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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Econometric estimation of an IRL-based market portfolio model. Part II: QED\n",
+ "\n",
+ "Welcome to your final course project on Advanced Topic RL in Finance. In this project you will: \n",
+ "\n",
+ "- Explore and estimate an IRL-based model of market returns (the \"QED\" model) that is obtained by a generalization of a model that you analyzed in the previous course\n",
+ "- Respectively, you are expected to re-utilize parts of your previous code from the course project from Course 3: RL (but you can also start from scratch - the template provided here is nearly identical to the one offered to you in course 3)\n",
+ "- Investige the role of non-linearities in price dynamics\n",
+ "- Investigate the role and impact of choices of different signals on model estimation and trading strategies\n",
+ " \n",
+ "\n",
+ "**Instructions for project structure and grading principles :**\n",
+ "\n",
+ "- This is a project that will be graded based on a peer-to-peer review. The project consists of four parts. The maximum score for each part is 10, so that maximum score you can give your peers (and they can give you) is 40. The parts are as follows (more detailed instructions are in specific cells below):\n",
+ "\n",
+ "- **Part 1**: Estimate the model using the DJI portfolio of 30 stocks, first without signals, and then using simple signals such as simple moving averages constructed below (Max 10 point).\n",
+ "\n",
+ "- **Part 2**: Explore the implications of calibrated model parameters for default probabilities of stocks in your portfolio. Present your conclusions and observations. (Max 10 point).\n",
+ "\n",
+ "- **Part 3**: Experiment with other signals and investigate the impact on model calibration obtained with alternative signals. Present your conclusions and observations. (Max 10 points).\n",
+ "\n",
+ "- **Part 4** : Show me something else. This part is optional. Come up with your own idea of an interesting analysis.\n",
+ "For example, you can repeat your analysis for the S&P portfolio.\n",
+ "Or maybe you can build a strategy using an optimal market-implied policy estimated from this model, and compare it with PCA and absorption ratio strategies that we built in Course 2. Or anything else. (Max 10 points).\n",
+ "\n",
+ "**Instructions for formatting your notebook and packages use can use **\n",
+ "\n",
+ "- Use one or more cells of the notebook for each section of the project. Each section is marked by a header cell below. Insert your cells between them without changing the sequence. \n",
+ "\n",
+ "- Think of an optimal presentation of your results and conclusions. Think of how hard or easy it will be for your fellow students to follow your logic and presentation. When you are grading others, you can add or subtract point for the quality of presentation.\n",
+ "\n",
+ "- You will be using Python 3 in this project. Using TensorFlow is encouraged but is not strictly necessary, you can use optimization algorithms available in scipy or scikit-learn packages. If you use any non-standard packages, you should state all neccessary additional imports (or instructions how to install any additional modules you use in a top cell of your notebook. If you create a new portfolio for parts 3 and 4 in the project, make your code for creating your dataset replicable as well, so that your grader can reproduce your code locally on his/her machine. \n",
+ "\n",
+ "- Try to write a clean code that can be followed by your peer reviewer. When you are the reviewer, you can add or subtract point for the quality of code. \n",
+ "\n",
+ "\n",
+ "**After completing this project you will:**\n",
+ "- Get experience with building and estimation of your second IRL based model of market dynamics.\n",
+ "- Develop intuition and understanding about the role of non-linearities in dynamics model. \n",
+ "- Develop intuition on whether the same model could be calibrated to both equity and credit data.\n",
+ "- Be able to implement trading strategies based on this method.\n",
+ "\n",
+ "Let's get started!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "help:\n",
+ "\n",
+ "https://www.coursera.org/learn/advanced-methods-reinforcement-learning-finance/discussions/weeks/4/threads/dBw8Q7LxEeiTjBLDL4RcNA\n",
+ "\n",
+ "\n",
+ "https://www.coursera.org/learn/advanced-methods-reinforcement-learning-finance/discussions/weeks/4/threads/-8YAn5DDEeimKw6zhoSwxg"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## The \"Quantum Equlibrium-Disequlibrium\" (QED) IRL-based model of stock returns\n",
+ "\n",
+ "In Week 3 lectures of our course we presented the \"QED\" model\n",
+ "$$\n",
+ "d X_t = \\kappa X_t \\left( \\frac{\\theta}{\\kappa} - X_t - \\frac{g}{\\kappa} X_t^2 \\right) dt + X_t \\left( {\\bf w} {\\bf z}_t \\, dt + \\sigma d W_t \\right)\n",
+ "$$\n",
+ "\n",
+ "In this project, you will explore calibration of this model to market data.\n",
+ "As in the course project for course 3 you analyzed the same model in the limit $ g = 0 $, you would be able to re-utilize parts of your previous code in this project).\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "import pandas as pd\n",
+ "import numpy as np\n",
+ "import tensorflow as tf\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "from datetime import datetime"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# read the data to a Dataframe\n",
+ "df_cap = pd.read_csv('dja_cap.csv')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
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+ " \n",
+ " \n",
+ " AAPL \n",
+ " AXP \n",
+ " BA \n",
+ " CAT \n",
+ " CSCO \n",
+ " CVX \n",
+ " DIS \n",
+ " DWDP \n",
+ " GE \n",
+ " GS \n",
+ " ... \n",
+ " NKE \n",
+ " PFE \n",
+ " PG \n",
+ " TRV \n",
+ " UNH \n",
+ " UTX \n",
+ " V \n",
+ " VZ \n",
+ " WMT \n",
+ " XOM \n",
+ " \n",
+ " \n",
+ " date \n",
+ " \n",
+ " \n",
+ " \n",
+ " \n",
+ " 2010-01-04 \n",
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+ " 9.055040e+10 \n",
+ " ... \n",
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+ " \n",
+ " \n",
+ " 2010-01-06 \n",
+ " 1.910015e+11 \n",
+ " 49338621810 \n",
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+ " 1.645038e+11 \n",
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+ " 3.313275e+11 \n",
+ " \n",
+ " \n",
+ " 2010-01-07 \n",
+ " 1.906484e+11 \n",
+ " 49921314620 \n",
+ " 4.519446e+10 \n",
+ " 37158179760 \n",
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+ " \n",
+ " \n",
+ " 2010-01-08 \n",
+ " 1.919159e+11 \n",
+ " 49885639550 \n",
+ " 4.475850e+10 \n",
+ " 37575407520 \n",
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+ " 1.767484e+11 \n",
+ " 8.960963e+10 \n",
+ " ... \n",
+ " 26121202640 \n",
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\n",
+ "
5 rows × 30 columns
\n",
+ "
"
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "start_date = '2015-01-01'\n",
+ "end_date = '2017-12-31'\n",
+ "\n",
+ "fig = plt.figure(figsize=(10,6))\n",
+ "ax = fig.add_subplot(1,1,1)\n",
+ "\n",
+ "ax.plot(df_cap.loc[start_date:end_date, :].index, df_cap.loc[start_date:end_date, 'AAPL'], label='Cap')\n",
+ "ax.plot(long_rolling.loc[start_date:end_date, :].index, long_rolling.loc[start_date:end_date, 'AAPL'], \n",
+ " label = '%d-days SMA' % window_2)\n",
+ "ax.plot(short_rolling.loc[start_date:end_date, :].index, short_rolling.loc[start_date:end_date, 'AAPL'], \n",
+ " label = '%d-days SMA' % window_1)\n",
+ "\n",
+ "ax.legend(loc='best')\n",
+ "ax.set_ylabel('Cap in $')\n",
+ "\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Part 1: Model calibration with or without moving average signals (Max 10 points)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To calibrate the model, it is convenient to use the log-prices instead of prices. Diffusion in the log-space \n",
+ "$ y = \\log x $ is given by the following Langevin equation:\n",
+ "\n",
+ "$$\n",
+ "d y_t = - \\frac{ \\partial V(y)}{\\partial y} dt + \\sigma dW_t , \\; \\; \\; V(y) \\equiv - \\left( \\theta - \\frac{\\sigma^2}{2} + {\\bf w} {\\bf z}_t \\right) y + \\kappa e^y + \\frac{1}{2} g e^{2y}\n",
+ "$$\n",
+ "\n",
+ "where $ W_t $ is a standard Brownian motion.\n",
+ "In terms of variables $ y = \\log x $, the negative log-likelihood of data is therefore\n",
+ "\n",
+ "$$\n",
+ "LL_M (\\Theta) = - \\log \\prod_{t=0}^{T-1} \n",
+ "\\frac{1}{ \\sqrt{ 2 \\pi \\sigma^2} } \n",
+ "\\exp \\left\\{ - \\frac{1}{2 \\sigma^2} \\left( \\frac{ y_{t+ \\Delta t} - y_{t}}{ \\Delta t} + \\frac{ \\partial V(y)}{\\partial y} \n",
+ "\\right)^2\n",
+ "\\right\\} , \n",
+ "$$ \n",
+ "\n",
+ "where $ {\\bf y}_t = \\log x_t $ now stands for observed values of log-cap. Note that because the model is Markov, the product over $ t = 0, \\ldots, T-1 $ does not \n",
+ "necessarily mean a product of transitions along the same trajectory. The negative log-likelihood should be minimized to estimate parameters $ \n",
+ "\\theta $, $ \\sigma $, $ \\kappa $, $ g $ and $ {\\bf w} $. You can try to estimate the model first without signals, then with signals.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(2080, 30)"
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# utility function to reset the TF graph to the same state each time\n",
+ "def reset_graph(seed=42):\n",
+ " # to make results reproducible across runs\n",
+ " tf.reset_default_graph()\n",
+ " tf.set_random_seed(seed)\n",
+ " np.random.seed(seed)\n",
+ " \n",
+ "# 30 stocks & 2080 days\n",
+ "df_cap.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 69,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Put the rest of you code and analysis for Part I here \n",
+ "class QED_MLE_Model:\n",
+ " \n",
+ " def __init__(self, ndim, learning_rate):\n",
+ " # stock assets\n",
+ " self.x = tf.placeholder(tf.float32, [None, ndim], name = 'x')\n",
+ " self.y = tf.log(self.x) # dim 0 days dim 1 stocks\n",
+ " # predictors\n",
+ " self.z_1 = tf.placeholder(tf.float32, [None, ndim], name='z_1')\n",
+ " self.z_2 = tf.placeholder(tf.float32, [None, ndim], name='z_2')\n",
+ " \n",
+ " # k mean reversion speed\n",
+ " self.k = tf.Variable(tf.random_uniform([ndim], minval=0.,maxval=1), name='k') + 0.0001\n",
+ " # variance of each assets(ndim)\n",
+ " self.sigma = tf.Variable(tf.square(tf.random_uniform([ndim], minval=0., maxval=1))) + 0.0001\n",
+ " self.theta = tf.Variable(tf.square(tf.random_uniform([ndim], minval=0., maxval=1))) + 0.0001\n",
+ " self.g = tf.Variable(tf.random_uniform([ndim], minval=0.,maxval=1), name='k') + 0.0001\n",
+ " \n",
+ " self.w_1 = tf.random_normal([ndim], mean=0.5, stddev = 0.1)\n",
+ " self.w_2 = tf.ones([ndim]) - self.w_1\n",
+ " \n",
+ " # mean of all stock assets delta is constant zero\n",
+ " self.mu = tf.zeros([ndim])\n",
+ " \n",
+ " self.scale = tf.slice(self.y, [0,0], [1,-1])\n",
+ "\n",
+ " self.z = self.scale * tf.cumprod(1 + self.z_1*self.w_1 + self.z_2*self.w_2)\n",
+ " \n",
+ " self.v = - tf.multiply((self.theta - tf.square(self.theta)/2.0 + self.z), self.y) + \\\n",
+ " tf.multiply(self.k, tf.exp(self.y)) + \\\n",
+ " tf.multiply(self.g, tf.exp(self.y*2))/2.0\n",
+ " \n",
+ " # Multivariate Normal Distribution, no need to implement the MLE function\n",
+ " self.mult_norm_dist = tf.contrib.distributions.MultivariateNormalDiag(loc=self.mu, scale_diag=self.sigma)\n",
+ " # the log probability of v \n",
+ " self.log_prob = self.mult_norm_dist.log_prob(self.v)\n",
+ " # tf.square(self.w_1+self.w_2-0.95) -> paper chapter 7 Experiments \n",
+ " self.loss = -tf.reduce_sum(self.log_prob)\n",
+ " \n",
+ " self.train_step = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(self.loss)\n",
+ " \n",
+ " "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "\n",
+ "def run_model(model, assets, sig_1, sig_2):\n",
+ "\n",
+ " reset_graph()\n",
+ "\n",
+ " model = model(assets.shape[1], 0.01)\n",
+ "\n",
+ " with tf.Session() as sess:\n",
+ " sess.run(tf.global_variables_initializer())\n",
+ "\n",
+ " for i in range(1100):\n",
+ " _,loss = sess.run([model.train_step, model.loss], \n",
+ " feed_dict = {\n",
+ " model.x: assets,\n",
+ " model.z_1: sig_1,\n",
+ " model.z_2: sig_2} )\n",
+ " \n",
+ " if i%100 == 0:\n",
+ " print(\"loss\", loss)\n",
+ " \n",
+ " \n",
+ "\n",
+ " theta, delta, k, g = sess.run([model.theta, model.sigma, model.k, model.g], feed_dict = { \n",
+ " model.x: assets, \n",
+ " \n",
+ " model.z_1: sig_1, \n",
+ " model.z_2: sig_2}\n",
+ " )\n",
+ " \n",
+ " print()\n",
+ " print(\"theta:\", theta)\n",
+ " print(\"delta:\", delta)\n",
+ " print(\"k:\", k)\n",
+ " print(\"g:\", g)\n",
+ " \n",
+ " return mean_levels"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 74,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "loss 182573120000000.0\n",
+ "loss 727991200.0\n",
+ "loss 697040640.0\n",
+ "loss 683100600.0\n",
+ "loss 671947600.0\n",
+ "loss 667412200.0\n",
+ "loss 663714560.0\n",
+ "loss 658315970.0\n",
+ "loss 654600900.0\n",
+ "loss 654437200.0\n",
+ "loss 650740030.0\n",
+ "\n",
+ "theta: [0.999995 0.9999976 0.99812365 0.9999978 0.9999985 0.99999833\n",
+ " 0.99848914 0.99971706 0.9990651 0.99974763 1. 0.99999815\n",
+ " 0.999999 0.99957436 0.9991969 0.97185814 1.0000002 0.99828565\n",
+ " 0.99296236 0.94642043 0.959738 0.9999987 0.9720296 0.99979424\n",
+ " 0.5718796 0.9983212 0.9999983 0.9999473 0.99974924 0.9999745 ]\n",
+ "delta: [3.309517 1.7753448 1.490827 2.127008 3.7270079 2.972592\n",
+ " 1.4456012 0.51459074 2.334206 1.0505652 2.9060168 1.4698379\n",
+ " 2.9769585 2.1353028 2.620034 0.95785147 3.392444 2.4328341\n",
+ " 1.5330924 0.1816716 0.7251418 1.9699159 0.78586614 3.3798058\n",
+ " 0.06016935 0.50767636 2.9002986 3.4537618 3.476372 2.5041633 ]\n",
+ "k: [5.6854844 4.415414 4.513262 4.9351535 5.878345 4.7603393\n",
+ " 4.087988 2.4592676 5.096154 3.097801 4.758635 3.5201404\n",
+ " 5.3482566 4.605661 5.006421 3.6826215 5.6027927 5.0411067\n",
+ " 4.308202 1.4537201 2.755195 4.2749486 2.8591683 5.0689545\n",
+ " 0.21238759 3.0136015 5.4308896 5.122197 5.3509235 4.867964 ]\n",
+ "g: [5.744686 4.7518163 4.478614 4.590043 5.981322 5.0087485 3.5538218\n",
+ " 2.5429685 4.728201 3.4188 5.3993397 4.1020393 4.6394925 4.599128\n",
+ " 4.962713 3.9913027 5.600853 5.151676 3.7527955 2.082434 3.3434951\n",
+ " 4.0904465 3.068817 5.7133336 0.7221537 2.5209265 4.9979615 5.1343102\n",
+ " 5.150924 5.114405 ]\n"
+ ]
+ }
+ ],
+ "source": [
+ "stock_assets = df_cap[window_2:] / df_cap.sum(axis=1).mean()\n",
+ "short_rolling_pct_chg = short_rolling.pct_change()[window_2:]\n",
+ "long_rolling_pct_chg = long_rolling.pct_change()[window_2:]\n",
+ "\n",
+ "reset_graph()\n",
+ "\n",
+ "mean_levels = run_model(QED_MLE_Model, stock_assets, short_rolling_pct_chg, long_rolling_pct_chg)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Part 2: Analysis of default rates (Max 10 point)\n",
+ "\n",
+ "For a particle in a potential $ V(y) $ with a metastable minimum $ y = a $ and a barrier with a peak located at $ y = b $, the famous Kramers' escape formula gives the following expression for the escape rate $ r $ (see e.g. the book by van Kampen):\n",
+ "\n",
+ "$$ \n",
+ "r = \\frac{\\sqrt{ V''(a) \\left| V''(b) \\right| }}{2 \\pi} \\exp \\left[ - \\frac{2}{\\sigma^2} (V(b) - V(a) ) \\right]\n",
+ "$$\n",
+ "\n",
+ "Here $ V''(a) $ and $ V''(b) $ stand for the second derivatives of the potential $ V(y) $ at the minimum and the maximum, respectively. This formula applies as long as the barrier height $ \\Delta E \\equiv (V(b) - V(a) \\gg \\frac{\\sigma^2}{2} $. \n",
+ "\n",
+ "Apply the Kramers formula to the QED potential and parameters that you found in your calibration. What range of values of $ r $ do you obtain? Do these values make sense to you? Can you think how you could use the Kramers relation as a way to regularize your MLE calibration?\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$$\\lambda_1 \\max(y_b-y_0,0)$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 82,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Put the rest of your code and analysis for Part 2 here.\n",
+ "class QED_MLE_Model_With_Reg:\n",
+ " \n",
+ " def __init__(self, ndim, learning_rate):\n",
+ " # stock assets\n",
+ " self.x = tf.placeholder(tf.float32, [None, ndim], name = 'x')\n",
+ " self.y = tf.log(self.x) # dim 0 days dim 1 stocks\n",
+ " # predictors\n",
+ " self.z_1 = tf.placeholder(tf.float32, [None, ndim], name='z_1')\n",
+ " self.z_2 = tf.placeholder(tf.float32, [None, ndim], name='z_2')\n",
+ " \n",
+ " # k mean reversion speed\n",
+ " self.k = tf.Variable(tf.random_uniform([ndim], minval=0.,maxval=1), name='k') + 0.0001\n",
+ " # variance of each assets(ndim)\n",
+ " self.sigma = tf.Variable(tf.square(tf.random_uniform([ndim], minval=0., maxval=1))) + 0.0001\n",
+ " self.theta = tf.Variable(tf.square(tf.random_uniform([ndim], minval=0., maxval=1))) + 0.0001\n",
+ " self.g = tf.Variable(tf.random_uniform([ndim], minval=0.,maxval=1), name='k') + 0.0001\n",
+ " \n",
+ " self.w_1 = tf.random_normal([ndim], mean=0.5, stddev = 0.1)\n",
+ " self.w_2 = tf.ones([ndim]) - self.w_1\n",
+ " \n",
+ " # mean of all stock assets delta is constant zero\n",
+ " self.mu = tf.zeros([ndim])\n",
+ " \n",
+ " self.scale = tf.slice(self.y, [0,0], [1,-1])\n",
+ "\n",
+ " self.z = self.scale * tf.cumprod(1 + self.z_1*self.w_1 + self.z_2*self.w_2)\n",
+ " \n",
+ " self.v = - tf.multiply((self.theta - tf.square(self.theta)/2.0 + self.z), self.y) + \\\n",
+ " tf.multiply(self.k, tf.exp(self.y)) + \\\n",
+ " tf.multiply(self.g, tf.exp(self.y*2))/2.0\n",
+ " \n",
+ " # Multivariate Normal Distribution, no need to implement the MLE function\n",
+ " self.mult_norm_dist = tf.contrib.distributions.MultivariateNormalDiag(loc=self.mu, scale_diag=self.sigma)\n",
+ " # the log probability of v \n",
+ " self.log_prob = self.mult_norm_dist.log_prob(self.v)\n",
+ " # tf.square(self.w_1+self.w_2-0.95) -> paper chapter 7 Experiments \n",
+ " self.loss = -tf.reduce_sum(self.log_prob) + tf.reduce_sum(0.001*tf.maximum(0.005-np.min(self.y), 0 ))\n",
+ " \n",
+ " self.train_step = tf.train.AdamOptimizer(learning_rate=learning_rate).minimize(self.loss)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 83,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "loss 182573120000000.0\n",
+ "loss 727991360.0\n",
+ "loss 697040830.0\n",
+ "loss 683100800.0\n",
+ "loss 671947800.0\n",
+ "loss 667412400.0\n",
+ "loss 663714750.0\n",
+ "loss 658316160.0\n",
+ "loss 654601100.0\n",
+ "loss 654437400.0\n",
+ "loss 650740200.0\n",
+ "\n",
+ "theta: [0.999995 0.9999976 0.99812365 0.9999978 0.9999985 0.99999833\n",
+ " 0.99848914 0.99971706 0.9990651 0.99974763 1. 0.99999815\n",
+ " 0.999999 0.99957436 0.9991969 0.97185814 1.0000002 0.99828565\n",
+ " 0.99296236 0.94642043 0.959738 0.9999987 0.9720296 0.99979424\n",
+ " 0.5718796 0.9983212 0.9999983 0.9999473 0.99974924 0.9999745 ]\n",
+ "delta: [3.309517 1.7753448 1.490827 2.127008 3.7270079 2.972592\n",
+ " 1.4456012 0.51459074 2.334206 1.0505652 2.9060168 1.4698379\n",
+ " 2.9769585 2.1353028 2.620034 0.95785147 3.392444 2.4328341\n",
+ " 1.5330924 0.1816716 0.7251418 1.9699159 0.78586614 3.3798058\n",
+ " 0.06016935 0.50767636 2.9002986 3.4537618 3.476372 2.5041633 ]\n",
+ "k: [5.6854844 4.415414 4.513262 4.9351535 5.878345 4.7603393\n",
+ " 4.087988 2.4592676 5.096154 3.097801 4.758635 3.5201404\n",
+ " 5.3482566 4.605661 5.006421 3.6826215 5.6027927 5.0411067\n",
+ " 4.308202 1.4537201 2.755195 4.2749486 2.8591683 5.0689545\n",
+ " 0.21238759 3.0136015 5.4308896 5.122197 5.3509235 4.867964 ]\n",
+ "g: [5.744686 4.7518163 4.478614 4.590043 5.981322 5.0087485 3.5538218\n",
+ " 2.5429685 4.728201 3.4188 5.3993397 4.1020393 4.6394925 4.599128\n",
+ " 4.962713 3.9913027 5.600853 5.151676 3.7527955 2.082434 3.3434951\n",
+ " 4.0904465 3.068817 5.7133336 0.7221537 2.5209265 4.9979615 5.1343102\n",
+ " 5.150924 5.114405 ]\n"
+ ]
+ }
+ ],
+ "source": [
+ "stock_assets = df_cap[window_2:] / df_cap.sum(axis=1).mean()\n",
+ "short_rolling_pct_chg = short_rolling.pct_change()[window_2:]\n",
+ "long_rolling_pct_chg = long_rolling.pct_change()[window_2:]\n",
+ "\n",
+ "reset_graph()\n",
+ "\n",
+ "mean_levels = run_model(QED_MLE_Model_With_Reg, stock_assets, short_rolling_pct_chg, long_rolling_pct_chg)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Part 3: Propose and analyse your own signals (Max 10 points)\n",
+ "\n",
+ "In this part, you will experiment with other signals. Propose a signal and explain why it is interesting to \n",
+ "include this signal in the portfolio analysis. Then add your favorite signal or signals to the previous benchmarck signals (or alternatively you can replace them), and repeat the analysis of model calibration. State your conclusions.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 84,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Put the rest of your code and analysis for Part 3 here.\n",
+ "# Put the rest of your code and analysis for Part 2 here.\n",
+ "stock_assets = df_cap[window_2:] / df_cap.sum(axis=1).mean()\n",
+ "short_ema = df_cap.ewm(window_1).mean()\n",
+ "long_ema = df_cap.ewm(window_2).mean()\n",
+ "short_ema_pct_change = short_ema.pct_change()[window_2:]\n",
+ "long_ema_pct_change = long_ema.pct_change()[window_2:]\n",
+ "\n",
+ "reset_graph()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 85,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "loss 178187760000000.0\n",
+ "loss 708432800.0\n",
+ "loss 678417400.0\n",
+ "loss 665999500.0\n",
+ "loss 654074430.0\n",
+ "loss 650760200.0\n",
+ "loss 647156900.0\n",
+ "loss 640599360.0\n",
+ "loss 636509250.0\n",
+ "loss 637568640.0\n",
+ "loss 632901760.0\n",
+ "\n",
+ "theta: [0.999995 0.9999976 0.9981251 0.9999978 0.9999985 0.99999833\n",
+ " 0.9984888 0.9997176 0.99906605 0.99974793 1. 0.99999815\n",
+ " 0.999999 0.9995743 0.99919677 0.9718497 1.0000002 0.9982855\n",
+ " 0.9929596 0.9463958 0.9597439 0.9999987 0.972032 0.9997943\n",
+ " 0.57187843 0.99832124 0.9999983 0.9999473 0.99974954 0.99997455]\n",
+ "delta: [3.3083217 1.7749254 1.4902204 2.1270297 3.7260587 2.9719894\n",
+ " 1.4455361 0.5147332 2.3337493 1.0506996 2.9052808 1.4699283\n",
+ " 2.9765904 2.134781 2.617355 0.95771897 3.3923216 2.432303\n",
+ " 1.5317701 0.18169905 0.7247302 1.9696428 0.7858456 3.379148\n",
+ " 0.06016934 0.5075528 2.9001231 3.4534073 3.4754407 2.5042193 ]\n",
+ "k: [5.6856375 4.415317 4.5133963 4.9353085 5.8789077 4.7603545\n",
+ " 4.087988 2.4591434 5.0962973 3.0979059 4.7587056 3.5203333\n",
+ " 5.348496 4.605775 5.0067134 3.6824272 5.6028576 5.0411234\n",
+ " 4.308278 1.4532471 2.755459 4.2750244 2.8591483 5.0689497\n",
+ " 0.21238588 3.0135908 5.4309034 5.1221232 5.3511767 4.8682423 ]\n",
+ "g: [5.7447867 4.751727 4.478546 4.590154 5.9816995 5.0087295\n",
+ " 3.5538468 2.542199 4.7281747 3.4187748 5.399374 4.1021957\n",
+ " 4.639656 4.599242 4.9628716 3.9911065 5.600911 5.15166\n",
+ " 3.7528608 2.0818546 3.3438318 4.090508 3.0687296 5.713285\n",
+ " 0.72215194 2.5209107 4.997977 5.134258 5.1508946 5.1145644 ]\n"
+ ]
+ }
+ ],
+ "source": [
+ "mean_levels = run_model(QED_MLE_Model_With_Reg, stock_assets, short_ema_pct_change, long_ema_pct_change)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Part 4 (Optional): Show me something else (Max 10 points).\n",
+ "\n",
+ "Here you can develop any additional analysis of the model that you may find interesting (One possible suggestion is \n",
+ "presented above, but you should feel free to choose your own topic). Present your case and finding/conclusions.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "# Put the rest of your code and analysis for Part 3 here."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 105,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Index(['AAPL', 'AXP', 'BA', 'CAT', 'CSCO', 'CVX', 'DIS', 'DWDP', 'GE', 'GS',\n",
+ " 'HD', 'IBM', 'INTC', 'JNJ', 'JPM', 'KO', 'MCD', 'MMM', 'MRK', 'MSFT',\n",
+ " 'NKE', 'PFE', 'PG', 'TRV', 'UNH', 'UTX', 'V', 'VZ', 'WMT', 'XOM'],\n",
+ " dtype='object')"
+ ]
+ },
+ "execution_count": 105,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# show pca \n",
+ "import datetime\n",
+ "asset_returns = df_cap.pct_change(axis='rows').dropna()\n",
+ "\n",
+ "normed_returns = (asset_returns - asset_returns.mean())/asset_returns.std()\n",
+ "\n",
+ "\n",
+ "normed_returns.columns"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 91,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "train_end = datetime.datetime(2015, 1, 1) \n",
+ "\n",
+ "df_train = None\n",
+ "df_test = None\n",
+ "df_raw_train = None\n",
+ "df_raw_test = None\n",
+ "\n",
+ "df_train = normed_returns[normed_returns.index <= train_end].copy()\n",
+ "df_test = normed_returns[normed_returns.index > train_end].copy()\n",
+ "\n",
+ "df_raw_train = asset_returns[asset_returns.index <= train_end].copy()\n",
+ "df_raw_test = asset_returns[asset_returns.index > train_end].copy()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 96,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "11 components explain 80.00% of variance\n"
+ ]
+ }
+ ],
+ "source": [
+ "import sklearn.decomposition\n",
+ "import seaborn as sns\n",
+ "\n",
+ "stock_tickers = normed_returns.columns\n",
+ "\n",
+ "n_tickers = len(stock_tickers)\n",
+ "pca = None\n",
+ "cov_matrix = pd.DataFrame(data=np.ones(shape=(n_tickers, n_tickers)), columns=stock_tickers)\n",
+ "cov_matrix_raw = cov_matrix\n",
+ "\n",
+ "if df_train is not None and df_raw_train is not None:\n",
+ " stock_tickers = asset_returns.columns\n",
+ "\n",
+ " cov_matrix = df_train[stock_tickers].cov()\n",
+ " cov_matrix_raw = df_raw_train[stock_tickers].cov()\n",
+ " \n",
+ " pca = sklearn.decomposition.PCA().fit(cov_matrix)\n",
+ " \n",
+ " \n",
+ " cov_raw_df = pd.DataFrame({'Variance': np.diag(cov_matrix_raw)}, index=stock_tickers) \n",
+ " # cumulative variance explained\n",
+ " var_threshold = 0.8\n",
+ " var_explained = np.cumsum(pca.explained_variance_ratio_)\n",
+ " num_comp = np.where(np.logical_not(var_explained < var_threshold))[0][0] + 1 # +1 due to zero based-arrays\n",
+ " print('%d components explain %.2f%% of variance' %(num_comp, 100* var_threshold))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 99,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "if pca is not None:\n",
+ " bar_width = 0.9\n",
+ " n_asset = int((8 / 10) * normed_returns.shape[1])\n",
+ " x_indx = np.arange(n_asset)\n",
+ " fig, ax = plt.subplots()\n",
+ " fig.set_size_inches(12, 4)\n",
+ " # Eigenvalues are measured as percentage of explained variance.\n",
+ " rects = ax.bar(x_indx, pca.explained_variance_ratio_[:n_asset], bar_width, color='deepskyblue')\n",
+ " ax.set_xticks(x_indx + bar_width / 2)\n",
+ " ax.set_xticklabels(list(range(n_asset)), rotation=45)\n",
+ " ax.set_title('Percent variance explained')\n",
+ " ax.legend((rects[0],), ('Percent variance explained by principal components',))\n",
+ "\n",
+ "if pca is not None:\n",
+ " projected = pca.fit_transform(cov_matrix)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 107,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Sum of weights of first eigen-portfolio: 100.00\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pc_w = np.zeros(len(stock_tickers))\n",
+ "eigen_prtf1 = pd.DataFrame(data ={'weights': pc_w.squeeze()*100}, index = stock_tickers)\n",
+ "if pca is not None:\n",
+ " pcs = pca.components_\n",
+ "\n",
+ " best_weight_total = pcs[0,:].sum()\n",
+ " # normalized to 1 \n",
+ " pc_w = pcs[0,:]/best_weight_total\n",
+ " \n",
+ " eigen_prtf1 = pd.DataFrame(data ={'weights': pc_w.squeeze()*100}, index = stock_tickers)\n",
+ " eigen_prtf1.sort_values(by=['weights'], ascending=False, inplace=True)\n",
+ " print('Sum of weights of first eigen-portfolio: %.2f' % np.sum(eigen_prtf1))\n",
+ " eigen_prtf1.plot(title='First eigen-portfolio weights', \n",
+ " figsize=(12,6), \n",
+ " xticks=range(0, len(stock_tickers),10), \n",
+ " rot=45, \n",
+ " linewidth=3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 108,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "def sharpe_ratio(ts_returns, periods_per_year=252):\n",
+ " \"\"\"\n",
+ " sharpe_ratio - Calculates annualized return, annualized vol, and annualized sharpe ratio, \n",
+ " where sharpe ratio is defined as annualized return divided by annualized volatility \n",
+ " \n",
+ " Arguments:\n",
+ " ts_returns - pd.Series of returns of a single eigen portfolio\n",
+ " \n",
+ " Return:\n",
+ " a tuple of three doubles: annualized return, volatility, and sharpe ratio\n",
+ " \"\"\"\n",
+ " \n",
+ " annualized_return = 0.\n",
+ " annualized_vol = 0.\n",
+ " annualized_sharpe = 0.\n",
+ "\n",
+ " n_years = ts_returns.shape[0]/periods_per_year\n",
+ " annualized_return = np.power(np.prod(1+ts_returns),(1/n_years))-1\n",
+ " annualized_vol = ts_returns.std()*np.sqrt(periods_per_year)\n",
+ " annualized_sharpe = annualized_return/annualized_vol\n",
+ " \n",
+ " return annualized_return, annualized_vol, annualized_sharpe"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 109,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "First eigen-portfolio:\n",
+ "Return = 8.37%\n",
+ "Volatility = 14.21%\n",
+ "Sharpe = 0.59\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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ua/MTODW7h3Beh3fjfJDzP/ZV4H6ckpidOO85aH2dtPf8dkV774mbcD4E7Abew/lw8rd2rtXh+9c9/wmcD5d7cD5g3BTk2HCcJ9IhYwP2FRIRGbiMM5TZk9ba7I6O7Q1u1qsMmGSt3dPX7ZH+yc0qb8QZYSas2dH+9p4Q6SvKGIuI9AFjzCeNMQluTec9OB0D9/Ztq6S/McZcYpzxitNwMssvqWRApOcoMBYR6RufwvnK+hBOWc4VVl/hSVtfxSmz2YXTjyFQJz0RCROVUoiIiIiIoIyxiIiIiAigwFhEREREBOjDme8yMzNtTk5OX91eRERERAaJ1atXF1trszo6rs8C45ycHFatWtXxgSIiIiIi3WCM2dfxUSqlEBEREREBFBiLiIiIiAAKjEVEREREgD6sMQ6koaGB3Nxcamtr+7opYRUXF0d2djbR0dF93RQRERERCaJfBca5ubkkJyeTk5ODMaavmxMW1lpKSkrIzc1l3Lhxfd0cEREREQmiX5VS1NbWkpGRMWCCYgBjDBkZGQMuCy4iIiIy0PSrwBgYUEFxi4H4mEREREQGmn4XGPe1yMhIjj32WGbOnMnll19OdXU1APn5+VxxxRVMmDCBefPmcf7557N9+3YAFi1axJAhQ7jwwgv7sukiIiIi0g0KjP3Ex8ezdu1aNm7cSExMDA8++CDWWi655BIWLlzIrl27WL16NXfddRcFBQUA3HrrrTzxxBN93HIRERER6Q4Fxu049dRT2blzJ2+//TbR0dHccMMNnn2zZ8/m1FNPBeCss84iOTm5r5opIiIiImGgwDiIxsZGXn31VWbNmsXGjRuZN29eXzdJRERERHpQvxquzVvO917psWvv/dUFQffV1NRw7LHHAk7G+LrrruPBBx/ssbaIiIiIHG3WHihj8YY8LpkzimkjUvq6OWHTbwPjvtJSY+xtxowZPPfcc33UIhEREZH+o7GpmesfX0VhRR1LNhfw1rdPHzAjcKmUIgRnnnkmdXV1PPTQQ55t69evZ9myZX3YKhEREZHel1deS2FFHQB7iqs4WFbTxy0Kn36bMW6v3KG3GWP473//yy233MLdd99NXFwcOTk53HfffYBTcrF161YqKyvJzs7mkUce4dxzz+3jVouIiIiE3yG/QHjjwXKy0xL6qDXh1W8D475SWVkZcPvIkSN55plnAu5T5lhEREQGi0PlvoHxhoPlLJo5oo9aE14qpRARERGRkB0s9Q2M1+eW91FLwk+BsYiIiIiE7GBZrc/6vpLqPmpJ+CkwFhEREZGQ+dcYF1fW9VFLwq/fBcbW2r5uQtgNxMckIiIig5P/KBTV9U1U1TX2UWvCq18FxnFxcZSUlAyoQNJaS0lJCXFxcX3dFBEREZFuKayoZVdR24EKBkrWuF+NSpGdnU1ubi5FRUV93ZSwiouLIzs7u6+bISIiItItL6/LI1D+sqiijrEZib3foDDrMDA2xvwNuBAotNbObOe444AVwBXW2i5NExcdHc24ceO6cqqIiIiI9KAteUf49f+2Btx3w5Nr+Mz8bG45ezIxUf2qIKFTQmn5Y8Ci9g4wxkQCdwOvh6FNIiIiItLP3P3aVmobmgFIiYvi7GnDPPuKK+v40zu7WLK5oK+aFxYdBsbW2qXA4Q4Ouwn4N1AYjkaJiIiISN/bkFvO/W/uYPW+UpZuby11ffAL85g2IrnN8fsPH91Dt3W7xtgYMwq4BDgDOK7bLRIRERGRPlfb0MTVj35ISVU99y7Z7tl+wrh0Tp6QyeZDR9qcU9fY1JtNDLtwFIHcB9xmrW3u6EBjzPXGmFXGmFUDrYOdiIiIyECyNb+Ckqr6NtsvnD0SgNHpCW321dQrMJ4P/MsYsxe4DPiTMebiQAdaax+y1s631s7PysoKw61FREREJNye//ggFz/wfsB9J43PAODUSZlMHpbks696sAfG1tpx1toca20O8Bxwo7X2+W63TERERET6xO0vbAy4PTMplglZzrBsCTFRLL75VO66dJZnf1X90T3RRyjDtf0TWAhkGmNygZ8A0QDW2gd7tHUiIiIi0quami0VtYED3BPHp2OM8axHRUaQEhftWT/aSyk6DIyttZ8L9WLW2qu71RoRERER6VOH/KZ8bjE+M5GbzpzUZntCTKRn+WgvpehXM9+JiIiISN/aU1zVZtvim09l2ohkn2xxi3ivwPhozxgfvVOTiIiIiEjY7S3xDYzv/vQspo9MCRgUg1/GuKFzNcYNTR0OatarFBiLiIiIiId3xvjWc6fw2ePGtHu8T2BcF3rG+NUNeRz7s9e54qEVNDXbzje0BygwFhERERGPvV6B8bjMxA6PT4hprcztTI3x155aQ1V9Eyt3H+aldYc618geosBYRERERDz2lrRO65yTEUpg7N35rmvDtW0rqOjSeeGmwFhEREREAGhsaubAYa/AOLPt7Hb+fDrfNXSt8119Y/+oNVZgLCIiIiIA5JbW0OjW+w5LifUpkwgmJjKCyAinY15Dkw0pyLXWt6ZYgbGIiIiI9Ct7vEakCKWMAsAYQ0J054Zsq23wDYQrahtCbGHPUmAsIiIiIgDc/+YOz3IoHe9aJMR2bsi2spp6n/WiyrqQ79WTFBiLiIiICK9vyufj/WWe9YlDk0I+t7MjU5TX+GaIC48oMBYRERGRfqCqrpE7XtnsWc9MiuHSudkhnx/fyVKKsmrfwDhQxthay6Gymjb1yD1JgbGIiIjIINbQ1MwF9y/jwOEaz7bHrjme9MSYkK/hO2Rb5zPGZdUN1DX6nvfd59Zz8q/e4san1oTcju5SYCwiIiIyiG08WO4zdvHQ5FhmjEzp1DXiOzmWsX9gDFBS2Vp33NxseXZ1LgCvbsznYFlNm+N7ggJjERERkUFsS57v5BpXHDcaY0ynrhEb1RpShjL0Wnl128DYO1iu9AuuV+093Kn2dJUCYxEREZFBbEveEc/yqZMyufmsSZ2+Rox3YNwUQmAcIGPsXXdcUesbGH+4R4GxiIiIiPQw78D42gXjiIrsfHgY43VOQxcD43KvIdz8xzVeva+0023qCgXGIiIiIoNUc7Nla35rKcX0EZ2rLW4RHdm5UorS6vo227wzxkdqfDPGe0uqemV0CgXGIiIiIoNUbmkNlXVOEJqeGMPQ5NguXce3lKLjAPZwVYDAuMa7lMI3Y1zb0ExJgHPCTYGxiIiIyCC1Oa/cszxtRHKnO921iOlk57uAgXE7NcYAB0t7fmQKBcYiIiIig9RmrxEppg3vWhkF+NYYhxIYB8r+etcdH6ltW4Oc2wuBcVTHh4iIiIjIQOTd8W5aF+uLwTdjHKjzXUVtA099sJ89RVV8/sSxlAYMjL073wXIGJdVt9kWbgqMRURERAapTQe9Syl6LmN8/eOrWbG7BIC3thXS2Ny2Dtm3813fZIxVSiEiIiIyCB0sq+FQeS3gTOk8eVhSl68V3c44xo1NzazcU+JZL6qoC3gNn8BYNcYiIiIi0lu8Z5ObM2ZIl8YvbtFexri4sp5gI61lJMZ4lsvbGZUC6JVpoRUYi4iIiAxCq/a2Tpoxf2x6t67VXsY4rzx4QDs+K9GzXFZdj7WWNzYX8MaWgjbH7j9czeINeaw9UNattrZHgbGIiIjIILTeq7543ti0bl0rtp2McZ5brhHImPREIiOcIeKq6pt4bPlevvz4Kmob2tYpV9c3ceNTa7j4gffZWVjRZn84KDAWERERGURqG5r4yQsbWeeVee1Oxztof1SK9gLjzKQYUuOjPes/e2lzSPdbvquk44O6QKNSiIiIiAxQjU3NNDZbVuwu4c9v7+KMqUMprqzj7yv2eY7JSIwhq4sz3rVob0ro/HZKKcZmJJIaHx1wwg+A5NgoZmWntgmEAw3nFg4KjEVEREQGoN1FlVz65+VA64gPH3p1uGsxqRujUbTwzhi/ujGfbfkVTBmeDLSfMZ4xMsUnY+xv9ughZKfFtwmMg41s0V0qpRAREREZgB5fsY+y6gafYdACie7GaBQtvANjgKseXkllnZPVbS8wnjI8mSEJwQPjr5w2vs21AYorFRiLiIiISIhW7WubHQ7k8vmju32v6Ejjs15cWc8/PnDKNQorWgPjoX4lG3HRkQwJkjH+3nlTOW1SJhceM7LNvq35Fby2MZ+a+qbuNt2HAmMRERGRAaa6vpEteW1HbvjzVXN59Jrj+OiHZ/O540dzw+kTOH/m8G7fLzZAVvffqw9irfUpe/jmOZM9yxfMGgHAkISYNuc+fu3x3HD6BIwxHJeTxgNXzuXKE8Z49u8srOSGJ1fztadWd7vt3lRjLCIiIjLArM8tp8mddjkywvDpuaOYPzad89xgFOCuS48J2/1iIiPbbCutrqeyrtEz9FpcdASfmT+aTYfKyS2t4bZFUwEC1hhnJrVmlo0xXHDMCI4fl84/Ptjvc9w724rC9hhAgbGIiIjIgLMl74hn+dI5o/j1ZbN79H7RUabNtrrGZp9s8dDkOCIjDHdePMvnuECBcaBRMtIT22aWAay1GNP2/l2hUgoRERGRAWZXUaVnefKw5B6/X0yADnz1foFxsCHh/DvfRZjAQXDLRCD+GpqCzDfdBQqMRURERAaQ1zfl8+TK1pKDCUMT2zk6PAKNbFHX2ESR1+gRWUmhBcbpibFBg+DMpLYBczg74CkwFhERERkgtuYf4YYnfTukjc/s/jjFHQnU+a7ZQr7XUG3BMsap8b7BbqDgt8XXFk5ss62mQYGxiIiIiPj5zWvbaParLMhOi+/x+wYaaxhg5e7WIeOCBcajhvi2b2hKXND7XLdgHB/+4CyfcxQYi4iIiIiP0qp63tpW6LMtMSaSqDBM4NGRYJOEvLGlwLMcLDAenhrH7RdOJyk2isgIw2Xzstu919CUOJLjWsePCGcphUalEBERERkAlu0sxvpli286a1Kv3DtYxtjb9BEpQfddt2AcV50whur6pqCjT3iLj2kdHi6cGWMFxiIiIiJHoZr6JnYVVTJjZArGGJZubx3T9/rTxnPFcaMZn9Xz9cUAUUE6y7U4YVw6s0cPafeYuOhI4qLbjoccSLzXcbUKjEVEREQGr7rGJj75x/fYWVjJl04ay7fOmcKrG/I8+xfNHN5rQTHQ4TjCXz19fFjv5x0YByqlqG1o4rZ/r6eitpG7Lp3VZn8wCoxFREREjiKr9h7msgdXeNb/vmIfmUmxVLkB4uRhSRyb3X52trelJwauL+6quA5KKf709k5eWHsIgHv+ty3k66rznYiIiMhR5Ccvbmqz7XdvbPcs33D6BCI6KG3obekJHdcNd4ZPxjhAYPzo8r2e5WdX54Z83Q4DY2PM34wxhcaYjUH2f8oYs94Ys9YYs8oYsyDku4uIiIhIyKy1bDp0pM32liHakmKjOH/WiF5uVcfS2xmbuCs6KqWoqG3s0nVDyRg/BixqZ/+bwGxr7bHAtcDDXWqJiIiIiLSrrLqh3f2fmDEs5A5svSUmMoLEmPC2qTOjUnTm3h0GxtbapcDhdvZXWusZHCQRCN+E1SIiIiLikec1k1wgn5w9spda0tY1p+QE3J6eGNNh57zOiusgY+xtSCfKOMJSY2yMucQYsxV4BSdrHOy4691yi1VFRUXBDhMRERGRAPKP1HiWZ45qOy7wgomZvdkcHz++cDovfP0Uzp421Gd7WgjjEneWdynF4ap6qutbSye8lwESwpkxDoW19r/W2qnAxcAd7Rz3kLV2vrV2flZWVjhuLSIiIjJoeGeMpw1P4ZtnT/asf+HEsUFnoOsNxhhmjx5CSny0z/aMHgmMWx/nEyv3Mf/ON9iSdwRrLQdLa3yOre7EzHhhHa7NWrvUGDPeGJNprS0O57VFREREBrt8r8B4RGocN54xgbrGJkqr67ntvKl92LJWsVG+GdoeyRj7ZYGr65s47/fLSE+M8ZkuGqCyLvSOeN0OjI0xE4Fd1lprjJkLxAIl3b2uiIiIiPjyzhgPT40nOjKC7y7qHwFxi1i/6aF7JGMcEziEPVxVz+Gqep9tVeEMjI0x/wQWApnGmFzgJ0A0gLX2QeDTwBeNMQ1ADfBZr854IiIiIhIme4qrPMsjUuP6sCXB+QfGaWEewxh8a4w70tgceljaYWBsrf1cB/vvBu4O+Y7Lc6p2AAAgAElEQVQiIiIi0mlHahtYe6DMsz4rO7UPWxOcf2Ac7jGMoXOBcWdoSmgRERGRHvDK+jz2Ha7iiyflkBTbGnK9tjGPlbsPs6uokoSYSL50cg4nT+h4NInlO0tocrOfM0elkJkU3mmWwyXGPzDuiYxxTM90MlRgLCIiIhJmaw+U8fV/rAHg169t48ypQ/n2JyazZl8pt7/gO6Xz/zYVcM/ls7lsXna711y5u7UL12mT+u/oXv6d79J7oMY4MbZnQlgFxiIiIiJhtC2/gosfeN9n21tbC3lra2HQc37wnw0smJjJ8HbqhnNLvccw7p9lFBAgY9wDgXGq35Bw4dJ3g92JiIiIDDD1jc184ZEPOn9eUzMvrz/U7jEFR1pHpBiW0j873kGAGmMFxiIiIiKDz+7iSgor6jo8Li0hmq+eNp4fXTDNs+3OV7bwwNs7g56T5zeGcX8VFek/KkX4g9j46EiiI8M7zTQoMBYREREJm+0FlSEd99zXTub750/jomNHYrziu9+/sYOy6vo2x9c3NlNS5QTcxkBWcv/seAdQ0+A705x/oBwOxpgeyRorMBYREREJkx0FFW22fecTkzlxfLpnfe6YIYzPTARgaHIcXzl1vGefU1KR51l/fMVeLrh/GQ+/t5uWWSKykmL7dOrnjnRmQo3u8J96OhzU+U5EREQkTLb7Bcb//tpJzBubzhXHj+GV9XkkxkZx/qzhGK808Q/On0ZmUgy/XLzVOWdNLp89bjQVtY387KXNNDVbNh064jm+vQ56/YF/jXFP6Wgs46+cOo5tBZUkx0bxpxCv2X8/boiIiIgcRRqamtl4sDWAffmmBcwb62SKM5Ni+dLJOVw2L5uEANMZXzZvtKdm9uP9ZUz64avMvWOJZ9xib/254x3A5fNHe8ocvn9ez01X7V+i8cR1x/uszxyVyuPXHs8DV80N/ZphaZmIiIjIIPfo+3s4WOYMqZYYE8nEoUkhn5ueGMMZU4by+uaCDo8d3s8D46TYKJbeegb7D1czc1RKj90nKsK3812S39jGGYmdr8NWxlhERESkm6y1PLlyv2f95rMmEdfJaYsvndv+BB/gdLw7c9rQTrevt6UmRDMrO9WnZCTc/APj5DjfmuOuDBOnjLGIiIhIN1hreeS9Pew/XA1AQkwkV5+S0+nrnDk1cMAbExXBS99YQFV9Iylx0Z3KRA9kUZH+gbFvWJuZ1PnAWBljERERkW54aX0ed76yxbN+8oSMNtMihyImKoIvnTS2zfb7PnssU4YnM3dMmoJiL1ERvmGsf2CcpoyxiIiISO96aZ3vjHWnTc7q8rVuPmsSOworOVxVzwnj0jlj6lAWTun/pRN9ITHW98NHQkwUp0zM4P2dJZw1dWiXhrRTYCwiIiISAmstT390gKdXHWBCVhJXn5zDmIwEVu4q8RyTHBsVUq1wMBlJsfzjKyeGo7kD3nc+MYVXN+ZjLXzPHf3isWuOZ8PBcmaNSu3SNY21bYcB6Q3z58+3q1at6pN7i4iIiHTWEyv3cfvzG4PuH5Eax/LvndmjHc7E15r9peSW1rBoxnBi2hk/2Riz2lo7v6PrKWMsIiIiEoJXN+S1u3/BxEwFxb1s7pg05o5JC9v11PlOREREpAN/eXcXy71KJvzFREZw/Wnjg+6Xo4MCYxEREZF2LN9VzF2vbvXZlhATybyxzigREQZ+9qkZTBqW3EctlHBRKYWIiIhIO/675qDP+vWnjecH508DoLGpmcZm2+nJPKR/UmAsIiIiEkRdYxOvbcr3rE/ISuRrp0/wrEdFRtCFIYuln1JgLCIiIhLE1rwKKmobARg1JJ43vnW6OtgNYKoxFhEREQliZ2GlZ/mY7FQFxQOcAmMRERGRIHZ4BcaajnngU2AsIiIiEsROBcaDigJjERERkSC25B3xLCswHvgUGIuIiIgE8Mh7ezhYVgOAMTA+U4HxQKdRKURERESAwiO1vL+rmMYmy66iKh58d5dn3wWzRhAfo3HZBjoFxiIiIjLo/fb1bTzw9k6abdt9c8cM4VefPqb3GyW9ToGxiIiIDGpvbingD2/tDLhv8rAknvryicoWDxKqMRYREZFBq7Sqntuf3+hZz0iMYXxmIgCREYafXTRTQfEgooyxiIiIDFq/WLyFQ+W1AAxJiOb1b57GkIQYlu0oIjMplpmjUvu4hdKbFBiLiIjIoNTQ1MxrG/M967+6dBYZSbEALJwytK+aJX1IpRQiIiIyKK3ZV0plXSMAo4bEc+6M4X3cIulrCoxFRERkUHp9c4Fn+bTJWRhj+rA10h8oMBYREZFBZ0veEf6+fK9n/cypKp0QBcYiIiIyCD3w9k4a3UGL544ZosBYAAXGIiIiMsjkl9f6dLq74+KZREaojEIUGIuIiMggYq3l9hc2erLFx49LZ8ZIDckmDgXGIiIiMmhsOFjOEq9OdzefOakPWyP9jQJjERERGTRW7S31LJ89bRgLJmX2YWukv1FgLCIiIgOStZZlO4p4bWM+TW7pxIaD5Z79p0zM6KumST+lwFhEREQGpI/2lvKFRz7khidX8/zHBwFYn1vm2X9M9pC+apr0Ux0GxsaYvxljCo0xG4Psv8oYs94Ys8EYs9wYMzv8zRQRERHpnF8s3uJZ/vaz66isa2R3cRUAkRGG6SNS+qpp0k+FkjF+DFjUzv49wOnW2lnAHcBDYWiXiIiISLdYa33W95dU07JpbEYC8TGRfdAq6c+iOjrAWrvUGJPTzv7lXqsrgezuN0tERESke1Lion3WD5XVeJZHDYnv7ebIUSDcNcbXAa8G22mMud4Ys8oYs6qoqCjMtxYRERFplRLvm//LK1dgLO0LW2BsjDkDJzC+Ldgx1tqHrLXzrbXzs7KywnVrERERkTbion1LJW5/YZNneaQCYwmgw1KKUBhjjgEeBs6z1paE45oiIiIi3VHX0Bx034jUuF5siRwtup0xNsaMAf4DfMFau737TRIRERHpvur6xqD7VEohgXSYMTbG/BNYCGQaY3KBnwDRANbaB4EfAxnAn4wxAI3W2vk91WARERGRUFTXNwXdp1IKCSSUUSk+18H+LwNfDluLRERERMKgtiFwYBxhYLhKKSSAsNQYi4iIiPQ3gTLGMZER3HLOpDYd80RAgbGIiIj0Q9sLKvj5S5uZODSJ7y6aQkJM50OWGq+M8dJbzyA9KYaoCKOgWIJSYCwiIiL9yp7iKs69bynWwns7i/l4fyn/vP7ETgfHNV4Z4/iYSJJiFfZI+8I9wYeIiIhIl/1uyXbOuOcdvGdzXpdbzo+e39jpa3lnjDX9s4RCgbGIiIj0C+9uL+L3b+4IuO8/aw7y8f7SkK9lrfUNjFU+ISFQYCwiIiI9bldRJWXV9SzZXMC3nl7L2gNlbY55ZtUBz3JaQjTfXTSF82YO92y7P0jQHEhdY7Mn6xwbFUFkhOl642XQULGNiIiI9KgnVu7jdr9SiPd2FrPstjOIjXIyuYUVtSzZXODZ/8/rT2Tq8BR2Flbw6sZ8AFbtLcVaiztvQruq61VGIZ2njLGIiIj0mOr6Ru59fVub7YUVdby49hAAFbUNfOvpddQ3OlM4zxyVwtThKQBMyEoiwQ1sK+oaOVRey79X5/L1p9bw5Mp97d63RYLKKCREyhiLiIhIj2hqttzw5BpKqxsC7n9y5T4amy13Ld7CkdrWQPb7503zLBtjGJOewNb8CgBO+dVbnn2LN+Zx+uQsRqcntLm29+QeccoYS4gUGIuIiEhI2itjaGxq5ulVByiprOe8mcOZNCyZ/6zJZen2oqDXW5dbzrrcDT7bbjh9AqdMzPTZNtorMPZtj1O7HCgw9i6lSFBgLCFSKYWIiIi0q6nZ8uW/r2LuHUv436b8gMc8tnwvP/zvRu5dsp0L7n+PvPIa3vUKik+fnMXtF04nMyk24PkjU+O4/3Nz+N55U9vsGxsg8G1ReKQu4HafMYxVSiEhUmAsIiIi7XpvZzFvbCmgtLqBb/xjDdZ7kGHX29sKPcv1Tc2s3F3Cil0lnm23LZrKdQvGsepHZ/Pnq+a2Of+lmxZw0eyRAe8/JiN4YFxwpDbgdu/yjfguzJong5NeKSIiItKu5buKPcsNTZaNB48wKzsVgCWbC1ixq4T3d5b4nPPjFzZR4dYNpyfGMHV4smffJ2YMZ9SQeA6W1QBwwTEjyAiSSQbIyUgMuq+gInBg/NzqXM/yxKykoOeLeFPGWEREpAOBMqSDyYbccp/1l9c7o0nkl9dy41Or+dv7e9qcU+HVme7saUOJ8BpHODLC8Mcr55AaH01iTCRfXzix3fsfPy6dWaNSPeveQXZuaQ1f/8caPvXA++wsrARge0EFb25tHfrtqhPHhPIwRZQxFhERac8zHx3g1//bykWzR/HjT07v6+b0urrGpjaTcby8Po9bz53CY8v30tDU/oeG6SNS+J7XKBMt5oxJ4/3vnUlUhCGugxrguOhI/v21k3ludS7lNQ0ck53KVQ9/AMA721rrmG95+mNuWzSVX7261TO5x1lThzJBGWMJkemrT8Hz58+3q1at6pN7i4iIhCrne694lpd88zQmDUtu5+iBw1rLu9uL+NYz6zhcVd+la4zPTOSFb5xCclx0WNuWW1rNgrvfDunYl29awEyvbLMMTsaY1dba+R0dp1IKERGRIJqafZNHGw+VBzly4PnTO7u4+tGPuhwUA1x9Sk7Yg2KArOTg9cjeLp+XraBYOkWBsYiISBD+QeH2gso+aknvamhq5tH39/psG5+ZyMs3LehwTODL52UDMDYjgcvc5XCLjYpk1JD4do8Zn5nI7YOw9EW6RzXGIiIiQRRV+I6R++d3dnHl8WMCTijRk55YuY9nVx3g8yeO5TPzR/f4/RZvyKO4svWx/+ayYzhz6lAykmJ56ssncNfirew7XEWB3xjC3zhjIt88ZzKfnpfNlGHJJPTgMGnnzRzOw+/5dvrLyUhgeGocXz1tAvNz0nokWy0Dm2qMRUREgnh3exFf+tuHPtumj0jhlZsXBJ0BLtwqahuYd8cb1Dc1AzBtRAq/vXw200em9Mj98strOed373pGlfjawgnctqjtpBvNzZbPPrSCj/aWkp0Wz22LpnLujOHERPXOl9Fb8o5w3u+XedYnD0vi9W+e3iv3lqNPqDXGyhiLiIgE4Z8xBticd4SX1+fxySCTUYTbgcM1nqAYnIDwqodX8tXTJ1BV18jCKUMZk54Qct1tR15Ye9ATFGclx3LdgnEBj4uIMDxx3QnsKqpk6vAUIiN654NCi2kjUrjmlBz+vnwvURER3HD6hF69vwxMCoxFRESCCBQYA3z7mXWMSU9g9ughgDOCQ1V9E0mx4f+3mlta3WZbaXUDv3p1KwB/eGsnAJ+YPozfXD6b1PjulQ+sP9jawfDGhROCTuEMzjBqM0b2Xee2n3xyhieb3dGQbyKhUGAsIiLipby6gZ1FFdTUN3P3a1s92685JYf/fnyQsuoG6pua+dQD7zMsJZbjx2WwPb+C3cWVXHvKOL54cg4jU+PCVmrRMjscQGZSrE/tr7fXNxcQ9Z/1/Omqed26n/dkHvPHpnfrWr1BAbGEkwJjERER18PLdnPP69uobWhus2/WqFTOmjqMzz/ygWdbwZE6Xlp3yLP+l6W7+cvS3YzPSuSlbywgMQwZ5IOlrYHxNafkUNvQ5MkS+1u8IZ81+0uxFp76YB8ZiTFcu2AcI1KDj+Cwp7iK37+xncykWC6eM4r9h50MdXSkYfJwTYwhg4sCYxEREeBQWQ2/WLyFYH3ShybHccrEDEanx3PgcE3gg1y7i6pYsrmAi+eM6na7vDPG2WnxXDR7JCeNzyAlPprHlu/ludW5Psdf9dcPqGlo8qyvzy3n6a+e5FmvbWjihbUH2VNczQWzRvDVJ1ZxqLwWwGeUh6nDU4iNUjZWBhcFxiIiMqg1NVv+8NYO7ntjh8/2mKgI6hudzPH4rESOH5eOMYbzZo7goaW7O7zuofL2g+dQ5XpljEcNiccYw8kTMwFnGLU7PjWTwopazr1vKbUNzT5BMcDmQ0c8y4VHavn8Ix94xmN+8N1dQe8bjqBe5GijwFhERAa1h5ftbhMU33XpLC6dOwpr4UhtAxmJsZ5RF246cyKVdY0cOFxNhDG8u70IcOp/rz9tHL9c7NQlF7hZWG9NzbbTozd4Z4xHpfmWRBhjiI+JZGxGIj++cAY/+O+GNudX1DXS0NRMhDF8+fFVIU1ScsmcUVxzck6n2ikyECgwFhGRQe3pVQd81mOiIjh3xnBPGYF/567kuGh+ecksz/q9r2/jf5sK+OY5k2hoaq3DyPMLjF/dkMd3nl3HrOxUHrvm+JA6jVXXN3pm34uONAxNjgt67JUnjCExNpL/+9faNvvKqht4Y0sB63ODT2n9w/On8cqGPC48ZgTXnjKOiF4efk2kP1BgLCIig9b+kmp2F1V51hdOyeKK48aQnhgT8jW+9YkpfOsTUwD4aO9hz/aCI05g3Nxs+cvS3Z4RLlbuPsyf39nFsaOHsGBSJtGRwSfEOOSVLR6RGt9htvlTx45ifW45j/jNCFdSVccfvTrsTR6W5JM5To6N4iunjecrp43v6OGKDGgKjEVEZNB6Z3uhZ/mMKVk8es3x3bre8JTWjG6+Gxj/e02uz7BvAL9/s7V0Y0RqHKdPzuKi2SM9tcMtDvjVF4fih+dP44rjRnPL02vZ5NYX/2fNQU9JRlpCNP+58RRO/OWbVNY5E3mcO3N4qA9RZEDrnXkbRURE+qFXN+R7ls+YOrTb1xvmFRgXHKnjtY35vLYxv50znJKLf310gCsf/oAfPb8B6zUshvdQbdlpoQXGERGGScOSfdri3VnwiuPHkBQbxRPXHU9iTCQxkRF8Zv7okK4tMtApYywiIoNScWUdH+wpAcAYWDSj+1nTmKgIMhJjKHHrgm94cnWnzn9y5X4+PTebOWPS2F9SzY+e3+jZ59/xriNDEgLPgPe548YAMGdMGsu/dxaNzc1ktDO7nchgosBYREQGpXe3FdHsJmePG5vO0JTgHds6Y0xGgicw9ve7z85m7f4y/r5iX9DzL/nTchZOyaK0usFne6ilFC3SEtrWSc8bm8aYjATPemqQ4FlksFJgLCIig9K2ggrP8kkTMsJ23W+ePZmfvLiJPcVVPtvjoyO5ZE42l8zJ5mefmkllXSNHahoYOSSe1zflc/0Trdnld7YVtbluZzPGaQGC3vNUSyzSLtUYi4jIoLSrsHVUholDwzf18WmTs3j7OwvZfud5jPXKzp7i17EuKTaKkW4W+NRJWcREBf+XHB1pmDsmrVPtGBIgY3xM9pBOXUNksFFgLCIig9LOotbAeEJW+ALjFjFRETx9/UkcO3oImUmx3HjGhKDHxsdEMm14ctD9q28/J6Rxj70FqjGeNiL4PUREpRQiIjII1TY0ceBwNeB0vBufldgj9xmeGsd/bzzZvU/7YxBPG5HCugATcEwZlkxKXOdrgdP9MsbZafEkd+E6IoOJMsYiIjLo7Cmu8nS8G52W0OlsbGcYYzoMigGmBskYt1di0Z65Y9OI9Tp3tsooRDqkwFhERAacusYmahuagu5fta/Uszx5WP8oL5gQpM55WErXhlKLi47kxW8sYMqwZDKTYjSrnUgIVEohIiIDypMr9/HTFzfRbC2fP3EsP//UzDbHLNveOurDKRPDNyJFd8wdk8aQhGjK/IZpu/aUcV2+5pThybx2y6k0WzqcTlpEFBiLiMgA8tHew/z4hY2eMonHV+zjugXjGJvRWkPc2NTMil0lnvVTJ2X1djMDSoyN4u/XHM/S7UVcMncUxZX1RBrDrOzUbl3XGEOkYmKRkCgwFhGRAePxFfs8QXGLNftLGZOewMrdh4mJiqCsup6KukYARqTGMaGHOt51xezRQ5g92qkFzk5L6OBoEQk3BcYiItJnGpqa+dPbu7BYvnLqeBJjA/9bOlhWw1tbCzllQgb3LtlOaXU9v7lstmcc4Bbrc8vanLtmXxnNzfDtZ9e12Tc/Jz2kjnEiMjh0GBgbY/4GXAgUWmvbFGoZY6YCjwJzgR9aa+8JeytFRGRAemLFPn73xnYA3tpayORhyazZX8oNp0/gM/NHs3xXMT/878Y2s8gB3LtkO/dcPtuzXl7dwL6S6jbHrdlfyuHqwFM0zx2jkRpEpFUoo1I8BixqZ/9h4GZAAbGIiLQrv7yWe1/fxvs7iwF4dWOeZ9/63HKeW53L7qIqfvbiJg6V1XDjU2sCBsUAz63O5bWN+Z71jYdaxwDOyUigJRG8Nb+CTQfbjg8MMG9s52aTE5GBrcPA2Fq7FCf4Dba/0Fr7EdAQ7BgRERGAW59bx/1v7eSaxz5iR0EFa/a3LX0AqKpv4jvPrmszQoO/G55c7Smf2OgV/J40IZNJ7vBnTc2WvQEyyWkJ0UwbkdLVhyIiA5DGMRYRkV5RUlnHsh1Opri+sZlzfreUJq+ecjNH+Qapy71GjmjPks0FAOwsbJ3iedqIZOaOaZsNTkuI5tkbTuKz80fz58/PIzpS/wZFpFWv/kUwxlxvjFlljFlVVFTU8QkiIjJgvLw+L+i+7583lZdvOpU7Lm475rC31Pi2Uxr/4a2dbDpUzq6i1sB4fGZSwMB4fFYSx+Wkc/dlx3Di+P4xfrGI9B+9OiqFtfYh4CGA+fPn2w4OFxGRAWJXUSW/WLwl4L70xBiuOnEsACcFCFbTEqJZ/aNziIgwNDVb6hubqWloYu4dSzzHXHD/ez7nTBiaSHZavP+lGJ/Zf4ZmE5H+R98hiYhIj3vkvT3UNzYH3PeLi2eS5A7TNnFoEjefNcln/7CUOCLcWdsiIwzxMZGkJ8Ywa1TgiS9ioyIYnhJHTmYiP75wOiNS4wAwBhbNHB6uhyQiA1Aow7X9E1gIZBpjcoGfANEA1toHjTHDgVVACtBsjLkFmG6tPdJjrRYRkaPKx16d7LKSYymprOPSudn85rJj2owj/K1zJpNXVsOzq3MBOGf6sIDXvOPimVz8wPttttc1Nnuuee2CcVxzSg47CyuJjDCMz0oK10MSkQGow8DYWvu5DvbnA9lha5GIiAwoVXWNbMt3ciXGwFvfPp3YqEhiooJ/afmTi2YAUN3QxNUn5wQ85tjRQ1h886mcf/8yn+2Xzh3ls26MYdKw5G48AhEZLDTznYiI9KgNB8s90zRPGppEclzbDnT+kmKj+I3X5B3BTBuRzBXHjeZfHx0AYMbIFL562oRutVdEBi8FxiIi0qP+7ZZEAMwZHd4JNYwx/OrTx/DLS2Z56pBFRLpKne9ERKTH5JXX8J+PD3rWPz2vZyrvFBSLSDgoMBYRkR6z7kCZZxKPuWOGcPy49D5ukYhIcAqMRUSkxxRW1HmWpwxXBzgR6d8UGIuISI8pPNIaGGclx/VhS0REOqbAWEREekxhRa1neWhybB+2RESkYwqMRUSkx3iXUigwFpH+ToGxiIj0GO9SimEpKqUQkf5NgbGIiPQYn4xxijLGItK/KTAWEZEe0djUTHGlExgbA5lJCoxFpH9TYCwiIj3imVWtM96lJ8QQHal/OSLSv2lKaBERCStrLTsKK/nh8xs8204cn9GHLRIRCY0+vouISFg9vmIfn/jdUqwz4R0ZiTH85JPT+7ZRIiIhUGAsIiLdtj63jEff30NpVT1/fHunz74vnpTDUI1IISJHAZVSiIhIt2w8WM6n/7ychibLPf/bRlV9k8/+C44Z0UctExHpHGWMRUSky6y1fO8/62locuom/IPiOy6eycShSX3RNBGRTlPGWEREQra3uIrtBRWcPiWL2KhI3t1exMaDR9ocZwy8ctOpTB+Z0getFBHpGgXGIiISkvW5ZVz+4ArqGpu5bsE4fnj+NP7w1s6Ax14yZ5SCYhE56igwbkdRRR1x0RFU1jUyPCUOY0xfN0lEpE80NDVz7WOrqGtsBuCJFfvITotn9b5SzzEnjc+goKKWmSNT+fGFGoVCRI4+CowDKKms48cvbOKVDXmebVefnMNPL5rRrevuK6ni3e1FLJoxXD20ReSo8uLaQ55Z7ADqm5r52UubPes3LpzAdxdN7YumiYiEjQJjLzX1TXznuXX8b2M+jc3WZ99jy/fy6bnZzMpO7fR1t+Yf4XBlPdf9fRU1DU28vqmAJ798QriaLSLSoxqbmvnzu7uC7k+Nj+b/zp7Uiy0SEekZCoy9vLD2IK+szwu6/6Flu/nD5+Z06ppPrtzHj57f6LPtvZ3F1DY0ERcd2aV2ioj0pqc+2M/Owsqg+y+ZM4rYKP09E5Gjn4Zr87LpkG/P6kevOY5/fuVEz/pL6w6xau9hrLX+pwblHxS32F1U1bVGioj0smdXH/As33ruFG5cOMGznhQbxRdOGtsXzRIRCbtBnzF+a2sB9y7ZznkzR7CjsMKz/eEvzueMKUOpbfAdk/OyB1dw1QljuPPimdQ1NlN4pI4xGQme/f/9OJd/fXiAL56U0+6g9jsKK9RjW0SOCofKaj3Ll83LZlhKHN9dNJUteUcYkhDNiNT4PmydiEj4DPrA+JeLt7KzsLLNOJyThjkD0sdFRzJqSDwHy2o8+576YD/Hj0vn/jd3sKuoim+dM5mbz5rE/zbl882n1wFO9nnu2CFB77u9oCLoPm/WWu57YwcbD5bzwwumMT5LA+WLSO9paGqmtLoecMYmzkiM8eybNkIf7kVkYBkQgXF9YzN/e38PBUdqWTRjOCeMzwjpvOZmG7BuLjYqguy01izwuMxEn8AY4P/+tdazfO+S7dx81iTue2OHZ1tlXSMvrj0U9N7b8oPX67Woqmvk169t5e8r9gFwsKyGxTefSkSEho0Tkd5xuKqeluqx9IQYoiJVgSciA9eA+Av39+V7+dWrW3n0/b1c8deV7C1uv373cFU9u4sqOexmQfyNz0oi0iv4jIvu+Gkqr2lgV5FvsPvMqgM+65OHtWZ739xa4O09nOgAACAASURBVDP0kT9rLdc8+pEnKAbYml/BX5ft7rAtIiLhUlTR+ncqMym2D1siItLzBkRgvHRHkWfZWvj4QKnP/l1Flfzfvz7miRV72VtcxRn3vMOZv32XPwaZsem4nDSfde/scTArdhVT7w5833rf1gD9tkVT+d8tpzFqSLynnfPvfIPNh9pOpQqw/3A1H+493Gb7Xa9u5aMA20VEeoL3B/jM5Jh2jhQROfod9YGxtZaNB8t9tm0+dITymgZeXHeIl9cf4v/+9TEvrD3E7S9sYuE971Be0wA4YxP7S0uI5qYzfcfjvG7BOGKjnKdq4ZQsYqMiiPcbam3xhvygbYyJiuCiY0dijOGc6cP8zgs8PNzyXSVBr/f6puD3EhEJp+LK1m/WspQxFpEB7qiuMf7pi5t4fMVe/Obi4K/L9vDXZXs6fb2zpw3l62dMJCvZ94//6PQE3rvtTMprGpg4NImGpmaiIyN4aOkufrl4KwAvrgteT3z1yTmeTPGlc0f5BOQlVYHLObwD47OnDeXcGcO59bn1AGwr6Lg+eaCqb2wmOtJQ19hMbmk1E7KSNFW3SA9SKYWIDCb9KjC21nKktpHU+OgOj91ZWBkw49tV3zhjIt85d0rQ/VnJsZ6AOdrtfDI/Jz2ka58/q3XYtmOyh3DtKeP42/tO4F4aJDBes6+1HOSWsycTH9Oaod6eH9qIFgPNy+sP8e1n1jEuM5Gq+kYOHK7hq6eN5/vnT+vrpokMWL6lFAqMRWRg6zelFHWNTZz3+2XMv3MJD4fQwSzU4c5CNSyl83/w545J49pTxnV43DGjfKeRPnvaUM9yoA6AdY1NHCp3RsEwxhk6bmx6AjFuOUf+kVrKqxs63d6jmbWW376+nbrGZrbmV3DgsPP8/GWpOiNKeO0pruLeJdvblGgNVj6BsTLGIjLA9YvA+M/v7GLKj15ja34FDU2WO1/Zwvs7i9s9Z//h6pCufd2CjgNXgGEpcSEd5+97500lIca33vgbZ0wkOtL5ev/qk3PaDK+W5jUOaKCM8cHSGs/wSCNT44mNiiQqMoKJXmMYb8kP3GlvoNqaX8GeIKONVNc39nJrZKCqqW/iqr+u5P43d3D1ox+16VA7GHkHxv5lZiIiA02fl1I0NjVz92tb22x/YsU+TpmYGfQ8/yHZJmQl+owCAXDS+Axuv3A6nzt+DCt2FXP7C5uCXq+rA9XHREVw4vgM3tpa6Nm2cEoWZ00byo7CSj55zMg256R7B8YBMsb7vIL+0emtM0rNHJXC5jwnIP7fpnxODHG85qOVtZbbX9jI8p0lpCYEL6/Zf7iaqcM10YB03ep9h/npi5vZ4JUlLq6sY2v+EY7JDj5RTyBLtxdxuKqei2Y77/2jfdxx3xpjjUohIgNbnwfG+UdqA27/aO9hrLVBO1b5Zw/v/cyxfOqB9z3rU4Yl84cr5wAwcWgSzdavh56X8VmJjE7veEi2YL540liW7SjCWvjMcaOZOyaNiAjDnDFpAY8f4hXkFVfW8/Cy3Zw8IdMzRfT+ktbAeGx6omf5otmjeGZVLgAvrD3E98+b5imvGIi25FXw5Mr9HR5323PrefaGk0N+Ltp7Xcngs6+kiiv/+gF1AbLDD767i/s+O4eoCBNSgLt8VzFf/NuHANzy9FrioiOYMTKVc2cMIyoigk/Py6aqrpEH393FzFGpXD4vG2vh6VUHeHNLAfExUVx5/BhOmtB/PvRqVAoRGUz6PDDeEWSEhZKqenYVVREbFcF7O4s5e9own6/x9pa0BsbvfGchOZmJPuffcfFMn3q48ZmJ5GQksLekmhPGpXP2tGH8YvEWAH5+0cxuPYaFU4bywQ/OJirSkBLXccfB2KhIkmKjqKxzSgDufGULkRGG0WnxzBmTRk19k+fYMf/f3n3Ht1Xe+wP/PJZlW5b3TLyS2EkcnD1JGJkQoIxAUiizQHuBALcpUGbvBS6UC/RHb3rphbILpYyUWcKeISEJZO+d2Em8996Snt8fkqVzpCNLjmVLlj7v14sX9jlHR48UH/t7Hn2f7zfZEbDPyUvG8PgolDd2oK61C/vKGt0G38HAXR75h7edgXe2FuPtzdYGKrtKGvHoJ/vw2KUTez1fp8mMX76yGcdrW/Hs1dO8XjxJwe2jnWWaQTFgLcP42Z7PMSwuCo8sGY/zxg9ze56VXx3CX5xqo3d0W7DtRD222RbTrjlUhchwHb45UAkAKK5rQ1lDB97fXmJ/zCe7y7Dmd66/0/zBuR208tMuIqJg5NfA+Iu9FVj+xja3+38qrMUL646huK4dH+WWYtXNcwAAZQ3tqGyyfryn1wlkJVrTDVZeMRkPf7QPC09Lc2nSEa4Lw1s3zcbGY7VYOC4NcVHhSI+PQrIxoteUDW/19Q9GQrTeHhgDgNkicby2Dcdr1bnTIxSBsS5MYGpOAsptNZMLq1uDNjBu7zK7zSkekWzEKKeg4Y2fTuJXZ45Cri0Pu6KxA//2+hYICDx79TTkJEdj1eZibCqyNkf57aqd2HD/woF9ETQk7C5xpE88cME4TMyKx9UvbVIdU9HUgVvf2IZ3bpljv6GyWCTe21aCr/ZXoLC6FYUeOm4CwA9H1Gsn/k+jyZCUwN6yxoAIjNkOmohCjV8D40c/dp/zC1hz9XqqD/xUWIeObjMiw8Pw7lbH7Mrs3GT7L+ul07Jw6ZRMtx95ZiQY8PPpWfbve3IA/SHJGIGS+naPx+U4pXjkpjgW4PW0oJZS4lh1K+IN+qBYHPPu1mL8/sM96Da7pr8YI3RIjNZjTHqsy75vDlTiZltgvPLrQ9hbas3HnvvUGlw4cbhqBrq0wfN7T6FhT2mD/esF49KQnRiNlJgIVQoBAFgksPLrw3jrptkAgH/8dAIPr3b/O2zWyCT8YmY2Pt9bjm8OVLk9Tkt9gFSdYQ1jIgo1frv9L6lvR1mja37x2WMcs7c7ixtU+z7bU47TH/8Wf/7msH3bRZOGq44ZKgtdvEm5ANQ5xoA1H7pHYXUrzBaJO/65E+esXIuz/993bmdZh5IX1hVqBsUAYLblB581OgVzx6aq9pXbfp7+9OUhey52j0/3lONIlTpt54EP9uCdLcU+HDkNNZ/tKbd/+mTQ65CXGgNDhA6v3ThLM2d947FarNpszXvfXOS+NfuDFxXgneVzsGx6Fl6+fiZ2PbQY44a53swpXaiod97gpr75YGM7aCIKNX4LjLWqMbxy/Qwsn5dn/75KMVsBAL97d5dqW7xBj8UF7nP+ApkyRcKdeIPepRpDrqJkW2FNC1ZtOYmPdlq77nV0W/DO1qEd6LV3mXG0yn1nv45uay6oXheG1381C09fOcW+r6rJWkXgmTWuH09reXvzSdz7/m7sKWG92lDU1NGNO1bttH8/ITMOOtuN9YTMePz0wCKMSjHCoNepqsM8tHofKps6VOsclF68bjp+deZI1bb4aD0+vO1Me0v4MAFMynLUN184Lg2Tsx3f7yppgHSzYNjddiWT2YKv9lX0u947F94RUajx++I7pbHpsegyu68bqvx7EBEehldvnKmqCTyU/PqsUThS2YK0uEg8fPF4fLSzFI99ekB1jHMaBaCeMT5e24Y1B6tV+7/aV4H7zh83MIMeBAc91Ge+alaO6vu0WEf96YqmDhx2Wsx52/w8xBn0+OMXB+Eunvj7j8fxp8snn9J4aejaX9ak+n1z2/zRqv1Jxgh8e9c8mCwS3WYLlv51Iw5VNqPLZMFL6wpV1WOyEg0oqW/HpKx4nFuQrln1xBChw/PXTsc3ByqRGhuJqdkJ2HqiHocrm3HRxAx8ub/Cfuw3B6qw/I1teOG6GapzPPrxfry7rRh3njMWvzprFMwWiTABCCFgMluw/I1tOFDejMjwMBTWtEKvE1hz93xkJZ5a1R2mUhBRqAmYwPi3i8YgOynaq2YNsVHh2PnQYvvszlCUmxqDd5bPsX//b2fnYtWWYtVsaY7GrHJclB4pMZGoaelEl8liX93e41h1K45VtyAvNQbHa1px65vbEW8Ix8vXz0RMZMD8c7vVU6e5R0pMJK6fMwLrjlSjy2TBikXq4GVYvCMwrmzqQJkid3hxQTrutd0kbCmqw7cHtfM8a1vUn0yYzBZsOV6P04bHIiFafePVbbZgx8kGFGTEDYn3k9xTptacNz4dC8aluRwTFiYQESYQER6Ge87Lx7+9vhUA8PL6IvsxxggdPl1xNrafqMf0kYm9lgLUhQlVZYuZI5Mw07aYL9HpZ+3LfZVo6TTZf86OVrXYW8k/+sl+TM5OwM2vb0VkeBjuOHcsLBbpksvcbZb4Zn8lbtDo0PlTYS0+21OOObnJSDRG4PRRSS5j36ZoTR8M6xeIiDzx+JddCPE3ABcBqJJSutQ1E9bfpE8D+BmANgA3SCm392UQk7MTcOe5YwEA0RHhiDfo0djufvHJjBGJQzoodmdYXJQqMB7hprZybqpRlfvn7Ov9lcibF4MHP9qLA7ZA869rjtqDxEB2QBEY33f+ONw635pa85tFYzSPT1P8sS6pb8fLPzgCllmjHOXYfn/hafjhSI3mJxLOi6we+/QAXtt4HOlxkVh7zwJE6R2dDX/3zi6s3lWGccNi8clvzgrZVfpSSry9uRiVTR24ZV4uoiOG3k3CUUWawZRsz9VdFp2WhswEg8vCzeykaMQb9JqBdV8kajSxqWjswOg0a/rUF3vLVfuWPbfR/vW97+12e95yjbUcNS2duPHVLWjvNuP1H08AsOZFKzuF7i9rUt14z8tPdTkPEVGw8eav+msAzu9l/wUAxtj+uxnAc30dRGe3WfX98Pje2zP7orxaIHLuKtXzB9FZXmrvZZw+32v9SFZZGuqT3eXuDg8oykodnl4nABgjwxGrmLlV3jBkJjjyQvNSY/D6r2dhfIZrh7zi+jZV3uZrG48DACqbOlXvodkisXqXNZ/7YEUz9paFVltupU92l+P3H+7B098ewVNfHgIANLZ144cj1eg0mT08OjAo027GuLnWlIQQqsXBPZxbwp8qrbSwSkUDpC/2Vbjs94ayjJzFIrH2cDUe+Xg/2p1+7/7hk/04ocib/rGw1v714oJ0dpckopDgMTCWUq4D4H75NbAEwOvS6icACUKI4b0c72KF02zgMA+BsbLkWjBxrqjhrpmAsmRbj6VTM9Hz8F3FDXj9x+Oq/WaLNfDbfrIeqzafDNjgRZnTmBbX+89Bj3Q3Py8ZisAYsJb2e+xS12YuDW3d9ud1fl96Unu2najHx7aguIeyfXCoefwzRz78qxuOo7KpA8ue34jrXtmMW9/o0wdGfiGlxJEqx4zxmHTPgTEAnKURGC86Ld0nY3JOpQCsM8YA0NFtxv4+3IhF6R2/2gurHTcAf/3+KK7/22aXn+Ue8576Hh/usFZ0qVdUxijQuKEkIgpGvvgcOBOAshRCiW2bV+45L98lAJym0bQiwvaR9YqFo13yPoPF4gLHH9g7zxkLo5sc1lyNmdRJWfG4QFHu6dGP96v2Symxt7QRv3jhR9z/wR7c9Po2WCyeV7cPNmXVkTQvcxrT47SPcw6M3W0DYG+sUtag/ti5rrULaw5VYdlzG3HHP3eq9u08qS4nGCr2lTW6fDx/+uPf2tOAvjtYFbA3Xj2OVbfYU2iMETqvF6fNG5uqyrW98cyRuG7OCJ+MKd7gmkrx7JqjeHbNURwob0JfLtcN9zma1xyrbkWnyYzq5k48u+aYx8fe+95unKxtQ52ichA73hFRqBjUxEAhxM2wplsgYthoXDI5A7cvGO1y3C/njMBL6wrRbOsM99TPJyF/WCwqmzpxzmn9y+MLZOcWDMMTSyeis9uM6+aMdHucsmRbj+ykaPx8RjaK69qwu6QRJqe/ol1miSc/P2ivD7zucDXe216CK2Zk+/Q19IfZIlUL4bxdBT8i2YgNR2tdtidr/DF3d87jta2YNSoJJ+vUnQcrmzrtjUKc7Siu19we7NYdrvF4zMnaNs0mLP1VXNeGbw5U4vwJwzA8Xvsmxxtf73csUps7NtXrNQuxUXp8+puzsK+8CXNyk1X55/2lNYbCmlY89eUhzQo17uSnxyI5JhLD4qJQYUvFuPAv62EyW+zpE7kpRtx41igsHJeGPSUNWK6Y5e82S/xrZykaFIFxsE5GEBE588WMcSkAZXSVZdvmQkr5opRyhpRyRrIxAvPdLOZIiI7A40snIi4qHOcWpGPJlExMykpwWwYpWOjCBK6alYMbzhzV6x/qnKRoVV5tz7aYyHCsvGKK5mNqWjqx/qg6oFl7qFrzWH+pbe20z4olRus1GyxoydcIwGbnJmk2e3H3vvbkVha7BMYdKG/U7pJXVNOK1k7PVVSCzYajngPjY9W+bzTTbbbg2lc24ZGP9+OyZzeiucP9Al2T2YLuXko/fnfQsajs3IK+pUKkxUVhQX6aT4NiT5xv2NyZnJ2ABy8qAABcMcORcna0qkXVbv6Oc8fiutkjkJlgwPkThuObu+bhtvmOGvKf7i5Hfavj/dVaGEhEFIx8ERivBvBLYTUbQKOU0uNKr4wEA5ZOc58rfPHkDOz+r/Pw0i9neB0ghQpdmMCUnATVtp6PgkenxaBguHf5gIHWJa+yUZlG4V1+MQDkO3UUi40Kx//+YmqfnvvZNcdwz7u78OMx9cxzZVMH6tx0IZPSuggvlHR0m7H5uGPJwfr7FmjOZi5/YxvO+/M6lNR7F9B54/O9FThhC+4qmjrw3PfaaQEna9sw58nvcOaT3+G4m59xZeA+Jy/ZZ2Psr5VXnFo97fAwgXX3LMBHt59pz4P+7TljXbpD9nCelBidFoPbF4xGpO137aHKZtUnIlr5z0REwchjxCmEeBvAjwDyhRAlQohfCyGWCyGW2w75DEAhgKMAXgJw24CNluyccyINipXx7v4YOjte2+pVF62B9v62Eix7biMufma9fVtfaqaOdZoxfnTJeI8LOLW8u60En+5R39NVNHWgtF57xhhQl5cLdmUN7bj+b5vRZbLOxOamGpGVGI2/XDUV00ckunyKcaiyGS+sLfTJc397oBIr3t6h2vb+9hLNY1es2oHq5k5UNXe6NM0BgC6TxX6zEyb6dhM20JZOy8IP9y7o9Rjn1tK/O3csXr1xpkvdc12YwF22MphKM0cmarakN0aG4yxFxZ+eLpOAdsUMIqJg5E1ViquklMOllHopZZaU8hUp5fNSyudt+6WU8nYpZZ6UcqKUcuvAD5sunuxYaDd9hHqx4s8mum+TPTk7AbFR1gCmrcvs0nZ7sJU2tOPe93erGgkAQEIfPrp1XhiUZOw9qFa2kfaksLrVnutu0Ouw5T/Owb3n59v3OzckCVZFNa245Jn12FTkmC3uCaKmZCfg/VvPwPPXTXd53D9+OuGT59eaHa5s6lSVM+uxs9ixKHLrCdeCOsqSfskxkQFXEz0r0aC5EG9UihGPXDJetUgXsNb4PnuM9s3wlOwE3HNevr2kXJgAbjo71+1zu6tVnMQZYyIKEUOvKj8BAM7IS8Ft8/OwuagOD/zsNNW+SVkJeGLpRPzhE2ut0mXTsjBrZBKSYyIwc1QSrntlM3bZgofC6lake1kWbSB8e6DSXkpOqa+1YW+Zm4sX1hViRHI05uT2/tH4JZMzMDLZiDiDHje8utn+8bwnWYkGpMZGYnxGvH3bwRAJjJ/57qhLIxTneuKTsuLhrOcmrIfZInsNRGtbOvHWppMwROjQ3GHC0mmZiI3SY+sJ7YWOe0oakV7g/udXKwXgVCqfDCYhBP64bBKWv7ENgPU9fO3GmZiWY+2qV9PSidd/OoGGtm7831WeU4ZuXzAaty8YjZZOE9q6TL3OkM/VCLAjw8NUn0gREQUzBsZDWG+d7K6alYPLpmai02RxmX3KTTHaA+Oimla/5lh+vb9Sc/vCcX1bEHX/BeNw8eQM5KXGeMxJF0JgcrY1R/vvN87CAx/sUTUzcCcr0VoFYVSyo1yeVlexYKSs+QsAep3AbKcbkNgoPW44Y6S9QQoANHeY0NTRDYNeh2tf3oRDlc34y5VT3ab7PLx6n6oZzdPfHlHtHx4fhfMnDMOrG6zPsae0Eef0snhO65MH5SyzP28Ke3Pe+HTce34+dhc34u7zxmJ0miN9IiUmEhvuW4jmDlOfUoZiIsM9tjEfmWLEuGGxqtx55hcTUShhYBzEovQ6zZXzPQEeAM2PogeLxSKxWfHR/Ib7F2JXcQPChDUw6AshBCZkus5YejIyxYi3b56NiQ9/aU+ZcGeELSBW5j/XtHTCYpGaFTCCSYXiBiAtNhL3nJev+XH/HeeMwZbjddinaEZxpLIFJ2pb7WkY17+6GUVPXOjyWCmlxw6NY9JjVTPTzk1WOpy6ufUEdas2n8TbW4qRYNCrutwF4owxYP15vm2+aynLHsbIcLd1zvvr2tkj8J//2qsYy4A8DRFRQGJgHIKUNUmVtUoHS0unCW9vOon2bjM6bQu5EqL1yEwwqNo4D6aU2EiPgXFPi25DhA6xkeFo7jSh2yzR2N4d1IuTTGaLKi93/X0L3c7KJ0RH4NMVZ+P2N7fbFzIeqWy2N/8ArNU8tFR7ke8+c0QiJmY6KrLsLmmElBJCCJQ1tOPclWtdHlPa0I77P9hj/37tYUeZwkANjP3psqmZqsBYq6EQEVGwYh20EKSsSdrQ7r4WrK+ZLRIr3t6BCQ9/if/+7ABWfn3Yvi+jH80afCHVi2YiyplG5axxdYt/FzAOtJqWLnt96WRjhFflE5WVEw5XtrjMqDe2uf7ceVrIGKUPw4WThiM3xQijLee1pqUTlU3WWfvlb2xDa5drS+8jle5L6qUGaCqFPxkjw/HJb86yN8hZMtnrRqZEREMeZ4xDkDJnsF4jQBko3x+qwupdZZr73LVqHiwpseoZ3zABlxa8o50C40Jbjdzq5k6XknFDkZQSm4rqkGSMUL2eU8nJVXa9O1zZjBan2fij1c2YPiJJte1AuSOAveb0HNw6Pw+HK5sxJTsRrZ0mROl19huS8Znx9jSc3SUNyEmOxu4SdVoFALR3W3rNA+eMsbYJmfFYf99C1LZ2et0um4goGHDGOATFK2eMBzGVYpeijJYzZd6zPzjnyy6Zop4lSzJGIFkxq6yaMfZzyTtfeXPTSVz54k+44OkfsK/MEWRWqAJj7wLJsemOm4j1R2tUJdQA4KGP9sHidOdxqMIxY3za8DhkJUZj4bh0JBkjkJ0UrXrPJynyyXcUN+BfO7RvuDq6zChv0K5DHR4mMGtkkuY+sqYMMSgmolDDwDgEJapyjAdvxth5oZRSRoJ/P9JudEopmekUMCnTKAB1YFzVPLQrU7R1mXD1Sz/Z80rNFolXfiiy71fOGHtbBWFEsrHXlIt9ZU0Y9+AXeHdrsX3bCUXb47zUGK2H2c0Y6ajd/dz3x/D8Wked4ynZjhzk9m4zytzMGK/+97OCOjeciIj6joFxCEpQzI7WD9KMsZQSe0odM4J3L1Z35PJ3KsVlUx3tyW+Zm+vSNEQZbAFOgXHT0Jgx7jJZcNub27DgT9/jd+/ssqc3vLXpJDY6tcLeoZjhVVak8DaVQhcmPAa3XWYL7nt/t71tdLEiMHbu4uZsfn6a29Jjt8x1NLBo7zajvFF7xrggw7vW6UREFDoYGIegOIPeXoKpucMEk9nS+wN8oKq5017ZwBihwy/PGKna7+96sgvHpeG+88fhlnm5uOOcsS6B8dQcdXdBZZOEz/dWuJQJC0Qf7ijBZ3sqUFTTive3l+CPnx8EAHy00zUNoaimFeeuXIsv9pbjeG2rfXtfqoYsmZLh8RiLBNYfqUFrp8neQESvExjm4echSq/D+RNcOzwmGyMwQzHb395lRnmD64zxf154mss2IiIiBsYhSBcmVDm1zmkEA2GPYmFUQUYc4qL0+MWMbADWBVATT6EGsS/pwgRunZ+HBy44DYYInapyBwBMy1HPGE9VfF/a0I53t5UMyjj7wznP941NJ/DF3gq3KS5Hqlpwz3u7VYvi8od5v8jw5rNzcdv8PNU255QUwNo2+oiinFtWYrRXbZpvnZ+n6pAYoQvDS9fPUDX1aOsyoUwxY/zABePw4EUFuMHpxoyIiAhgVYqQlWDQ2/OLG9q7VQvLBoIy+OppxPHIkvG4cNJwjM+I02xE4k+ZiQbERIajpdOE7CQD0pxmMPNSY/Dz6Vl4zxYQ7ylpADDCDyP13t5SdTk0KWFvOwwAiwvSMSrViBfWFtq3NXeY0NxhTbkQQl2Zw5OwMIF7zx+Huxfn40RdG3YW12Pe2DRM+8PXquP2lTXh0mc32L/PTvJuwVdeagyeu3Y6fv/BHuSlxeCFa6fbWxeHhwmYLBIWCXR0Wz8RiY7Q4ZZ5eb2dkoiIQhwD4xCVEB0B1FpzOgejMsVeRWDcMzscpde5bQ3sb9ER4Xjm6qn4Ym8FrpujHfCeN36YPTCuCvDKFF0mCw5VuK/nC1gbO/TW5SwnKRrREX3/lREWJjAqxYhRKd41ishJ8j5dY97YVGy4f6HLdkOEzh7Q90hlaTYiIvKAgXGIUn7cXN86sKkUFovUnDEOdPPz0zA/P83tfmXpssoAX4B3uLIZXbZc8tiocLR2mlR1muOiwrFgXFqvizF9Vat5fEacqmW0sxkj+l9CzaB3DYxTBvhTESIiGvqYYxyilDnGTR0DGxh/trfcPqMaExnusVrBUKFcgFcd4CXblC2ZZ+cm4/RRyfbvo/RheOryyYjS6zA83uB24duc3GTN7X31xNKJyHcTZF88OQMXT/a8aM8TQ4Rrak5KDEuzERFR7zhjHKJioxz/9M5dyXztJUVN3Gtm53i1sGooSImJgBDWXN2ali50my3Q6wLzXrOw2hEY56XG4Bczs/HC2mNIi43E5TOyVXm9Ty6biBte3aJ6/LWzc3DN7ByfjGVSVgK+vHMuAOAfPx7Hgx/ts+/78xWTffLzYdDIWeeMMREReRKYf8Vpq4oG8QAAFWlJREFUwMVEOmaMnT9y9kZHtxl7Shq9KvVWpAjKbjxjVJ+fK1CF68JUwVYgd8A7VuMouZabas33fXLZJNy1ON9lsdv8/DQceux8ZNtyfa+cmY3HLp2IyHDfL5C8ZEqmfSZ3xaIxCPfRjYXWjPFALzAlIqKhjzPGIUo5Y9zXwNhskVjyzAYcqmzGlTOz8eSySW6PNZktaFJUNQi2BVBpsZH2gLiqudPvjUrcKax2BMZ5qZ4XwUWG6/D5b+fiSGXzgJbSizfo8c1d83Cyrg0TMnz3PFozxqlMpSAiIg84Yxyi1IFx33KMD1U041CltcLBqi3FqGt1v2BLWSM5LkofNGkUPZSNSZStkwOJxSJRVOOYtc9N8S7HOyYyHFNzEn02i+tOQnQEJmUlIMyHPxtMpSAiolPBwDhE9SfHuEjxsTwAfLmvwu2x9W2OwNi5aUYwSIsN7FSKvaWN+OfWYnst3yRjBBKNwT9zGqW1+C7IPq0gIiLfYypFiHKXY3y4shlS9t7h7JgiZxgAvj1QiatmaS/Mamx3zCbHRwdfQJageE2D0UGwL15ZX4Q/fLJftW3umBQ/jWZwxUW53oQlh8ANARER9Q9njEOUVirF3zcex+I/r8N5/7sO6w5Xu31soVNgXNrgPoVAWSM5GGeM4wyO97EpwAJjrZl8d81Kgo1WPnGw5bcTEZHvMTAOUc6L74pqWvHwakfZrFVbTrp9bKFTKkVNi/sUAmXDiMQgnDFW1oMOtBnj0vp21fcXThyOaTmJfhrN4HIOgo0ROsRqzCITEREpMZUiRMU6pVJsKapT7f/hcA1MZovLwispparCAQDUtXbBYpGai6caFDnGCcE4Yxw1eI1SvPHyD4VYe7ga/75gNCoUiwHX37cAw+KiIHrr+RxEnBfapbtpWkJERKTEwDhEOS++a2hXV5Zo7jRhV0kjpo+wzjD2BL6N7d0ui/XMFonG9m7NRV3KGeMEA2eMB9KW43V47NMDAID9ZU0w23o+p8ZGIisxureHBh3nGWMGxkRE5A2mUoSoGKfAWFk9osehimZ0mSy44vkfMfO/v8HGozUocfp4vkdRbavm9gZFsJhoDL4Z40AKjJ/+5oj961pFCb3MAK2tPJBcZ4yZX0xERJ4xMA5Rel0YovTWf36zRaKi0XUBXUtnNz7YXoLNx+tQ29qFq1/ehNIG7cB46V834oittrFSg3LGOAhzjOMUgXFT+8C21u5NUU0rNhyr0dyXmRh6gTFnjImI6FQwMA5hypJtJfVtLvubO0w4WKEOdm/5xza353v62yMu25TNP4KxKkWgzBj/bX0RpNTelxWCM8bGyPBevyciItLCwDiExSnSKYrrXGeCmztMiNZolODO1uP1LtvKFKXchscH36ydMle7qaMbFoub6HQAtXaa8P72Erf7x6S7r0kdKoKt4yIREQ0MTqOEMGWecYVGO+PXNh7v9fHhYQImRSBojFQH0WaLRJki9SIzIfgWgOl1YTBG6NDaZYaUQEuXSbO5xED6fG8F2rrMmvuWTsvERZOGD+p4AkW8QW+fxe9ZREpERNQbzhiHsL7MBmuZMVIdbBTXt6tmTCubOuyBc0pMBAz9fL5ApcwzbtRYxDiQOk1mvLD2mP37FQtHIzfVCF2YwF+vmYaVV0xBlD4433dPXr5+BiZmxuPGM0didm6yv4dDRERDAGeMQ1hMP/IuYyLD8dilE3H58xvtFS26TBaUNbbbS4MpK1hkBnG5sHiDHuW2xYuN7d3IHsTnfvOnkzhSZe1EaNDrcO2cEVixaAxMFhmyAXGPmSOT8PFvzvL3MIiIaAjhjHEIi444tcB4xcLReOum0zE6LQYb7l+Isekx9n1HKh3toovrHAv6soK4MoIydaKxfXDzjLeddOR1r1g0BmmxUQjXhYV8UExERHQqGBiHsFNZqX/a8DjctTgfk7ISAFiD6zPyUuz7P9pZCgA4XtOK3727y749mAPjYYpFhde8vAmTHvkKqza7b6ntS/WKqh/jM+IG5TmJiIiCFVMpQphRI+e3ZyGZlojwMPz1mmku25dNy7Iv1PvXzjLowsLQZbaojskO4lSK3FSj6vuWThPu/2APrpyVM+DPrSyHl6TReZCIiIi8xxnjEBatMWPcW+vgbf95DkalGF22T8yKx4RMx2zl+9tL8PGuMtUxi8en92OkgS0vNUZz+/ojNQOeVsHAmIiIyHcYGIewmEjXGePegqveFuudNTrV7b5nr56GtNjgq2Hcw3nGuMe1r2zCBztKB+x5pZSob1M2UGFgTERE1B8MjEOY1uK73vKOhXDfJGHWKPd1YocFYWMPpdwU7RljALhbkWfdX1VNHfjfbw5j/ZEaPP7ZASxauRbdZuuMtEGvC9pyeERERIOFOcYhTGsG2LlJh7em5yS53ZcWG3lK5xwqDBE65CRF42Sda1ttX3rk4/34dE+55j6mURAREfUfZ4xDmFaDD60Z43iDHk9fOaXXc8VH67FwXJrmvtQgD4wB4J7z8pExwDPj7oJigIExERGRLzAwDmFaQbAxQofFBY6Fcl/dORc7HzoXS6Zkejzfs1dPcwm2E6L1IVFT9+LJGdj4wCIsm5Y1IOc3OVX5cNafZi1ERERkxb+mIUwrMI6OCMdDFxdgWHwUJmclYGx6rNfnM0TocNnUTLy5yVHDN9jTKJwlx6hnbntJy/ZafWsXCmtaez2moqmj/09EREQU4hgYhzDNOsaROmQlRuPRJRNO6ZzJMepAOJirUWhxnjHX67Q/lDGZLVhzqBqj02IwKsWIj3aW4lhVC248cxQSFWkRxXVtuODpH9DSaer1eaUcvG57REREwcqrwFgIcT6ApwHoALwspXzSaf8IAH8DkAqgDsC1UsoSH4+VfMzdjHF/pDjNmOYkB29jDy3dTikPXSYLOk1mRIarA+YnPj+IV9YXISYyHE8snYjfrtoJAGjqMOG/LhlvP+6LvRUeg2IAuGtxvg9GT0REFNo85hgLIXQAngVwAYACAFcJIQqcDvsTgNellJMAPArgCV8PlHzPqFmurX/5wMlG9YzxwnztBXnBKifJ9Uagsb3bZds/txQDsHbJ+83bO+zbezoI9iiu773Sxf9cPhlPXzkFF04cfgqjJSIiIiVvFt/NAnBUSlkopewCsArAEqdjCgB8Z/t6jcZ+CkDRGkGwVrDcF7FR6sefNSalX+cbai6dmolxw9R52U0agbE3s8AA0NLh/ri8VCOWTc/CkimZ0IX5IJmZiIgoxHkTGGcCKFZ8X2LbprQLwFLb15cBiBVCJPd/eDSQ9LowRISrfwR6a/DhjRkjE5EYrQcA3HDGyJCoSKEUGa7DZyvOxug0R9MPrRljQy/vS2Ob4/jKZu1FdXqdOOU8cCIiItLmq8V3dwN4RghxA4B1AEoBmJ0PEkLcDOBmAMjJyfHRU1N/JEbrUdnUaf9eq7ZxX0RHhOOrO+fhUEUzZo1y3/QjmIWFCWQkGHC0qgWAa2Dc3mVGe7fL5WF3oq4Vk6ITAED1b5MSE4mRydGYNiIRP5s4HFOyEwZg9ERERKHLm8C4FEC24vss2zY7KWUZbDPGQogYAMuklA3OJ5JSvgjgRQCYMWMGl9EHgJykaFXw1d8ZY8Da0CMUmnr0Jt6gt3/tHBjXt3X1+tgTtW2YlGULjBsdM8Zf3zlXVbGCiIiIfMubVIotAMYIIUYJISIAXAlgtfIAIUSKEKLnXA/AWqGChoDsRPVisf7OGJNVvMFxg7H2ULVqn6fAuKe1dGunCc22XOQIXRgSovW9PYyIiIj6yeP0oJTSJIT4dwBfwlqu7W9Syn1CiEcBbJVSrgYwH8ATQggJayrF7QM4ZvKhbKcqCv1dfEdWBcPj7V//a2cZbpqbCymBoppWvLet90qGJ2utgXFVs2MmPy0uEsIX3UKIiIjILa+iICnlZwA+c9r2kOLr9wC859uh0WBwCYzZWtgnlk7LxPNrj9lnfy/8y3qvH3uiztrlrkKRRhFqHQSJiIj8wZtUCgpiw+LUnemcq1TQqYnS63DRpFOrLdwzY1zW0G7flpFg8Mm4iIiIyD1GQSEuO4kB10DJTDy197a8qQOdJjNKFYHxqZ6LiIiIvMfAOMSNSDZiyZQMhAngznPG+ns4QSUjvm/BbKwtjUVKoLiuHaX1jsA4izPGREREA44JpYSnr5yKxy+byPxiH+tL+kNMZDgmZMbjx8JaAMBfvj2CulZH9QrOGBMREQ08RkIEgIvuBkJGQpTHY/50+WRsPFaDq2fl4IMdpfbAePWuMtVxmQnRWg8nIiIiH2I0RDRAYqM81x3++fQs/Hx6FgDrgr23Np3UPI4zxkRERAOPOcZEAyizl3SKHKdSeRMy4/HgRQUux8Ub9IjhjD4REdGAY2BMNID+48LTkKzRxlkXJvD0lVNcts8bm+KyLT2ONYyJiIgGA6ehiAbQzyYOxwUThqG6pRNn/3ENOk0WLMhPxVOXT0ZKjGvAm5sSg3iDHo3t3fZtSRqBNREREfkeA2OiASaEQFpsFN666XTsKm7E0mmZSIjWDnbDwgRGpRixs7jBvi3ZyBljIiKiwcDAmGiQTB+RhOkjkjwe55w6wRljIiKiwcEcY6IAkxarLvPGwJiIiGhwMDAmCjBpseoZ4+QYBsZERESDgYExUYBJj+OMMRERkT8wMCYKMKnMMSYiIvILBsZEASbdKceYVSmIiIgGBwNjogCTxhljIiIiv2BgTBRgkpxqHCdG6/00EiIiotDCwJgowITZ2kVPzUnAyismI1zHy5SIiGgwsMEHUQBaMiUTS6Zk+nsYREREIYVTUUREREREYGBMRERERASAgTEREREREQAGxkREREREABgYExEREREBYGBMRERERASAgTEREREREQAGxkREREREABgYExEREREBYGBMRERERASAgTEREREREQAGxkREREREAAAhpfTPEwvRDOCQD04VD6AxgM4TqOcKxDH5+nyB+hoD8fUBQAqAGh+cJ1BfXyCOKxDPFajvuy/PFYhjAnx3DQKB+V756nyBOCZfnytQX2Mgvleneq58KWWsx6OklH75D8BWH53nxUA6T6CeKxDHFCqvMRBfn+18QXsNBuq4AvFcgfq+B+pr9PG5fHINBup75avzBeKYQuF9D9T36lTP5e31FgypFB8H2HkC9VyBOCZfny9QX2Mgvj5fCtTXF4jjCsRzBer77stzBeKYfC0Q3ytfnS8Qx+TrcwXqawzE98rX51LxZyrFVinlDL88ORHxGiTyM16DRIPH2+vNnzPGL/rxuYmI1yCRv/EaJBo8Xl1vfpsxJiIiIiIKJMGQY0wDSAjR4mH/90IIfhRINMB4LRL5F6/B0MDAmCjIefplTkQDi9cg0dDBwJg8EkLMF0J8ovj+GSHEDX4cElFI4rVI5F+8BoMfA2OiECCEiBFCfCuE2C6E2COEWGLbPlIIcUAI8ZIQYp8Q4ishhMHf4yUKNrwGiYYGBsZEoaEDwGVSymkAFgD4HyGEsO0bA+BZKeV4AA0AlvlpjETBjNcg0RAQ7u8B0JBggvomKspfA6FTJgA8LoSYC8ACIBNAum1fkZRyp+3rbQBGDv7wyEu8FocuXoPBgddgkOOMMXnjBIACIUSkECIBwCJ/D4j67BoAqQCmSymnAKiE4xd6p+I4M3jDHMh4LQ5dvAaDA6/BIMeLj9wSQoQD6JRSFgsh3gGwF0ARgB3+HRmdgngAVVLKbiHEAgAj/D0g8h6vxaDAa3AI4zUYOhgYU2/GAzgGAFLKewHc63yAlHL+II+J+qDnlzmANwF8LITYA2ArgIN+HRj1Fa/FIYrXYNDgNRgi2PmONAkhlgNYAeAOKeVX/h4PnRohxGQAL0kpZ/l7LHRqeC0ObbwGhz5eg6GFgTFRkOIvcyL/4jVINPQwMCYiIiIiAqtSEBEREREBYGBMFDSEENlCiDVCiP22Dlq/tW1PEkJ8LYQ4Yvt/om37OCHEj0KITiHE3U7nShBCvCeEOGjryjXHH6+JaCjx1TUohMgXQuxU/NckhLjDX6+LKJQwlYIoSAghhgMYLqXcLoSIhbVRwKUAbgBQJ6V8UghxP4BEKeV9Qog0WEtGXQqgXkr5J8W5/g7gBynly0KICADRUsqGwX5NREOJL69BxTl1AEoBnC6lPDFYr4UoVHHGmChISCnLpZTbbV83AzgAa3etJQD+bjvs77D+EYaUskpKuQVAt/I8Qoh4AHMBvGI7rotBMZFnvroGnSwCcIxBMdHgYGBMFISEECMBTAWwCUC6lLLctqsCjja07owCUA3gVSHEDiHEy0II40CNlSgY9fMaVLoSwNs+HRwRucXAmCjICCFiALwPa4moJuU+ac2d8pQ/FQ5gGoDnpJRTAbQCuH8gxkoUjHxwDfacJwLAJQDe9fkgiUgTA2OiICKE0MP6B/lNKeUHts2VttzHnhzIKg+nKQFQIqXcZPv+PVgDZSLywEfXYI8LAGyXUlb6fqREpIWBMVGQEEIIWPOCD0gpVyp2rQZwve3r6wF81Nt5pJQVAIqFEPm2TYsA7PfxcImCjq+uQYWrwDQKokHFqhREQUIIcRaAHwDsAWCxbf49rDmO7wDIAXACwBVSyjohxDAAWwHE2Y5vAVAgpWwSQkwB8DKACACFAG6UUtYP5ushGmp8fA0aAZwEkCulbBzcV0IUuhgYExERERGBqRRERERERAAYGBMRERERAWBgTEREREQEgIExEREREREABsZERERERAAYGBMRBRwhxH8JIe7uZf+lQoiCwRwTEVEoYGBMRDT0XAqAgTERkY+xjjERUQAQQvwHrF3RqgAUA9gGoBHAzbA2WjkK4DoAUwB8YtvXCGCZ7RTPAkgF0AbgJinlwcEcPxFRMGBgTETkZ0KI6QBeA3A6gHAA2wE8D+BVKWWt7ZjHAFRKKf9PCPEagE+klO/Z9n0LYLmU8ogQ4nQAT0gpFw7+KyEiGtrC/T0AIiLC2QA+lFK2AYAQYrVt+wRbQJwAIAbAl84PFELEADgDwLtCiJ7NkQM+YiKiIMTAmIgocL0G4FIp5S4hxA0A5mscEwagQUo5ZRDHRUQUlLj4jojI/9YBuFQIYRBCxAK42LY9FkC5EEIP4BrF8c22fZBSNgEoEkJcDgDCavLgDZ2IKHgwMCYi8jMp5XYA/wSwC8DnALbYdj0IYBOADQCUi+lWAbhHCLFDCJEHa9D8ayHELgD7ACwZrLETEQUTLr4jIiIiIgJnjImIiIiIADAwJiIiIiICwMCYiIiIiAgAA2MiIiIiIgAMjImIiIiIADAwJiIiIiICwMCYiIiIiAgAA2MiIiIiIgDA/wfrESosUgBS+gAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "needs_background": "light"
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "if df_raw_test is not None:\n",
+ " eigen_prtf1_returns = np.dot(df_raw_test.loc[:, eigen_prtf1.index], eigen_prtf1 / 100)\n",
+ " eigen_prtf1_returns = pd.Series(eigen_prtf1_returns.squeeze(), index=df_test.index)\n",
+ " er, vol, sharpe = sharpe_ratio(eigen_prtf1_returns)\n",
+ " print('First eigen-portfolio:\\nReturn = %.2f%%\\nVolatility = %.2f%%\\nSharpe = %.2f' % (er*100, vol*100, sharpe))\n",
+ " year_frac = (eigen_prtf1_returns.index[-1] - eigen_prtf1_returns.index[0]).days / 252\n",
+ "\n",
+ " df_plot = pd.DataFrame({'PC1': eigen_prtf1_returns}, index=df_test.index)\n",
+ " np.cumprod(df_plot + 1).plot(title='Returns of the market-cap weighted index vs. First eigen-portfolio', \n",
+ " figsize=(12,6), linewidth=3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
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+ "pygments_lexer": "ipython3",
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+}