{ "metadata": { "name": "", "signature": "sha256:7aeddf5fc2de9c686a8999de37518b0edac5fa9cd21921f59b1b4303d1b1a9a4" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Gold vs. SP500 returns :: XAU vs. SPX" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Long-term comparison of two asset classes: we boxplot their return distribution and also compute geometric mean returns. Correlation between the two is shown to be nil. We then look at the history of projected returns using Holt-Winters method, which also gives the latest forecasts. \n", "\n", "To conclude, we closely examine the relative value of the two assets in terms of gold troy ounces per equity share. **Analytically *short equities vs. long gold is favorable for an investor with log utility*, but hardly profitable over the long haul.** " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Dependencies:*\n", "\n", " - Linux, bash [not crucial, cross-platform prefered]\n", " - Python: matplotlib, pandas [recommend Anaconda distribution]\n", " - Modules: yi_1tools, yi_plot, yi_timeseries, yi_fred\n", "\n", "\n", "*CHANGE LOG*\n", "\n", " 2015-02-23 Code review and revision.\n", " 2014-08-05 Uses new boxplot routine with paste of dataframes." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# NOTEBOOK settings and system details: [00-tpl v14.09.28]\n", "\n", "# Assume that the backend is LINUX (our particular distro is Ubuntu, running bash shell):\n", "print '\\n :: TIMESTAMP of last notebook execution:'\n", "!date\n", "print '\\n :: IPython version:'\n", "!ipython --version\n", "\n", "# Automatically reload modified modules:\n", "%load_ext autoreload\n", "%autoreload 2 \n", "# 0 will disable autoreload.\n", "# Generate plots inside notebook:\n", "%matplotlib inline\n", "\n", "# DISPLAY options\n", "from IPython.display import Image \n", "# e.g. Image(filename='holt-winters-equations.png', embed=True)\n", "from IPython.display import YouTubeVideo\n", "# e.g. YouTubeVideo('1j_HxD4iLn8')\n", "from IPython.display import HTML # useful for snippets\n", "# e.g. HTML('')\n", "import pandas as pd\n", "print '\\n :: pandas version:'\n", "print pd.__version__\n", "# pandas DataFrames are represented as text by default; enable HTML representation:\n", "# [Deprecated: pd.core.format.set_printoptions( notebook_repr_html=True ) ]\n", "pd.set_option( 'display.notebook_repr_html', False )\n", "\n", "# MATH display, use %%latex, rather than the following:\n", "# from IPython.display import Math\n", "# from IPython.display import Latex\n", "\n", "print '\\n :: Working directory (set as $workd):'\n", "workd, = !pwd\n", "print workd + '\\n'" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", " :: TIMESTAMP of last notebook execution:\n" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Fri Mar 6 08:29:39 PST 2015\r\n" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", " :: IPython version:\n" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "2.3.0\r\n" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", " :: pandas version:\n", "0.15.0\n", "\n", " :: Working directory (set as $workd):\n" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "/home/yaya/Dropbox/ipy/fecon235/nb\n", "\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from yi_1tools import *\n", "from yi_fred import *\n", "from yi_plot import *\n", "from yi_timeseries import *" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# Get SPX daily:\n", "sp = getfred( d4spx )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " :: S&P 500 prepend successfully goes back to 1957.\n" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# Get Gold daily:\n", "au = getfred( d4xau )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "# Create their dataframe:\n", "assets = paste( [au, sp])\n", "assets.columns = ['Au', 'SP']" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# Compute returns as YoY percentage, assuming 256 days/year:\n", "returns = pcent( assets, 256 )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can explore returns as far back as 1968-04-01, or any sub-section in time. The gold bubble crashes to its low point around 1982-03-19." ] }, { "cell_type": "code", "collapsed": false, "input": [ "start = '1969-07-01'" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "# Show subret distribution:\n", "boxplot( returns[start:] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEKCAYAAAACS67iAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nos0AAAAASUVORK5CYII=\n", "text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " :: Finished: boxplot-tmp.png\n" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The red line within the box shows the *median*, while the red dot plots the most recent data point.\n", "\n", "Gold shows a wider range of returns to the upside. To best summarize performance, we compute geometric mean returns." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Geometric mean return for gold in chosen period:\n", "georet( au[start:] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "[7.2, 9.2, 20.02, 256]" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "# Geometric mean return for US equities in chosen period:\n", "georet( sp[start:] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "[6.59, 8.0, 16.78, 256]" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "For start since 1970, gold's *geometric* return exceeds that of US equities by 65 bp. Note that dividends are not included in the SPX index, so we are not comparing total investment return. (Geometric mean returns implicitly penalizes volatility, and is compatible for an investor with logrithmic utility.) " ] }, { "cell_type": "code", "collapsed": false, "input": [ "stats( returns[start:] )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Au SP\n", "count 11918.000000 11918.000000\n", "mean 10.613677 7.976448\n", "std 28.282301 16.759750\n", "min -41.473587 -48.779458\n", "25% -6.891652 -2.075755\n", "50% 5.086154 9.821511\n", "75% 22.170530 19.348908\n", "max 261.010830 65.300874\n", "\n", " :: Index on min:\n", "Au 1982-03-19\n", "SP 2008-11-20\n", "dtype: datetime64[ns]\n", "\n", " :: Index on max:\n", "Au 1980-01-21\n", "SP 2010-03-02\n", "dtype: datetime64[ns]\n", "\n", " :: Head:\n", " Au SP\n", "T \n", "1969-07-01 0.734394 -3.786541\n", "1969-07-02 3.580402 -3.218233\n", "1969-07-03 3.615960 -2.562848\n", "1969-07-04 6.393862 -2.715109\n", "1969-07-07 6.488550 -3.234317\n", "1969-07-08 7.397959 -4.527675\n", "1969-07-09 8.636364 -4.739430" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " :: Tail:\n", " Au SP\n", "T \n", "2015-02-25 -9.739652 12.804777\n", "2015-02-26 -9.629768 12.644292\n", "2015-02-27 -9.756551 12.118613\n", "2015-03-02 -9.193035 12.744670\n", "2015-03-03 -9.765625 12.284982\n", "2015-03-04 -10.900650 12.363263\n", "2015-03-05 -12.005857 12.463334\n", "\n", " :: Correlation matrix:\n", " Au SP\n", "Au 1.000000 -0.103213\n", "SP -0.103213 1.000000" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Without the effects of volatility, the *arithmetic* mean of gold is 260 bp greater than US equities -- which might compensate for its lack of dividends cash flow." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Correlation and regression fit" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "We expect practically zero correlation between gold and US equities in most periods." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# This also runs a linear regression: Au = f(SP)\n", "stat2( returns[start:]['Au'], returns[start:]['SP'] )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " :: FIRST variable:\n", "count 11918.000000\n", "mean 10.613677\n", "std 28.282301\n", "min -41.473587\n", "25% -6.891652\n", "50% 5.086154\n", "75% 22.170530\n", "max 261.010830\n", "Name: Au, dtype: float64" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " :: SECOND variable:\n", "count 11918.000000\n", "mean 7.976448\n", "std 16.759750\n", "min -48.779458\n", "25% -2.075755\n", "50% 9.821511\n", "75% 19.348908\n", "max 65.300874\n", "Name: SP, dtype: float64" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "\n", " :: CORRELATION\n", "-0.103213213575\n", "\n", "-------------------------Summary of Regression Analysis-------------------------\n", "\n", "Formula: Y ~ + \n", "\n", "Number of Observations: 11918\n", "Number of Degrees of Freedom: 2\n", "\n", "R-squared: 0.0107\n", "Adj R-squared: 0.0106\n", "\n", "Rmse: 28.1324\n", "\n", "F-stat (1, 11916): 128.3076, p-value: 0.0000\n", "\n", "Degrees of Freedom: model 1, resid 11916\n", "\n", "-----------------------Summary of Estimated Coefficients------------------------\n", " Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%\n", "--------------------------------------------------------------------------------\n", " x -0.1742 0.0154 -11.33 0.0000 -0.2043 -0.1440\n", " intercept 12.0030 0.2854 42.06 0.0000 11.4436 12.5623\n", "---------------------------------End of Summary---------------------------------\n" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "History of projected returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the Holt-Winters technique to plot projected annual returns. Resampled monthly data, rather than raw daily data, is used to see the broader trends.\n", "\n", "The projected annual returns gives the best linear slope forecasts, thus it is a compact representation of many point predictions using the Holt-Winters technique. It may not be accurate at major turning points, but its path very far away from the (seemingly stationary) mean could indicate overbought or oversold conditions in the market." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Forecasting gold" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Gold: projected annual returns using monthly data:\n", "aupro = holtpc( monthly(au), 12 )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "# Gold projections for the last 40 years:\n", "plotfred( aupro[-480:] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEYCAYAAABWae38AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnXmYFNX1v9/DIjsOi4CALC4gooARN0QdBY3RuEQTNSZG\nYjRGY0w0G2qMmsUv0RjNoolJVNyN+RmNK4pKo2IUF3ABWRVlHZFNEJDt/P44VU5P091T3V1dfWfm\nvs/Tz0ztn66qPnXq3HPPFVXF4/F4PI2PZpUW4PF4PJ7y4A28x+PxNFK8gfd4PJ5GijfwHo/H00jx\nBt7j8XgaKd7AezweTyPFG3hPwYjINhHZtdI6PB5PfryBbwCIyAIROTLhY/YUkYVl3H9KRL6TZ/kA\nEfmviHwkIitEZIKIDMhY52IRWSoia0TkVhHZIW3ZhSLymohsFJHbM7brFzyk1qZ9Lq9H7ygRmSUi\nn4rIcyLSJ0PHfBH5RERqROR2EelQz/5+JyIfB59xGct+LSJvi8hmEbky334inIfOIvKQiKwL7qOv\nF/s969OdZV/9RGRSsK93RWRUxvIzROSDQNtDItKpvu/qKQxv4BsGCkjCxzwWeLKM+6+vh92OwMPA\nAKA7MBX4b7hQRL4I/Bw4EugL7Apcnbb9YuDXwG15jtFRVTsEn9/mWklEugIPApcDnYDXgH+lrfJf\nYLiqdgT2BPoE6+ba33nAicCQ4HN8MC9kLvBT4HHqOU8RzsNNwEagG/AN4K8islcx3zOC7kzuA14H\nOgf7/H/BMRCRwcDfAk3dgfXAzfm+q6cIVNV/HP4AdwFbsR/AWuAnQD9gGzAG+BBYAXwP2B94C1gF\n/DltH2OAKcCfgdXAu8CR9Rz3P8BJOZZtA3YN/j8OmAasCbRcmbZea+Bu4ONA01TM0PwW2AJsCL7T\nnyKch87BcTsF0/cCv0lbfgSwNMt2vwZuz5gXnr/mEa/Bd4EX06bbBtdjQJZ1uwATgR/m2d9LwDlp\n098G/pfj2l9Zj7ac5wFoB3wG7J62/A7g/4r5nlF1B8sGYA+WdmnzJgPnBf9fA9ydtmzXQGu7fN/X\nfwr7eA/ecVT1TMxwflnN0/x92uIDgN2B04E/Apdhntxg4FQROSxj3XmYAboS+E+uV2IRaQkcihmq\n+lgHfFNVd8SM/fkicmKw7CygI9AbM9DnARtU9XLgBeD7wXe6KMJxDsMM16pgei/gzbTlbwHds3yn\nfG8+H4jIQhG5TUS65FlvcPqxVHU9di73/vwgFm5YAywHlqvqH/PsL5v2wXnWz0e+8zAA2KKq89KW\nv5l+LBFZJSIjgslc3zNcP69uEXlURH6Wtq/3VPXTHMfOPNZ7mIGvE4bzlIY38A2bX6vqJlWdiHnC\n96rqx6q6BDOg+6at+5Gq/lFVt6rqA8BszCBn4zDgzYwfZ1ZUdbKqzgj+fxu4Hzg8WLwJe6DsocY0\nVV2btnmksJOI9Ab+AlySNrs99tYQ8knwNzP2nS3EsRwYjoVS9gu2uSePhHZp+08/XvvPD6J6b/CQ\nGwAMEpGL8+wvm/b2Odatj3znoX0W3WtJO0eq2klVXwomc33PcP28ulX1eFW9Nse64bHD9dtlWZ5+\nLE8MeAPfsKlJ+39Dlul2adOLM7b9AOiZY7/HYvHfehGRA4OGtI9EZDXmpYfe8F3AU8D9IrI4aKBr\nkbZ5vZXuRGQn4GngJlVNj3uvw94OQnYM/qY/QCDLQ0RVP1XVN1R1m6p+BFwIHC0i7USkT1rDa2js\nMo8VHi/zWATe8jjgW4H+y9L2F8aYs2lfl/UE1E++8xBZd459Za5fiO4o+9oxz3JPDHgD3zCIo+Rn\nr4zpvmxv9EO+BDwRcb/3Yo2hvVW1Cms4awagqltU9VeqOhgYAXyZwPARzbh3woz7w6r6fxmLZwDD\n0qaHAjVpIZyQQs5dM1X9UGsbXkMDNSPYf6irHbBbMD8bLbHYNap6Tdr+Lsij/Z0c+6pPf77zMAdo\nISK7RzxWfd+zEN0zgF1FpH3G+un7Sj/WbsAOgWZPTHgD3zCowX5ohZLuvXYTkYtEpKWIfA0YSBYj\nLiL9gVaqOjviMdoDq1R1k4gcAJxBYJREpFpE9hGR5phnthlrMK73O4lIR8z7f1FVL8uyyp3Ad0Rk\nUPAguAK4PW375iLSGmgBNBeRVoEOROQAERkoIs2C2PufgEkZ4aN0HgL2FpGTg31eCUxX1TnB/s4J\n3jQIMlTGYtkoubgTuEQsFbUXFnoan6a9RXCc5kBLEWktIrl+qznPQxBi+w/wKxFpKyIjgeOxN6uC\nv2d9utMJtpkOXBnoPxlrswjPyz1YFs7I4EHya+DBKGFBTwFUupXXf+r/ACdgIZVV2I+qH2Yom6Wt\nsxA4LG36LuCy4P8xwIvUZtHMAkbnONaF1JPVEhw7zKI5BViAxU8fxYzlncGy04NjrQOWATeGmoGD\nsHaAlcCNWY5xFpbpsg57OKwNjtE7bZ2Lg/2uAW4FWqYtuyrYPv3zyzRd7wX7XoIZqW71fOdRWPbR\neuA5oE/astsCHWuD7/QzQOrZ3++w7KcVwLiMZeOzaP9Wnn3lOw+dMMO9LrhOp2dsuxY4JMr3jKD7\nCWBs2nRfYFKwr+0yt4CvY/f1ukBjVaV/a43tI8GJzouI3IY1yH2kqvsE8zpjObJ9gxvnVFVdHSy7\nFDgbMwQXqerT9R7EUzZEZAzwHVU9NMK6j2MplhPKLszj8ZSVqCGa24FjMuaNBSaq6gDg2WA6fEU9\nDUupOga4Oc/rpcc9UsHH4/E0cCIZXlV9AQsPpHMC1mmC4O9Jwf8nAvep6mZVXYDl0R5QulRPCSgR\nGxtV9TpV3VhmPR6PJwFK8ay7q2qYlleDdTcGS71blLbeIrbP4PAkiKreoaqH1b+mx+NpTMQSOlEL\n5OfzEP3I3h6Px5MwLepfJSc1ItJDVZeJyM7AR8H8xcAuaev1Jku+tYh4o+/xeDxFoKqReoGX4sE/\ngqWyEfx9OG3+6SKyQ5BTvQdWZCqbyIp9rrzyyoqnMLmiwwUNruhwQYMrOlzQ4IoOFzSEOgohkgcv\nIvdh9UW6itUI/yXWHfsBsZreC4BTA6M9U0QeAGZiFQMvUFXnvPUFCxZUWgLghg4XNIAbOlzQAG7o\ncEEDuKHDBQ1QuI5IBl5Vcw0SMDrH+tdg5UA9Ho/HUyGabH76mDFjKi0BcEOHCxrADR0uaAA3dLig\nAdzQ4YIGKFxHpJ6s5UBEXIzceDwej9OICJpAI2uDJpVKVVoC4IYOFzSAGzpc0ABu6HBBA7ihwwUN\nULiOJmvgPR6Pp7HjQzQej8fTgPAhGo/H4/E0XQPfUGNqjVUDuKHDBQ3ghg4XNIAbOlzQAD4G7/F4\nPJ4AH4P3eDyeBoSPwXs8Ho+n6Rr4hhpTa6wawA0dLmgAN3S4oAHc0OGCBvAxeI/H4/EE+Bh8DubO\nhfXrYejQSivxeDyeWnwMPgbuuAP++c9Kq/B4PJ7iabIGvr5Y1uLFsHp15XUkgQsawA0dLmgAN3S4\noAHc0OGCBihcRylD9jVqFi+GHXaotAqPx+MpnpJj8CJyKfBNYBvwNvBtoB3wL6AvwWhPqro6Yzun\nY/CDB0OnTvDii5VW4vF4PLUkFoMXkX7AucAXVHUfoDlwOjAWmKiqA4Bng+kGRVIhGo/H4ykXpcbg\nPwE2A21FpAXQFlgCnADcEaxzB3BSiceJnXyxrE8/hTVrYNWqyupIChc0gBs6XNAAbuhwQQO4ocMF\nDZBwHryqrgSuBz7EDPtqVZ0IdFfVmmC1GqB7KcdJmiVLYKedvAfv8XgaNiXF4EVkN+BR4FBgDfBv\n4EHgz6raKW29laraOWNbZ2Pwb7wBZ58N77xjufC+sdXj8bhCITH4UrNohgMvqeqK4MD/AQ4GlolI\nD1VdJiI7Ax9l23jMmDH069cPgKqqKoYNG0Z1dTVQ+ypSiemNG2HTphTt2sHq1dV061ZZPX7aT/vp\npjudSqUYP348wOf2MjKqWvQHGAq8A7QBBIu3fx+4Fvh5sM5YYFyWbbWSTJo0KeeyZ59VPeII1d13\nV509u3I6ksIFDapu6HBBg6obOlzQoOqGDhc0qJqOwHZGstElefCq+qaI3Am8hqVJvgH8HegAPCAi\n3yFIkyzlOEmzcSO0bg077ujj8B6Pp+Hia9Fk4cEH4Z57LIvmiivgyCMrrcjj8XgMX4umREIPvn17\nWLeu0mo8Ho+nOJqsgQ8bMbIRGvgOHcpv4PPpSAoXNIAbOlzQAG7ocEEDuKHDBQ3ga9HEQmjgW7Tw\nHrzH42m4+Bh8Fq6/3jo7qULv3nDJJZVW5PF4PEaSefCNktCDb94c1q6ttBqPx+MpDh+Dz0KSjawu\nxPZc0ABu6HBBA7ihwwUN4IYOFzSAH5M1FjZs8Fk0Ho+n4eNj8Fm48EIYONA6Ok2cCHfdVWlFHo/H\nY/g8+BLxefAej6cx0GQNvI/Bu6UB3NDhggZwQ4cLGsANHS5oAB+Dj4WNG6FNm2Q6Onk8Hk+58DH4\nLHz5y/C970HfvnDGGfD225VW5PF4PIaPwZeIz6LxeDyNgSZr4H0M3i0N4IYOFzSAGzpc0ABu6HBB\nA/gYfCz4LBqPx9MY8DH4LAweDP/6l/1t0QI++8z+ejweT6VJNAYvIlUi8v9E5F0RmSkiB4pIZxGZ\nKCJzRORpEakq9ThJEmbRiHgv3uPxNFziCNH8EXhCVQcBQ4BZ2DisE1V1APBsMO0U+WJZn3xihh3K\nb+BdiO25oAHc0OGCBnBDhwsawA0dLmiAhGPwIrIjcKiq3gagqltUdQ1wAjYAN8Hfk0o5TpJs22ZD\n9XXubNPeg/d4PA2VkmLwIjIMuAWYCQwFXgd+BCxS1U7BOgKsDKfTtnUyBr9qFfTrB2vW2PR++8Et\nt8Dw4RWV5fF4PECy9eBbAF8ALlTVV0XkRjLCMaqqIpLVko8ZM4Z+/foBUFVVxbBhw6iurgZqX0WS\nnu7du5ouXWqnO3SoZt26yunx037aTzft6VQqxfjx4wE+t5eRUdWiP0AP4P206ZHA48C7QI9g3s7A\nrCzbaiWZNGlS1vmvvKI6fHjt9HHHqT76aPI6ksQFDapu6HBBg6obOlzQoOqGDhc0qJqOwHZGstEl\nxeBVdRmwUEQGBLNGAzOAR4GzgnlnAQ+XcpwkWbECunSpnfYxeI/H01ApOQ9eRIYC/wR2AOYD3waa\nAw8AfYAFwKmqujpjOy312OXg7rvhySfhnnts+pxz4KCD7K/H4/FUmkTHZFXVN4H9sywaXeq+K4H3\n4D0eT2OhyZYqCBsxMknawOfSkSQuaAA3dLigAdzQ4YIGcEOHCxrA16Ipmfffh169aqe9B+/xeBoq\nvhZNGqrQsydMmQK77mrz/vIXePdduOmmymrzeDwe8PXgi+add6Bdu1rjDtC1K3z0UeU0eTweT7E0\nWQOfLZY1Zw7ss0/debvuCu+9l6yOpHFBA7ihwwUN4IYOFzSAGzpc0AA+Bl8SK1fW1qAJ2W238hp4\nj8fjKRc+Bp/GtdfC8uVw3XW181ShqsoaXzONv8fj8SSNj8EXSTYPXsR78R6Pp2HSZA18tljWqlXQ\nqdP26+65J7z1VnI6ksYFDeCGDhc0gBs6XNAAbuhwQQP4GHxJZPPgAY49Fv773+T1eDweTyn4GHwa\no0bBpZfC6IwiC6tWwS672N+WLSujzePxeMDH4IsmV4imUyf7LF6cvCaPx+MpliZr4LPFsnKFaAD6\n9oUPPkhGR9K4oAHc0OGCBnBDhwsawA0dLmgAH4MviVwePJTPwHs8Hk+58DH4gE2brEzBZ59BsyyP\nvcsug7Zt4Re/SF6bx+PxhPgYfBF8/LHVnclm3MF78B6Pp+ERi4EXkeYiMk1EHg2mO4vIRBGZIyJP\ni0hVHMeJk8xY1kcfwU475V5/112tVk25dVQCFzSAGzpc0ABu6HBBA7ihwwUNULkY/A+BmUAYcxkL\nTFTVAcCzwbTTLF+e38AfeCC8/jps3JicJo/H4ymFOMZk7Q2MB34LXKKqx4vILOBwVa0RkR5ASlX3\nzNjOqRj8vffCI4/A/ffnXufAA2HcODjiiOR0eTweTzpJx+BvAH4KbEub111Va4L/a4DuMRynrCxf\nDt265V9n5Eh45ZX4jrlpEyxcGN/+PJ6Gynvvwb/+VWkVjY+SBt0WkS8DH6nqNBGpzraOqqqIZHXV\nx4wZQ79+/QCoqqpi2LBhVFfbbsJYU7mmb7zxxjrHe/XVFDvsAJB7e1WYPz8+PS++CA8/DK+9Vl32\n75tvOj2uV4njh9PTp0/nRz/6UcWOn34OKnk9YPv7s7Ffj7//PcVjj8Fpp22/PMr9+dxzKZo1a5zX\nI5VKMX78eIpCVYv+ANcAC4H3gaXAp8BdwCygR7DOzsCsLNtqJZk0aVKd6XPPVf3rX/NvM3GianV1\nfBr+8hfV3XabVO965SbzXFQKF3S4oEHVDR1JarjuOtXu3YvTsW2bap8+qkuWxK8rqoakmDRpkga2\nM5KNji0PXkQOB36iFoO/Flihqr8TkbFAlaqOzVhf4zp2HHzxi3DBBXDiibnXef99OPxw+PDDeI55\n+eVw550+TOPxjB0Lv/udDXDfrl1h265YYSnOd98N3/hGefS5RCXz4EOLPQ44SkTmAEcG086yciW8\n/DIceWT+9XbZxdIp48qkWbrU8u89nqZO+DsoZtyF99+3v889F5+exkJsBl5VJ6vqCcH/K1V1tKoO\nUNWjVXV1XMeJi/S43uOPWwXJDh3yb9OiBfTsGZ/HvWQJbNyYYv36ePZXLOnnopK4oMMFDeCGjiQ1\nLF9uv6/58wvX8f770KcPvPZaebRF0ZAUherwPVmBd96B/faLtm7Xrubxx8HSpfbXe/Geps7HH1uY\n9D//KXzbBQugujq+0GljwteiAU46Cc48E045pf51jzkGLrrIBgEplZ12Mq/liSdg331L35/H01AZ\nOBDuusuM/OzZ9acsp3PBBTBokMXxly2r/028oeNr0RTInDkwYEC0dbt0sUadUtmyxapX7rmn9+A9\nnuXLbezjffeFadMK2/b996F/fwvT+ISFujRZAx/GsrZutRtk992jbReXgf/kE+jYEURSLF9e+v5K\noaHGFxurBnBDR1IaPvvMsmeqqrIb+Cgx+P79LQmiXGEaF64H+Bh8wSxYAN27Q5s20daPy8CvXm03\n9E47ea/D07SZPdscrObNC/fgt22zKq99+5oH7+PwdWlSBv6vf4Xp0+3/sMdYIeEZiN/AH3podcXL\nEIfnotK4oMMFDeCGjqQ0zJgBgwfb/4MHw6xZ0XWEMff27ctr4LNpmDp1e63lptBr0qQM/N13wzPP\n1J03e7Y18ESlc+d4smhCA9+3r71FeDxNlXQD36OH9TWJyoIFFp6B5GPwv/+9dVR0mSZl4OfPN4MO\ncMstKe6+u/Ie/PLlqYob+IYaX2ysGsANHUlpeOutWgPftaslHWxLK12YT8eHH5phh/J68Nk0vPlm\n8h58odekpGJjLrNpk8X0mje36XXroKamdtCOSy+1LJbhwy1NMipxGvgdd7T4/wcfgCpIpMQnj6fx\nsG4dPP883H67TbdsackHK1easa+Pjz6y3xCUt5E1k/XrYe7cWvviKo3Wgz//fLjxxtrp996zAbVn\nzzbj/+mn1Rx9NCxeDAcfHH2/nTqZcS6V0IM/7rhqWrWqTKpk2A3BhXgvuKHDBQ3gho4kNDz1lP3+\nunSpndetW90wTT4dNTW1Br53b1i0qK73H4U33jBjnY9MDTNmWGj3vfdg8+bCjlcKPgaPXeBHHrGb\nJ2TePDjkEFi71l4Je/eG3/zGalAX0jGiY0dYs6Z0jaGBB+jXL/nxXr/ylaZRmMnjNjNnbt+LPNPA\n56OmprZTVJs29puqqcm/TTqzZtnxL700+jZghn3vvS13/+WXC9s2SRqlgX/tNWtV/9//LMcWLF42\ndCjssYcZ/qqqFPvvD4ceWti+O3a0HPZSO+GGBj6VSlWkofXdd+G+++z8uBDvBTd0uKAB3NCRhIa5\nc7fvg9K9e10jnU9HeogGrD1txozox3/2WXP8Xn01/286U8OSJdCrF1x4IVx/ffTjlUqTyoP/7W/h\n1lu3n//EE/C1r9nT9c03bd6rr1q8feBAePJJKxpWDK1aWdxtw4bidYO9BVTSgw/fWt54I9njejzp\nzJu3vYEv1INPN/DV1TBpUvTjT50KZ51lYZZshc5ysWSJ2ZAvf9lsi6s0aAP/4IPmhWby+ONWK2bo\nUAvHqJpXP3y4PeGnTIHDD68u+rg77mhefCmEHnx1dXVFPPiFC2HUKPPkXYj3ghs6XNAAbuhIQkMU\nA19fDD69bs0RRxRWNnjqVBtredQo8+Zzkalh8WIz8N26WZmFpMpqNZkY/OrVlhHzyit1je2aNWa0\nRoyAIUPMwC9ZYst69YKdd7b/zzij+GOHYZpSyIzBJ2ngN22yLIXqajtXHk8lWLvWslG6Z4zYHNWD\nV90+RDNoUG19+Cjbz59vTl9o4Ddu3H5s2Oee274hNQzRtGoFbdtaRp6LlGTgRWQXEZkkIjNE5B0R\nuSiY31lEJorIHBF5WkSq4pFbyxtvWLfmww6Dxx6zeTU18Kc/wRe+ADvsYB78G29YTG7vvS0N8dRT\n4f77Yc6cVNHH3nHH0hta02PwPXvWlg5OgsWLrUPJ3nubgXch3gtu6HBBA7iho9waamrsPsxMD44a\ng1+xwtIq00eA6tTJjG0Uj3rVKjPOrVtbldhnnoGTT4bTT6/NarvlFjP+11xTV0MYogn1FtI5qxSS\njsFvBi5W1cHAQcD3RWQQMBaYqKoDgGeD6VhZvNg6Npx2Wu0T98c/hl/+sjbtccQIy4u96SbYay+b\n17WrbVMKcXvwO+2UbJrk4sWWRTRsmL2ihg3RHk+SfPxx3fTIkKge/Ntvwz771H1AtG4NzZpFayNL\nj9/36AHnnWfFBw891DJjVOG66yzlOj0jb/Pm2hBNqLeQzJ0kKcnAq+oyVZ0e/L8OeBfoBZwA3BGs\ndgdQQFeiaCxbZhflxBMhlbLW+Mceg1/9qtaAt21r4zw+8khtT7mQUuKLcaRKpsfgw957SbF8uT1U\n+vWzh+D8+dWA3dylNh6XQlOJO0fBBR3l1vDxx9k7M0WNwYcGPpPQi6+PzAbaa66BCRMsdPnSS5aF\n16oVjBsHb79dzYYNZtx/+1sYObI2USFJD75iMXgR6QfsC7wCdFfV8JlWA3TPsVnRLF1q8fQdd7Sx\nVH/6UzjoILjiCgvRhJx6qv3NdiMUS6mNrFu3wqef1t4g7dtbffikjOvKlbWe05lnWtYR2Lnq2rWw\nbAJP0+Wtt+y+LZaoBj4XcRt4EfuMHm2/iSeeMAeyY0drz3vxRTj7bEvi+NOf6uptlB58iIi0Bx4E\nfqiqa9OXBcM2xd7GHBp4gO98B/77X/NGM2ne3AzqyJF155cSXyzVg//kEzPuzZqZDhES9eJXrKg1\n8AcfDM8/n0LVsotOPdXCXJWgKcSdo+KCjnwaVq2CAw6AG24ofv8rVmQ38B07WiJA6PDk0jFvXvZC\ngVF7m2ca+JCRI+0t9/bbbYQpgD32SHHBBfZQmTy57nG7d7eIQhIkngcvIi0x436Xqj4czK4RkR7B\n8p2BrM/jMWPGcNVVV3HVVVdx44031hGfSqXyTr/7boqaGps+7jgYOTJFt27Z1w8Nafr206dPL+h4\n6dM77ghvvhl9/czp1auhVau6y1u3TjFhQnH7K3R6xQpYsyb1eQNv27bwxz+m2LAhxZ/+BK+/Dr/+\ndfmOn2t6eljLOaHjuTxdyv0Z13S+63H11Sl23z3FuHHmQBWz/9dfT31u4NOXi0DHjin++9/828+f\nn/rcyUtfXlVlTkt9x586NfW5gU9f3qwZfPe7KYYPT33enjdo0HQOOSTFQw/Z7yV9/T59YOrU8l2P\nVCrFmDFjGDNmDOPHj6cgVLXoDyDAncANGfOvBX4e/D8WGJdlWy2FAQNUZ84saRdF87vfqf74x8Vv\n/8YbqsOG1Z03erTq00+Xpisq55yjessttdOnn656yimqRx1l0w89pDpiRDJaPJVnyxbVVMr+pnPn\nnaqPPpp9m5NOUr3vPtV99lF96aXijpt5H6Zz8MGqzz2Xf/uqKtUVK7af/81vqt5xR/3HP/vs3Mcv\nhFRK9ZBDSt9PVALbGclGl+rBHwJ8EzhCRKYFn2OAccBRIjIHODKYjpWwkbUSlBqDDytJptO1K4kN\n3ZceogEL0/znP9aWAdY778MPLcbqafy8+KI1LI5Ny3VThV//2joTZuP1163j4DHH1M0wKYRcMXiA\nww/P3yN1wwbLoe/UaftlUWPwCxdaBcpS2XVXq03jIqVm0byoqs1UdZiq7ht8JqjqSlUdraoDVPVo\nVY2h/mIt27ZZmdFMI1kI6a9DhVJqDD49RTLUsdNOlTPwrVpZO8CZZ9p0ixZw7rlw883J6Akp5Zo0\nJg2QrI6pU63n95131nboee01+OCD1OelPtL56CNzcHbbzeLV//tfccfNlSYJ1tAZDs6T7VzkyqGH\n6AZ+wQLLJItCvuvRs6clLiSRJFHofdEge7KuW2dxsGYVUl8OD75Hj+Q6O2Ua+D32gBdesJ55IWef\nDQ88YI1dnsbNq6/C179ufUUuu8zmTZ1qnQhnzdq+F+fLL5v3LmLd/KdOLbxEL9TtLJTJIYdYg2Yu\nRyrfG3wUA79tm72l9u0bXW8umje3/UTtQZskDdLAr11rXnQplJoHX4qBTx/MINSR5HBj6WmSAEce\nWb1dBlLv3rDnnlZS+dNPk9EVd971W29ZznIlNRRLkjqmTrWMmAcfhLvusj4l06bBySdX06vX9mmz\nTz8NRx1l/3fvbgY1HEgnKqrWWSjdqUindWtLe06lsp+LUg380qX2Ft22bTS99V2PkSOth3y5aRK1\naMI0w0pRaqmC5cu3jz0mNRrNtm3bG/hcnH++Vev829/Kr6scXHihpfElVQiqIVJTY/fy7rvbeMPf\n+AaMH2+D0w8bZmGYdAOvap2BwvRBsPovhRr4jz+2EgP5DGx6mCaTpUvzG/j60iQLCc9E4Ze/hD/+\nsbg3mXL7SbQsAAAgAElEQVRSUQNf7MlYu7Z0A19qDL4UDz69cSk91SoJD37JEvsht2pVOy/XuTjz\nTGt8TcrAxxl33rrVYsPNmxf24GxqMfhXX4X9968Nd551lj3U582D1atT7LprXQN/113m+Q4ZUjuv\nmHs3SgPnUUeZgU9PHw5ZtMjeMrNRVVW/Bz93rjWORqW+69G3rz2sFi+Ovs9iaFAx+JUri9suDgNf\nCnF48DvtVHder17mlWzdWpq2bGzZYlXywOKE4Sj0URg+3GrVN7RY/IoV5sntv79lfHz4IVxySf1D\nszU1pk61cxQyZIjdi2edZSMk7babxeGvv94aV2++2br0p7d/FTPYdT4DHTJsmP1WTjjB2oTSs3XS\nB9vOJEqIJhwAKE4GDHDv/qrooNvLlkUbWDeTTz6pbAy+Qwdr6N22rbiG3nQPPtSxww4WNlm2LHdc\nslguvdReH2++2Y6T+Wqa71w0b26vwkuWxPtKm404484ffWQP0cMPh7vvhj/8wR5SH34I/+//JaOh\nFJLSMWGC1VpJ56GH7F5s166a1avhJz+xchoffWSVWQ87rO76u+xiDaKFsHBh/Qa+WTP44Q/hvfeq\nmTLF4vGzZ1sFyXxvAFENfHqYqT6iXI899jADH6Ybl4MGFYMvtntvpT345s3tdWzduuK2z+bBg92w\ncYdpNm60mOpjj1me84QJhXnwYA+cOF49S6lbUigffWQ1Qr7/fQsx9O5tdb1ff93KWnjs9zd37vZl\nPPr0qS3BO2SIOQUPP2wPyQMPtAbQzPUzPfjFi+G7383d/jFtWm2F13xccYWVDJg1yzSFaZulePCq\ntp9hw+o/fiGEBt4lmqyBLzXGWUocPlsMHsrT0HrDDZZydvTRZuDvu297T7y+c9G7d+kGPpUyzytf\nEak4486hgW/b1n7M999vXugNN9jbTBIaSiEJHXfeaeGPHXbIrWHXXa2c9KhRFg+/6abt18tm4J98\nEv7xj9qxGtJRhYkTazNx6iOVsn4ahxxi9ZK2basteZ2Ntm3NmchVBvvFF+33V0hHySjXY489Cm9s\nLpQGFYMv1sBXOosGiu/stGWLPaCy9cArR0PrrbfCVVfZ/z/+scUxTz65sH306mUx01IIS2jMmlXa\nfqKS6y3pyCOtYdHXwDdj/aMfRV//8MOzF/faZRf7LaS3qaVSZsCzFSObP9/amvbcszC9I0aYgQ9T\nHDPfJEJE8nvxN9wAF11U2LGj4GIMvkEa+ErnwUPxDa0rV9rNGcbu03XE7cGrmmEeMMCmRcyT79y5\n7nr1nYs4QjQffmjfL5+HE3cMPn2szpCOHc1ITZ1afg2lUJ+Oq6+ufXAXw/Lldv/mC1NEPRfNm8N+\n+9UdfPrFFy2kM2PG9uUO3nrLSnpn64WaT8dRR5nnn0rVzeLJRlVV9lTJ+fPh+edhzJhox87UkI/d\ndrP0y3IkShSiI52KGvhie25WOgYP9rq/fn3h233ySe4SC3F78FFyjaMQh4EPB/ku9ytsSC4DD/Cl\nLzX8OPxf/mJGvtjfUPowlnFwwAG1D801a+wBstde1hv63HPrvgHOnGm584Wy885WJ+lnP7MHSj5y\nefD33We5/unD/MVFmzb21phEf5aoVNTAh4NhF0q2rv6FUmqMs23b4gz8+vV1DW45Y/BRUtEyNWSj\nd+/SQjSqtQZ+9uzidRTC0qXZa32Djbl5//3bd8GPW0Mp5NOhanVPRo2yhuNieOcdM/DFashk5Egb\ntBrs4bHXXvaWevjh1p8ivS/Fu+9Ga2DNpuPii81uFGvgX355+yygQjXko9xx+AYVgy/WwGfWUqkE\nbdsW14U/08CnE7cHH9XA10epHvzy5fbGM2xYch78okW50+gGDzbj9rvfJaMlbmpqzFv8ylcKN/Br\n15qD9Nxz9Rv4Qhg1yjJjli/ffqSlr361bg77u+8W58GDhXauugqOOCL/etkMvCq88oplApWLvn2T\nKzkShSZr4EuNtcblwafr6NbNXm/DTkmlEtXA13cueva0a1Vsz+Mw/r7bbtbRKle6ZJzx7/ryrP/+\nd2tsy3xjaggx+Pnz7VwedJBVfSyEo4+u7VQXVg8tRkMmbdrYwDt33mmx+PQY+f77m1Fft84at2fN\n2n6M5EJ0XHll/f1nshn4BQssY6gYpyfqudh55/IWDWxQMXjV4lINXfHgizHwGzbk9uCbNTNjWmrG\nSsiMGblzhQuhTRvzwIsdUjBMaWvTxlLTPvigdE352LjR7qtcMXiw8/LtbxdeEnnlSsutf+ih0jSW\nwty5ZuAHD7b/o2YErV5toZmVK62MQ6lhzkzGjoXrrrNz85Wv1M5v3dpCKv/8p3n5AweWJwaeTjYD\n/8or1lZQTkJnyBUqauCLPRlxGPhSY63t2sUfg4f4wjRz5lgDV5RsgSjnopRc+GXLasfPHTgwd5gm\nrvj3okV2b9XXy/j0080Ypdfhr0/Dv/5lIYjvf7/4gS6ikE/HAw+YJ966tRn6GTOi7fP5583rT69D\nVKyGbAwZApdfbtoyy/D+/e9WmfSee0xDIRRzX+Qy8MWGZ6JqKLcH70wMXkSOEZFZIjJXRH6ebZ1e\nvQo38GEeeThgRqWIK0STSVwNrQ89BKedFl/Zg969i9eVXtp1wID8Da1xkC/+ns5++9ngJrvtFr2g\n2jPPWA/N8ePhBz9IvlLlhx9atsqpp9r0F79onZVqaurf9q23rLZQOfnBDyxTJZOBAy175eabTW+5\nyUyT3LzZ2h3KGX+H8hv4QimLgReR5sBfgGOAvYCvi8h2zSrFdKBZtcpeLZs3L01jHDH4YhtZ27TJ\nrSMuDz6zpGs+opyLffYh6+g+UUg38LvskvuaxxX/zldnPB0R835fecXKva5dm1/D1q02jNyRR1pO\n9tatxZ+T+sil4+GH4fjja++h3//etNx5Z/37XLiwsJBd3O0RF19snvyXvlTYdsXoyPTgr7nGjG9m\nWYa4NWQz8N/7HnznO/Hkx7sSgz8AmKeqC1R1M3A/cGLmSv37Fz4KigvxdyifB19qSiKYt/LKKzbO\nZlzsv3/djiyFkG7ge/Ysv4eTLwc+G4MGWercPffkX2/aNPsePXvaw+GrX4V//7s0rYXy6KNwYsYv\nacyY7F5zJnGNQVos/fqZoUuCTAP/9tvW5tKyZXmP26OHvU2FCQnvv2/F7WbNgttuK++xs1EuA98L\nSPdDFwXz6pBZazoKcRl4V2Pw3btHe93Ox5w59kNu3z7a+lHOxfDhlrFRTEgi3cDvvHP2sNzq1fHF\n4HOVKcjHuedaI2A+Dc8+a4NQhIQGvhxhmlw6Zs7cPgf8oIPsmq9dm3+fhRr4htAnIBeZBr7U4fmi\namjdum5npwcesFDplVfWlusoBVdi8JFu+czRYqLQ2D34bt3yF+SKwltv1c1DjoM+fSwsVkwee6aB\nz/TglyyxkEpcnbw+/rhwAz96tJ33efNseutWazA85BAbp/Q//7HaLene8/Dh9rYUdvApN5s328Mr\nbLAOadXK8sNffjn/9mG6alMg08B/8EE8GWVR2GsvexCDvfUdfLCFht58M7nhL0PKVQ9+MZB+K+2C\nefF1+POfx/Dmm/246iqoqqpi2LBhn8eYwidV5vSKFdV06ZJ7edTpcF6x28+fnwpi5YVtv359NT16\n5F7eq1c1NTWlfb+334YOHVKkj2eZb/3q6up69z95coqhQ+HJJ6sZODC6nsMPr2bZMpg9O8WHH8LQ\nodUsXWrLFy2CCROqufdegBTvvMPnlPL9ly+Hmpro3x/ghRdSHHEETJ9ezaJFcOKJKbZsgWuvrWby\nZPj1r1N861swalTd7f/5z2rOOANuvTVF+/bF349R7k8LPVXTosX26/fpk+LOO+Goo7Lv7/HHU3z2\nGXTqVJiedC2lfJ9SpqPcn5nT77yTCrKjqtmwAVauTDFrFvTsWZyecF6U9QcPhkceSdG2Lbz9djWX\nXgpTp6bo3x/+979qRo8u7PipVIrxgfvfr9BBGVQ19g/24JgP9AN2AKYDgzLW0a1bVVu3Vl23TiNz\n3XWqF18cff1y8eyzqtXVhW93zjmqf/977uWrV6u2b1+8LlXV445Tfeih0vaRjYceUj3ssMK2Wb9e\ntVWr2ult22qv+cCBquefrzprluq4carnnhuPzkMOUZ08ufDtPvhAtXNn1W9/265T1PtyzBjVK64o\n/Hi52LYt+7GnTFE98MDs26RSqsOH597n1Kmq++wTj76GwNatqs2bq27apDp7tuquuyZ37H/8Q/Ws\ns1Q3brR7feNGm//jH9t9HpV161R/+Uv7LumY2Y5mi8sSolHVLcCFwFPATOBfqvpu5nrNmlnDSyEN\nrY09Bt+xo72KF7PvkEJDNFHPxbHHWorju9tdydysXl03pVXEQgyPPGIprzfdZCl0o0fDU09F01Ef\nxcTgwV7hhwxJ8cADFjON2hnnyivte6Tn0xfLLbdYOKtTpxQ//Wndejn5eiaPGGGdnnKF96ZMsXBT\nIZT6G4mLYnQ0a1Zb8TW9H0YSGgYPthDNnDmWSBL2O9hnH/ttRuX55+FXv6rb+F/ouShbHryqPqmq\nA1V1d1X9v1zrFRqHb+wxeJHS4vCrV1vssdBRm6Kwww5wxhkWj47KmjXb91nYfXcrJfvVr9ZWMxw2\nzNYttJfrgw9aHZT08gfFxOBDfvELO/eFdGfv1886TV17bXHHDPn0U0vXfOQRa5x7/nmC8JWRL7+/\nZUtL33z66ezLX3yx+BTBhkoYh1+xorihQYtl0CBzgubNqzuw95AhhRn4F16wVOdLLy0+dl/Rnqxg\nJ+C996Kvv3JlPAY+PbZWDOWoRRPSvXvxBv7tt82DaFbAlS3kXOy/vzUcRSVb5c8wI+fgg2vnNW8O\nJ5xQzRNPZN/P5s3WSSa988q6dXDeeXZPXH21ZbNs2WJlCrINqBKFUaOqiyqvfPnlloVT7ChfYLXO\n99nHOuOcdFI1P/xh3fFja2pyV8gEOOYY6/+QycaNVkP98MML01PqbyQuitWRbuCTrF1VVWX3/OTJ\ndQ38oEHm1UfNh58yxQbpGTLEHvoAPXpE1wEOGHjvwW9Pt27Fp0rOn187wEc52Hffwg18pgcfpvll\n9io89lh4/PHt97FihYUXLr/cOsqE+73iCvNKH3/cPN5HH7UHx6BBpXeEK5SePS2TZfLk4vcxaVLd\nNMzjjrMMnTCnet26/KmvX/yiefCZaZsPP2zXLY7Kog2J0MCnD5GZFIMH23CF6W/SrVvbOBYrVkTb\nx8yZZtxHjIDp0y1UU2gF0CZr4OOIwcfRkzWbjlI8+OXLC+vkk0tDLvbYw7RlGy0nG2vWbO/Bjxhh\nYZXMMTHbtUvx/PNWkO3aa+GNN2z+X/5icfonn7QY9bZtcPfd5q1edZUZ13HjLJ3x1lsL7ymZTin3\nxejRVsqgWMJesqGOHXe0h2PYb+DTT/O3C/Tta8szS0E8/nhtaYNCaMgxeIjXgy9Uw/77m13LDJXu\ntFO0tpqwqmy3bjB0qKVY3nEH/OIXhemouIHfeefChu5zxYNv08aMdaGdXDZtqr/YUykefLENjFFp\n3tw81VxD3mWSzYPfeefshrBDB4vF33OPhVy+9jW73n/7m43ic+CB9rB4+mnz1C+5pHbIuZNOshon\nt99u/1eCkSOtB3ExrFtnMdt99607v3//2hBmfQYerEduZhG0qVMLL/DVGKiqqvXgk7YZ559vfzM7\nV3XrFs3Az59v4R0RM/DTp9s9X99QhZlU3MB37px7cNxMVOMz8KXGF1u2tDh3tlGB8rFpU93u0nHH\n4Avtpp9LQz4OOQReeinauoWMvlVdXc2xx9pA0OecY9f56KPNcO+zj93s558Pf/2r3ezphbNErN7I\nli11Y/uFUsp9seeexQ+6/NZb9lof3huhjvRyHlEM/Bln2FvN/ffb9KpV9gZQyAhKIY0pBl9qiKZQ\nDb162T06dGjd+TvtFO23PW+eJSOANayvWmWfk08uTIcTBj59NPZ8hANhpIc4KkkxcfjNmy0bJR8u\ne/BgBn7KlGjrZsuiyceJJ5qHf+WVlpmydGndkZfOOMOyC5Yti3dEojjo2tXCR8XUzX/jje29d6hr\n4Nevr9/Af/GLZtx/8xtziF57zd64km6TcIFOnczBqNRb/377bZ/sENWDD2v+gzkv48dbyYNCqbiB\n79jRbtwonnB9jUyFEEd8sZiKkpkefK4YfJIGvtBzse++0dO9soVo8ukIMw06d7bSs6++Wnf7du0s\nhPO//5WncFQp94WINXAXU87h5ZfrvpGEOjI9+CgZPkcfbcb9+ectPFPsIBeNJQYfRyNrXOciqgc/\nZUrdJISvf90e3M7kwUdFpDZWVh9RXlGTpJjOTps2RfPgS2lkLbcHv/PO1hAapaG1mAHSw9z4li2z\nl/390pessddFijHwmzbBE09Y1kwmhYZowM7fuedaqOa558o/ipGrdO5s5aBraqwh3gWiNLJu3mz9\nFuKIkFXcwEP0OHycBj6O+GIcIZpcMfhSPPhyx+BDTzXKwB2rVkXPSXch5luqhkIN/MaN5nEPHlz3\nYVZsDD7k/PMtXbQUA+/C9YDidYwaZQXWzjjDIgWV0JBJlBDNtGl23bOFlQrV4YyBjxKH//TT+EI0\ncVCMgc8M0WSja1frMFPo4Nvr11sniiTecgYOjGbgS+lV2hCJel5CJk+26/bYY9mX9+5tb3OffVaY\ngW/VyjqGlVomtyHTqZO114wbV2kltUQJ0cyaFV/7khMGvlOn6AY+LuMVVwy+VA8+m47mza0uyoIF\nhe174UIzCGGIIyrFnIuoHvzy5dHjny7EfEvVUKgH/9hjNkB1Zhgr1NGiRe1wicXc/6WUB3bhekBp\nOvr3L917L1VDOlE8+Llzc3dWbHAxeIjuwa9b514MvpBGVlUz8FEaB3ffvbY2eVQWLLC6KEngPfjs\nhNct7H2aj82bbcCQk0/Ov17//rbPzz5zJ4PMUxxRPPg5c+JrY3LGwDeFGPzmzeaRpXvYuXQUMxjK\nBx8U9zpezLmIYuA3bLDvHDWs5kLMt1QN7dvbG0uUazdhgj0QBg7Mr2PgQMuGadu28LezUnDheoAb\nOuLS0KWLJR7kq0eTz4Nv9DF4lzz4Ygx8fRk0Ia578AMGmL58N2rovSdplFzg+OPrVoHMxQsvRCur\ncMgh1nu3mCJoHrdo3txC0rnq0aja7yrMgS8VJwx8U4nBZ2tgzaWj0CqbYB58MQa+mHPRrp15qnfe\naTVUslFo/rELMd84NJxzjnVMqa+Mxdtv567bn65j5EjrOZy0c+PC9QA3dMSpIV+YZvVqc4hyZZ41\n6hi8a1k0hebBF+LB9+1bd4zS9evJWUo3ZMGCZDMmLrzQ6sR8/evZB3yuRBU/F9h3X/uR1tcZ7K23\notUWCccSLbTR3eMm+Rpa434LL9rAi8h1IvKuiLwpIv8RkR3Tll0qInNFZJaIHF3fvqLG4ONsZI0r\nBl9II2s2Dz6Xjr59zSNXtQa7b33LOsLk8wqL9eCLPRc//7kV1xoxwhoLMym0gbWxxFpF4JRTbDSe\nu+7Kvs6qVfZQzPVAztRx553bV98sNy5cD3BDR5wa8nV2qq8dLckY/NPAYFUdCswBLgUQkb2A04C9\ngGOAm0Uk73EqEaKJg2JCNFE9+DBtbsUK+Pa3rWDUDjvk7gC1aZPdNJXosTdqVPbiY3PnJtcm4BpX\nXmkNat/7ntXjySR8GEdtnzjzTKvL42n45AvRxP0WXrSBV9WJqhomg70ChMMJnAjcp6qbVXUBMA/I\n25euEo2slahFky1Ek0uHiF3om2+Gd96x8rr77Ze7WuHChdYTspiiUqWei4MPttowmRRaB6UxxVrb\nt7fBSQ480B5+r79uQ6+FLFmS/2HcmM5FqbigI04N+UI09b2FVyoGfzYQRoh7AovSli0CslQUqaWh\nZtF06GBho6hE6cWaTp8+NrDFySfbw2SPPXJ3okk6/p7OkCH2ZnHrrbXzVEsrdNVYOOwwy4C5+274\n4x8tdRTqN/Cexks+D37ZsnhDcS3yLRSRiUC2w12mqo8G61wObFLVfIlhefMJwrKeqvlfWeOsJhlH\nTK1jx8LG4MzmwefTUV1tDauHHmrTAwZY5kU2SmmcKfVctGhh1e9GjbKek0cfbbHnrl2zFwsrl444\niFvD2Wfbm1fz5lZU77nnrC2lPgPfGM9FsbigI04N+Tz4VavM4Y1LR14Dr6pH5VsuImOAY4FRabMX\nA+kdpHsH87ZjzJgx9AuskkgVTzwxjOOOqwZqX0XCL5RKpVi0CNq1y7086en58+GTT6KvP3MmtGwZ\nff399oO//rWagw6y6f794YYbqrn8crjjjhTdu8OZZ9r6kyengtrTlTkfS5emOOccuPrqavbYA37w\ngxQ33lg5PS5NP/oo3HVXijVr4NVXqznuOHjttVSQ61x5fX462emddoK5c1OkUtsvX7Wqmk6d6q6f\nSqUYP348wOf2MjKqWtQHa0CdAXTNmL8XMB3YAegPzAcky/aazi67qL7/vublwANVX3op/zpRmTRp\nUsn7mDpVdfjw6OtPnqw6cmRpOs45R/U3v1Hday/Vq6+unX/mmaq3317QrorWkIstW1T791fdd1/V\nX/2qcjpKoZwa7rhD9Ywz7P/jj1d9+OHK6IiKCxpU3dARp4YZM1T33DP7st13V501K7+OwHZGstOl\nxOD/DLQHJorINBG5ObDaM4EHgJnAk8AFqvWPXBqlRoOLMfhSQzSF8r3vwe9/byOup4drii1TECfN\nm8PFF1sJgwsvrKwWF0kvRLZokdXV9zQ98qVJFlJeOwoSwfaWBRGpY/ePP956AJ54Yu5tdt0VJk6M\nrxtvqSxZYvHVqOlrTz5pDW0TJpR23H/9y2Lut91WWw+mb19IpbYfxT1pPvvMRoBv6o2r2Vixwu7d\n996z9pKaGl88rCmydauVc9640dqvQlQtCWPDhvzJGCKCqkZKsHWiJytYg9OSJfnXca2aZMeO2Xtw\n5iIODx5sbMZLLrGerhs22EDTy5ZZWdlK06qVN+656NLF3nLuuAMOP9wb96ZK8+bWkJpZj2btWrsn\n4hyKskEZ+DhLFYSNGKXQrp0Z2HwFt9IppBZNfbRsad763LmweLGNAlXsjRHHuYgDF3SUW8OIEfDb\n32Yfni9JHVFwQQO4oSNuDdlSw6OEZwrV0WAM/LZtZkxdqqgnYg+cqF58IT1ZoxCW7I07d9ZTPkaN\nMs/t2GMrrcRTScIBwdOJO/4O9aRJJkmvXvkN/IYN0Lo1QSpg6YTpSaXSoYMZ+Kqq+tctNA++PgYO\ntEa7Nm1KG1QjrnNRKi7oKLeG446zXPiwgFildETBBQ3gho64NRRr4AvV0WA8eNcyaEIK6exUaE/W\n+giHzVu+vGmNmtSQ2WMPeOSRSqvwVJps9bfKUX3VGQMfjjuZi7gbWOOKqRVi4AupRROFQYMsVbJU\nA+9CjBPc0OGCBnBDhwsawA0dcWvI5sFHMfANNgbfpYsZwGyV98BdDz4M0UQhbg9++HB7KE6b5j14\nj6chkcvAx/07dsbAh9UTP/gg+/K4B/uIK6ZWVRWtlj1kb2QtRUfLltZYd//9PgbfmDSAGzpc0ABu\n6IhbQ7YxMKJ48A02Bg/W+SOfgXfRg486WAnElwefTjimp/fgPZ6GQ7EhmkJxzsDnGpYsbgMfV0wt\naqljiDcPPuSII+xvly7F78OFGCe4ocMFDeCGDhc0gBs6kojBL1/eiGPwYCGaXAbetV6sIYUY+PXr\n48/j33lnK+FQ6To0Ho8nOkl58M7UogEbFOGJJ+DeLJXl//EPePnluoNKuMBtt8ELL8Dtt9e/7ne/\na7Vrzjuv/Lo8Ho+7LF4MQ4daJ8WwHk2fPmZL6nPWCqlF40xHJ7Du9rnGHC1HL684KMSDX7OmdqxV\nj8fTdOnVy0LSL75ob+CtW0cL0RSKUyGaHj3siZaNOXOsk0hcVCIGn83AN8b4YrG4oMMFDeCGDhc0\ngBs6yqHhrLPglFNg771t2MvBg+sPQzfoGHw+D372bOu56Rreg/d4PMXwgx/YUJeLFlmp4BNOiP8Y\nTsXgt261V5X16y3bZPNmuP56G7j4K1+xDj2uDVRcSE34vfaCf//bntQej8cTMmmS2YVu3epfN9F6\n8CLyYxHZJiKd0+ZdKiJzRWSWiBwddV/Nm1sMKhzZ6dFH4dJL4dprLU3SxRFwQg8+ynPSe/Aejycb\nRxwRzbgXSkkGXkR2AY4CPkibtxdwGjY26zHAzSIS+Tjdu9fG4adMgZNPNkM/YoT1do2LuGJqrVtb\nK/j69fWv62Pw+XFBhwsawA0dLmgAN3S4oAGSj8H/AfhZxrwTgftUdbOqLgDmAZHH+OnVCxYutP+n\nTIHzz7dwzVe+UqLSMpJtdJZMtmyxIbriLLfg8Xg8+Sg6Bi8iJwLVqnqxiLwP7KeqK0Xkz8DLqnpP\nsN4/gSdV9cGM7bOOxX355eYR//CHNmLR0qXw5z/Dd74TfwpRXAwdasOwDRuWe52VK208zqhlDTwe\njycbseXBi8hEINtYQZcDlwLp8fV8B8z6FBkzZgz9+vUDoKqqimHDhrHfftX84Q8we3aKYcOgbdtq\nfv7z2leTsNiOS9OdO8Nzz6VYvTr3+k89laJVK4DK6/XTftpPN5zpVCrF+PHjAT63l5FR1YI/wN5A\nDfB+8NkMLAC6A2OBsWnrTgAOzLIPzcaCBaqgus8+qk89lXWVWJg0aVJs+zrlFNV//zv/OtOmqQ4Z\nUl4dxeKCBlU3dLigQdUNHS5oUHVDhwsaVE1HYDsj2eqierKq6juBMQcgI0TzCHCviPwB6AXsAUyN\nuu8+feCuu+DrX7esmoZAlFx4n0Hj8XiSJpY8eBF5DxiuqiuD6cuAs4EtwA9V9aks22gcx3aBsWOt\nLvzYsbnXeeQRq6fz6KPJ6fJ4PI2PxGvRqOquGdPXANfEse+GQOfOVgkuH96D93g8SeNUqYIkCRsx\n4thUo3cAAA2cSURBVCBKmmQuAx+njmJxQQO4ocMFDeCGDhc0gBs6XNAADbwWTUOlSxcfg/d4PO7h\nVC2ahsozz8C4cfY3Fz/7mT0Ifv7z5HR5PJ7GR6K1aDxW4nPduvzreA/e4/EkTZM18HHG1Nq1s2Jo\n+fAx+PpxQYcLGsANHS5oADd0uKABfAy+IrRvn93Ap0egvAfv8XiSxsfgY6CmBvbZp7bMcUjLlnDT\nTTYW64gRcN11cMghldHo8XgaBz4GnzDZQjSffmoVJJcvt2nvwXs8nqRpsgY+zpha27ZWCnjbttp5\nQW0gPvsMbrgBZs70Mfj6cEGHCxrADR0uaAA3dLigAQrXEUtP1qZOs2a1Qw22bw+LF1vZ4/POs2EG\nX3oJ/vY3q3Xv8Xg8SeFj8DHRrRu8/baNSPXcc3D11XDRRfDVr8K3vmX14j0ej6dUfAy+ArRvX5sL\nP28e7L577RiLX/hC5XR5PJ6mS5M18HHH1NIbWjMN/NChyekoBhc0gBs6XNAAbuhwQQO4ocMFDeDz\n4CtGsQbe4/F4yoWPwcfE6NFWZ2b0aOjXD558EgYNggkT4EtfqrQ6j8fTWPAx+AoQevCvv24ZNYMG\ngYg37h6Pp3KUZOBF5Aci8q6IvCMiv0ubf6mIzBWRWSJydL59VIpyxODXrTPP/YQTzLhXQkcxuKAB\n3NDhggZwQ4cLGsANHS5ogATz4EXkCOAEYIiqbhaRnYL5ewGnAXthY7I+IyIDVHVb7r01fDp0gLVr\nLf4eDIzu8Xg8FaXoGLyIPAD8TVWfy5h/KbBNVX8XTE8ArlLVlzPWa1Qx+MsvhzZt4OmnLQf+iCMq\nrcjj8TRGkorB7wEcJiIvi0hKRIYH83sCi9LWW4R58o2arl2t7syCBdC/f6XVeDweTz0hGhGZCPTI\nsujyYNtOqnqQiOwPPADsmmVdgKyu+pgxY+jXrx8AVVVVDBs2jOogvhHGmso1feONN8Z6vOXLU0yf\nDjU11fTuHX37cF65v2++6UwtSR8/nJ4+fTo/+tGPKnb89HNQyesB8d+fDfV6uHJ/VvJ6pFIpxofF\nrQpFVYv6AE8Ch6dNzwO6AmOBsWnzJwAHZtleK8mkSZNi3d+TT6rutptq376V1VEMLmhQdUOHCxpU\n3dDhggZVN3S4oEHVdAS2M5KdLiUGfx7QU1WvFJEBwDOq2idoZL0XOICgkRXYXTMO1Nhi8K+9Bvvv\nb3nwEydWWo3H42msFBKDL6Wa5G3AbSLyNrAJ+BaAqs4MGmBnAluACxqVJc9B1672d9CgyurweDye\nkKIbWVV1s6qeqar7qOp+qppKW3aNqu6uqnuq6lOxKI2Z9LheHBRr4OPWUQwuaAA3dLigAdzQ4YIG\ncEOHCxrA16KpGO3aQatW3oP3eDzu4GvRxMjXvga33AKdO1daicfjaawUEoP3Bt7j8XgaEL7YWAQa\nakytsWoAN3S4oAHc0OGCBnBDhwsawMfgPR6PxxPgQzQej8fTgPAhGo/H4/E0XQPfUGNqjVUDuKHD\nBQ3ghg4XNIAbOlzQAD4G7/F4PJ4AH4P3eDyeBoSPwXs8Ho+n6Rr4hhpTa6wawA0dLmgAN3S4oAHc\n0OGCBvAxeI/H4/EE+Bi8x+PxNCB8DN7j8Xg8xRt4ETlARKaKyDQReTUYlzVcdqmIzBWRWSJydDxS\n46WhxtQaqwZwQ4cLGsANHS5oADd0uKABko3BXwtcoar7Ar8MpgmG7DsN2As4BrhZRJx7U5g+fXql\nJQBu6HBBA7ihwwUN4IYOFzSAGzpc0ACF6yjF8C4Fdgz+rwIWB/+fCNwXjPi0ABuM+4ASjlMWVq9e\nXWkJgBs6XNAAbuhwQQO4ocMFDeCGDhc0QOE6ShmTdSzwooj8HntQHBzM7wm8nLbeImzwbY/H4/Ek\nSF4DLyITgR5ZFl0OXARcpKoPicjXsEG4j8qxK+fSZRYsWFBpCYAbOlzQAG7ocEEDuKHDBQ3ghg4X\nNEDhOopOkxSRT1S1Y/C/AKtVdUcRGQugquOCZROAK1X1lYztnTP6Ho/H0xCImiZZSohmnogcrqqT\ngSOBOcH8R4B7ReQPWGhmD2BqsQI9Ho/HUxylGPjvAjeJSCtgQzCNqs4UkQeAmcAW4ALfo8nj8XiS\np2I9WT0ej8dTXpzLT/d4PB5PPHgD7/E0cUSkpYh8U0SOCabPEpG/iMh3ggSKpHTcICIjkzpeoYjI\nLxM8VteM6TNF5M8i8t1CrkmTCNGIyJHAKcAuwFZgNvBPVZ2XoIaWWA/fj1V1goicBewPTANuS6Kd\nQkRuAB5U1RfLfaxiEZFfquqvEjhOV1X9OG36TKxD3tvAP5JsN6r0/Skit2KdFnfA2tNaAQ8CXwY+\nVNWfJqRjOfAB0A24H+swOS2JY0dBRBaq6i4JHWtaUCUAEfkFcChwL3A8sFBVL460n8Zu4EVkHJbL\n/yxwEvA+lvFzPvB/qvpAQjoq/iNy/QcEyf2I4voBxaCj4veniMxQ1cGBE1ID7Kyqn4lIC+ANVR1S\nbg2Bjmmquq+IDABOxxyiFth1uU9V5+TdQTwa1uZZ3EZVS0lMKURH+v05DThUVdcF12iaqu4daUeq\n2qg/wDtp/7cAXgr+7wTMSFDHjOBvS2Al0CpN01sJaZgW/B2A1Q+agXmLVwIDEjwXa/N8tiR5LsL/\ngfZp1+edJDQEx6v4/QlMT/v/qYxlbyZ4LqZlmTcUGAfMT0jDh0CPHMsWJnguZgFfAPbLvB8LuSZN\nIQa/VUS6BP/3Imh3UNVVCevYHBx3M/Cqqn4WTG8h4Z6+qjpHVX+lqoOBU4E2wJMJSlgF7KGqHTI/\nWI2jJGgjIl8Qkf2Alqq6Dj6/PlsT0gBu3J/LRKR9cNwvhjNFZGfgswR1bIeqvqmqY1V1t4QOeRfQ\nJ8ey+xLSALAMuB74PbBcRHrC57H5zVF3ksjrRoW5BnhDROYCA7FXX0SkG/BmgjqWiUgHVV3r0o9I\nVd/EzsPYBA8b/oiWZVmW1I8o/AFB8ANS1SWF/oBioOL3p6oek2PRJ1gIMSkOS/BYWVHVy/Ms+1mC\nOqpzLFpFAeep0cfgAQIPaVdgXgU897yISDssPFCTwLE6qGq+GGOTR0SaA61V9dMEjxnen3NVtSJl\nC4PMjAOxtwjFqsNO1YQNRFBa/IBK68iGiOypqrMako5Gb+BFZIiqvlVpHQAi0gf4RFVXi0h/YDjw\nrqq+05Q0pGnZH+iNhUTmVOLHIyLDqc1eqYiGQEfFzkUwKM/NWGnvRcHs3liZkQtU9ammpCMXSWbR\nxKWjKRj4rcB71GaNzKyQjrHAecAm4DrgJ8AU4CAsTfL6PJs3Gg2BjsOx8MhqrBHpJWxMgc3Amaq6\nsClocEWHiMwCjlEbvyF9fn/gSVXds9waXNEhIn/Os3hM0E5UduLS0RQM/DTgTOAMrEFxPZZ2dX/m\njVRmHTOxH3A7YAHQX1WXByGaqUGDZ6PXEOiYDhwVHLs/cIOqniQiRwE/VdWyD/PoggZXdATx/72C\nBub0+TsAM1V193JrcEVHkCb5E6xdLN04CnC9qnbJuqGjOppCIytB+OEy4DIRORDLsX1RRD5U1REJ\nydiiqhtEZBP2kFkZaPtURLY1IQ0AzVR1efD/h0DfQMdEEfljE9Lgio7bgFdF5D5qQyO7YL+T2xLS\n4IqO17C0xCmZC0TkqoQ0xKajSXjwGnQYyJjfDDhMVVMJ6QizQ9ph2QltgIewUss7qOo3m4KGQMft\nwDZgEnACsEhVLwneJF5P6FW84hoc07EXNtxmz2DWYuCRpEOaldYhIp2Bjaq6PonjlVtHUzDw31DV\nexzQ0RrzRJaq6lMi8k1gBNah4ZYwL76xawh07ACcCwzCUgFvU9WtItIG6J5E6MwFDS7p8DROGr2B\n93g8+RGRKqwfxElAdyzm+xHwMDAuqdRNF3S4oCFOHY2+J6uIdBCRX4nIDBH5REQ+FpFXRGSMAzpe\nTlKHCxry6Ej0mrigwSEdD2AdaKqBzqraGTgCy+xJpFaTQzpc0BCbjkbvwYvII1ic+Rnga0B7LGXy\nF1i887KmosMFDa7ocEGDKzpEZI6qDih0WWPU4YKGWHVoQsVzKvUho5AX8FrwtxkwuynpcEGDKzpc\n0OCKDmAi8DMs5h/O6wH8HHgmwXNRcR0uaIhTR6MP0QCfisihACJyIrACQFWTTAt0RYcLGlzR4YIG\nV3ScBnQFJovIKhFZBaSALljfkaakwwUN8elI6olUqQ9WbvRVLHY1BRgYzN8JuKgp6XBBgys6XNDg\nmI5BwGigQ8b8Y5LS4IoOFzTEpSMxsS5+gLMrrcEVHS5ocEWHCxqS1AFchI0L8DA2IMxJacu2q9He\nmHW4oCFOHYmIdfVDggX8XdfhggZXdLigIUkdwDvUDnjSD3gd+FEwnaRRq7gOFzTEqaPRlyoQkbfz\nLO7elHS4oMEVHS5ocEiHaO2AJwvECqA9KCJ9sdonSeGCDhc0xKaj0Rt4bPzRY7Cc0kxeamI6XNDg\nig4XNLii4yMRGaaq0wHUxv78MnArkMh4rA7pcEFDbDqagoF/HHvV2W5waRGZ3MR0uKDBFR0uaHBF\nx7fIGMVKVTeLyFnA3xPS4IoOFzTEpqPRd3TyeDyepkpTyIP3eDyeJok38B6Px9NI8Qbe4/F4Gine\nwHs8Hk8jxRt4j8fjaaT8fxhADShSMpm/AAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "# Long-term arithmetic mean return is 10.6%.\n", "# Latest forecast of gold return for the coming year:\n", "tailvalue( aupro )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "-4.884878533176684" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Forecasting SPX" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# SPX: projected annual returns using monthly data:\n", "sppro = holtpc( monthly(sp), 12 )" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "# US equities projections for the last 40 years:\n", "plotfred( sppro[-480:] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEYCAYAAABbd527AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n", "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "code", "collapsed": false, "input": [ "# Long-term arithmetic mean return is 8.0%.\n", "# Latest forecast of SPX return for the coming year:\n", "tailvalue( sppro )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "10.944655163915927" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Relative value between SPX and XAU" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# SPX priced in USD per share:\n", "plotfred( sp['1968-04-01':] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEYCAYAAAC5q4bCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text": [ "" ] } ], "prompt_number": 42 }, { "cell_type": "code", "collapsed": false, "input": [ "# XAU priced in USD per troy ounce:\n", "plotfred( au['1968-04-01':] )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEYCAYAAAC5q4bCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhmEkmP8P3xZuptiZ1WcAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous section on forecasting looked the assets separately. **Now we shall look at SPX priced in terms of XAU, which can be interpretated as troy ounces of gold required to buy an equity share in the US.**" ] }, { "cell_type": "code", "collapsed": false, "input": [ "spau = todf( sp / au )\n", "# Units are thus expressed in troy ounces per share." ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 44 }, { "cell_type": "code", "collapsed": false, "input": [ "# USD as common denominator drops out, and \n", "# Y plots the US equity in terms of troy ounces of gold:\n", "plotfred( spau )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAWYAAAEYCAYAAABvDlynAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDbOiKIpjqGFWFEVxjP8HWldqPLvbjKwAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 45 }, { "cell_type": "markdown", "metadata": {}, "source": [ "That spike to 5.6 ounces is very noteworthy indicating overvalued equities, and a signal to buy gold. In fact, it is the all-time high since 1880." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Longer view using monthly Schiller \"data,\" back to 1880, but in terms of grams:\n", "Image(url='http://pricedingold.com/charts/SP500-1880.png', embed=False)\n", "# 1 troy ounce = 31.1 grams" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "" ], "metadata": {}, "output_type": "pyout", "prompt_number": 46, "text": [ "" ] } ], "prompt_number": 46 }, { "cell_type": "code", "collapsed": false, "input": [ "stats( spau )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Y\n", "count 12244.000000\n", "mean 1.565869\n", "std 1.217546\n", "min 0.131882\n", "25% 0.644588\n", "50% 1.163509\n", "75% 2.306488\n", "max 5.565022\n", "\n", " :: Index on min:\n", "Y 1980-01-21\n", "dtype: datetime64[ns]\n", "\n", " :: Index on max:\n", "Y 1999-07-15\n", "dtype: datetime64[ns]\n", "\n", " :: Head:\n", " Y\n", "T \n", "1968-04-01 2.453050\n", "1968-04-02 2.483646\n", "1968-04-03 2.485904\n", "1968-04-04 2.539648\n", "1968-04-05 2.521351\n", "1968-04-08 2.562753\n", "1968-04-09 2.532000\n", "\n", " :: Tail:\n", " Y\n", "T \n", "2015-02-25 1.754605\n", "2015-02-26 1.746940\n", "2015-02-27 1.733526\n", "2015-03-02 1.746301\n", "2015-03-03 1.738017\n", "2015-03-04 1.749504\n", "2015-03-05 1.747953\n", "\n", " :: Correlation matrix:\n", " Y\n", "Y 1" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 47 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Over the long haul, it took an *average of 1.57 troy ounces of gold to purchase one US equity share*." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# What is the long-term trend?\n", "plotfred( trend(spau) )" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " :: regresstime slope = 9.67148719065e-05\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAEYCAYAAACTG3dtAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSpsRNnwlwN4AAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 48 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simplistically, US equites has arithmetically doubled in value in terms of gold (from 1 oz. in the 70's to over 2 oz. recently). That trend looks good, going as far back as 1932." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Compute the geometric mean return:\n", "georet( spau )" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 49, "text": [ "[-0.7, 2.71, 26.12, 256]" ] } ], "prompt_number": 49 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Conclusion for relative value\n", "\n", "The arithmetic mean return for spau is approximately 2.7% per annum (which is the trend shown graphically above), however, due to high volatility the geometric mean return is sub-zero. **This analytically implies *short equities vs. long gold is favorable for an investor with log utility*, but at high risk with hardly any profit over the long haul.** \n", "\n", "Including dividends in our analysis would reverse this conclusion as to positions, but would still leave us indifferent as to a definitive choice between the two assets. A complete treatment should also account for the taxation on dividends and capital gains (financial vs. commodity assets).\n", "\n", "Notice that the spau volatility is greater than that of SPX, and also that of XAU. **Opposing the two assets in a portfolio does not diminish risk, but rather increases risk.** \n", "\n", "It is worth noting that dividends are reduced generally when industries are not doing well. Interest rates may decrease in order to induce economic activity (cf. Great Recession), which would decrease *real* interest rates. Since gold has no income stream, it thus becomes more preferable over equities in such situations.\n", "\n", "Real interest rates also become negative when monetary policy allows inflation to rise above nominal interest rates. This is the classic scenario where gold is preferable because financial instruments will have difficulty merely preserving wealth." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### TODO\n", "\n", "- [ ] - do a portfolio analysis with SPX and XAU jointly long.\n", " - What allocation between the two assets has been risk minimal?\n", " - Can the allocation be improved by using real interest rates as a factor?" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 49 } ], "metadata": {} } ] }