZoSoRuB3TivulZUdISNHQs0FFl8bzMBgMfLH1X/Nx2xoRfDtchBwQlF7EilvgdnwtvApnrj/DkG/3uvT6FxLl0AtNIkN597FGJTbHpUDgCsSKW+B2fFTK9UFGAUITOMPtDMnZZkzXWvxf73ouvbZAUBIRK26B2/HxVtpuO/JeLCynr0txUB5sZBuOVSAojQjBLXA7vlaC29/n7sKepmRp+ervC2w4IUX+u5YiReYTXoyCewWhKhG4HWtVSZPIUAc9neO+97eQppHULZdm9WHHuSTqVQpxGEBKIChtCMEtcDvWqhJr70mNVoeXF/jlsxK/nZHD7Yxss9AGeHPVMU5dL9qQsQJBcSNUJQK3Y511fNXhq+aywWCg3qQNdJy1Jd/rtHj3L3p8vF2RhX3pvssAdK9XwdFpAkGpQwhugdvJayvySrKkn05Kz8mjl5LjV1Ns6mIqiWBPgnuHfFUler2eKVOmcPbsWdRqNdOnTyc6OtrcvmDBAtatW4eXlxejR4+mZ8+ebp2woPRw/EoK87ZfcMm1AkWeR8E9RL6Ce9OmTeTk5LB8+XKOHDnCrFmz+OqrrwBITU1l0aJFbNy4kaysLB577DEhuAVOcfJaCrFf/ON0f4PBkGd75bCAu52SQOAx5KsqOXjwIJ06dQKgWbNmnDhxwtwWEBBAlSpVyMrKIisrS+TaE9jF3teiz+fOC22ANCunne+fbs03w1qajyuEuDHsoEBQwsh3xZ2enk5wsBxXwtvbm9zcXHx8pFMrV65Mnz590Ol0PPfcc+6bqaDUk5OrN+cVtSbRmD8S4OUedehqTPD7xoP1mLX+DI2q3p2JoUDgSeQruIODg8nIkGNB6PV6s9Devn07N2/eZPPmzQCMHDmSFi1a0KRJEzdNV+CJRAQ5txp+Y9UxIsMCGNoumgpl5GzsG04kMHrxQQBWPNeeNjXk5Bmju9RidJdarp2wQFDCyVdV0qJFC7Zv3w7AkSNHiImJMbeFhobi7++PWq3Gz8+PkJAQUlOFTa1ASY1yQaxxIqHBqkNX+XzLv8xaf8ZcZzAYzEIboFywCNcqEOS74u7Zsyc7d+5k4MCBGAwG3nvvPRYuXEhUVBTdu3dn165dPPnkk6hUKlq0aEHHjh2LYt4CD6NxHt6Slcr4k5CqMR/vj79tLlsm/QWoHCo2IQWCfAW3SqVi2rRpirpateRH03HjxjFu3DjXz0xwTxA38yGuJGfR6YOt5jpLD8r5Oy4q+geohdmfQCAccATFipeXF+WtLEL+vZkOQJpGy+w/z5rrh7WLRiAQCMEtKEJqVwg2Z3y3xN+B88yU1afM5WoRAUx6uIHb5iYQeBIiyJSgyPjz5c4A1Hrrj3x6SpuSvxy6Yj4e06W2Q1NBgeBeQ/wSBEWGt8oLb4skCo2qlrHpM7FPfQBSNUqHm0Ftqrl3cgKBByEEt6DYWPtiJ3N5VOea1CwXZNZ3J6ZpFH2FV65AICMEt6BE8NZD9dnyalez4L5p4SlpvXkpENzrCMEtKFFUCJE8Js8mpJnrNk/oUlzTEQhKJEJwC0oUFcpIq+upa2SLEpGSTCBQIgS3oEQRYpXWrFm1sGKaiUBQchGCW1CisN6E7FFfpCQTCKwRgltQ5HSqU47IcOdijjzarKqbZyMQeB7CAUdQ5Cwa2TbP9skPN2DaWknH7cirUiC4lxErbkGJI7psoLns5yu+ogKBNeJXIShxBFtsUPoJN3eBwAbxqxCUOHy85a+l2lt8RQUCa8SvQlDiqFEuyFwWru4CgS35bk7q9XqmTJnC2bNnUavVTJ8+nehoOS7ytm3b+PLLLwFo0KAB77zzjvixCe6KiCCRnkwgyIt8V9ybNm0iJyeH5cuXM2HCBGbNmmVuS09PZ/bs2cybN48VK1ZQtWpVkpOT3TphgUAguNfJd8V98OBBOnWSorg1a9aMEydOmNsOHz5MTEwM77//PpcvX6Z///5EREQ4upRA4DTnZzyIVqcv7mkIBCWSfAV3eno6wcHB5mNvb29yc3Px8fEhOTmZvXv38ttvvxEYGMiQIUNo1qwZNWrUcOukBaUfX28VvmJjUiCwS76/jODgYDIyMszHer0eHx9J3oeFhdG4cWPKly9PUFAQrVq14vTp0+6brUAgEAjyF9wtWrRg+/btABw5coSYmBhzW6NGjTh37hy3b98mNzeXo0ePUrt2bffNViAQCAT5q0p69uzJzp07GThwIAaDgffee4+FCxcSFRVF9+7dmTBhAs888wwAvXv3Vgh2gUAgELiefAW3SqVi2rRpirpatWqZy3369KFPnz6un5lAIBAI7CJ2fwQCgcDDcHt0QJ1OB0BCQoK7hxIIBIJSQ14y0+2COzExEYAhQ4a4eyiBQCC4J/AyGAwGdw6g0Wg4ceIE5cuXx9tbxFYWCAQCZzBpK6pWrWo2wTbhdsEtEAgEAtciNicFAoHAwygRgjsnJwetVlvk4xbnw0Z6ejqpqanFNr5AUFrR64s2xo1GoyE7O7tIxyx2wf3DDz8wffr0Irc6+e677/jyyy+Jj48v0nEBli9fzoABAzh27FiRjvv777+zceNGNBpNkY4LsHbtWv7++29F+ISi4Oeff+a3334jKSmpSMYzLQb27dvHtm3bFHVFxY8//siXX37J7t27i3Rc02d9/fr1Ih0XYPPmzbz//vtFPu6iRYt4++23iYuLK9JxvadMmTKlSEc0cvnyZQYOHEiVKlV44YUXqFChgrnNYDC4LaZ3Wloa48ePx9fXl2bNmqHX66lSpYrbxwXYsWMHM2fOJC0tjfj4eEaMGEFISIjbxjORmJjIM888Q1paGufOnSMhIYGYmBjUavfHvb558yYjR44kMzOTxMREjh07Rnh4OOXKlXPr552amsrYsWNJT08nOzubHTt2EBoaSuXKldHr9W4b13Td2bNnk5iYSPPmzfH393fLWNakpKQwduxYtFotjRo14scff6RatWrm77e7SEtL4/nnnyc1NRWtVmuOGhoUFJT/yS5izZo1LF68mF69ehEREUFubi4qlfvWpTdu3ODRRx+lWrVqvPLKK1StWtXc5m45AsW44tbr9bRt25YuXbqwcOFCPvnkEzZt2gS4N+tJZmYmNWvW5Omnn2bXrl3s37/fvDJx94d98OBBhgwZwowZM4iNjS2yle/169dp2LAhs2bN4tlnn+XkyZOKiI/u5Nq1azRq1Ijp06fz7LPP4u/vz2+//Qa49/POzs4mOjqa6dOnM27cOBo3bszXX38N4NYfNMD69euJj4/Hy8uLDRs2uHUsSxITE4mOjmbatGn06dOHRo0a4efn5/Zxk5OTqVq1KjNnzmTgwIEkJSURGhrq9nFBVouEhITw8MMPY1qHWlthuJrw8HBatmxJs2bN+Prrr5k+fTo//fQTUDRZm4psxa3RaHj//fc5f/48WVlZ1K9fn82bN7N582ZatmxJhQoVWL9+vbnNVXcty3Gzs7MJDg5mwYIFeHl5ERkZSUhICOvXr0ej0VCvXj2X3i1NY585c4acnBz69+9PdHQ0Go2GTz75hF69ehEeHu7yO7Rp3HPnzqHT6QgPD2f79u1kZ2ezadMmjh8/jlarJTU1lejoaJeuQC3H1uv1+Pr6smDBAoYOHUpAQAD79u0jPj6e8PBwIiMjXTKm6fNbunQpFy9epF69epw/f56NGzfywAMPoFariY6OZufOnWi1WmJiYlzymdsbF0CtVtO8eXMqVqzIsWPHqFq1qsv/z/bGvnjxIkFBQdStWxeAjz76iF69elG2bFmXjW1v3P/++4/KlStTvXp15s6dy/r168nIyODq1as0bNjQZd8ve2MbDAbS0tJYsmQJs2fPZv78+ezdu5eIiAi3fr9SU1P577//+O2332jbti0dO3Zk2bJlJCYm0qJFC7c+1UERrbhTU1OZNm0a/v7+NGnShKlTp3L58mWaNWvGo48+Sv/+/YmNjaVPnz6cP3/eZW/aelxTWrXw8HD++usv+vbtS2xsLD169OD06dMu/bAtx27evDnvvPOOOeStv78/HTt25OjRo4Br79CW4zZt2pS3334bgBEjRrB69WoyMzP54osvUKvV/Prrr2i1WpetQK0/77feeovy5ctTsWJFZs6cycKFC7l8+TJRUVEufdowfX67d+/mm2++Qa/X06xZM/OPDSAgIICOHTty7do1lwkxe+MCVKxYkTZt2hATE0NoaKhZ1+3K/7Pl2F9//TV6vZ5WrVrxyCOPALB//34CAwPNQd9ctWFn7z03btyYLl26ANC1a1f++OMP2rRpw6+//kpOTo7Lvl/2xlapVCQnJ5sXgj4+Puz///bOJaaptI3jP8oURIYRbAFBGEABLVWhikRRiUpcqFU3BkUFlAVmYhoU75rJDERNNCYuXGAUEpxRUfEC8ZK4YOEtYkYUoxI0KgERYeqMOuClCvZbGPt9ZuSboT3lWHx+65P++n+b85zT933PeX77jfHjxwPKrC98zhsUFER8fDzz588nIyODMWPGYLFYqKurU/Sc6gm3fvrHpya1Wi3t7e0sWbKE8ePHs3DhQkpLS0lPT2fmzJmOjebNzc0MGzbM5dA9eTMyMigrKyMvL4/79+/z6NEjvL29aWlpYejQoYoMdk/uRYsWUVpais1mo7u7G39/f0X/xvbkzczMZM+ePej1eqxWK5s2bSI6OhqtVovBYECr1brFnZKSQkZGBiUlJRQVFTF16lT+/PNPCgsL0Wq1ijyM9dELHwpVUFAQQ4YMcbwULT8/n8rKSu7du4dGo+HJkycEBga6XEB78m7btg3AMaYRERGMGjWKxsZGxRYKP+cOCwtzuD+eS01NTWRlZdHQ0EB+fj6XLl1S3Pu/mT9eGBITE9Hr9dhsNlJTUxVZR+nJvXXrVuDDHHtZWRnV1dWUlZURGxvL7t27Adculj15t2zZAsDkyZOZM2cOnZ2dADx8+JBx48Ypck79E255AKetrY3du3fzxx9/kJ6ezsiRI7ly5QphYWHMmTMH+HAHmJOTg81m48SJE/j6+mKz2VixYgWjR492mzcnJ4c1a9ZQW1vL7du36ejo4O3bt1gsFsaOHev2zJmZmcyYMYNjx45RWVnJgQMHnHb+W+/SpUtZu3YtR48e5fXr19jtdp49e0ZeXh4pKSludS9btowlS5ZgNBqprq6moaEBq9XKhg0biI6Odtk7ffp00tLS0Gq1PH/+nPDwcGbMmMHBgweJiopi3759tLe38+jRI969e0d+fj6JiYlu85aXlxMZGenoEmW1Wjl//jwmk+mTt2q602232/nhhx9obGwkKiqKxYsXO+6I3emtrq6mpqaGJ0+eYLPZyM3NZeLEiW7NfOjQIb7//nvq6+tJSEgAoLGxkZaWFkfLRXdmPnPmDNXV1bx69Yru7m6WL19OcnKy05n/LW6Z4/7ll1/w8/Nj+fLl1NXVce3aNXx9fenq6iIgIIDBgwej0Wg4deoUFosFo9HId999R0FBAaGhoW71ent7c+TIETZv3kxycjJ6vZ5Vq1YRFhbm9szffPMNFRUVzJs3j4SEBDQajWNe1J1eLy8vKioq2LFjBxEREfj7+7Nu3bpPVsLdmbmqqoqFCxfy8uVLfHx82LBhA4GBgYp4r1+/zuXLl5kyZQqhoaFotVr++usvKisrMZvNJCYmkpycjE6nIz8/nyFDhrjVW1VVxezZs/Hy8sLLywt/f38SEhJc7sXam8w2m43Dhw+TmZnJxo0bnb5A/lvvyZMnMZvNREREMGLECAYNGkRBQQGRkZFuzfzixQuqqqowm80EBwcD0NXVhU6nIyoqqk8yR0dHk5KSwuDBg1m5cqXbd/B8RLHCffz4cfbv38/du3dpaWkhOzubyMhI9Ho9jx8/pq2tDZ1Ox7Vr15g0aRJ1dXXo9XpMJpNjvqivvCEhISQlJeHn5+dSf8zeum/cuEF4eDhJSUkAThft3npv3rzpGOvg4GCXLhbOZA4JCcFkMhEZGcmoUaMU9YaGhtLQ0EBzc7NjXCdMmEBRURGxsbEMHz4cHx8fp4tXb72FhYXExcUp0nfVmcwxMTHEx8czd+5cp/9ZODvWsbGxBAQEuNQFqzfuiRMnUlRURFxcnOP3dXa605XMAwcOZNiwYU5ndgZFCvfOnTu5desWubm5nDt3jjNnzuDj48OkSZPw8/Pj/fv3WK1WUlNTuXv3LocOHaK+vp6cnByX7kSc9WZnZ7t8B6SWW62xVtP9T15vb2/u3LnD6NGjHXumDQYDQ4cOVcUbHh7u9rH+f5l1Op3TawhqjbUrblfHW83MzqLIZseOjg4WLFiA0Whk8eLFhISEcPr0acxmMwaDgaCgIF69ekVSUhJGo5HW1laX/r6p7VXTLZn/7tXpdNhsNgYOHOjYMTJ58mSP9arplsx9m9lZXL7jfv/+Pb6+viQmJuLj48PevXuZNm0aBoOBkpISTCYTFy9epKmpialTpzJgwACX5jfV9qrplsyf9164cIHm5mbS09MVW9FXy6umWzL3bWZXUHRXSWdnJ0uXLqW4uJjg4GCKi4t58eIFT58+Zf369Y4FBKVRy6umWzL3f6+absnct5l7i6LPhba3t5OamkpHRwdbtmwhLi6O1atXu/0qpZZXTbdk7v9eNd2SuW8z9xq7gpSXl9tHjBhhz83NtVdVVSn50V+kV023ZO7/XjXdkrlvM/cWRadKjh8/jtVqJTc3t0/ePKe2V023ZO7/XjXdkrlvM/cWRQu3vQ9eZ/gledV0S+b+71XTLZm/bKTnpCAIgoehegccQRAEoXdI4RYEQfAwpHALgiB4GFK4BUEQPAz3NmYTBJW4evUqK1euJDY2FrvdTldXF9nZ2cyaNeuzx7e2ttLQ0MD06dP7+JsKQu+Rwi30WyZMmMCuXbsAePnyJVlZWcTExGAwGP52bE1NDQ8fPpTCLXgEUriFrwJ/f38WLFjA2bNnOXDgAG1tbTx79oy0tDQsFgt79+7lzZs3mEwmIiIiHO2pAgMD2bZtGwEBASonEIT/InPcwleDTqejvr6epKQkSktLKS8vp7y8HG9vb/Ly8jCbzaSnp/Pjjz/y008/8euvv5KWlkZJSYnaX10QPkHuuIWvhtbWVkwmE7du3aKmpoZvv/2Wt2/f/u24Bw8eUFhYCMC7d+8U6WYjCEoihVv4Kujs7KSiooL58+fz+vVrioqKaGpq4ujRo9jtdjQajaNTeUxMDNu3byc8PJza2tpPun0LwpeAFG6h31JTU0NWVhYajYbu7m4sFgsxMTEUFBRQW1uLn58fUVFR/P7778THx1NcXIzRaOTnn39m/fr1dHd3A7B161aVkwjCp8i7SgRBEDwMWZwUBEHwMKRwC4IgeBhSuAVBEDwMKdyCIAgehhRuQRAED0MKtyAIgochhVsQBMHDkMItCILgYfwHH0jIgP8+0ZsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c25b2fef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas_datareader import data as pdr\n",
    "import fix_yahoo_finance as yf\n",
    "yf.pdr_override()\n",
    "\n",
    "start_date = '2005-01-01'\n",
    "end_date = '2015-01-01'\n",
    "\n",
    "# Get returns for SPY and TLT\n",
    "etf_returns = pd.DataFrame()\n",
    "etfs = {}\n",
    "for symbol in ['SPY', 'TLT']:\n",
    "    df = pdr.get_data_yahoo(symbol, start=start_date, \n",
    "                            end=end_date, auto_adjust=True)\n",
    "    etfs[symbol] = df\n",
    "    etf_returns[symbol] = df['Close'].pct_change()\n",
    "get_equity_curve(etf_returns).plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c25b3dbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style('white')\n",
    "fig, ax = plt.subplots()\n",
    "get_equity_curve(etf_returns).plot(ax=ax)\n",
    "ax.axhline(1, c='k', linewidth=0.5)\n",
    "ax.set_xlabel('')\n",
    "ax.set_ylabel('NAV')\n",
    "fig.tight_layout()\n",
    "fig.savefig('SPY_TLT Buy_Hold Equity')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ideal f calculated in 104.5985779762268s\n",
      "SPY          0.457094\n",
      "TLT          0.495551\n",
      "ghpr         0.032737\n",
      "drawdown    19.833778\n",
      "Name: 1810, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "f_etfs_dd = ideal_f_multiple(etf_returns, bound_factor=4)\n",
    "print(f_etfs_dd['optimal_f'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c266e81d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "optimal_idx = f_etfs_dd['f_curve']['ghpr'].idxmax()\n",
    "optimal_weights = f_etfs_dd['f_curve'].loc[optimal_idx, ['SPY', 'TLT']]\n",
    "\n",
    "pivoted = pd.pivot_table(f_etfs_dd['f_curve'], values='ghpr', columns='SPY', index='TLT')\n",
    "pivoted.sort_index(ascending=False, inplace=True)\n",
    "pivoted.index = np.round(pivoted.index, 2)\n",
    "pivoted.columns = np.round(pivoted.columns, 2)\n",
    "pivoted = pivoted.iloc[-25:, :25]\n",
    "optimal_x = optimal_weights[0] / pivoted.columns[-1] * 25\n",
    "optimal_y = (1 - optimal_weights[1] / pivoted.index[0]) * 25\n",
    "\n",
    "sns.heatmap(pivoted, cmap='RdYlGn', center=0, ax=ax, cbar_kws={'label':'GHPR (%)'})\n",
    "\n",
    "ax.scatter(optimal_x, optimal_y, marker='*', c='red', s=200)\n",
    "fig.tight_layout()\n",
    "fig.savefig('ETF Returns Heatmap')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08597973675489645"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_ghpr = f_etfs_dd['optimal_f']['ghpr']\n",
    "(1 + max_ghpr/100)**252 - 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Non-Linear Optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sharpe_ratio(x):\n",
    "    return np.mean(x) / np.std(x)\n",
    "\n",
    "def rolling_z_score(series, lookback):\n",
    "    mu = series.rolling(lookback).mean()\n",
    "    sigma = series.rolling(lookback).mean()\n",
    "    return (series - mu) / sigma\n",
    "\n",
    "class Portfolio:\n",
    "    \n",
    "    def __init__(self, returns, regularized=False, c=1e-6):\n",
    "        self.returns = returns\n",
    "        self.regularized = regularized\n",
    "        self.c = c\n",
    "        \n",
    "    def fitness_function(self, weights):\n",
    "        weighted_returns = calc_weighted_returns(self.returns, weights)\n",
    "        neg_sharpe_ratio = -1 * sharpe_ratio(weighted_returns)\n",
    "        penalty = self.c * np.linalg.norm(weights, ord=1)\n",
    "        if self.regularized:\n",
    "            return neg_sharpe_ratio\n",
    "        else:\n",
    "            return neg_sharpe_ratio + penalty\n",
    "\n",
    "    def optimize_portfolio(self, display=False):\n",
    "        num_strategies = self.returns.shape[1]\n",
    "        initial_guess = [0.5] * num_strategies\n",
    "        optimization_results = cma.fmin(\n",
    "                self.fitness_function, initial_guess, 0.25, \n",
    "                options={'bounds':[0,1], 'verb_disp':display, 'tolfun':0.0001}\n",
    "        )\n",
    "        return optimization_results[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create Strategies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "rolling_z_score() takes 2 positional arguments but 3 were given",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-27-b3e1f126c7c9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mspy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0metfs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'SPY'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mspy_returns\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mspy\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Open'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpct_change\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshift\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mstrategies\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'SPY_5'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrolling_z_score\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mspy\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Close'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m \u001b[0mstrategies\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'SPY_50'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrolling_z_score\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mspy\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Close'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m50\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mstrategies\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'SPY_100'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrolling_z_score\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mspy\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Close'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: rolling_z_score() takes 2 positional arguments but 3 were given"
     ]
    }
   ],
   "source": [
    "strategies = pd.DataFrame(index=etf_returns.index)\n",
    "strategy_returns = pd.DataFrame(index=etf_returns.index)\n",
    "\n",
    "spy = etfs['SPY']\n",
    "spy_returns = spy['Open'].pct_change().shift(-2)\n",
    "strategies['SPY_5'] = rolling_z_score(spy['Close'], 5, 20) * -1\n",
    "strategies['SPY_50'] = rolling_z_score(spy['Close'], 50, 20)\n",
    "strategies['SPY_100'] = rolling_z_score(spy['Close'], 100, 20)\n",
    "\n",
    "tlt = etfs['TLT']\n",
    "tlt_returns = tlt['Open'].pct_change().shift(-2)\n",
    "strategies['TLT_5'] = rolling_z_score(tlt['Close'], 5, 20) * -1\n",
    "strategies['TLT_50'] = rolling_z_score(tlt['Close'], 50, 20)\n",
    "strategies['TLT_100'] = rolling_z_score(tlt['Close'], 100, 20)\n",
    "\n",
    "for column in strategies.columns:\n",
    "    symbol = column[:3]\n",
    "    if symbol == 'SPY':\n",
    "        strategy_returns[column] = strategies[column].multiply(spy_returns)\n",
    "    elif symbol == 'TLT':\n",
    "        strategy_returns[column] = strategies[column].multiply(tlt_returns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize Portfolio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "portfolio = Portfolio(strategy_returns)\n",
    "results = portfolio.optimize_portfolio()\n",
    "optimal_weights = pd.DataFrame(np.round(results, 2), index=strategy_returns.columns, columns=[''])\n",
    "optimal_weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determine Leverage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ideal_f(returns, time_horizon=250, n_curves=5000, drawdown_limit=20, certainty_level=95, steps=200):    \n",
    "    \n",
    "    start = time.time()\n",
    "    f_values = np.linspace(0, 0.99, steps)\n",
    "    max_loss = np.abs(np.min(returns))\n",
    "    bounded_f = f_values / max_loss\n",
    "    f_curve = pd.DataFrame(columns=['ghpr', 'drawdown'])    \n",
    "    for f in bounded_f:\n",
    "        # Generate n_curves number of random equity curves\n",
    "        reordered_returns = np.random.choice(f * returns, size=(time_horizon, n_curves))\n",
    "        curves = get_equity_curve(reordered_returns)\n",
    "        curves_df = pd.DataFrame(curves)        \n",
    "        # Calculate GHPR and Maximum Drawdown for each equity curve\n",
    "        curves_drawdown = calc_max_drawdown(curves_df)\n",
    "        curves_ghpr = calc_ghpr_eq(curves_df) \n",
    "        # Calculate drawdown at our certainty level\n",
    "        drawdown_percentile = np.percentile(curves_drawdown, certainty_level)\n",
    "        # Calculate median ghpr value\n",
    "        ghpr_median = np.median(curves_ghpr)\n",
    "        if drawdown_percentile <= drawdown_limit:\n",
    "            ghpr = ghpr_median\n",
    "        else:\n",
    "            ghpr = 0\n",
    "        f_curve.loc[f, 'ghpr'] = ghpr * 100\n",
    "        f_curve.loc[f, 'drawdown'] = drawdown_percentile\n",
    "    optimal_f = f_curve['ghpr'].idxmax()\n",
    "    \n",
    "    elapsed = time.time() - start\n",
    "    print('Ideal f calculated in {}s'.format(elapsed))\n",
    "    \n",
    "    return {'f_curve':f_curve, 'optimal_f':optimal_f, 'max_loss':max_loss}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimal_returns = calc_weighted_returns(strategy_returns, results)\n",
    "leverage = ideal_f(optimal_returns)['optimal_f']\n",
    "print(leverage)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "leveraged_weights = optimal_weights.multiply(leverage)\n",
    "leveraged_returns = calc_weighted_returns(strategy_returns, leveraged_weights.values.flatten())\n",
    "np.round(leveraged_weights, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_style('whitegrid')\n",
    "fig, axes = plt.subplots(2, 1, figsize=(7,7), sharex=True)\n",
    "\n",
    "eq = get_equity_curve(leveraged_returns)\n",
    "dd = calc_drawdown(eq)\n",
    "\n",
    "eq.plot(ax=axes[0])\n",
    "axes[0].axhline(1, c='k', linewidth=0.5)\n",
    "axes[0].set_ylabel('NAV')\n",
    "\n",
    "dd.plot(kind='area', ax=axes[1])\n",
    "axes[1].set_ylabel('Drawdown')\n",
    "vals1 = axes[1].get_yticks()\n",
    "axes[1].set_yticklabels(['{:,.2%}'.format(x) for x in vals1])\n",
    "axes[1].get_legend().remove()\n",
    "fig.tight_layout()\n",
    "fig.savefig('Leveraged Portfolio Equity Curve')"
   ]
  }
 ],
 "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": "3.6.4"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "332px"
   },
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}