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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# INTRODUCTION\n",
"There are several ways of making money in the stock market; here we explore a few of them using techniques from data science and finance. We explore alpha generation from the perspectives of:\n",
"\n",
"- leveraged finance (ETF decay) and similar tricks of the trade\n",
"- digital signal processing\n",
"- portfolio construction using MPT (Modern Portfolio Theory)\n",
"- bayesian Natural Language Processing using Twitter data, attempting to perform sentiment analysis\n",
"\n",
"##Initial Question\n",
"\n",
"Thus our initial question is: Which of the above methods will generate alpha, and of course what are the caveats. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Motivation\n",
"\n",
"The motivation of this project is to apply knowledge from 209 to finance. The motivation is to make money. We not only want to just maximize returns, but also minimize volitility. You will see through the statistics we employ, that we focused on these two ideas. That is our motivation. \n",
"\n",
"## Related Work\n",
"\n",
"In terms of related work. Many of our funcitons are derived from other works (like the butterworth filter). We have sited them in our .py files. In addition we have used what we learned on bayesian tomatoes quite extensively. Most of the other work we have done, comes from our own experience. \n",
"\n",
"## Data Munging\n",
"\n",
"We colleted the initial data from Quandl, and have included it as files in the .zip. In addition, we collected twitter data. That process is descibed below. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exploratory Analysis "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Grappling with timeseries data is essential to our task of stock price prediction, since a stock traces out a series of datapoints with regard to time. Fortunately, pandas includes an API for time-series manipulations. In the following, we introduce some exploratory statistics and methodology and begin to analyze stock data from a returns perspective.\n",
"\n",
"The pandas time-series API includes:\n",
"\n",
"- 1.) Date ranges from files and from scratch\n",
"- 2.) Shift, resample, and filter manipulations\n",
"- 3.) Field accessors\n",
"- 4.) Plotting\n",
"- 5.) Time zones (localization and conversion)\n",
"- 6.) Dual representations (point-in-time vs interval)\n",
"\n",
"\n",
"Let's import some code. From datetime, we need\n",
"\n",
"- datetime\n",
"- date\n",
"- time\n",
"\n",
"From pandas, let's get the timeseries tools:\n",
"\n",
"- Series\n",
"- DataFrame\n",
"- Panel\n",
"\n",
"In addition we need:\n",
"\n",
"- matplotlib\n",
"- sys"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Code to allow inline plotting, derived from psets\n",
"\n",
"import warnings\n",
"warnings.filterwarnings('ignore')\n",
"from helperfile import *\n",
"plt.rc('figure', figsize=(10, 6))\n",
"\n",
"%matplotlib inline\n",
"\n",
"import json\n",
"\n",
"import requests\n",
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"pd.set_option('display.width', 500)\n",
"pd.set_option('display.max_columns', 30)\n",
"\n",
"# set some nicer defaults for matplotlib\n",
"from matplotlib import rcParams\n",
"\n",
"#these colors come from colorbrewer2.org. Each is an RGB triplet\n",
"dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),\n",
" (0.8509803921568627, 0.37254901960784315, 0.00784313725490196),\n",
" (0.4588235294117647, 0.4392156862745098, 0.7019607843137254),\n",
" (0.9058823529411765, 0.1607843137254902, 0.5411764705882353),\n",
" (0.4, 0.6509803921568628, 0.11764705882352941),\n",
" (0.9019607843137255, 0.6705882352941176, 0.00784313725490196),\n",
" (0.6509803921568628, 0.4627450980392157, 0.11372549019607843),\n",
" (0.4, 0.4, 0.4)]\n",
"\n",
"rcParams['figure.figsize'] = (10, 6)\n",
"rcParams['figure.dpi'] = 150\n",
"rcParams['axes.color_cycle'] = dark2_colors\n",
"rcParams['lines.linewidth'] = 2\n",
"rcParams['axes.grid'] = False\n",
"rcParams['axes.facecolor'] = 'white'\n",
"rcParams['font.size'] = 14\n",
"rcParams['patch.edgecolor'] = 'none'\n",
"\n",
"\n",
"def remove_border(axes=None, top=False, right=False, left=True, bottom=True):\n",
" \"\"\"\n",
" Minimize chartjunk by stripping out unnecessary plot borders and axis ticks\n",
" \n",
" The top/right/left/bottom keywords toggle whether the corresponding plot border is drawn\n",
" \"\"\"\n",
" ax = axes or plt.gca()\n",
" ax.spines['top'].set_visible(top)\n",
" ax.spines['right'].set_visible(right)\n",
" ax.spines['left'].set_visible(left)\n",
" ax.spines['bottom'].set_visible(bottom)\n",
" \n",
" #turn off all ticks\n",
" ax.yaxis.set_ticks_position('none')\n",
" ax.xaxis.set_ticks_position('none')\n",
" \n",
" #now re-enable visibles\n",
" if top:\n",
" ax.xaxis.tick_top()\n",
" if bottom:\n",
" ax.xaxis.tick_bottom()\n",
" if left:\n",
" ax.yaxis.tick_left()\n",
" if right:\n",
" ax.yaxis.tick_right()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's sample some data from the SPX.csv data file, sourced from Yahoo Finance S&P 500."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with open('SPX.csv', 'r') as ff:\n",
" print ff.readline() # headers\n",
" print ff.readline() # first row"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"DATE,OPEN,HIGH,LOW,CLOSE,VOLUME,ADJ\n",
"\n",
"2013-09-13,169.13,169.46,168.74,169.33,72459700,169.33\n",
"\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use lists or dicts for parsing dates."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"data = pd.read_csv('SPX.csv',parse_dates={'Timestamp': ['DATE']},index_col='Timestamp')\n",
"data"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"
\n",
"<class 'pandas.core.frame.DataFrame'>\n",
"DatetimeIndex: 5195 entries, 2013-09-13 00:00:00 to 1993-01-29 00:00:00\n",
"Data columns (total 6 columns):\n",
"OPEN 5195 non-null values\n",
"HIGH 5195 non-null values\n",
"LOW 5195 non-null values\n",
"CLOSE 5195 non-null values\n",
"VOLUME 5195 non-null values\n",
"ADJ 5195 non-null values\n",
"dtypes: float64(5), int64(1)\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 3,
"text": [
"\n",
"DatetimeIndex: 5195 entries, 2013-09-13 00:00:00 to 1993-01-29 00:00:00\n",
"Data columns (total 6 columns):\n",
"OPEN 5195 non-null values\n",
"HIGH 5195 non-null values\n",
"LOW 5195 non-null values\n",
"CLOSE 5195 non-null values\n",
"VOLUME 5195 non-null values\n",
"ADJ 5195 non-null values\n",
"dtypes: float64(5), int64(1)"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at some of these more recent values:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"history = data.ix[:, ['OPEN', 'VOLUME']]\n",
"history.head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" OPEN | \n",
" VOLUME | \n",
"
\n",
" \n",
" Timestamp | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" 2013-09-13 | \n",
" 169.13 | \n",
" 72459700 | \n",
"
\n",
" \n",
" 2013-09-12 | \n",
" 169.34 | \n",
" 83098200 | \n",
"
\n",
" \n",
" 2013-09-11 | \n",
" 168.64 | \n",
" 94272700 | \n",
"
\n",
" \n",
" 2013-09-10 | \n",
" 168.64 | \n",
" 102432800 | \n",
"
\n",
" \n",
" 2013-09-09 | \n",
" 166.45 | \n",
" 83392900 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
" OPEN VOLUME\n",
"Timestamp \n",
"2013-09-13 169.13 72459700\n",
"2013-09-12 169.34 83098200\n",
"2013-09-11 168.64 94272700\n",
"2013-09-10 168.64 102432800\n",
"2013-09-09 166.45 83392900"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compute a VWAP (Volume Weighted Avereage Price, a weighted avereage of price with volume as the weights, often used as an anchoring quantity for algorithmic traders) using resample."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"volume = history.VOLUME.resample('1w', how='sum') # weekly vwap\n",
"value = history.prod(axis=1).resample('1w', how='sum')\n",
"vwap = value / volume\n",
"print vwap"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Timestamp\n",
"1993-01-31 43.970000\n",
"1993-02-07 44.554778\n",
"1993-02-14 44.845201\n",
"1993-02-21 44.021129\n",
"1993-02-28 43.816993\n",
"1993-03-07 44.786620\n",
"1993-03-14 45.346889\n",
"1993-03-21 45.133627\n",
"1993-03-28 44.827772\n",
"1993-04-04 45.121409\n",
"1993-04-11 44.453826\n",
"1993-04-18 44.844166\n",
"1993-04-25 44.560004\n",
"1993-05-02 43.723734\n",
"1993-05-09 44.391409\n",
"...\n",
"2013-06-09 163.200245\n",
"2013-06-16 163.581478\n",
"2013-06-23 162.626114\n",
"2013-06-30 159.262948\n",
"2013-07-07 161.399900\n",
"2013-07-14 165.689620\n",
"2013-07-21 168.265996\n",
"2013-07-28 169.031879\n",
"2013-08-04 169.393906\n",
"2013-08-11 169.890286\n",
"2013-08-18 167.850913\n",
"2013-08-25 165.400218\n",
"2013-09-01 164.397174\n",
"2013-09-08 165.588047\n",
"2013-09-15 168.435810\n",
"Freq: W-SUN, Length: 1077, dtype: float64\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can conveniently index financial time series data as follows."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"vwap.ix['1993-01-31':'2013-09-15']"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"Timestamp\n",
"1993-01-31 43.970000\n",
"1993-02-07 44.554778\n",
"1993-02-14 44.845201\n",
"1993-02-21 44.021129\n",
"1993-02-28 43.816993\n",
"1993-03-07 44.786620\n",
"1993-03-14 45.346889\n",
"1993-03-21 45.133627\n",
"1993-03-28 44.827772\n",
"1993-04-04 45.121409\n",
"1993-04-11 44.453826\n",
"1993-04-18 44.844166\n",
"1993-04-25 44.560004\n",
"1993-05-02 43.723734\n",
"1993-05-09 44.391409\n",
"...\n",
"2013-06-09 163.200245\n",
"2013-06-16 163.581478\n",
"2013-06-23 162.626114\n",
"2013-06-30 159.262948\n",
"2013-07-07 161.399900\n",
"2013-07-14 165.689620\n",
"2013-07-21 168.265996\n",
"2013-07-28 169.031879\n",
"2013-08-04 169.393906\n",
"2013-08-11 169.890286\n",
"2013-08-18 167.850913\n",
"2013-08-25 165.400218\n",
"2013-09-01 164.397174\n",
"2013-09-08 165.588047\n",
"2013-09-15 168.435810\n",
"Freq: W-SUN, Length: 1077, dtype: float64"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"selection = vwap.between_time('1993-01-31', '2013-09-15')\n",
"vol = pd.Series(volume.between_time('1993-01-31', '2013-09-15'),dtype=float)\n",
"#vol.head(20)\n",
"# attempt to fill possible missing data\n",
"selection.ix['1993-01-31':'2013-09-15'].head(20)\n",
"filled = selection.fillna(method='pad', limit=1)\n",
"filled.ix['1993-01-31':'2013-09-15'].head(20)\n",
"vol = vol.fillna(0.)\n",
"#vol.head(20)\n",
"# now for visualization, plot the volume weighted avereage price, along with volume, with respect to time. \n",
"vol.plot(style='y')\n",
"filled.plot(secondary_y=True, style='r')\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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cCxcuxNVXX43Dhw9j1apVwVyaIKKDY8eAOXPYDEFtagURfqNv1EjZphVYO3ey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\nMcacjBtYjDHGGGNOxg0sxhhjjDEn+3+4x77Al5umlwAAAABJRU5ErkJggg==\n",
"text": [
""
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Regression analysis of S&P 500 data\n",
"----"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"BB = history.OPEN.resample('1w', how='ohlc')\n",
"week_range = BB.high - BB.low\n",
"#week_range.describe()\n",
"week_return = BB.close / BB.open - 1\n",
"#week_return.describe()\n",
"#week_return.head()\n",
"MM = week_return.between_time('1993-01-31', '2013-09-15')\n",
"#lagged = MM.shift(1)\n",
"lagged = week_return.tshift(1, 'w').between_time('1993-01-31', '2013-09-15')\n",
"# Ordinary least squares\n",
"pd.ols(y=MM, x=lagged)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"\n",
"-------------------------Summary of Regression Analysis-------------------------\n",
"\n",
"Formula: Y ~ + \n",
"\n",
"Number of Observations: 1076\n",
"Number of Degrees of Freedom: 2\n",
"\n",
"R-squared: 0.0012\n",
"Adj R-squared: 0.0003\n",
"\n",
"Rmse: 0.0222\n",
"\n",
"F-stat (1, 1074): 1.2743, p-value: 0.2592\n",
"\n",
"Degrees of Freedom: model 1, resid 1074\n",
"\n",
"-----------------------Summary of Estimated Coefficients------------------------\n",
" Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%\n",
"--------------------------------------------------------------------------------\n",
" x -0.0344 0.0305 -1.13 0.2592 -0.0942 0.0254\n",
" intercept 0.0014 0.0007 2.07 0.0383 0.0001 0.0027\n",
"---------------------------------End of Summary---------------------------------\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And VWAP:\n",
"----"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"MM = vwap / BB.open - 1\n",
"MM = MM.between_time('1993-01-31', '2013-09-15')\n",
"lagged = MM.tshift(1, 'w').between_time('1993-01-31', '2013-09-15')\n",
"pd.ols(y=MM, x=lagged)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"text": [
"\n",
"-------------------------Summary of Regression Analysis-------------------------\n",
"\n",
"Formula: Y ~ + \n",
"\n",
"Number of Observations: 1076\n",
"Number of Degrees of Freedom: 2\n",
"\n",
"R-squared: 0.0018\n",
"Adj R-squared: 0.0009\n",
"\n",
"Rmse: 0.0122\n",
"\n",
"F-stat (1, 1074): 1.9175, p-value: 0.1664\n",
"\n",
"Degrees of Freedom: model 1, resid 1074\n",
"\n",
"-----------------------Summary of Estimated Coefficients------------------------\n",
" Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%\n",
"--------------------------------------------------------------------------------\n",
" x -0.0422 0.0305 -1.38 0.1664 -0.1020 0.0175\n",
" intercept 0.0003 0.0004 0.91 0.3610 -0.0004 0.0011\n",
"---------------------------------End of Summary---------------------------------\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Intro to Leveraged Finance: Decaying 3X Leveraged ETFs.\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So the S&P did very well this year. Why can't we just invest into a 3x ETF and make 60 percent a year!\n",
"\n",
"What are leveraged ETFs? First, ETFs (Exchange Traded Funds) and financial instruments that trade similarly to stocks, and attempt to replicate the return of a basket of other assets. In principle, it would require many costly transactions for an investor to replicate the exposure of an ETF, so they are seen as convenient cost saving tools (Example: one SPY purchase gives you the same exposure as buying every stock in the S&P 500). Some ETFs purport to replicate a multiple of the return of the underlying asset; these are known as Leveraged ETFs. Leveraged ETFs have an interesting behavior; many market participants have noted their long-term downward tendency. This is because they have an asymmetric distribution with a large chance of decay. While the chance of decay is large, the expected value of each timestep is the same as for a similar nonleveraged instrument. Let's attempt to demonstrate this through a Monte-Carlo approach."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"###Use randn to simulate historical data###\n",
"\n",
"We want an etf security with normal historical returns. Average daily return should therefore be 0, with a standard deviation of 1%."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# numpy/matplotlib\n",
"%pylab inline\n",
"history = randn(10000)\n",
"plot(randn(10000)) #plot the 10000-day historical price vector.\n",
"title('returns') \n",
"xlabel('day')\n",
"ylabel('return [%]')\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"WARNING: pylab import has clobbered these variables: ['load', 'info', 'mpl', 'datetime', 'save', 'set_printoptions', 'unique']\n",
"`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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H4enpiTZt2qB///4ICgoy6riEEEL4wSphWFtbY9KkSZyeODExEU2bNoWPjw8A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\nO5KqKj5K+mJdw4oPO/u+hy/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"text": [
""
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"h = hist(history,100)\n",
"print 'Mean:' , history.mean()\n",
"print 'Standard deviation:%.2f' % history.std()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mean: -0.00286332404091\n",
"Standard deviation:1.01\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
""
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is very near mean 0, standard deviation 1.\n",
"\n",
"Starting with an investmnt of k dollars, on day n our investment would then have a value of $k*r[t]*r[t+1]*...r[n]$. We can simulate these returns by using the cumulative product function."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"price = 100*(history/100+1).cumprod() # normalized price with a starting asset base of $100.\n",
"plot(price) # cumulative sum\n",
"title('normalized price')\n",
"xlabel('day number') \n",
"ylabel('price [$]')\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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kMn65epLbN7U+F9FxEX0qvPjiixpP1qaPMleuXEFYWBj3n7OzMz7//HMUFxcj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\n4syZMzh37hz27t2LQ4cOIS4uDpGRkUhLS0NERAT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"text": [
""
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now employ a monte carlo approach, creating many simultaneous price paths."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"history = randn(1000,5000)\n",
"prices = 100*(history/100+1).cumprod(axis=0) # normalized price along axis\n",
"h = plot(prices[:,:300]) # plot first 300\n",
"xlabel('day number')\n",
"ylabel('price [$]')\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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GprRoYzNVs+nT29m7/N8YS3yOFerOEd7PHqWb8vs+xvDQCJSdw6nvLBvag4fI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cAAAg\nAElEQVTS+J74LDpR5SspLZ6vIPLR2Q/TMJxALhOQSZPQi9SOR+gpNqOK2sK7UeqnO5rH6skBVgPD\neitl+SE6et30RxP8fo2Pj3drRoFPLoe0iYquzQw1HWK0+gyO2WIGG44tuveZlMDCU/bWIvz6EwiA\nAQUjImp/CP7i38HlgyduQ/A7UVCJRqwgZYdqbHGJS0ecvJaUcMnpBX6pr79kp2jKwLVTcJUnwQm3\nwPG8NKKqYO/X5vZbzRmfWccTa8qJGL9PSsgAX24/PoorrHnK96zrxyUPQpsHZV5/T0puescq2Pgu\ndQIvyFsZF7XFry53mOlwDr6oncfadvDFzb/XmhelIOXR8mQAiUGt82AyIdIqN7N84wA2U4xz0Uwu\nT1K0PAECHLcsZ3kwo+DckRQfPOzlVxsLFpTgIlFV9GmVhCyCqhIteoOxYBSwoNoCkDuJNBiihAkk\nY4SeEnifPsqS+ijJwn2YEzk8erqSQbGEFCIyCleey1Cn/+zSQtpqtGU3IQuQkjmbrwdzJhG/wyfx\n6nh51m29/6RMwfIgggDfkkfZPeOgqT1KGoETVVaKTSZGQxqySlaTXO1/Dbs/zFXiAZ6J7eTEyK3v\nUJ76HxPp2+9A5CQIAnfccQef/OQn3+6Q/3L5zne+81/CPZX0nSQy8DP0rnUI4p+ew5nd90lif3Cg\nm1uCuvQ0rDsCfbUI8xSdsqmXMqUVxTRFfiiJTgijCmnkgDYxDRNb0E+vRY7lYkqm6S2wMSeVEZJy\nGTS1IIlBVEQUjCi6SVImLW9hj8coD87hM1jI9VahopLSxwnmzFB1fj0qKpawE13KQP54HTFTkOZW\njaZeGK4keKqZfU29bBjPY+NwHk8nWjBFvVnP1mMppN2ePbgnDDm4I0EOp6q4W7iVDz20CV1SJmGN\n0ud2MGUJkxuWUBHpXPI69rRmhfqVFozCJN6kSJvViY5zWeeNxWV8ASNpRXtvQsICkuYFDZcUcFTR\nyPO2zp2jIjSFJdmB3RzHYk5hERL8NDFfHNhp59f2taQuWHBDsoFiTwqdoDKZo6fCG6dhJM73y36P\nENSxZWwSt3Magy9OXUR7B3MBI4mkxJTPjDGdZFVgCIvqQy/MMalso2+FjvWlexmPpkkYosT0MWI2\n36LxIQhQkj8fOrj/cwgpbawJCKhiktjNv0Ixe5HM4Cs6g66jBb9O5o1SPxYhyZoJK36dSm46wUfH\nx6n21JIT19OZlwlHXNHnwpzU3puYtFMasLNk2sKSGSvmlLTonrS+7jKbeqc5V+giqtcWuRs7WimK\nxBbu0ZZKssH+m6zfWtQoZaqWK+pNriAoyXRJtey2Xka/WkGz0sOwUMQBeR0IAtc3HeSK+mO4TAHa\nJ2qJpQxUG0awixFEI8TaId4GifNanUTaIHKv+DGGhRKOjTZT6pik3VtLdTjMXUeb2DriIi2oDDti\nxNMG5O2DvJZrpd+7iU6pjpXxHpaORyicU+nP16POR1HKiZNUJFYMBrn1xDQb+wJs7AuSF5/mvAMG\nxVKWRQa5ZagdS84MObIPQR/jCrePal0cQQDJCLmWGEf6l5MUZI7KK1EQSAh6XKoG7khKAsPueQ07\n54RjW2CsAiaKwT1JyaiRsz2XkH6LPd+bEyc6VMlR9ySdp1fRMbSVNnU5XTRzxfHtnHHYmfZq3HEt\nSjdLFA1O7VbnyFNn6Bar/4/ony6Ud1QaAAMDA5w+fZqysrKFavBoNPr/DHb7X6E00jEvI3uWMDL5\nOjYlhD5/G4FTXyDS/1MMhbsQpHd/dlVVUVMhZp//MmLHaqRIKXHTcZKNJ4jpXyHp7AJFT7zshYXF\n7005tnQG2V+HI5hdiBY06DhXrDnP5dJvKJcfJVd6gwLpVWxCF1ZdBwA5fitV0zFMQoCqI5+jeLiF\n0sHlOGaLSemj5HqqENXsQZn3FgSNIWbFn38Ce28D52yDmOc5eFRgQNfAz8u2c9ilLdTbpzvw6t0k\nRRGf3srRnFpOGStoGddxc6vmc4du+xnTLR46nccpGWrGFZXYV2anQD5PQGkiqpZhFXsRhSQmMRvA\nX+COEI5mK+5u5W5c8uvMOlUes7QQUJ3Ui16+YXiR6Rnt+0z5TBTlhTk0eAW3ml9ii66fNt9lDObG\nWZYcxytlQl1juXqm7XoQBOZsMqakhavdx2lReqk0TjE+8BFWR57NuodQJGOfG9QkemEOBQMbGjtY\nX/5HxLwpfAEDsaS4SGEU5oYJRfSk0iJFiRyU3TcgTRYRtPl5bamds/kFTLl9GPssyOfWoN+/E9Py\nHqSj2/jx6mESkkqJ38zNV/6S9PmNXK67D2y9CGkDxZP1zFkjbNvwPNv2rSXXv7hLlEERFxSGSjaC\nTgBMSS1pumTcz/HqXG4M3EWu9Skmrz5Bu+s8uVE/tvKMwvBjpUesokDVChljqomak5/mUJ2Fk5f2\nYJ74EqLZxPKwk5/pm1EFEb2Q4tbm10BUcVsC+KI2vCE3E+YwzTYvOoOWXFcCoNssMZ2fx6Nz1xBL\nGcgP6zGlRI7NViGocNfRTDPTar+ZfRUa8usNtYYRKlF9ecwJDhqVPnJSUcSERPV4mmeKViIJKT43\nqGfto9upUI/wrLyd1+QNlCvjWIjSLjUwKeZSK/Tjxse00YqoKEhhPV923MrZZCFLgmNYzdo8Pj5b\nRzymKYYxsYhuqYZl6XPoSVIyl6Cr2ExckuDoBbTyKR3qeAXBuYoFhZFb3MNNh5tpz5/vqqmamB1b\nwkwiU4QVFyVWjeSSM2bjXG4YUU3zwWR2uNOt+lmldlJww3vLm72bvCt6qrKyclFOQxAE+vsv3s7x\nP1v+T9BTobiP+w/+BS3FO7ii6VMXPUZNx5h40sIfUi46VC0UskYMsVEM4hLSzLm+S9TxEVatzobZ\nzc5E8IwHON89RW6uhVdePEtD3kHWeu/BdOAjyP4GInW/JOXMWNC9eUYqZmLICsj5mYrTyU168uJu\n7D+/EyGWCcfEJZEHLqsjJaus1H8eMSXTeGYHSUMUQRGw+vNp2/A0qw/ehjl88X7ab5X++sNUn7/k\novs+/oFJzpRI3Oo5zFr/AH7ZxD7dNQT1dZwpykBAPtvbynTkIwzYzwECxyqTCCq8cY8LnSLwRmWC\nL9wSpDriJSnI3Hi0jDuOm/DaFPorQlzSoS3eRy/7DRGbjzQCh5wNtBBhqXSW+so5hietHPOUEhdl\n4qKOgP/bjDhG6C/sxqvXkRIkfmF6mGZ5gkhM5lj74th1Q6WPb0S/xg26R7m+qIvDqUq+EL3los9e\n6ndzq3eKotQfQczmQLKaEoSiF89PuR1RWuozUNWBMRtD4xnlpDeZybVNUl/hz+rdAFDZvY6q8+t5\nJ5kzJPnhOu3df3i6k3xbNqV6RNQxOXY3y0ZcqMtbEc6suthpsuRYywBF6dOUdl2PwGLPIy2HiS55\nAMU0yYzRxKDdyerJTO1El1jDC7ptWNUwH0g8jQEFj+/DvL6xDXtUx6pDN/F8i+Y5O8NxVk3u5cn8\nFNf05bGmthUuf5GECi/2reHkwAowhblx5dOssGghm8Ssi3sP30JYrykyS0LiK0c1g+XxxgkSosIH\nu7KRTWM5QQYtKcoCRk4UBThToCXXC5VJpkQX7eU2BoozObE9b3QiJ1/gjNjIXp3mlW5ItbIp3crP\nLTfhS7lZaT2CQ9aUvymR5HPL7lj4/aeGXiFebOIx3RqUmMz209m5I9UeYFvyKCX+MB65kI7yfCZH\nF0OdL5S/PVRDXFL4x0sG3vG4ap8Jn8PDFamDCP56iu0HmRUcyLFC7IZuxoV8RBS2/ML7jud5r/Ku\ndRoXa6L0P1W+sXsL0WSAnqljNBVtocy5uNV6dOQxFJUFhQFwQrESVCXeL8+QM/tNnnvFRGSghjXX\nbeO5rn9nqftKfvbDYUQhjXoBadjpkc2cZjMfTZ/FBUQNCgJ6JJL8dkMeO7p8RIUcZGuUvNVxkj0w\nkzCTa08xSwz71/4O3w/+iWeXlnHtmXGc0ST5wRh+l2aJ15zbSMF4dnqrquNyTO9RYRy88gE2vHoH\nCTHOnR+IkZBUevLT/PNTVrb1GMgLmoAEjxVdgqiqPFa0AUUQYZ6zU1DhlR/l8FLjZorig3z5nOYF\nff2aIEOuNLr5oPoja7UQ1JRYyc7+Fo7UTHF5t4/igERBR2ZBXXPwNl664g/8r8bLiEh6WoU5nrZq\ni+IvjVfybE2mfwMcmv+rTXx9SqZzfAtLSp9gLLyKuopOeoay34M/pOertj3U52pJ5EvkQZ6yPMiN\n4b9YOGb7aIy9pUZGHTPc4xD52x4R2wVIxfoKH8X5ERJJkWMdhRgNKURTisC0tvjn2DUFM+pvIpp0\n4LZmYvtWU4I1zZkk+IQLdBfQVA3VnaC8bxVS+uLh0La8IE80ejGocQrU6UUKA8CsJHnq0laW/XYn\nnFkBQNo0gZA0I6bs7KvPJy3CjnOahfJCSzFni5dQKY3xcpGVj726uH5CSlnQ932IWPM9uGNR/PrM\nYptC5HVZg5yGBAtTA3czWFVAf3UF7v5NzNb+mjdWTUJSUxpzFpknbzrIirYy1nhqEDzb8PU10lYz\nSutyDZlJ1MJTwXpmYz6WHFtJ8eENfAX41zWD+Ewp6mczc/OWc4Wk5cUMFSVzNkrm32150ERnboiU\npDIhatDaak+MpE4g35eks9LM3zfo2HRucxZ9yxF5FSfkFlIpHQIKFimD6pqUHQiKSumUVuh0f/mO\nBYTUnSdN3Hw6l7N5YZ5vGUPvlwmknHSEN7FPP3/v82CwwpCerWMFPNowkuXt3XA+H0kVMKckEk4D\nQjpE3qSJOWOK2lkzlw27eGiFdpJ+Z5SPx/eQQwjV7uWQtJqj8kr0ksDnBpfxuxptXr43Mp53l3cN\nT0WjUf7t3/6Nf/7nf+axxx5jfHyclStXIsvvqm/+U+RPCU/FkiGGfO3s7/n1wrZIIsDq8quzj/M8\ny9zR25lE5oSSjXmfQcelYgBRgCbxJQz7fs9rnT/m0FgRbS/nEam/H93MYotdUFQu6Z1Fp6g83HQL\nx6230+/MZ5P3dWJiDeM2lSm9jfKiAN8xX0+jQ6DU5CFHjIEAxk0vU152CNO0DXkyD6/dhMn9G2yx\nFEtO7VqAcr4plqCTVxti1Mxkvo/XauB3GyrpLLOxfFiLrZ5e/xRl9eO8un2Ku5eXMuJSmLVoHlyz\nR2bZuI6d5w0sH5N5cUmCdnsZqiDQMibz/ANONg7ocEUELh0wsNSro3Y6c70dPQau6zAgqQJPLI/x\n6DyUt26miNKgG3fMDmkfNTPZHqOoSrxcUMPW8yZ2ndOzt1zGIQcZS+Rzn7qWd5L66SIsY5dybPQ2\nzk9vwZ+qZ0XxK8z6MwtcKKKnKr8PkzGjBWzEF/Idt0inuDH4MmfkMvzzzaMcqQgVMS3kUlXip6xQ\nyxUcHbudN1KX01V3hkBSR24A0qJKfm6S/ulSfjH4SUr0MWpzTzM+ZUdRoKo0oPXhBtq8W9hrD5IW\nwPkmp6OgMlR3gmiqhjyfGRWVKfc0xriBUVucR5o9SGqaDyWfYk26I+v5h8wVdDmKqevYyqZBkUTJ\nq+hnVpE2ThJu+SGJ4oOcdG7neHkFk3YTDd4Aoqqyd0kBKUlkTl1NXLRwqtxN1VSIWM4A6eqfoZ/U\nxrSUtJDIPQlyDGdc+55JQSKNgFmNs9p0iFrdAK8VfxqfSVPWUZ2JdGA9xlSYhJo7nz8QEZI2ZqoP\nsvmwBpE2BW1UDpcwVjXMjNsHc26YLMYzWsuOY0uR5/N/S6eszFmnuLHXjahk4M+ioilZ5cvfRXgj\nu5PgmzJnTOGxZqg0ZAUKfUlsUYVqT5xRi4NUcHEbWmXe83LLUxQZNIVvlpPsdS6BOQdLh6MU+JLY\nI2k8bh0IAg/+3oE5KVAc1DFi9uPXqxiTKhEh2xio9pn4eFsp+WGZiC6Nxxpn25CLj7aXUBTWnm/P\nSi8PrTPQl2fhF48Xs23YxfIpG46ETNw4w6hVm/8GkpSrHg5I6zguzxsLIhx2Zcb/f1lO4wMf+ACB\nQIA777yTdevWsXfvXn73u99x6623vtPP/tPkT1EaPz9yN3849d2sbeP+89TkrcFlKiMWS3L/jw9T\n7rsGUVDoUY10qyb0M800Dv8ZSu5hokhMJ3NYKvtB0KpfO1sshHq/hoCEfiZD455wHyfHshsxVMuS\nsRgN3iBzJh3HqnNBEIinqujjFgS5F6PgRUBl2GNjm+48tbkjiyggjHIYOapH6G7CahgjkP86zSeu\nxRxdXBgoQpbCiMkiP99SS0Ins7r+EQqv+zEdJa3EbX7KK33cmbydqE67oCOZZpcnDzEqsm5Ym6il\nfonrOgzsbo6TkOH5BzR20fyQRL1Xxpi+OF+FpGrb798cYcOAjq/N7mcudNVCL+iQKYcCfwxHLDuf\ns3ZYR/OEjvopGXMC/rGigleVTF2LIaVj2YyTwkAB06YA4vyCsnGkHr2i483ofCBeQFwoYteyFyjK\njTDq1YwA74wZkyHFKe9SXh9cRkthP1vkXtZKw1wZ7mBkwsby4BCvubUaiJQgcqv9NNWlAfJcsYVv\n89TgR/EvuQ8EgYgRonroKRPI6wlT3zvJZFxH1NhCS+E+SvKDVBYHsFuTjPqr+GXrT+mbvRSddxuT\n1QeZyUkhRoqxpjRLNpzfwXM7T3Ou+TgJdxutKzt4xWlCSetYFhujOTkC0vwCmNYT6/8ixaNrqfLZ\nMXiXIYfL0c1oFXbJ3BOkc3oJinm8mDff0kAQOFdox1PswWp9gTn1zRCWREoSiRTvp9r8U7CF0X/o\nAPFjm5DTEmEhF9GRqXJ+I7eWYVsOa0K9HHJsp039TpYRI6cUbjkxzNauFAlZpHflk+jmliHGCgmV\n72G4fJQV7Y2Z49MifSs6ME+4iasGdgy6qfZnvAqDItI8mbegMIbrDuCY1QhlVLcXYcsB0ge3IioS\nE7YU1oRIyOZFn7BiTelpLdDmbkwnIGdYSABwBTIbPrX2KWZjNqIxmdQ8dL3Z0sqm126naPMxbEe2\n02HNRe9X0aU1w8caU4gaRNYFA+xscxOV0nx/0wB+PcDF58j6cQdlQc1DrfdZuHTYyd4mWDWqXfPO\n2/280BImJmqhUGM6yrIJmDArPNngxZVzkEGhFAQBv2CjUhnled3Fu1zWzprZdOuVF933H5V3dRc6\nOzvp6spgwrdv305T0+Kwzn9naR15HtB6Vl/W5sI97qS/wMC9fIgG8ZN4jjQjCQpyWYpkyELh7lso\nW99BEIneGQP6iQIonKVLUvjXZCG7TH5mi6y06e28ddnOtz2AQ3ydref9pNOvYun5BqDnQJMRBAUB\nBad4HJvQg1XIJoQZ9tgY9tgw6FOI1kYKXAFyjB5yTBNQp7nu+WMO8sc+vegZR5xmFEGlYjY7vKBr\nPMPWst20T13PsoLdiCI01c1yPFHDV5OXolxQvSwm7dhml2BW4kAmZ1UYlPiHp62MOrPj+I7428AW\n5yVoSXBb6UH0uQ72DH4ta7BFDDKPr6ugcipE0VyUY9VuvvhKNlvcpX1m/mVHlOKgk4gcp252lrrp\nVaiitpBUjc2RMhWjSDKGWFSDr1wgvTMb+UXr/Uz438Cls9NofBKAswMujgWXYBWj7D+hFfOtb+qn\ntV8LXRiVFN8+/we+X3sDfZZCHpPXYhLjjCUCNIRSCEMfZ7bh/oXrfOLABO2lZibcDibsepZ4otyc\neo6vSKXcBkgCkDCAIc6e7i2kVe09CmkzjtYfoEhhhoofoyjsQU4aSBpiXHLGTeFoA2HrLCvHGqg0\nmrCnUtRP1wLb8Ja18vVdcG1rGTfOzidGg9m1KIoc5li5H9FeQiCZobp1pQYoVU6xLPUInWI+l8wc\n4gXb3zEnlVGUbGdVRGvqpa+FwVAT3pYuNpxYgWuikW7T5ynK/REI8GDVVsbMTgor55gw5pAbbmfb\nQDPX9LZSM6xHTup5kyKqdtLLAftxrMqlhMRy5GAZ/dX9fOubP+aa57ey7mQLTedqaTpXiz+3nzea\npmgKapDcjtwgzdPZoBC/Lcij13bzlR9qQRe/JUlQMfHMnY9Sfa6Rb6+sRkeK29rX8fFD/ZQGdPxF\nVyHBa56mtKKHx9t2YDeGEFE57cmEeBtMMxTd81dsbD7Ob5wZhSUJKcYNMjUP3YU9LbM+OcOBch/u\nmMiMUXvI5f0RanxmEqJCe352geKbYo2LhAza8WLZHzhc6WbD4RuIl76IFCmiL7eW998xR6NX5lRp\nClk1cu+p39IyT3QZWClzWL+OmOCiLjmIS/HzR/2VBAUrv9S/b+E6myfqOFSo1XflxXXkG3MX38yf\nKO+qNFatWsXhw4e55BLNTT1y5MgCeeH/BAnH51DneZjqe/NR1Ummi2YJOK1c/cIWJoueYbLhQXaJ\nhcRVgfZDV7L2bCOfONvIUO4ce4uGKDL6qe+bIC6L/GFNHo/hhmWgm8pOMtbFX2V1ZA9hg0RUkonM\nXYUzqWe8yIOx+H5aVJmYWoxVfGf2sHhChtleXvbeTUit49q+TuoG0iiCsmBZXyjHqtxMrOvjkuLH\nUR+5FmEyU98grjnMqop+VlVo7KsB1cAPz9/Msxd0RayeKaDf7cVnChOXkngcAs+0uEmLApv7guSF\n4qwf1rN+eNGl31EmCmWOnvurrG3JlIdVxS9yduZW2p2zHCuJYU4aaJ4U2dtYwPZzXs4W2qn3BigK\nqNxxagMJOZOcvfDxTfpmjMlXmQylCatxrMbLkERtcVHVBIKgxx8rwqC/jqigZ0ARsDOMXThPsT6A\n84KEQmtXpqPk+pYJhvU67kgc5afJzfw+laGJ0Nt/B1U/B70WonGO2DEEE+SGtEXCb85Mqdsij/OZ\nwQ9y38+1YrC2pd34ijYhS2BMDSKIDpYNBVnbHyZiWo6oLsUesqGiZFGRAGQTVUDByCou7/Bw46m3\n0BkDJ9f9kU7jKqr1r/C1Zddiie3iir4WBGBD/O85WGThmoGDGJQ0+ZEQFjXAzYHPERMcmNQM75dg\nNOLpiBAvOkjAVoU96KBhoIT21NfQxS3k1EUYM6eYMGrhqGlLkD82HearL7gX3ZMzDHf84sMUz4TY\nvXyKfr6EknOE/Og4dSPZyXfHdDUtHTU4A/Ph0unFdPYhwczh4PvoLAmzdMzCD5odDISupyb3dQYv\n8ZBOVpMfdpAUzXQW5LF2cJaSWSvKa5cSvrObRyoaeTnvByiqsKA0Jp06tnS2oKAycgEh4jLLcSJp\nK+35QewJmccbx5ieR0pd1VtAfljPPeu1PF+fM8rPl49lhcI+f6Kc3bWTDObEkFAoDuoZtyWonCrC\nlHuI4NoL6nesd5A2w+4WbTyu8A0vKAwAQUyxM5VpS2FSF7PXqqJEW1U9YmwcRQ2zr9HM711x7lh0\n5J8m76o0Tpw4waZNmygrK0MQBIaHh2loaKClpQVBEGi7gPfkv6N4Ar1YSFMtr2DDESc9LVoCsNQX\n4sDW/aw5D8sHQM4/z0nVjnsmk8uomM7hfSGJkMmHPVhC2jbEyuEQ/W4jxvN/SUjJuNabJl+iQXcf\nIgrWuMKIsZjSqUoApstOcNZayMOll+JOBPnC4AhmJYPIWdvsJRKV6ezLnmyK7VnEyDLKB4t4ubGU\n7We9C72dA3Yv9kABn7klSG1gCXcvnS/d+dy9qH01MFoOuVNZ9NcAHeliXs6vwB7TEdbFSIsqzd4y\nRl3j1KrTNLb8DT2DH6C3WAtvLPHGyQu9M63y+dpBntzUxZ2PX01PXoL7Nkf51ovF7K7NruGQhVFm\ni89QYTnA+ug5/pduHafm6Zv7nBPUNLRyT/lfgCDgPJygMBAjPxBj1LUYMvqmxMQdOHXPMZuAWKIL\nk2E5ieQg8VQPVuMOJNGMOE+YNZfauUBZ3aD7ewzC9KLzdZULrHotTWFaZbzwY9BwPmv/kcQ2Gszt\nONGURO5gBXp9F46IFlKYzZc5Xmll7WCI1WN+1h3LIKmWdTbwSK2HrbPH2NkeR1AFdH5tDOmDGRTV\nWxXG28ltR4suuv2sex3TyuWohgkSoo6rh5YiIOM3RPhiyzZUQcWcSnDH0BsLnezSgpilMEQrnA+a\niJvDvOJeyrENEl+db2XeMqIpiX/cncO1n8x+h/Jb6I0euiTCxn49TV6ZsvnCzBtPT/P0CgMT8dVM\nGzbwQnM7lx83kBfMjLPSWW2gK8C400TBXJQLaaf2NMUZcSr83S4dl3c78ebYOCckOBfLjDnbfPh2\n1Glm7aD2HcTRcnp8NcwZRb4fuIa/GRjjptpjfJPL0GGgcVqmrdrDiCMMaTdlhn5cumnG42Wczw/R\nlp9pKuaMylT4TegVkYo5I0M5miHxVoXhlmJ8WJrgn5MuPnuiEgSISwpmvUwk9xCooJteg2F8G18P\nPkbapimgV3LX0hjIIJ5+obuZZuU8a9OZvi06UhQrfsZFB0ZdC6JgQBJzEAQRi3EzihJBMUwQ1S0e\n63+qvKvS2LNnz/+1i/1XSToyTNLXSmLmdSzn7+HLOlBVD+112Vw9ay5YD8YmrVTvv4SK3my+eoMi\nYzz1l+iSRlQxwZb091iiz+U1XTWqwU9asnLL2E+oat9JeEkZadsQKjCnN9Po16xAv9PDS3kat9GM\n3sY+9xKuntIqoXNjOVhMY1hMKeZe+xw/ujTCn/VUUaf7AbZQI2Zk7ttRj4pMVK9jV4eHU7VRLjmb\nx6HN/Rwvt1NxdpaBtAuvamODPAQ1fQy5rXxfvYRbkgl2yOcZVx0UC35OpMrZMdBCTiyzECtSiMvV\nfRjNE5xGhPqHuO2R21nSn3vRaOzrtXqcnKd6uIizjf08vaWTzRM9GB0W3OFNfOFgKU/OQ5KNiSRz\nwiBp/QjWVY8hSRIvTzn59BMf4ruCyMddaX69fIaIFKYprWCzPck+tYVZo0phgEVKo2guQq34AH73\nCG3Je7TvLV+DWZgimdhPMj5IXDHzkY5qjtelGXde5AGA7tQ3NOpq4RRx1Y1MGIO3hFQAACAASURB\nVEmIYZmwoKRFJlOXYY/nURSYwmPP1FjMKIUcSeRxpeExpMEa8vKO4vcY8ZgvR1Jb8Qk60v5VmLtr\nIG1EDlVkXfcfn9YB7wy1BEjKCRQ5hiFmp2P1CxSM1TNYd5yIbZYNr96BIZ55J0e2/xqrP4+q7vWc\naJpmUtFIGwelq1k9nsY033nwWPlp1HnCu5cKlnLHUMZi9ZotKCUyJaUy8YCBXNcoI912nitYzhFn\nA+TFSYjwzRczRlVuSOHKsTDbTlTQWaRwbM1J9NOVC/sHXCkeWROjzCfQ5M1eam44PUZMFvnJ9nom\ndC08uTLJzSeHcYez4c0Pbypjxmpl2cgsO7syC+hv5hF5tb5qAjYbjTPQWTCKJWFkw0gdE9Y57GqI\no8U97K73c7xE4f0njTR7ZIofX8/7l/n5/Esb+PWSSfqdUVYRASJ46o4TKOyh36/F/8vGGxhsDOMJ\naKE/Q0okL6KncTaHmDXI6WXHKBip4HrT/aTDZvr0hXRI9SiI1CkT2K59AZ75BGLbMu6SVAzzxamG\ntAiJSrrD21nZcwlyQvOmLGc/TWD1N0FKsnM60772ZXkTs6KTA+J6RCRWp7Xc0ln9FYTMt2NTE4hi\nNluCKOgRJT2OeIANQ//3wlPvieX2v5O8W51GV1cXrY/dzZbCV9DlQiRh4NRILQnfHPPzhaAJbG9B\nFprCDjbs/cjC//uv/gkFow14Krowhu1s2PthItY5ksV7OFNYySVvrEefkvjKzR6+tTsPS0ImbZwk\nUfA6I8Ue/LKLtQdvJ2LxsW/n7/nb+lsQVK2Qqj7s4f6Tv+Gwu5Km+iSl7jGe7/5Lvpev56ruOr6y\nZ5qHdhQRF7MbEL0p5liMT275IAkB7jn050TVFPtW24kIej6VbiN5/naiSRcxKYnXNo0rneSF8lFS\nkoI9qXDt2cXgu3D9j0nlZBolFXny+NRDGsWEAtx/WR3N434aPT4e26wjWNxKrGA/q2UfneEc1p64\nhCFRwGb34Yl9lDRGrLEkN50c4eHLXsW/MpNAXXG6kZt273zbbzjgiFPl15KdaQHay2Ypn3Lgimph\njJn8QdrW72Y6vZGR9IcWfmcRelHQUx88SqflOlKC8aLnfzsR0hFSQhpJtOEOB5kxm1EFkT11p/GZ\nwujSEsl5KvBdIw7cs024IinWDMxystKFUPA4pTNJduzfsOjcM8YE7lh2TkgV4wiKgVPlEs3B06DK\n9DW24jx7IwXzBXnBFd+jN0/HnDHjicyQx/t2ay1rT6x+gzN5K6jW/Yyp9FZG0xen/EkZhkimi4jJ\nCSRF4tnGk3yp+0V2TnZxzlbIRIuTS8Ugv22/lwnrHHurOxadwxKHH/3BhmAfpbG3DF1KR1yXxJDU\nvKx/+NJP+dSD7ycnaKW79hyHV56iIjZNucdOzYk7OJ+XorsozHVtmXH9em0u1VMhciLJhYLCN+Xl\npgLayzREk4JC43iAXV0eHtgU5lfrY6wZq6Z+JlOfsa+yk13dbrb2qOxvzCchS/Q4x+l39mNN5nF5\nt5mb+k9ydNlh5lJucnwFnDQtRky9KcY0fO2NGgQEDpTO8nrpHJ9pLcOR0KEI8HTtFKcL/ciKwN1n\nJaScIyRz30KHrgpY2r6EFM8s2s/UTlLpN7Fs6uJdJM8Vhji15jmunjy1YLQ9rruKYbEEAQM203ZE\nBJzpIXxSBaqQCe9VBs/ik6oZcYaxx7Of7Z9++HYtHP9j8v8GN/ufKPfeey9QiTjSzH55PQ7Jx0rb\n0YWX31sM+mApxb4EwZwpXN5ajq7q5aYnM6iDs8tfQZHSeMo1AEDMEmC4tpWn1o4ipB188IWlTJvh\nox+e4qqzBiwJ7TVKsXxMQzeh0x+lJKZZZNMGG53CjejSEjv7GhFVPc/XC3y59vNsGDGzy/pDBoYu\n5fVIM42Tfr75/BSnyp2LFMas2Ut73gybhhuIGI10+TYTT44TS6qMu41EBD3OqIVXIrsYaDjHrt5l\nSIpIxZwWwqicS9DrmmBL38Whq2KsEDjL5tdXcWhTK56iKXbf9ALXPHklKVFESXk4XpPP3mt/gr3z\nmxhGKzCM3kR3/Y/4mL6Nn4nLUVGYCtnRy0bSSoANnefIC9m4rLcYb0Ll2No2FFGlYmQxxfSF8qbC\nAI1eacVw9uA3RmwkVCf2OZVl4S6cc26OVrsJ6zWU1RnrW8Ji+EmReZ+xxHmM+sX0bapkXihtm7HY\nkAwdJKMNXNZTSUQdwpyUmHRZOVYxgVfOoSA5y58f0tz+lrE54OK5vmerp7CqYS4bqAQg6TpDwnWa\nxMgHccZh5XCa7iVByqMT1LZfihzOeBGG8e1UCPuYK5FASDOeuo6tR5YQlUL050R5NedqdGoRPUkz\nIfXiXd0A0v4jNJn78ce3MKtu4rYzS/nBcri39gpSEhSEFWY6VqGaVF6r6sCYAFWA+DxKdMNwHXl5\nT/LYxzqRBIUv/uRmXDNFCwoD4Gs/yLAbWcQxdpwppLdhmuGiAMPX/YiIqMMRE6EtUxezqTc7bBI0\nithiWj7hXFHmm4mIHKvS8+0rZkAAQ0rOUhgAn369hKs6PKiohJ299Oe6aQw+gWkGTotfJWLW0bbk\nt5wMbdZ+8C7EDhtHXAtosC2jLraMZsahqMLOoQLOu4LIqoB1tpJ0xAAIKIYZ0tZhhJQVIWleoCoB\naCvNoa0kzJQleFGlcag6wV03x4GdVHryWSq9SKdYy7L+Fm6bdnCk2syrjaPkxiqYlRd7rDe9AQL9\nzJoUvnHdGHVzS1EFEUW+eGL+T5H/T3kaqWScz37uC5A/DnEjOHysDQ1imc8f9BWDONbIh/ZcBkte\nIrnpEPEX12IauQHTPKXC3NL76S1KMmWWMKoZy6fTWsIvSzUMuD2eZutAmt2Neh74nZ3Vo2/PTfVi\nUy6dZdnJymfrTxIwRvncfjMfGZrjwSVbiBg0xbNqcIbWSi23sXnwFLawib/fKdOdOwECbB5qpNyv\nWS1D9idxTOfTU+5k2BVgV+9ybAkT7fnDtBcO0+wtZJn37WnY40UvIUaL0M21oBqH2DZ0gpWnl3By\nZSe7r90HwK0n6sifcvHjIgWWtSJFyrB2ZTOhqroJhGRh1rZoopNK70RWpe7xdYfprevk8j03kzvj\nJFj/K0LRjRSN1KGg8mT9JKVBA+s9716c+IuN1dxwZhTXBeGMx9aUM+q24ArFWT04y/FqN1XWvwLV\nyCn1n1BVlXjyHPFULyZ9C3q5EgBrNEnI9N75xUK6GOWTXXz02NuvOglRQT8fijhaPMv6cRfxwn3E\ny15ESNixnfnr93w9AK9zlo4GH9uOViKqGcvy4eYZRvOLMOgyTMKptIcq42OMJDWSTLvQQaH4KyyS\nVmNyNvkNVnROsXFE83z63KkFmPa3rgpxpDLBEz/LISbDzZ+YIz/k4J4nzYTyzjGZP02p10RNT6Yf\nysVERQUxTv/6BxnO1RbNlAgBMxwtzaPy8PV85lB2OEURVD56h4dPdg0QUFZz1r1y/l2m0M83HRu0\nD3OkfJia2ULWjmtj26Ke5aoTZspntSK/c8v24qnIUOgrqoCKgC/aQkdiscGy0f4qkpDmRHATUUVT\n2C2TVt7XXbjo2AslqhMZdIoEdDHWj2Xb32nHMGKwAOGCepLjlS4O1udzfesIxmSKUr+W++jLifDr\n5nGiNpG9zRlFWT8pcfsxLydzJRojGynzp7nrJi2m/rcv2MmNFtEyNsfBunzOFTswJlJ85rWerPs4\n3Bzg9JZTTLg6eeAD71xZ/l7lXes0/rvJW+s00kqKBw99mv2d9zJ1rpO+kqdpinjJNY3hK5+hxJdG\nN7/2DxRBzvGtrPTmMF58gh8vlxHGl7BkVKPRjJW+yL8s/QIe5QYer3RySUBLOAUlI/9esWu+GhoK\nAjJff8HF7SeNNE5pg+Xz7wswkBtj3VB2SOSVpSUk38KoOWGdI2CMcqwySSRVTlKfSYB7crSJlBLS\n3LtxGK8tSmtpcAHqrTdNUDJTCcC43UZZvJmSUB5NU6UY5iuJFUFh0DnFiolqzMmLtzwbWvVtZGcr\nFnUIYWYrQsrBtUdEZBWKJ/IZahpkzhImWTxOZywXf3MnOt8qTIO3IaSzJ7vwlkJIRQwQjbXjMyZY\nOWvEOG+NWsJG0vEG6gdziesT/OK2Q3gIc7BQpHNdN+dtUXqsCh5rnJis0JcToSJgIi2o3HPXL1jW\n3oh+/lwrR3yLwhlLx/0kLSPsaItRNhdh5bCPqt61VPYvBTHJkMlL/fgE0+YEcd0kLt0hPr/HxOqh\nWS7pm+aSvmlssSR9+RcPG6jpAIJoIC+k8LHDGcvtjcooZXPaff12fSV7lphJJ4ep8mtKpXQ+yS2H\nKnmyJYV7aAU5gYsnsQFmHR4eXt1GnS8PQ0I7rzVmonrUtShJLstOhvPMqPOosWRqkjm1k1lDnFLF\niySkKJGewCxlEvJ50gFqJm1YA7kIiLiimXNu69UjqrBmVI85KbCr28XHD6dxxNLkzTipHC7BNZvP\nu4mAgKDK2Gcq8ZZ24XHDyQYBr0tAJ0eYqjhPv9KAPSZw+0fn6Nj5GH+zoYw5owFD5GrmjBl036GK\nc1TO5VHsi/BXL09xWZ8TW6qYkFGHTTzFHXsV3GHNO/HneOhqfgNJ0P5XVTgW3Ep/bAmT6cXftVg/\nRL5+AlFQKU8GiVjT6AUTv1pn54qzRiwJgfEcE/ZYCoD9DfnsXVLA8hEf+rRKXlihNJh5f36jwqdu\nC9DhsrC115RVt1IyF8WYSLNkIsBvlwwQ1hs51FTLiTI9McY51GTLYt+dsajIKSuGpJGEvZGDVX5G\nc7T82v66OMtHYqwYEznYkE9cJ3F1+glyBvN4eccb/PqDz9DefJ6aVS9y7YSCpaeWhis/+K7f7b3I\n/3hPY3D6DM+8spMbJR//FKmkfixB3jwIZCQPSqe09barAia9S2GinE+3FvHUrbupHc5lx6s7EBCI\nF+7nfPUM91V8nPaCIQqSY3x2+BXarGU8XKo14ymOzWJMp/jOE3UseUtib92XZlAE+O2vHNTPK5Jf\nbaxixqYpkYA+gj2hLbZ+g5/nGjSFtKu3hdyIA30qReKCKvvn61qZM2XTI2yenGB50evsG7+L5d7s\nBOs7Sdw0gSGasZpyrX9HX5OWVCwZK8Dc9WUmHdrC5gzFufHUKD/fUk68YB/x8qcQI0XYOrLJzs7m\nDtM4m4egZFvbSXsX0eqHkaLFGAdvoyq+n/e9uNgqPba6neeu3r/4XserMJzXko6qAKKi/aV0kEo5\nyJ8/fNOi3wy7ZMpnU+/6HgbtESoD2jf4l7t+zmUH1rGmVbu34boTlPdkgK3jOSYO1+QylKspxOtO\nDlE1E2bSpqc4kClI/PFlxRwrn6FiRsGZrFmgkrihdYSaqQzS5r2I1+ElIFr4Y/0kG5VWivHyhvpp\nXFE313RmkvHnC2wcr3JzzZkxOkocC0WjF8reqg4qpwbZEhkmT16cn7hQzEEnTad2YfPno6IStfgJ\n2aZRpDR5E9VvS2uiVPQiDmU82Z98+mdsPLQpq2AP4NimZ9izdYi0lLnHtd1JAolc7qnLZmW4vHcZ\neRE7gprGrkzwammEuKWD0piPf/3ZBkKOKcwhJ1JaR2ulGcm1m+bTW5EUGZ97hN1Nw/SRT5P5DPl6\nD+G0lePB7GZa1/gnMU3vIJ33HCbnG/hSy5GmdjJsL2PIlYeCioiANZpETqcYdios86hMWwyETDrS\nuikuP5NixUgGsh3SK7zQlOCpZTG6CzRj5rMHzPz7lgirRmQeeNS+iL3hTc/4TMEQnQUjC9ubBiMM\nFpqIGLXjV4wWoFf0HCsf4a3SMm6mZXoV5niKT5zdz2+vPkh/yRS13ghXdAWxlSfRH/kE4kAthW+J\nEPyp8j9aaUz2H+Pe12/kqrkIfR47o3lQfZEeLikJ1ozOck6oZI9xE0YxzAa71oPbGLGxdt+tHFrn\n4ZDrck61PEKxNIzFk8cVU53cW3YDo2YLCHDH6AHKujdzY6sWbvLmTTLnDDBZ9RpdOTn8tHw7ORGB\n2/sDBNJXLkxk19L7uNXxIg/NbCXVfTcAOturPFHs4Jrzq5AUgRcbD9A40YQjbuZoSS8zluwY5LXj\nA0heHam4hTM1NrZ4LlvYl5Ci6NMXD5XMmmfYpPwtRkVlXNiILT2FTewhZIIJSwGX7V/PucIcemyL\nk7cA/pavYu/6VpZ3IeEjGN9Hd6Gb9ZEowVANKf0YqTWPzX8kaDhbjTvmQy/MIqYltj7/mYXf91YP\n87vbniP1Vnzmm+ItgqQOSoYJn92EZXLeQmxox5mET//22oVY+lDRJN/bFeXBX2WU6LQ1iansIdRg\nDeF4OQVTjRe7yoIoAvxkRwkfbX0V62z2sWeL7LiDcfIvAjt+aEsNAdPFiQsBvvjSWXzmELlhK3Fn\nBwZfRnkGrWFaV3YRMkfwm/3EhiuRbYVYBRm7MsGa6COIpOkXy3jauJ1ISYrSmTR/PnKQB0t/AqqK\nOxRfMEreKtOmAKOOWVZNFLJcr/VnEWc2UuKLMlbZjiIvVrKmoBtFShB/S+c8c9CJea6Mc1U+wg4v\nVzzxIQZtSQarj3DjWAjDyJWcXrePp3cMYozp2fnqRgYrx6gYKmTdSa2J+Xe+/u8oooo7mKRiIo3b\nL1IUDtJvKuCvl2mkkUUBJ9sGNYTj1vAPqUvsI6AzMGGxYp+uYKxEM3QKZ/SUpLRQS0BvoN/hRExa\nSBpiHJzbSXq+inuL9RUOhDKAiwZdD4XmXqZDH2dMv4rVwSdYkX4YgN/k/IiYUE5aP4OUyIa+q6gU\nGH+DN/YhQGV45XepOvHX3PVKpt7qSzcG2F/39o24v7fbyhXnNK8/JQo8sqGStuIInfkjTF8w11cO\npCn2BtClJQ4tdzBtzV6et/TqsKWW8lxjJuH+Z53rWDsY5vKuCWL6BB3LT1EvaIWsaQQkVAyjV1Hx\nSjZL858q/6PDU797+CYaLeNM9TiQVcgJaV5FQDIQlE0LtRAjaiHfb9qF6HMgiynW2w8unC+lS3Cg\nJMxZeT0J9RA1pm6uP9jEFa2FEHdgn67kX56y0xjrZ7q+ja2tDeQEbDxy/UH2XLuX9uZeTIkU5aEQ\nCVsMi8GHIb4EKa5Z9kLxS1TlP0+rYmHUEEQ3swYxZUVJVNMwU4yIwIw5RHv+JCM5M/S4J1D0flZ0\nx2kciWKKKzjCadwpD+qclsvICSU5WRWj0l9AxNFGtyNCYUgb6CkhvUDVMepoY1v8HvxOBY8bRipG\niNhmKZgFQwpckTAvXdrDsMuj3ZeweAEUxxuQBe26aWWOUHQf0eQg/5u89wyP47zyfH+VOncDaIRu\nZIAASIJgzjmLVLSClaNlS9Z4xtdpPNKsPbNre3ck2RM8lpNs2ZKjspUsyRIlkaKYSTATBAiCyDk0\nGujcXeF+KIjNJkBJ3ntn76Pnnk9AdYW33qp6T/qf/9ENkZxQgmhcQ9WHsRk6al8VeAdwqDpzevuZ\nOdaNO5kgaLOwy1LMvMEs9te28adbX0cXP8JWcYXBY1I+WLw9JhdRwgYjPuKjBRys6UKzxKkYzsER\ns1K//m3cAwUUB11sr4nx0tZtLBk/SYMxl5mdUzSsvkh+unE6SdnOkDxMxXgSOWU5bxXmhxM4k5OV\nmw7snDk55n37vjZOlpo43wNV+cR9DXgLfsh701R+NtvH9AGBU0UjvH7zn2ma2cqAy0uy/xvEHbOJ\nyhUEpTIG5FmogoUS9Rg5xjhJZR2J5DXozGHM6qBYf51eYToJ2wXhFsNAJo4+wW/kUK10eoZY3Oli\n0wE/tpiHuobZ5A1WUtwxm848EWy9GWNXrTE0JRPyCpCyxolmDeDQx8mOafzrChfvV4qcdfkY0CWO\nV7ZRv96MpauyRvP0dgYLAsiqwuzTNQCUtfupGunDH4ogalZKQ+N44wmK46Pc0bmfGeNB7ut4C7s+\nxrAti40hs+LeqmvkxmO4xD5GbXayEnHKYmnL0Kpp+KNhuj1mS9XOeBXGxPvfkUwniq9tLmDd2Qpi\nVh2X3E5lah9V2nbkid6zTZZrSYhuxAuMo1jBLsRoKSIiEXUeAgJxS4htuU4a8/vpyVb58doIcVsF\nzy/4aAbZ7TOS3HnITmdxG6npT9DlnMEzs7qJWjLnuyR/Fz41TDySzeo2G4cuyHXbkvDkH7PpystH\nxE6Pxww5JmSVm47H8EZ0ZE0iXLkNlz7CK0Xz+fLCu/htxSpmsJO5l0/dCO6vlU+lp6HrOtu2vU3b\nuXvoxjqpUfvFMpz0cVBfzIbRfhy+oxiijqjKWONOYk5zcQqpHkbVXLbWr8E/OjXUNSWpKJoZQvrX\nrz1J2B2lREhQ1HEdZ/onw9liZS+S9O/I2GZvuRdLILO+96y3j0MlptVS2xFlxtA4KXXqXAQ5w+Qx\nQl4yisvQ+e7czWBA7VAxoiHSktvPrMESEmon5X3D3NsKgYI4f77qfQRd4Gs/uYuELczppX86f8pT\nkQV4knYC9s+iYaDqI1jk0ozLRhOHSWm9F48GAKsQI2GkPZ05liNsCWV2bnvMcg8pQYalu8ERQRle\nSiovXQkr6QaOhEbIPhnQJ3TWYrRODsfddbKI6qCDdv8wFf1pSGPjjFYq2guxJ6b2vnr9gyScvVSe\nm0+7185LSyqY2znK5sZP1mr0YEUbS9srickij28oJyHLRC0J+lyj3LO/jwNVizPaCeRo7Zws2sUH\nBRVsPJYilzkkfe8hSKM4BiZTwgA49AC3jd1LXMjij9m/m/S7YWgIE1BLR0LlumON+IISAgK/XFtN\n2K585D39Yl01gr2NHLEeARUBDQ+NyJIZUssZKiHsGSFlncx6+7x/GYeyzcS7K55klfMNZN0AS4Lb\nDwwSHi/kRLVIe3mS7z78f2Ucm7CFscbTOTDVfY5Y9dMYSrppVL9Sij81ORSjwyXLHkdsdsSUyHPS\nZ4gITjxGiAgO1qn7ma63EQmv5S9ru7j1eBNWbfKSd8J6HQcd957/f3zBQxhKmF2xa7ji1BZ0waAx\nv5uYnORc7kcriE1DnZywlRNyJLi25xhBi53382eyaqSFL53bQW7SvNdfV6zmzcK5jFrM5Pt8ZS9F\normY2U7PYkd+HX96Kp/fr+5jWWIbc45fhjVcwutzszhcJnKwsJWBbDN3c3ViOw88t56e/BGmO35D\nULFzw8ovnx9TTjLCyQd+/JHj/qTyqVQaT7/4bRzDv+NIoAZXdBBfPIpNldAsk3sRa4bEnrFN3Hmy\nlKqgaUUEvT1kB9KJtqZ579FXdhp3sIDFuz6+te1A/giDf/sTqsQ4o6HpPHfyB5P2McQY4wu+nSaW\nmxBpbDquM5kav77oHM15feSOpVgaOY7gHsfoLUW0RyHohejER2aLwrJdLGk0cCYNnilcwZGsyoxz\neSIq405z4RV1g02Hg2xqy+Ht2SmiVoU1zfDisgQuIUiONsqBnGqSkrn/+qNjOBI62XktBKxz8I6a\nrr2mBwnHd4EtgpychiRlIemniWpTI7YFQ+dvkk9jI0GP4KdfzGO+dpoe20x2LBpmVMnHfeJ76PYe\nkkWvsuScyvLA+wC8Vr2M1nwHmr0NFDOE4gnYGT+5yez/eYEUhaw8cKz04st/pExFxfLuqkY277k0\nXBWgvew0zxfaicsahqixPtHOuoNbMTBY8g8XJJnjYfxhB3N6J9fCqMSRSYeTBCmKcRGoQJciKKqE\n9glrTPqtx/jBa5kGRsgT4NfLVvK1d9K9W3qybBSPmd/HU6unMeqc6PdeeBBDLeSWo242N3ZzrnYv\nrtEiTmavIu5s4qrDLg5URumve5kcY3ziPkRe8i+hPqsSQxAp748zu91ULquGIxzItaCicNnYKIWp\nFFVNKz/yHgwpRmjBv4CY+XwHbS6SskhJeHzK43aGv8BK129R+Ph8FkBCy8cqDWVsa7atZHp8LyoK\n7+XcRke+g6hvD5pjFHfE4EByA31yGaIhTPIKMm8C1naXIlf9FDlUydjADfxL2wOImMtruyOXiujI\npMPGZDu3L/siq1N7qVHbGHEp7JOX06mZuaLqQYlvtTxPRaqVhGAh78B3acvV2DYziRSP8IuN5rvs\n1/u5seUkQauTywZOcyinkp/UbMq4Vve9j066/v+OfCqVxutfKkJUkrRo0ziVmk++GmfmiINw1R6y\n5CAVjSt4oxCGMKGbdUMubm76aPjcySWvU9gxm7zBCv6wOMaeaUn+fruTioBEdGYjntMmSaPqGUN6\n4CfgDvHDlB+54SHUSCZe2i61c13XMfZd/wrHjQnMfVIBVQFHFGvXtUgxP2LSi6FbGNb2Yx8TzA5+\ni/ZB1Ekq7kbJHSEsCQwZhbSm6sgzRtgY38vsnjhhycbDVZ9BFWXu6NnNvFAnWYFCxuxRHlxwFQDz\nWiKUDCeJWQT2zPaQsExtpzljGlW9cVr9Vub3DRLVPRQGUihSEbo1H9F2girHWdq9Q8RPrEDABYKG\nVY5jaDIJ3Yzl5opDjOiTuZAAZmtnKNBHEDDoKvPTHbgDWcxjQ+Q/qE59kLFvXHBjM0K8Oj+XFp+d\nq4+NMJwsYn90MoPnfceKzzOF7ikOMHPEhTeunA8vteREqB6d6B7ojHKmpo1Fx+omnQcgaoszmjNO\nZ2kvKw7OP7991+JmQqMeDhRlJra/0qSQM1zC7V9spcWTWUsi6gLF414kQ2RlVyaR4KVkuPzPiAXb\ncLXelcGajKETVt5CkrKxJ9ILcHnvGR65fIg1LQo/fHky4/HFcrQ0m5QkUhqI8i9bBvCEhlBlL3cf\n9jC7P20AvLywhLZ8N87UKA9sNz2V3y0tYDTHzlxLJpfYU8Vr6bLnct2JNooSATYlDyIAHXIdSQUS\n9hC1R7eQN5Bp3FwsqhKlc9l/kJdMz/HJPB9JSUY0dOb1BRElUzEFcfO6spEBMR+nEeW+5LPI6Jc6\n9SUlJsuczsunIjhGbjzKiaxiHplxJV9vfYvqhq28uLKFZ0suTcm/9UicQT9AJQAAIABJREFUHbMt\nJC0ifvpYZHv//G8bdq5kYfz5TzQOHbOI9bEtJdQnVzOgpw0h0dB5+4P/QJpQPkbKjefot86/3+/U\nRHj8sm6u6jvB7rwaTmRnGlEPNr1Jt93LjvxZHPq7n33Cmflo+VQqjba5/5M3V+zguF7N5a15rOjN\nJiZpPLa0jWsDQdSRGbxQOwAGzBp2ckuTCW9szYoy4EyyovfSdQA6BjfcF6Q7x3wJ17Z18t3cF+g8\neDW9OQZjSw+zwBDZmxBoVXJxn/guhpigeuHXWaMb7Aks43DOaQwlQsFADuGcMaIHN5gKQ9AgdxCG\nJ+CWBT1gSZrx+qHJEMy4Q8W25D0+LGU3DAGGilnf28W7uXPYlj+H6eE+7u/eQc5gKfMPXAfAgC3F\nP18VoHAwnWAL20Q+mOvBECcTg2w4MoYj+ck+Ol/NEQbOTu4Gl6/0s9H4gECskHeUNVMcmZYvpF7k\nHdfDxAU3d43ddcn9UiL0ZVspDSToFIp40XLllPtVBu0UhizsLTFDjd6oQkrSED1BxupO4RJVprWW\n0jqti6g9xmVvLKdoqIQh/xBLJtBT4xaVP9T1MpAVBV8v5ZYgUWecEXcEXZMRxnIxmjPZnS2agEdV\nqXQ10SQvY9DXxXa/aUCURAN0O7womsRNDZl9VkKWKO4JJJ2BQSi7idfL0lZoMZ2s7JiHMlaHQIJo\n0V9IlpjET9mnvogRnce0gbOI9jC6dy+7nJdx694YC8Y6EFLZSPGpFffFEq3+PY6WzPl/dmk5h9f9\nkIKz9yBFi/nGtrS38us1VZRm/XcUIdPyLxkfwxfLVKhjFist2bkgCJSeW0SB67X0j4aIGCnCefoB\nUkoKS8qci/aafcSLt+PQUoQsVtqtPkRBwx/Iozs4lxO5CZJT5N2K9H7yjFEuU/dMeZ89go9iY4CA\n4OEVeQujYjYPnMjBF3JxZNXLDGaPMXeknyw1HYo75/Zy/8IvZJzHomrcfMTJofIUK/qP4U1E6Nf9\nBC0WhJVpJKAtpfN329Oh3PcKatk0aLIt7LHfz89mluE1Glkxco7buw4AMOSUeWTFUo6lzN4uueIA\nS5SdlI3EuPXwYMY4pPFpWAZWII/OJuVuI177SwASoszj09YjYPCmfw4V4VEe/2CApPUYsrWfmb+5\nBPDkr5T/UqXx+c9/njfeeIOCggJOnjQhpoFAgFtuuYWOjg4qKip4/vnnyc42F/FHHnmEJ598EkmS\neOyxx9iyZcvkAQsCfbVmOKgtK3YeCw/w5rRhDly5DVpqIezms2d8GVWXAWuSHy/ppDrgwCUlaLUb\nzBnIYnNHGi2xbUaCb30mTF4wRW1nDE/UnOhVaj0Rx1rapXUYgmmVfchGmso5SrTmV/jVJMOygnoh\ntK67DFpmgS2MVZNIpP7K3uoL9kNWMGPTWN9SdueYMeV5PSG+97aCP1hwHhr5o0UdBCZYOMM2EUU1\nsKoGR2qcjHhkarpjGAZIgKBD6fBHuN2fUKw1R7iqr4GSEZUnPNcS+5DCoLgdJA0608Vny9SjZBlh\nJNHNLLUegEZ5LYOWatZEnwLgcGkeZ3JcSFEbt7U08q68kuOSuWh/KfEHzooVvKusvuR4PK4R7l3w\nNi+OlNMTy4fcISzOMa45GeKdscsY18zx5UUVcuIKZ70XdX+bewicIahfDSkLlJ1DGC3DiUY4dEHo\nSFKhsJtodAZBaxku634q4wN8rmMvv7Jfy9NLp+NK2PDGXORF3ZzN7SNkibMsIFAScRGP1tCZe46T\n+WMZl99ofQVXNB/N1k/FQIKdBTXki304hBhCMoucQBZz+jsQJuoRVBEsfVcgBFeypnkwA9ypObuQ\nIh8fxjuX7+LVhYWMLf0qlr7N2Luu5/rDnVQOmzH4PdV5RHLOovjTvcELImFKw2NTnq/dk42OwLTx\nNFw4LrgRki68Z25CipqFdhey+v5gWRtZrjasYoy2+AxcSZGV3Tlsm2YqVd0ZRog4ERA4XONkVWOc\n+AQKb2NqDwv0RvZU5HCgLAf3oQV48xvpmDlGbW+ULq+VUNNKGPNSFLKypbOQ92YkeXx1jHva92Rw\nccVEhatXfzWjmvtrTe+S1biBbnecssJ3WdRhpbFilEGvwemK9H7TBmNcf9QcbzRHpF31Iesa1ZFB\nRGBPcQk/rV5HP0Vs7T/FQ2f+gibAD2Zv4B3vYqqlU8yJRLBZmrnl0BCeuMYb5dNQYja2DKbbVHyc\npAw72ac/jxQpJVb5ApVvHPz4gz6B/JcqjV27duFyubj77rvPK40HH3yQvLw8HnzwQb7//e8zOjrK\no48+yunTp7n99ts5dOgQPT09bN68mebmZkQxM6RyodKYSkZtOu9WjCBaSvjsCTOfMGrXue7+IF+O\nnqD8ZA5vWNI0DaIBXzlUTk5CISkZbP5ygNL+BLOGSkkaARTDikWuQBAUJNE15TXz1ePYpRe4LHiS\n0z47b1VUgyUB9ijiwdXosamPm0p0JYnTgFjeIPSXQO4gm6T3UA2ZnXWmArQmdUraXPy89Cr+/i8K\nN55Oh0biksYjK9OVn8OVERYf99PuyYRR1gYVlnfk89S8tEWUsBjoiHgIsUA7xQcFNVSOBVgiHOI1\n4WoIp0Mg0pz9aCeXgyWOVH6GUqWVz058KD8v3EA0WIa48j10GZNwq3EeDGZ6U/n6CHekXuEN+yrO\nClXmIl3eBrkXxJ0NKG320NVnhmXuSL6C3zCpJ7plH89JVzNlkxtJRXSNoY+lDQJXYTv6UAFR1TF5\n/4vFGoW8QeipyNxsrSYx/TmTzvXkUqg7CDkB6C3FfaacLyafBeBd6zKOM4fDNU76cy8Ny71QquLd\nBB0KI7qPEqmVaqmB95Ppbms2omyyvQpAWT9M6zfQBPP2RR16cywMWypYftxH9bly8gI5jOW0IFQ9\nhbV3A4agg2Bg6956/pwJ3y6Svv1oQ1v5YFols/g9L6xRKW2pYDD0ELaUxlXHeygfSSeqm/KSnCot\nJs+2g4VaWoEELTY6Pdl4YzFKIpmKREi5OBx/lHjVL1n9wWWENA+PLzST3QVhhS8eL0XRRQ4UBnmz\n+hKMrDNOQmEPGDAeqKRBW8iKhkj68RtAQR/UHb/0JI974OhyxuwKu+em32dPKspPD75KyK4yM2SG\n5H4+bT2F8QCPV27g4aYXkQSN7thMcrUkSpaZsO7Og5YScwDFgzpzuiPUDZn3fqjCxb4qDyWjCdad\nGSMrpqILAr/a5CeGTJ9azjF1GQ82/YUtg6cZtrj43JJ7WeV8gxuO9zFjwPR8UiI8s6iQWNNW1kU+\nYKaeyVwN8LbjaraG3jZD3BeIPDIPx7nbAD49dRrt7e1cc80155XGzJkz2blzJz6fj/7+ftavX09T\nUxOPPPIIoijy0EMPAXD55Zfzne98h+XLM+sHBEGgfsWPKQ6aE3q60MOOWj/XHek6v+1Cafa5+cGW\nIY5NtOn8cfCP1HctZzjiJa4INJXZsaQMpgcl2nNtnPFpXH+kCPsUvC4AiVQLsuQ737cBQI3t4P74\nj9CReMz6ObrzLPTmWajsi+OIaTgTxqWad4GgIZa0oo36eL+6CEPRuWdXkMSMFgY7Z4Ihcn/yaTxG\nlLfrcjhVklZ47pjOxn3lLNh/GeMOnfdmdJEz6OP98nRi9tt7pjHsSPKLBd0Zl7XLcWLqBRbztDNQ\n1kbhCKxoDtJQ4OXqxiFQYqgi/HxdEcnuGZCy0OT38K9HXyOBRGOpwvqW9ALRkWOjubyKpuwoSetF\nuPWkBfZuzNi0MbWX7cpFiVJ/F7hC4OuDPRs5P3mGwSbeZ0xx0Jcso1fOw1PSyljnhTmDj8LYTCHW\nGFQ3gT0KwRzTK7xYBD2jkYc4twNsQXTbMIjpe9x6MoCsGwQUF3vtdQgd1UStIjsWpNF4tx5pYdts\nPwHLZEPiH8+9ygf+CvY6511yuFdYn0PEoLpHp2DYzr55cYwp3i3BgLIuDyNd0/li+JWM109IuXAf\n/ScirkG0mY9NSkDrgnn8PteNHM9djFXq5mvPlky6RqJgP4mKVwAIjm3GGajhpbqVRC0yt41/Hptu\nfo9GIhfP8W8gIHFozbMs2n0zv5rbQ48nDRJZ05nD5o5cOjxmP4pJUtQB0xsnb9+3zgzvfniHdUch\n/6PRTQCdLVs4WZI2KL79lgO70cA/XVHJY0f/yOxx05j6IK+GtcNpao4+h4tedxb6BC/XgVnmdQXD\n4La9IxSG02Cc1+d6OVN4kYESdmNpmk5eMsq4vIo9dc30iEX85OgfqQ31AdBSYKN6MH2eVxbk0kMB\n8WAJck8RK8XDzC44i73TnL9dlV5+6r6L0mSI+0514ZMayDYGQDQ9MFvbDYiJbEr2P/Gx8/JJ5P84\nYeHAwAA+nw8An8/HwID5gHt7ezMURElJCT09U7w8wFeMvdjsGiKQ651PmVLMsXLHlErjvVo/1Xo3\nedaXsAoJ3vKLJPJPEopUcMCSTna2FQFozOyIYhEn0yToRopkqpWE2gypJiQxG0UqIaX1oBlh/tP6\nBboLZNoL7DjiOkubLojxCpCXTGDzdLCjpAZnwEJRIEW2PMyS7P2kQhI/qKolalOYFeqmLH8fq165\njufnNtEuldAjFOIxzrGwI0RDcZoALWQXeXVjFz2FT3N4ehIj7Iaj6fj59WcKsOgiRWEbt/T18U6J\nQsBqhag7U2HUHYU88zn05cJLK7IBnf7CLHzjdpr9Ey/+NPPjmQl4EglEwNeSPk0kV6TDW44yFiHp\nmwLRYkmazYuS6WtPUhgA/WYoxdrtJ3HhcicIvMcGUDH1gs5FCgM+kcLIGwDvIIzkQ90J00zvKTXD\nmlOJIYKvBwZMxJ0eD4G3b9Jub89Je3zCKdOocBhR1h2DgFumdChJiFzWnOvh1dr0uLNSEVakGvFX\nDrBJi7CXSyuN46nlzFf20lIi0FKSXlgShpXjqeUM6WlupVUlb5NdWs/zgXxurh8ijAM3UQwlzO7P\nPEp9fgGrG0oQBJ14VgJfLExBLHK+Z8vK8IsEK96lsdjFuWlXUtZZjDIBBdflEMliM8+idt3OOaWE\n+qokosWOICg8l/3f2Jj6PnHJCkkPiyaoIJfsuhUNg2FHZki0zReAjlzKx+20F7mJKyr/9JaHUXuS\nD1YcJTW9aWLu7Yi2C77zFTuhpwwCeeAam6Qw5JSI+mFDJV0A0SBqOAiXD4JmKo31A+codR9EcgVZ\n1H0rP6nexONHzKK/CxUGQGE0zIjdwe46hYg9/W7edGiIwnDmPUWlKSrpnWGqbE345DBDyQC93XfQ\nXd7DL6cv54eHzYK8DxXGgFvhmWUFaKoNAh6oaUSRxomPq5yK5zLNnSAQd9LVvZjZtig7Fnj50qZc\nJH0+V54W+frI9wGIV740cfFPqdK4UARByMCzT/X7lHLzbEKihCulcjArQr2wnX8RXuAtx2Ya3Tew\nvmkARenklcsP42ipxTK8nGx0lMBCdDlMVjKPAqC55ihxOYUm6CRllfJANvODSxBF88OIygma8ns5\nl9NPSlRZc2ocjwpgoOmjaPpoxrBKBlWUVBzf6OTK0LMVKvXFC0lKCuTBonOn8FiakMaS7K/yMGYx\nF9I5oS6G8lM0rv49FWN+2ilht76ZmcfuptRzin/eV8SLVx3hdG06BFVfG4fRXGicc37btalR5g9W\nE1z270jxJJo/TmDpRIJ0zwb4kJMqK3BJy2zMIWd0olvSFuJQpbkY/nBrCTceGqIskF7WLaqduu52\nfrP2gkSsKplmq6STTwq54Bz9XbXU6uc4LdVM/XwnJBG/NG31JcUZgqgDDJMVlpU7kBtqUcN5UNkC\nRV1pr6/oAqPEEzS9DWcIylrhiKnMYladmANGyyWq4gEY88JIAUK2huEwFYdvLMlA1gUhqPEsGDYN\nI+YfxGWP4Br2w5BZaKiOFfDt1PPsbLwcT1RjfflRFpU1cnqgkryCfpYI73MotR4A0dBYYJzg8sMu\n/m1hBb2Uk0opVMsNeEUzjDOoFZ7f/0LZk9xKldSA5m2gscCFprrwJmRsmoqqO5gzEOUty0ZShoXF\n4m40l0hBLJJxjitPBdFEgZz8XxHzisSTHtwnHiRe8apZW5F08U7pEKetE4ZF7C1EwYMuDfMn/2Lm\nx1pYH2zj3Ow/8Lx7JbOHXHR64iRkUzMJcw5ieAN0InC0v4gFnU5++5yPhy8L8/jqXvKK68E74Tk3\n1SHWNELcCrYLoOzFnRhFnfToFcRTM+nVKiiWO0gaFoZ1PzO0ExQI/XB4OcFFZ9iTvIwPjYsFym5c\nZZ2cVWI0FWVzY9NL2LqhvtzF4o604ReWFFya+V3PHhlk9gfw9LJ8+rKt3LB7nNILiDPb3NnEZAW5\ntYr8cx607CCB2glPXzBoqwlj7QSXpZ9b+37EjGyBPp/K7xeUc9fRdNFZfYXbpF6REki6Qe32SiQ0\nTjhmEreIfCDawCZC0oY9aVASHqXL7UUT4c+zdfoDN/L9ky9Oei/+n8r/J+Gp999/H7/fT19fHxs2\nbKCpqYlHHzUxxP/4j/8ImOGp7373uyxbtixzwILAkfttXL/sy9zYXU9cUnilaAFV4WH+oflNmtyF\nXN5/ClHQ+NdFS/EMXoV1fD5TSUpUUXTQhRCHck+xbDiN+pGFI8QTpzjqK+Rs6UTy2jCwpAwq+xNU\n95rWwMEZLsoGE/inUBRBD2SPQ8wiEC4LUJ9bcZ70sCg2yh8O/ipj/8enrSVc3Yqi6Xz1vV5SyPzY\ncjfGxDH3HyvBYzsLFU8TsigkND9/WpMiLFtg33r4kCOo7ijenB6qkzFsXRqL28O8Ps+b9hga55hW\nsyWO1dvL7ccs2OUO8J7hZxtNS9UTVRm/QGFU9+lce6KXhiIHb11gUX/j7e7za3B7rpU/LTYVRm44\nRd2719Do7WPIo8D8+vPHTOtLsrYlQEdiBp1CISuyjjJsU/BPj/GbvTdN+awAbEac61LvkG2M8RvL\njcQvqmWwlrSQqG6BhBWOLYGYC+Sk6SEVTS4WOy8dlWglXXQZVSjEKZPbqdaSnBWs/Dl5Kx9qmfJU\nB7MPm3HwA7Ve8m1n+ULvO0zvVDmhzKB/VoRkoJKewYlCxNxBmHNBkWPMDgfWTbq8U4nhsMQZipiV\n5DbPCIm59SwYyOeKo5XsdedzdNkHHEzN56ySri9aZXmbv3l2NXdf75wyRPWh1Mn1TDeaWdkw+bfm\naB29SZNKPsdtY6HwJ0pCQfLik73286KLE4i+iaVDgHpPBblqiMqJWoTt0nKOyiYyrVTvpUucgg5/\n7iHwmvt3a5VEelbx7G/TyMbHV0XZXTuCu+AgBdJkz+5C6dVKOZq6NDBi2uA4vkHYNzsTmrzV+gKy\nMNkr9kRV7tw3QNAhUzie4sWCz1AY62VVqD5jvzB2XJhz9WFg9KRczTBeVqlHeV3eQJtUhsXTx2KO\nUz/HIKmkH5ZvQGbgAq9cMAyWnxsn4FQyQlv2uMGXdvYgAHulBeyTJ9PwF1a9y4msCjwhg33OBeiC\nSMIisLX/FC2uAnZ85TcfMYOfXP6PK40HH3yQ3NxcHnroIR599FGCwWBGIvzgwYPnE+EtLS2TvA1B\nEDhzT2YI4unSZfxqWrqYam6wi7ljXfyhfCWKJnFzwxKMv8KpKkydYFPkB+yQFtIgVtPvtWCIcLzK\niS4KyKrBrI4olaFhRMGgvrCQ8v44WdE0bHVRcRMlNW38YnQ9yzvP8Nn+es4583lm+lK2e2ZlNIu/\nUDTB7CHxodRLs9kpp8N2X0n8hjHBhdcYQ8RgwK3watYKQkMT/SHmH4DsTA9ITgqoFvOktpRI3JCg\ncxoM+FkTO8lSLd2y90SRi3cLZrD0dArZ0NmTX8HqaD/rDs0gUfoWhhTnucVFdPvND6VsJM6N9cMM\nuRV+v9J3/jz37u7HGzE/hheUK+ic33t+gfhQvOEUrrjG4o4QlcEE9kXwcsNaGlLpXhfVWhvdYiFJ\nFL6WfCojNr/HOYP9s6zgDVBytoLu6va0F5G0mEyH1sziSl2Vmf7+Flo2vwnAsFbAwrYEb5UtpFMv\n4F7LPh6wmiiaA5qTf47dyKiRDlduOhzEljLn0p7VhxHMmaS8zsucesg1vYG554qorwxg6SuAs1Pk\nTS4SWYfrutzM6TTn1LjxGXZVJfmGfulGOi4hyFbjDaJWiR6tkja1lhAefGI3iy27qOgzcMShw28C\n2nyjwGAVZ0Pp+fYJSW6OP41lioK5Y8JMfAxTaHx061ADeNxyO1Hh0oADMbufEyVeEp4ERVInzeoc\nwkYWVSMazz2Znu+IYnDTF4IUD43QXGrHYQ2c97LCqodj8bWUS820pmoJWz4BwOECKUt2882OVzPC\nipk3YiDqBtceC/Dyojwk3WBjY5DCYJL88GQj8T+rN/O1lncnsGDmO5JCok8ooMwwld6+aW721kzN\nOHGx+M/kQ84I/QXmunL94WGmDccZEbL5jeXGjH0Lq3awsr+bPTUe+rOtGHEbHFxDe4GDdp+VhWcj\nPPvDT0Gdxm233cbOnTsZHh7G5/Pxve99j2uvvZabb76Zzs7OSZDbhx9+mCeffBJZlvnRj37E1q1b\nJ51zKqUB8LNp68lJRQlYnPy5cJ4ZBjIMyqMjBKRiVnTN5Ex+D4POcbzJIPedljhr3TTpPP7ETq6O\n/sf5/w9Kc3nTtZyoTeJ4lZWl1hMsCoY5GytjIFvk71KHeemUWXRWlt3HlukHKckaQk9A/BhggHbB\nN2YAv6xYwwPtu/g46bW7KYqFGMfFE9ZbM36r1trYqO7DQOAJq4mOuCb1LjV6O79fUcCQZzJiZ0zP\noXhQ5vMnj5KQRfqkUmpimRwsF0JbPxS3EeaB0FtYu67AEpiHLuhs27yXfctN0jRnfw4R/yh5oRSV\nw3H+5F3D/zi8HW8qDWM9ZS8hkhehdDzCztoserPSVcyuuMZ9H/SRlEVsKZ12oYSEVcGSVKnUu2hT\nKtEcY9SMBTLGdcZn5/X5meRyHyUjegGHkuvQkMkXe3EJ47Rp0/ExRgA3j9pfY618LuOYX6eK+Lzc\ny5Dh4qrIl8gdS7G88ePZa31GkroNr3IQB3VilK3iGE/Gi0hJKpEjqwiHciGvH39SoH88rWztKZGY\nkjY+NrZ7WddlLmqqYPDF28YZcer0Z6XQLujYNk9tpVRq48aDvez2LyWg1qIlF/JqbT0iGpusrzCo\nFjMwMpsqx3EUUthdvci6xIrXrmCP10ya3pl8GZ8xQo/g41XLZ7g++fJ5JXFWKKfGSL8vXa4sjuUs\nZFHbOEXyYcBcJIcFL09brkU0NLKMcUYlDyCgWELsq8ljwDU1mlAixWXWl5h3uoqbXsr89u+5c4yG\nQlOR2QkTN5zYUwLRjwCmWVMaCUWa8rfVLb3UDQa4JfUX9k9zc7TQi7Mvh0JbO+XDcd4PfobQrDYT\njHHxODWDr72bafCdkqt4W1zPZ1NvUWFMnYsFiFhEfrfSRyLpRnOnvw/3gJNQqAQC+aDJE8AML7KR\nYva01zhW7sQdU7n/g34E4M/yRoqMAY6LsxgV3bB2m+nmxG1wbgayFEUdKktHH4Bf/OIXl56sv0I+\nlcV9Z78hoo8ACjAFsWSbI4/7Fn+Orf2neLD5LUKylS8vuIMuRy7faH4bbSiPftFHhRGl3bIIyWIm\nHjWxg3D4BPcmX8BrpBFB7xXU8oMZl5MSZb5pfZdbLEdp0Px8LnoXf6fspHYwjGaILCttQJrIIiaa\nIdk8eWwXigE0Owv4zuzreOTki1RE04uihsDVq7+KjsFjDb+jJTSPJmlyQ6XpWivNkon0+nri14gY\nBBwyf5mTQ3EwSVwRaSg2EVdf+KCP7NjkAp+YaOV04FZOew3sSQv5Si/dViuWYCEn/Sr2pM6CZDPT\n9TZaQ1u5ocEcx2N3vsdIZRrRcu+ufrxRlXPGMr4/dzE5DEwZU/3xxiIEXUCVyaDLBqjrieCJqSzq\nCGNVJ7+aDUUO3pmVQ11vhBOlkxefK0+MsGtaPiFXeuHdmbiSsDG1dfew7TUuU85wTsulSppM81Cv\nOVkoRhAFODFSQcyu0bRnJm1kcmHV2IOMiTpLhRAno7l0LK0nS4lRJcYok+O40fi9ZobuxISCHso2\nocVjOXDMDMFubcthSU8O/76sPUNx3HGqkOmjadTc7gU2Hl/UQ9NE//N7zh0mFvockjiZfvsvMw4w\nak1RLZ2iIDmKv8+BW41zc9chDuRWUJ9TRPGQgKFNozpSf97r/KXlFkKCmb+arZ5hq5Zp5ASsdo4U\n53CySsDYu4HcZJRRN2iRyVa7DvTnKhyvdpwPz04lFYku6rrDCO4Ale1lpPRl3LfL9BSTksGOmiQx\nxeCHG6L8zW47Nx2zceddY7QUmO+0qBlccWyAw7UO+h3pMJQ/EKffm+kNLh85xzea3yYrFeO0MP18\nzY/FSCKhERPsZn5r8Z5JyMctpwLM6Ukv+E8qNzIqmoavbKRYop0kmyDNSimXJ45gMzLh7pqZjycp\nC/xkkxluXHMizq6AWZyLYbBMO8ZqzVTE4zaJJ9aZcPXLd+nURdMw+R6hkGctV4GSACUJsgrj2ShC\nipRhwWIPkIx5Ea1hfv7YHy8593+NfCqVRu8LEu8fe4DFtc9gj40R3T15vyGlgPxUupKyxZnPsYJ8\nOkbnQMz8GCRDo0Zv4wp1Jyp2wjYNS1zESgLlIlqCbns2A1Y/I65rWFi2Db+7kTYxh2fGl3JYKebr\n1h2EDSvXW06g6tC23YM/nq6c/cC1mBXTGlBOTI4VP7Dwbu7o3HceqWEA3U4PbxbN5ZinHF80xH9r\nfp1GayljCR/HpZmkLqqMXaIeZ612KGNbq15HgeUsQ9kCvvHUJau+D+aVIkk6Ec1FX6qId2rKaHWm\nQwSSZnBVU4huWaRwNIVFNfj2vhqOzm3klWvfA2BBR4iNTWlFqwkCT1SuRdI17m9PP6Dd5fkc8eWT\nzB5HEAz8pOhnsrmYP55k66lRfKG0VSB6oHeZwp/IIy6aFqRF1bnmUoN8AAAgAElEQVT54BA7arNR\nVIPrjg4Tl0R0CayqwQ9mbmF/9gzuduxlv2F6N3lqlHuGoxz1O7nNchQuYNwdizlw2uIYgDJROPdi\n0MfmtgADfdkU6WYNSRQbH3hm0eh3MWvITW7cwoJjtfT7h3n25jfJCXj42k/NnvPbNu3h0MrDJC9A\ndskpCfXD7mBdFSCpVMUE7nr6M3zz3r241BC0p42E2REvNxrnYGYj1J6mdTSbHwcvIzqSR+FEPs2q\nzMSm1GDRw4iopAQ7qv0Qz9QYKIbGk8cepzg0BSw9y0tWMnm+qjsgO3lKMr1XTxJUJcQ9yVdxECcp\nSPzj3Bs5ll3GkpYRCjxnofXSNCkGcGiOwpAzU8HXxtrQ3WOUSO3EDCeBjsVUdIK0aLfJcjyWjXBy\nOct7prO2TcdxCdbxwyUpCsdFisYldAyis3/EU9MW8dsZaW/5zQ/+gzeK5qGikJ0Q+H6dmbsUDZ3c\nRIT5jQksCTtMMN4awGi2jjD7CDmy6WUJSYnrT/RTOZIZ7nxi7jLGz8y5YIuETZmFVakgpfZhU/dQ\nSDd2o5hjuoWt6vsZdRY92RYGPQrzOyOcEaexS15Cpd7FZjVdaJhC5hfza0n4RplxTuTqls6MMTzj\nuoY+tRzRCDPfdQC3bK47h0PLqcveTyKRg0sa584f/L/Tue9TqTQG36pjuD/I9vd+QMWsl5jjfBm1\nBxJWF1LHpUMH44qFF/13oweryNMTXBV5FAUzoR2RFcYtVnzR8JSgzb32+zltM+PJgqFSmfNDrq0z\nF8Prxr5Ij5iFgMEWuZEFre1saWtgxOLkZ1UbGLB6uLaggRssx3nv3DSWNpovTVyQsV1AwqchsM1f\nx58L51GeGOKop4K4aOHhk39iVqjvgv1EDkuz2SUvnRiPzl2pl8k3zFxGUhDptnsJKg6a3D68o4Vc\nOXgY3dmDoVkQpExo4DsFs/ht+SpGRTeGIBC3Tm0NipqBNaVj05J888g+ZoZj9GW58ElN5ManJpX7\nUMKShV1509k6cIqkKPOf8xfjz29juRjmDd00mXNJMUImTPGz8RHKzsVxVBr0ui08pWXCoT+3u5/c\niGriAC/BWyfkCbiWG+zW3Cj1i1n+hhn6MEo6oL8ICgbguhfRC/pJaBYSgsSeQ1dzVWE9WnbblEaJ\nPDwfe9uNCIbM6ZktvHLNdrSEG+QkG/fOZdX+TEr2737rZ4iSxnwxQv1Ep0P3uIOwK4ZxKZr4uA1O\nLoSIaTUvqO7k2sptABzonMVfzlwMVxbIta3mxvG/RyZBtzKX6uQeflu+kssGGiiKT125fbEEFBvv\n2xczruXQ4C6hN1ch4Urh1BN0OTLDgbaEzpqT41gu8goFwcagR+dgrTNje410ktJz17LptJ0Zxs84\nsegM0wbi/CV6A+H8MMw+mt456oSDa5BViW+c0XAGLt26+GJ5cd0+8i1HmB4ewKml33cDuHn5lxix\nZiqxpZ2VTAtlEan6BQ2hmbTmm57pPGU/UcOJhEq51IIsqEi6QUG/TKvPSlRwkt+wFTEoY1NmIolu\nVNc5YhXPII/VYuu64bz3p+tx7EaEFZH/xKu34zXGeVdemaEgVER0xPM5pb3SEg5LtSQLB2HmKfKC\nBlecCE5CuR2xXc2gs4t8OR0L1wwRSdCxqCoI8Nl/m5ql+q+VT6XSGNlzA4neV+Cp+yBmJ/6Fn2Gz\nmlbbkZZNePs7yDda0ENgnQX6OKQmlHOfPINhaSZHbTczJ/EyyytfRPBJYNU53FiAdyRCZU0YZIhP\nACXGRD8vZGXGAwtTx1jq/Q1+awedXi+/NlZz99mTWCMhCpOmh/PwzCt512eS41lJcZvlML+Pr2Td\nwBk0SaXZU8gfjzxxPsTWqG/gy+sXZVIXNG/jM33HSYkiZ7NzyQslKUiNkUTmKcuNhAUX6/R9LPU2\noF+ipqk5O5fpwRGMZBaCEgJBRx6Zg5p78vw+55x5NLv8hGQbI7KXg/nFdDjzmNedoiXfQsRqviZv\n/FLGVvlzBEtwymvFsWDj42lJnqhcyzNly3jI+jaSOECrlkuXYaNA6medOM47+sf3Cb+sSeMd5xy+\nbdmGUgKJJki2TL2v2HcL1uu3If/86wiptGejultBl0mUvk0kq4c3SmZR017M4sEg1u7Lia76Ploy\nUyG6D/1PBEMhLoscLffiTKhkh0P8ww0qQcsYv/uDG184M5aeVFIc/Psf4bca/FytxCX288ATN+MM\nevncV46Trccosx9jSjmdrqa3W8e4c977/Kb+SlK6qWAlMQvDUNGNCHWc5fLE5I6IACHZyhvuf0Ir\nfoOzOSn++67Dkwyk1wrnMqY48EldnM7285p7w6SugBdLXVuUioGEWSexaB8IIKQcvKFdc763xTxl\nHyVSO8OpEkpOfBOrpnDfge0w/UcARCUrL09fyYjVRyLvAOJEZXPtO2u4zrOd8apxPue+m+t2+/ji\n3k+W8D5TOUZh/iMAqFjM3hmGwB8L1/HrGUuwpWTiyidjyAXwid1kiQG8DCOcncm+ShMRZtWTrG0q\nI1+tpt97lu0l5ofoEQLMGCqhPGJBGa9FMCQC9jA2VUGJDaJaBukRB/jb4dfOJ8o77V7+ffpWmt0+\nVAl8iSTTWrPwpuJoS19A1A1WHzfITcQIK1ZqRwZABEUz+KAyn7YCC9XdAlG7wagLygdUqkbHyYvH\nmP5p4J76rxBBEIj1vcno7qsh6kD9/b3Is4+jrdiNdIlwqZGC8NuZ2wakGXRPX8VK4UkECygTBa8d\nQ2WMR+1UFbTQ2+3jWM8dDEpzSYimtZetdRKUTIjiysjPKdDOMC4WstP5NTTBSr7azDWhhxAFHTXb\nQW/lQh7P9rNfq6RoPIfVHTORDQk7I9xR9lWc/hB6CIKDMtZ8ndHObEaCEtWRTArn1MCVnPCsZkeN\ngw7POKu6/YTELG6s+wZlOT3ET6QV48eJASQkCaumXbJQ3RBg56y5LA/1QI/KoFhCHIGqyCCSZXDK\nY6JkMSJXU6KasVjB4JKV8P1WD3cuu5+q8CBbBhr4bfkqwooNKwnuV16ndbQQLbcbWZj8ojujfipG\nIswrHmC6NUDDwCbG4j7mFLwI75kKS3CBZXQJCSUdslOGFmFvu2liDgxi1X9A9U6BQ51CrF1bsQys\nAENGMEwk3s6Z2Rwun6LXd7KBL+2No+UdYn+Rkz+XTmfQrZMTFfjmuw72lIU4VRNESPjRlDIKI2au\nQ7eMEJr7HRB19M5bOeLrpUppIEcbhyPLIZZptUuiF6d1JYIgYI9tozK1j5XakcnjmZD/Xnctu3On\nc1ljERbjIGgam4X3mRcwn+cdS++jz256fQoJXMI4o4Y5ttLBBCG7hDumMbMzRkuJjTZ/Ok9Q2Rtn\nlnwUytoBE3SxO3k5AGVSC4Kh0aHXACLz+yqYNVSCI57ijvafYvjMnjOdymK2uf4ZgJLsn7KioJ4R\nNY95hWZycL9azgudc1kQ6OW6jnMYlnGE0bmcFW+i2v0dBM2O1Hovjov6r5/xufGNRxCEOJ6YRMCu\n8ofFPkZyPDTl9tL6Mf0xPolYVZVseYgBJr8PNdJJcsZFwiNzOF2mkxNzsrF1NpIu8nb1ceZ0DjPL\nPsKhgjGO2ia3Rv5QNk8UKNuSBssnKKiaynT6vRJ5oSRBu2z2GDdEk8UAmNUT4YpTZgTi/9dKwzAM\nDDWKmgjw5ddWIRiwZMDOlaVnJ+3fOLgWv/ss9pY+Uhc1a1IqINVu/u3cCBhgaCBdAOWOq06eO/Eo\ngVgZm8KPUJE6wHOeXxCWfFxKVkV+hl9tIEvvpdFzFb2WmXRomRjy5dEnmJ2Yuv2ijoRI+gGL2eBY\nBe9F55OwJPlpYi3ReB6XSWf5ds5zGCqE30ofP2Kz0+d0UxweJycxucdIr9NNn8u8yRkjg7jUFBev\n7wZwVtlAkXoS1xQQy4hkZb/ty7j0EdqVFYRE33mL1GYMIBoiBeIrNFhm8zdnY0jjI9iVFmzdWxme\n92OscoDT7sKMsNtJTzH/NmMrTjVBk7sQqxCjVGrFQMAhhLHoUHX2BuSISbO9cs73KBOCPHvCRLvp\nYoL5Vd+lujNOiVtl7JWvMpQFLVU9hJRsahN/YVazj1jldgQ+WagGwNp7GdbuNNKuvTjAkaIZtHvz\nLnlMi7efUwVdCEDEkhkH94+JDHh0rm1cguOiZlu6ZRjN3o88Vkdn1jDHCtup08+RL56AI5lsuTZl\nLlalHJse4Obx+7AY6Xdmv28aucEYSlJgUMyj2+rlJ4sXn39GWw6N8mFKxevs4e3qUgbtk8ECgqFz\nWf04ykWNiwwg6JLoyrfS5bMiGDqbLa8wThaze6287S+iW5uGWwhijSs89kwhd94dQtYldDGFOsG2\nfOOxErITHdwe+08MBMbb/henCovZcPkDWN2T8y+DmpP7Y7czv7eDL3XuxjXHics3REP7OmLNCvX2\nW2h1DPCvr348xP5b1xhsmxm45O/uuEjIpuOOpQjZp+6TvirRyBl7DsP6R7deuJSsb62j2d/IgCOJ\n9jFlASIa661/xi7EmN+sM5ht0FswNTrsQ8kfT3L3vkHaxPlsffLw/9YYL5ZPrdL4UJ47/B22N5vM\nqN+quoOhQz8hGpfpHXRiIBDTCxlT76Wg4AhrHL9GzofILjA+onbJthBkP3wI9BiOlPPasc9z4+j/\nQACO2m7isP3Ojx1rWfIgnZalGdty1HbytFbWRX/0kceOyiXkZXUj+0EpBUOH+IiItUBHFOF/DW/m\nobwdGCmD00e8VA8PowoCQw4Xg3YnqiRxKrSAe6KmYjrp96NpAs5UkpDFmhECKy8ap6fLiaJamRX8\nmDaIQKdlOs1Z02lX7//YfS8UWdWpGRhn1dA2KP9oJEezq4C/XXgXuiDiSsURtByuaZ5c0PTXyrXj\nf0++lo5h/dv0LezNrcamqsTI4pqhfeQnQoRkGzedTBKML+BXcytBLmGW3IyqljAaS/MwxWwtHPAn\nWNs+C3EKt0rHYH9pM+05QwgGlIzlMuwMkRt1sbZjIllrJLHEQwTlQdYk3uCwK7NnhYGOmnOcUNGb\nSE1lEMpGEKy4bes54e+lSn2dr7W8c37/LqGQ/5u9946zsy7zv993Ob1P730mmfSeQCgJJHQQBFQQ\nAXVZdEXUXfWnrv0nrm2tq7s2BFQQkS69JiGE9DKZJDOZ3uuZ09vdnj/uSc6czCQE99nn9ewun//O\nfe5evtf3uq7P9bm2uVYxrORObHqKbbTWmqGdRV1xaiY8HK5M0FNqegw21UJdsIghb5DwtFRH+Xia\nZZ0JRHuUVcphtljW4UjNuE7/JFubC4gafgQ0DEPkqoEj/LVyIYJh8OmWIezjGyjODNBaWkxEKsXp\n/CWKHOPBqnUn2VR/2PoY5fZOpGYHjrLcj3Ncd9GulrHemjsp3K1WsVrOute/OfQdVi34GY8pS9ke\nXcS8CYHz++CcYx5qg3MPyC/OS3PPpXFqgk6+8ZTAV64RaS+OoYk6NkVmzUADpbEAR4raGXeq1IQK\nOVzUT0ZSWTBeQZ10jETl0+zKbDzplV3S34IxXko6L8rummKSvLP6EbuisTwWxaa4yVS8yoBWS5+W\nVU+okdpYIO9HEGYP3eXBNGNeC4o8PXgZBlYFMlaBX9709t/22eC/vdGIpad46div2dB4KwFnCeHR\ndp794aacbYr6mxkrG6WgYJhFDRNoU5CYW3r/JNKFfkIV9TSUm9a5e8AHxzIUpJKkRIl++XxEQ8Vr\n3cUz5deix1Zy48i/8qbzTvotq+bcp08b5OrI57GTTdZ3Ws6jQOvAp4+gYMNCdlbaV7GOw+mFnFvx\nIK5DaSyazoDby6jLg9edJhBNQAQKUib9r8frZ8RRTGf6fUymelCm2UKyXMFUYQE4X2Nt6Aiy18AR\nTeFQs5SUoLaGXu12vNoQV0b/GZdhzsAMBA7ZrsNndFGeOUqvZS2vuz6TtaiARByHMMiUNYAlfXa9\nHG6e/BhO0fQyVKUAUYoiirkz8iGbj+J0mG7rBbzu+qeTyyPWJN5MVmJ+0BMkLSvUTZ3e+zsVXm0I\nw3qE+5s82DQLZZEARXEfOyrbychmnHv1xAAdznlc3jF3n/ERV4jXa1vRRYP6cJIfHXqAZ71fISI0\nzVpXFEZRjQDiKUyxSfsod788TsQ+xRPNg9yZeYiU4GGn4zaO2zbnrKs5Bokt/jaoMog6RriQZT1x\nNo2ZukzfbL4a25gXa9SKPqOGo0If5lJlK89bLmBHcTUt9S4cGQvN4xXsK88yaq5obcSvFZOwpHm6\naQ+ehMKaYyZd9HzbDtZOHee1/CV0yVUs0XaSiZSQ5+jnO8s2MkzVrGueN5HPyqHZel4+bZBLY9/E\nq49wxXmfIiVa+AIvcL23Zda6kZSbZ499mNeaxvil8+E5n8Nc+FFqA1dYWpknjTOl+NnW8XFkKc6j\nHivXbnNzzeFsaG246hBHGgQufnUxiiTQF3DwifeFmHBFaR4rZ/lILUF7DEMw8KWcjLkilMT8vFXR\nTr9/lHUcwuNoZzxeT1FrCWIyayRUzxJCPhlL5e/xWvvp1+ppUdfMdcrYVY1VR+JYVR1HZnqMc8QR\nGwcYi17AzuJsrtAvTLDKuhWbkGZH+mKq5A6qImE+ufswcZtE1C7xyKoCtBMxe83CL285TcLvHeK/\nvdE4HdLxINsfvIvRjlzqi9uRwedJo02BoklMaC68mSRV0TB2LTcplhZspAoE/BEzxGPMGNPitVas\nPQqWU85lR60HI1nGuHoVIWMpiu7jiug/kxbc1Cpv5az7WPFmIumPogrmALg49TgWI3HGjl9xIcC+\n/CZKleM0zCh20wSBQwUlbGt2YB38EM6wm2iyhZQoMlihUZmyUWIcxBB0flN5EQhw9XAb84IBZGL0\nabdmD2LoCBg0qk9SaHmOfXmbaIzuRCRFr3YbU7pZVyAIcQodPyRl1ahPjHHEVUafdT2LJwwKxNfo\ndl6Llo4wZKmgIJqrM+XTBliceoIu6/kMWZaCYXBF5BvIQhwB/aQ3oCHzO/8jlKsHacy8RpdUzn8s\nKuATW0rJ2JyEbXF+td6M2VaG8zm/1xykYpYUXXmjhG0JakNFtBYOcGnnYs5G0HBHZTvdgTEw4Mr2\nFfjSuTNFRVTZV9ZNZ142Fr4gMsC3Dz/GiDOPhwpvQcgsoCz69tpZ7wvdgdcwcwppwYZt+iV7Qv5X\n4tYaVItGhbqbbut5GBjEF38NzWHWk9w4rf0FMGZ38qV1m4hM1bKyPY6XKAdLC5n0ymwKtHLZWA93\n+K6hKRaize/LKQwEWNwVp2osg92yEBCJay2IuhmyPFpXzOrRlVh0jQ+E78BpmCQIA5iSqvlN3QKe\nL8uNxQeSLi47vgyrkcCtjTMl1+T8X6i2cU308wjA8Mo8mkpnh4n+sf1fKJto4KWGFlKOMNVJkfN7\nFnLriruxyYlZ658NUoqb3X3vZclfq/FPZnNEP9wY58FVKR7/tZ/KkMTWjb/jH1ddc9r91IYc9Htj\nqNPUb7MA3CAQVVnamcCVNnMKMhIO+0UYjgi6YwQhEyDkHUCq/CMhI58hrZpGvQ+p4y7y4vm4hU5s\n+qskWEO1/hZBpZ5x+2YUUeXJ+XtOTmgAfMIk5wxMEZi8jfb8YUKWbr5wfDv16nZ2uN/Lm+uz/TPy\nBxbw7c899zfds1PxP9ZonMBrv/kgI8fNwqTK837E069lsOhJVqR/RSDkZbykC21G79/8ZJyayNzM\noJmQAnDMV0Jjz0jO8j6/h79Ur8EXT1Adm6AinqDHtZgu1yquH/0BxdPSyc9V1/D9mhtYGhrjnOEC\n7GqKMeNSmuTv4InnsTzxzFldnw6EbA5CdjtTdnNw6y+E47YKVg+NsaJyjMJAkljCQs+El38TPoBV\nraC1IMymzsV4M7kD4ljBs2wMv4GFEIIAw04nbU1Jlo4qBIZlDENku/NKWvL8FHu3sN9YgaSKfL3j\nsZz9WC0axfkJwjErTrvKC/GrSCQ3UKa0EzTWn/GanHqQm8MfPvl7RF5AiZptPvOc/FHe/2auEfrh\n51/hQcPUGAtk4nz1yFMsCg9y3FPMFxZfT8TixJO2c3Xb3F7gqTieN4xHDlEy1oxgqBi+/+DBmmXM\nTP58xf4cxztWc9ij8MHhLSdbjiqCSEx0Ylc82IVRhnkfo4opcyMZSaxCApuc5NL4N/AkZpMKBuUa\n6vZ+iAxmjiFpi3LbbSO8d/QAD1cvYIWwm3XdYTb1mnpaWxu9HC1zEbNL7M2cx5hagT5Hh8a54CPB\nEmGQ/F1+lFN6vgtY8TguQhBy4/lp/2+onaxjSDJl7mszb/BqTQc7CkxK7PKhGmqnirFrFi6K3UOd\nsotBeQlD8hLK1Bae83yTfGcv6yseoH14HRsX/RK7qLBHreTu5A0UGDFGBB8SOg+77qVKNL/H16eW\nsSLWibcyt1huJu6LbeBG5w5c015rPOPDZZ0jfxX2QlszrytNbHzBZDje8YEwUWeKP91bzJGmLj5z\nmcikzTN721MgGwbqjHCvL5NgUWgAf58PVCtHqr2EPDaagpVURoqx6jLpkldQvW04Oz+MoJ1dY7a0\npJCWVF6payE5Y8wqjvq4vK8eNaVz/dAOKqYkhNFSDAx+ccsWtlcaBIRxHr1l9xn2fvb4H280Rju2\n8/q9t7Hsii8y77yPEgqF+fKXvodu6HgtK7EYBmX2+/GLZiVsXt8iqiYcSGVPnWQgnIDoAvtKSOxg\nzkr0E4hJNu6vOZdrhg5QmTRnwSlRwq6bmcfjRXaeXZxnMh0wRcps0+/AuqOg6Tb60p/ihsinABiR\nmjnouIEi9RjLU4+cPM6wPJ/BQARBFMj3J/E4FXqHPWZXPtGgtjxCRUkun3syVcyLbf/ESGx2QZbo\n+y3DLgXJ0ChPTVEVj+CeDqV1F8OkF1wJgZDVRcap4447KD2ykH9fXM4tw68zLzEMGLgcKiuax5Fm\niGhF4hZ2HC/Hppg3TpDsdDovIzxpdmccc/dRHvWiCH6sUpzNyX+hND47XHECDuMccMfRbEOkxDDO\nagVLqcmwGTtgZ+NIW+7zqD6XvKSbZPzDVAQjrO2a5JXmPFrLBDRBZ9g9wh/vE3l4TTU1Sx9nXWXW\n23vzlS/zpaVJ5id72es3k/B3ytv4qP0tEkmZ3a1FnLAkyRoXG/M6SR4TyIwK+FarCIMGw5FGWh2b\nOKfmYZzdQbQw2JpB8ps5Nj1iR8q4kUMLsPVfdrKT3bHGVj5+WSlRu3kvbZrCc2/8+OS57al2s2V+\nlp6c0ey8pLyHEx6VVYXMHOH8Gy37uNu2BbugMhJtIKNGea1zJd1TJ4QFBVaVOxmbbCQsvn3Xvzrt\nfl5tgqrxDYgRs1reaQlxa+Od/Da+glXuPjomAtjDCkc8V/HVph/kbL8j08Dd6evMc9YUqrQgP/c/\nQt50X3BjWo5H9IA4o7jb0GEkZKM0zzQSLytNbLJkpRi+GfwAF4StbKh94LTnHvzjneS3mc+1J6Ax\n5Etzbo+TLUv6+f4lYcKih6ZYiHplmLZ86MqsJCmJ2FD4XKSH/cPv55mmfXzmNScbOqzcfUOEPKGb\nvHgCcaiEl9YETk42ZB1KgxJVw1P44wL4mrk69AQhqYpD9vee9hxjHGHU78Of9hJIunm5/hATLtN4\nfsb2Kjdbc5PcoVeu4s/x+Ty9RGEiX8InJDh4+8/P9AjPGv/jjQaAoesIMzoAxuNxPv/Zf0TVwYdC\nBCfNnhHOueZ2XnmrnQ/fp2EIKpniNxGThYz7MvSveoV59SFcToWpoxbsPeYoLxUBKyQSL4NNfXtK\n286yQn4zfw3zLTO6ixkG87qslEazs4f9rnlUhguxCRNs82yiMDyPrTUtrAn2sXrMgmRk6Hady0XV\n/5eG0neW4Iqm83mp4y4GwospEZ/AJx7CyuTb0fFz4AiX4kramSgxY+IeZ4aAX8VpS1NSMHfoQFEF\nDrYVEEtYWLdkFLtNY1t3Beo4CILB78ou5L0Dx9mw4CA+j3kv9DjEdogImo5zPSTfAmM2IQwA1yZQ\nBiAz3dY6JUnYtewzGZfqecZzD9aMhTu2HEcy4BM3RthZo3DrLjt3b3HRf/5hKjb/IWe/Q7qX98Tv\nBAOqQgVUx9IsMLr58PzfQRTCipXDvQVk3DIXN/SR3AXaHKQcucJk5qVndOy0LQHrdDog1NJE4JGP\nAJC0pth63gt8f8lyQhYXgmHws0O/Z0Eolx76yIpC+gptoAsYhoggaXiDNoRQMYsHM6QmFrOt1M/8\nMYPbuxwEL97G/snFnN/iw3bHz0nY4Ze7/oBV0bhD+nd6S0bYe2wNccu5RDwmOyxh6ef1uh5k1csl\nnUspdHURS+cTxIEm6LiVXImOi+t/zpKSF9F1EUHQ6dAL8AgpCvQ4BwcKWVmT612puswDrbdyyB3k\ns20vnOzVLQXAsRaSu0GbofAiWX1IHVcRrd2OrPVhCPDXyqW8v2Y/1lwR2zmRSAs8JuVzkzSBJAAZ\nCzz1XoRDZu7q+5cO87kXTOpsX56DlxYU8JE3+lFFgV9d2EDcJtCb10dtOI6sNaEbVmrGY7x3n+n5\ndeepHCpTWdtroSQqEbbp+NIif1ma4jubs50G17dEqCNIzJLkrtG/EpRqOGa7jEPeelb693No9AZ0\nZzfxht+bDb+AcLyWko4LiHpSdMslpPI6eDRwek2pe1KXME8cZZOljeYb46dd753gf4XRmAuP//kh\nnn/l9ZO/P5p+GD9R8q75Z4RjK1D+kGVqiNfVsW/oR0wVmUwNwTCYHx3HbVNwrjdZjImUxJNtS2lK\n99E0Zj5gwybCKgtCawZC5jnftPbvGbX7KBH6WRIbpd9loXpc5+JJU8NJB35UczljNh8XBI/R4yik\nx5lNLq/qkfjI/koGFw1zxdIfYJVOM4JOY/fAdTyXbCA/Us+ivJ1cWPu7k/9NxEt5Y1DCHz7z/bSk\nHSi2M9DNgJULxvC4ct2vg8OX47BE0BO91JYMYbPqTGl2fmvcvHIAACAASURBVD+xkruLs0yEYNhG\n/4gbRRURBFi5ILdGxVDNGyNYQR01BxHAbHPqBn2OaIWlBnqmilHLBOpGR04O4v2Ocl5y/ITbO7fh\nG7dBYztc/QTqi5cjT+bDTVmDoeoy8nRXu/9Ir+e2qR1MtjnxRWMYEsT9NtwzZSVOo4V2JuiCwMQ8\nN0ksBDxpEt3n4nzjHH6xdgpffgvbCxpAgH/of4HVw4NYjKz325JfTEaWUUWQdAi54VA9GIKAO2Ew\nrx+KBmtZ/eblHLvpERbUH4YTxWzf/hpCykH03Dd4rjxMVdsq1h3KJRIEXVby4hmMpmO0r+zjYH2Q\nG63ZAsSb47dRJ0xwozqIlCxgMNJMgbOXleVPndW1fyN5OVcbPfT13MBUooyLvN/H396DyNxyN6fS\nwlWsbHHdTVgs55LYPbiNCQQXOFZCJF2LP78HYUa1/fhQOfb9gwg+6MCPp1imvjFLJ1eeugHrHjN8\n2TZ/O86x5eRFHbiU3NnUsWKRr14RR5OdXNAR4O+2h3FlcieMhpwBXUTQc928H24M8ciKNKoosVgd\noeigDZtmkApkOO7Nwy7FuHH0TfKVON2lduYfWc1baw4S8yQQdYE7fnsjBUGzlubBxX3cdGNWuXav\nWslP0ht4wPX72ffOgLIb/5fXafxn0dfXxz333ANAmT7CTcqMmgkD3MFPI3aWzFikE84bZv/6bOze\n7cxQXRqlMC934NbCoPSDtR5Eh/nAlH7Qdbg8cBcprHz1wB4czlxFVTkR4BeNKzjuMT/enz7iYdyj\nc2zFKNbSXSTEUf6p24eteXZBWs/UcoLJChKKGQefiNcyEF6IoufGS4tcnVy/4PPYrebgcUDNwzFg\nfqT3ievY76rh2tR+PujfRzxpwT6QwrX1eozofGLeCQZqDxIszno2bmeGVQtzB/lkxoX49Ea2KTfQ\nUhlAJIXP0sFNS7+O7dQWsKdBKi3R3uunpjyCd9oYDU34aOldyFR8M5XpA4SsNlI2DVcyn/XxX53c\n1phvxduQIZGx4rRmMAxQhyA1rVAhOMFSanqJUt7sgmddhzcPlCKkYe2aEWTJwMhA7MWzOnUUQaR9\nWRkNY6PYBhViThv51WnSM7qVqnWl6D2jWHXz3rf784na7JQRwaIbFIxnGXaTdgchm4P6aeJDr6OW\ndudSLHaJReVHGRiMoqnmfo6Xw2CheUGibrCyHda7wF93ivLqaDE8chO4YjBUAWt2QEU/StqO5a1z\nYbjM1E+fdxTe/+DZXfgpUHURWZxtACZ1Jx9LvJ8HXfejazZ+t/eXJNVsjcgFyZ/TXPgyWn9220Fp\nIS94voHDsoUPjP+Mbst5vOrO7Xl9Y/jj+PQhDBH2F5SyuHUR/ng9YryAkOEjvuQHeKdlE+QSEJc5\nOdy9kbLBXZRuGIeeGoR7P3ZW1/bo0hR/WZbiofvfXrlgJgx0+uZtY2TVAGsaWknpFuyKCM4kr/Ut\nhYzEfZm1lNUOcNkTi9lw1ItRMAbvedSU+3/kJoSUmYc01uyAq8ye8fE/foRflBTy9BKVD3l3cIct\nK02i6XC8K4+NXxif85zeKf7XGg1d17nnnnsYGBjgozddS96fbjLbeM6EZsN19O+REqYSpefLG0kN\njBALD2B9PMLh1c8wUdLNsmQV/gt2nPZYGUXEOq1a2jfiZvdAA/lG7gMsHK5n4Z7Laa2KsLsqg+YK\ncn6nlYg3zmg1XLzgWey22TGPBw9+n7FYPQYSgXia+kgrg3kyYW+UtC2NFrkQmQQqZkKvRHyGUvmv\n7Kpp4jMFW0+K8gEMaD7+qKziFuseykUzeXi4NUB1p46j41oQM6Sqn0S3JJDLwdYE0owi5eSUhcPx\nK9gzeAPL4u2sq36Itvg8XvRPErEI+B0J7vJnw3LjsUoK3XM3R2odK2C816QM+zxpZFFnMmwawClt\nJT3ah5nJhFqT+B2lagtvOO8ibvPxoSV34j5F5S7xVq5MPYClGuyLc5e9fqCRlvhXMAyZa5yfpGbF\nZI5qcdTjxROdQ2tLhO7KQr6TfzmbgoeoS46TFCw8U7yM5flDbN53GGtCoccTICVb8KRTNIXMuIsm\nCHT58mgITZ62Sh8gZfeyzXEXU7Yabl/xcaTpPtCxuIyYdJLsq2VLdZg+b4oEIu/TgzTYspOaUNSL\n33NmnbAz4tSueYCuihiGhGQx7/dWtZ5fpM+nUy+kSgjyFdsLBCZdPGxrxCOkuFxuxeGMUSya31tf\naDGPtn5r1qGaM8/jUYdRBRv7HDfP+EcBZhfbWfUoHwzfjjRDhCwj2BhkEYUxAbcrt4GStSErO2Od\nD7Z64A+3IxyfD4AhJdBtU4TFfL50RZq/2+FkVf/cRX4AmjWEWNuP0Jb7QqVWPYl10y6En34JIeGa\nc1vjYz+FstnaUKmOGuy1faYrCZCysfXxD1MhZKi98T4ESaf94Fq2hV14naP4jCjOdIaBmkKKx4JI\nho43naIj3Mwnf/v27RjOBv9rjQZANBpleHiYpqYmDF1DT4TRlSTRnQ8z8acZsxhDmNbEgNKPP8TY\ng59GC48ixsuQwg3Yhy5FX7udZNVxXAvNsFbqkRs4vGALiZSMrovMrw1SUmCGeLoGvIxMOFlUP4XX\nM/0Bxp0Q9sPLl8KmF03Z7NcvBsUKF74Cnlwhxu2am73jF6B13gnAorGjXDJD6224eJxfffQR7IpG\n3RAUzBgnWt3lPFaymn/xPM0aOVd7ZFSX2WO4uFKau2LaMDBDRacUoiYOCHR0L+CA5U4mA2Yi9Jye\nfaxst2OdbisX9MV4/LY/s8EzRCAtEfCG4dkr6YsbRJa9hWCB6qoYEd3OQ8euY2XyZTTDhkh6ljcQ\n12vpUD+Jjh1DDuHQIliIUyn/CZswjtOusHLhWI60jKHD5D4LckRFSsxI0tttOJZYcXui9O+opVX3\nYbNpjIjL0bV5XKt9BTlufrSOtRAvsHNoax0L48f56rxbGHSLfLRnGw9XrmbQEeCzrbtx2gbmvH+n\n4idVl/Klo88zP5Y7YKiCgGwYZPwS1lA2rGBfAZY5muCdDcYMmV+rRVwphVgmnj1lNTFSyrGeBRT4\nxnE9v5n8UD6UDsKHfw2KhbaDtUSdUwRKEvRMuNhiW8ZzpSb12aapfHvfVpYeOA9/KCuxYWCYXkzU\nC54oLY1WXs1cnlNf8rfAqw1yY/iTCNPyMzoinc5mitO9eLUY/X4f1ZYI+vgpY4hghrXkEuDhmyEU\noHvlFnbEbub8xL/hYIxWTyXV8UnK99yNNZMVPFQW7CM6/1UCy2bMSFoXwdPXQUUffOAPIGvQ0Qhv\nno/QMbuOB8AoG4DztphN1IpHzLbBgWCOCvOpOBCtYWdvAfOSc/T90DVqw1N4M2ZL5v/1MiL/1VBD\nw+iZJKO/+QjJ9jNbaClag2V8FenKZ5HdboT+eVgvLUVyvJf4r/fjjAfQbUmMu36E6PvbZ3nqq4tI\naW0csK5jx+I8yio99LX4MOQ4AQ5y4xObsaat+KLmC63IKq9seIuqgRIMMcOx+h5eqrUguMIUSiMs\niVRwfYFZO7Jbc7Ja+tu475m4TMcb+fiVKBgGzzrvI2o3k6NWRaMslCQ/lsZSK7D4tk2UFTvR3VHe\nePBWnM82UzKSz/NXPk7EF6HhHQhxjstNHGkaRQ43s3x0P041dwbsdadx2DQmQ3ZKChKMTjpQ1Oyg\nVBmZrRZ6AppuQxLTxGULrukiSF23cPzSElbZ+jEMeCCyimWuIf4jcx5dsWJu3adRnv/kGc85KVpQ\nBAnZ0Pn3yosZcQT44ZMSSz0/R5DMmfdAQx4Wp0pZYQKnQ0WLmuE1ax0Ip5/ozomYIfKIlk+fYZ3u\nJSfgQ+UWeYICVF7RvezXXSQRmUeSK+UQ7hnep6IKtBzPJxKzEXFCyCVwzaO34E7Y6Fz1EophYI/k\nkT9eTd54FZqkoEkKX7sszZv1ST7V8xwB1XyvxsQCjnoLeL5wBRbdypXtZWxM/Durtr0fSbPQvnAL\nA7UttKjfRDOyarr5sTRWRWNZ/xRtJV66ijyUB+MoksiYz4ZMHIkoabLW1K2PIJFAN5xEJTPMvCj1\nKClHJ5M2LzUhBzGhklXphyg8P0js2WVMBmqo25zb/0U3RFJpN/qbEYwTn4dqx7vv6wAYl/0Vzs2t\nBRuZcBAatDB/ae633tqRh/dYE+Xzx5EeyKop6HIMUZ27MZVa1seR8x5nMilgt2osbx7HZjWfTywh\n03Ioj5DDwrgfvHHwx83cj6TrHLeXkZ+Kc/G4yQx512j8f4x4y/OM/PrDaBGT+eFacgVln34SQRRR\nJvsZ+sm1pPtyVUrtdWuwp65Cf8KsAjYwSHzuOzg9ubP4TDdYa09/bEMVST1TjirlhnJ8G+9Ev/Iu\nonoEr62YN7r+CJqVJXtr8f6kZ859bV+3nxc3Z5PQNnTSuoR14lze5zlIg/fYyf/C2nxaR29l0egz\neJefUkIf8sG9H2OqsJdDTdtYff7n8Dtg+877ifU00+K8MVuNOgd0S5j4/B+jO3KZNLVDBpXjsydX\nsqSzpGmCfUdzpdGL4uWoTggKp++WdiqC2iqSRgUYIheFf4tbOztj2WNrQHB6WLR+/6z/DhwpIBTP\n1ZFq3reJoytewm5XMVwSfVEfP665AlUQAYMKMUzZhMpP76/jwLkPkyd0M+lwkjZ8rNx+A/b1b6J4\njpEOjmNdLWB1GyiqgEU+8/vfMb6ayWQ1S0qfZ+eoyOvFJqXIlTSoHzYIugUGik4fBLuBSTIdLiIx\n83okWeNoicRQQXYbV9IkhMSc2WWlIz6ueHEtwdIjBAvNd/XUo3QonyRqmF5IT8mfWDfVR30kjGCI\nxL1ZilRMr2WQc/FN+bnpzdz3KGGVcGQ03qjL8PONY3yqbS9x7yh75LuwpuvPeG9OhTOtUBUe5FhR\nDQALil7h0safzlpvZKIIcXcQVfczac+nat4kPtE6K6S090gh0bj5vS+dN07Aa7IAf5ksYli2s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a/0MR3fUIw7/4AILFTt2P+hCdfoRp7X81PIJodSE6sjHe5PE3kXwlWPIqEORTZ7XT63S+BQjY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\nNm2ipqaGd955h0OHDo1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"text": [
""
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's make a histogram of the last day of returns. This is the thousandth day, which is simply the end of the prices matrix."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"finalPrice = prices[-1,:] # get last row of prices table\n",
"h = hist(finalPrice,50) # plot histogram\n",
"xlabel('price [$]')\n",
"ylabel('frequency [#]')\n",
"print 'Mean:', finalPrice.mean()\n",
"print 'Std:', finalPrice.std()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mean: 99.3375039092\n",
"Std: 32.1103764376\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
""
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What about a leverage multiplier?\n",
"-----"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"history3x = history*3. # leveraged returns\n",
"prices3x = 100*(history3x/100+1).cumprod(axis=0) # normalized price\n",
"finalPrice3x = prices3x[-1,:] # last\n",
"h1 = hist(finalPrice3x,500) # histogram 1\n",
"h2 = hist(finalPrice,100) # histogram 2\n",
"xlim([0,400]) # setting limit of x axis\n",
"legend(['3 times','1 times'])\n",
"print 'Mean 3x:', finalPrice3x.mean()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Mean 3x: 98.0867193128\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
""
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The mean is close to our initial asset base, but the distribution is skewed to the right. No longer a normal distribution. Therefore, an equal probability of going up or down in percentage terms does not change long term expected value. The resulting distribution is however skewed involving a price decline more often, but it is compensated by the fat tails on the up side. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note what is happening here: the fat tail of the leveraged ETF is so enormous that while the peak of the distribution is below 50, the long term mean is still at 100. This suggests that the naive strategy of shorting levereaged ETFs is not likely to be as profitable over the long term as it might at first appear. \n",
"\n",
"So okay, our first approach did not work, but now to our next approach. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Signal Processing \n",
"==="
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"warnings.filterwarnings('ignore')\n",
"import signal_processing as sp\n",
"sp.example()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"[2013-12-12 20:04] DEBUG: Transform: Running StatefulTransform [short_mavg]\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"[2013-12-12 20:04] DEBUG: Transform: Running StatefulTransform [long_mavg]\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"[2013-12-12 20:04] DEBUG: Transform: Finished StatefulTransform [long_mavg]\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"[2013-12-12 20:04] DEBUG: Transform: Finished StatefulTransform [short_mavg]\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"[2013-12-12 20:04] INFO: Performance: Simulated 253 trading days out of 253.\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"[2013-12-12 20:04] INFO: Performance: first open: 1990-01-02 14:31:00+00:00\n"
]
},
{
"output_type": "stream",
"stream": "stderr",
"text": [
"[2013-12-12 20:04] INFO: Performance: last close: 1990-12-31 21:00:00+00:00\n"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"IBM\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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EfyJDeO/k31gbmBAy7qMqbQkhyLu4D4lUhlHrpyiKv0TG/m/JCfoLpDrYTV6J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74OHZT/r11T9hCA94PJXygSiQS2trYwMDBAy5Yt0bJlSxgYGMA2XS88p8pz48aNePPmDapWrYrR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\niI+PF5YX/FxkpciDgoIyrapWkIrOwsJCm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"text": [
""
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Dual Moving Average Cross (DMAC)\n",
"The concept of a DMAC is fairly straightforward. Calculate two moving averages of the price of a security, or in this case exchange rates of a currency. One average would be the short term (ST) (strictly relative to the other moving average) and the other long term (LT). Mathematically speaking, the long term moving average (LTMA) will have a lower variance and will move in the same direction as the short term moving average but at a different rate. The different rates of direction, induces points where the values of the two moving averages may equal and or cross one another. These points are called the crossover points. \n",
"\n",
"In the dual moving average crossover trading strategy, these crossovers are points of decision to buy or sell the desired product. What these crossover points imply depends on the approach the investor has in their strategy. There are two schools of thought: Technical and Value. \n",
"\n",
"The Technical Approach suggests that when the Short Term Moving Average (STMA) moves above the LTMA, that represents a Buy (or Long) signal. (Conversely, when the STMA moves below the LTMA, the Technical Approach indicates a Sell (or Short) signal.) The intuition behind this strategy can be explained in terms of momentum. Basically, the principle of momentum states that a price that is moving up (or down) during period t is likely to continue to move up (or down) in period t+1 unless evidence exists to the contrary. When the STMA moves above the LTMA, this provides a lagged indicator that the price is moving upward relative to the historical price. Buy high, sell higher. \n",
"\n",
"The Value Approach offers the opposite trading signals to the Technical Approach. The Value Approach claims that when the STMA crosses from below to above the LTMA, that the product is now overvalued, and should be sold. Conversely when the currency STMA moves below the LTMA then the product is undervalued it should be bought. The intuition behind the Value Approach can be thought simply as a mean reversion approach. Buy low (value), sell high (overvalued). \n",
"\n",
"Both strategies try to achieve the same goal, but do it in opposing ways to one another. In this paper, we will analyze both the technical and value strategies as applied to the SPY with the periods of 2 and 5. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us better understand what we are doing. We are looking for the underlying signal from a stock's price. We are then taking a value based approach and a technical approach using these signals. But what is a signal. Signals are tools for estimating future value of an asset based on its previous behavior, e.g. predict the price of AAPL stock based on its previous price movements for that hour, day or month. But what does it do? Consider below: "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# make a new dataframe from the original dataset \n",
"prices = pd.DataFrame(data.reindex( index=data.index[ ::-1 ] ).OPEN)\n",
"prices.plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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Zn1fxVfhIfBE2nFMtc1mcjpS3EjYgq6SAU3vmxuRDNdW4Pjm3Gwfv38DXlw7i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\nQticDORCCGFzPwG+Tf180/c3twAAAABJRU5ErkJggg==\n",
"text": [
""
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Notice how choppy the graph appears. It is hard to tell which direction the S&P is moving. Now consider applying a simple moving average (see included python files: filters.py)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"prices['SMA50'] = sp.sma(prices.OPEN,50)\n",
"prices['SMA200'] = sp.sma(prices.OPEN,200)\n",
"prices.plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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pNlB8o/1N/hunxCiomaUXiK7KpU5ly88+TTOryktqLqZfQqWSEzXSGzmtXV6u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\nRsbCkR25jIyMjIUjO3IZGRkZC+f/AR5U8RvYO8vwAAAAAElFTkSuQmCC\n",
"text": [
""
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now what you see is a smoother set of curves. Notice how the 50 period SMA follows the actual prices more closely than the SMA 200 curve. And the 200 SMA follows it more loosely. Why? The 200 curve looks a prices up to 200 days ago, vs the 50 which only looks 50 days back. That is why the SMA 50 reacts more quickly.\n",
"\n",
"Now that we understand what the true values/underlying signals of the market are. But how do we use this? Now we can implement a DMAC algorithm that based on these signals will produce equity curves (how much we will have made). Consider the code below. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"equity_curves = pd.DataFrame(sp.dmac(prices.OPEN,prices.OPEN,sp.sma,2, 5, 5, True),columns =['Value SMA'],index=prices.index)\n",
"equity_curves.plot(); remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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ud3Z2JiYmptB7jxo1ChcXFwBsbW3x9PTEx8cHeJzXKqycP+f1LP11XVZaH2DO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\n2prY2Fi962/duhXITcfUrFmT69evU69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PzJkzeeONN7Czs+PVV1/VpF6eRTuPxMREPDw8\nqFixIqtXr9btCyN5bpF70UgkClOvXj1CQkKoWrWq0lYkRoZM0UgkCiNz7hJ9IUfwEolEYqTIEbxE\nIpEYKTLASyQSiZEiA7xEIpEYKTLASyQSiZEiA7xEIpEYKf8Pii9dLU3BDEMAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Well hot dog! Looks like we have a winner. Well we should just go invest in this! It gives us 10x returns! Well wait, let's first put this in prespective"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"equity_curves['Technical SMA'] = sp.dmac(prices.OPEN,prices.OPEN,sp.sma,2, 5, 5, False)\n",
"equity_curves['Baseline'] = 100*prices.OPEN/prices.OPEN[0]\n",
"\n",
"equity_curves.plot(); remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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BjBo1SlsZEe8sEAiAh3m5PLX9S87cSeCH4GcZv2tVmXPKikVPzrpPp/WLS+y3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\nAABJRU5ErkJggg==\n",
"text": [
""
]
}
],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Okay, this is more reasonalble. It seems that we have beaten the baseline in our Value base approach (described above) and lost nearly all of our money with our Technical appraoch. But generally speaking just eyeballing our results is not the best strategy, there are certain statistics that we should veiw: "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" Standard and Poor's (SPY) 500 Total Return Index is a capitalization-weighted index of 500 stocks. The index is designed to measure performance of the broad domestic economy through changes in the aggregate market value of 500 stocks representing all major industries. The index was developed with a base value of 10 for the 1941-1943 base period.\n",
"
\n",
" Annualized Standard Deviation is a statistical measure of the degree to which an individual value in a probability distribution tends to vary from the mean of the distribution. It is widely applied to Modern Portfolio Theory for example, where the past performance of securities is used to determine the range of possible future performances and a probability is attached to each performance. The standard deviation of performance can then be calculated for each security and for the portfolio as a whole. The greater the dispersion, the greater the risk.\n",
"
\n",
" Sharpe Ratio is the amount of reward per unit of risk. The higher the Sharpe Ratio, the more incremental return is added per increase in risk as measured by standard deviation.\n",
"
\n",
" Sortino Ratio is a ratio that differentiates between good and bad volatility in the Sharpe ratio. This differentiation of upwards and downwards volatility allows the calculation to provide a risk-adjusted measure of a security or fund's performance without penalizing it for upward price changes.\n",
"
\n",
" Alpha is a measure of excess return, or the amount by which a portfolio outperforms a benchmark, such as the T-bill rate. For example, an alpha of 1.20 indicates that a fund is expected to rise 20% during a given time period when the return on the market (and the fund's beta) are zero.\n",
"
\n",
" Beta is the measure of a fund's volatility relative to the market. (Many fund managers correlate themselves to the SPY 500.) A beta of greater than 1.0 indicates that the fund is more volatile than the market, and less than 1.0 is less volatile than the market. For example, if the market rises 1% and a fund has a beta equal to 2.5, then the fund is likely to rise faster than the market ( and conversely fall faster than the market when the market falls).\n",
"
\n",
" Correlation is the degree to which the movements of two variables are related. The correlation coefficient is expressed as a value between -1 and +1. For example,a correlation coefficient of 1 would suggest that two asset classes are perfectly correlated, a coefficient of zero suggests no relationship, and a coefficient of -1 suggests an inverse relationship.\n",
"
\n",
" R-squared is a statistical measure that represents the percentage of a fund or security's movements that can be explained by movements in a benchmark index.\n",
"
\n",
" Maximum Drawdown is the maximum peak-to-trough percentage decline in value experienced during the given period.\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will begin by examining the statistics on our baseline."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"stats = sp.performance(equity_curves['Baseline'], time_frame= 251)\n",
"pd.DataFrame([stats.values()],columns = stats.keys(),index=['Baseline'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" sharp | \n",
" std | \n",
" sortino | \n",
" car3 | \n",
" car1 | \n",
" cret | \n",
" pos | \n",
" car5 | \n",
" aret | \n",
" max | \n",
" ave | \n",
" ytd | \n",
" 1000 | \n",
"
\n",
" \n",
" \n",
" \n",
" Baseline | \n",
" 0.4506 | \n",
" 0.169088 | \n",
" 0.868786 | \n",
" 14.479322 | \n",
" 17.134151 | \n",
" 284.648624 | \n",
" 0.526083 | \n",
" 5.947035 | \n",
" 6.967836 | \n",
" 56.70044 | \n",
" 0.033569 | \n",
" 17.134151 | \n",
" 3846.486241 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 21,
"text": [
" sharp std sortino car3 car1 cret pos car5 aret max ave ytd 1000\n",
"Baseline 0.4506 0.169088 0.868786 14.479322 17.134151 284.648624 0.526083 5.947035 6.967836 56.70044 0.033569 17.134151 3846.486241"
]
}
],
"prompt_number": 21
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So the baseline model (meaning let's just invest in the S&P 500) does pretty well. It gives us nearly 4x! But what else... The max drawdown was 54%. Pretty bad, during the morgage crisis the market really sank. The anuallized return was 7% a year! The sharp ratio (usually looked to be good at .5) was a bit above .45. But lets look at the statistics of all three combined. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"stats = []\n",
"for strategy in ['Baseline','Value SMA','Technical SMA']:\n",
" stats.append( sp.performance(equity_curves[strategy], time_frame= 251))\n",
" \n",
"pd.DataFrame([stat.values() for stat in stats],columns = stats[0].keys(),index=['Baseline','Value SMA','Technical SMA'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" sharp | \n",
" std | \n",
" sortino | \n",
" car3 | \n",
" car1 | \n",
" cret | \n",
" pos | \n",
" car5 | \n",
" aret | \n",
" max | \n",
" ave | \n",
" ytd | \n",
" 1000 | \n",
"
\n",
" \n",
" \n",
" \n",
" Baseline | \n",
" 0.450600 | \n",
" 0.169088 | \n",
" 0.868786 | \n",
" 14.479322 | \n",
" 17.134151 | \n",
" 284.648624 | \n",
" 0.526083 | \n",
" 5.947035 | \n",
" 6.967836 | \n",
" 56.700440 | \n",
" 0.033569 | \n",
" 17.134151 | \n",
" 3846.486241 | \n",
"
\n",
" \n",
" Value SMA | \n",
" 0.857395 | \n",
" 0.159222 | \n",
" 16.518197 | \n",
" 12.628268 | \n",
" 4.673404 | \n",
" 1021.574147 | \n",
" 0.337055 | \n",
" 14.389879 | \n",
" 12.847359 | \n",
" 24.042366 | \n",
" 0.051072 | \n",
" 4.673404 | \n",
" 11215.741466 | \n",
"
\n",
" \n",
" Technical SMA | \n",
" -1.141516 | \n",
" 0.109234 | \n",
" -1.163120 | \n",
" -12.432710 | \n",
" -5.102461 | \n",
" -94.240220 | \n",
" 0.307796 | \n",
" -15.226719 | \n",
" -13.299761 | \n",
" 20.924733 | \n",
" -0.050313 | \n",
" -5.102461 | \n",
" 57.597798 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 22,
"text": [
" sharp std sortino car3 car1 cret pos car5 aret max ave ytd 1000\n",
"Baseline 0.450600 0.169088 0.868786 14.479322 17.134151 284.648624 0.526083 5.947035 6.967836 56.700440 0.033569 17.134151 3846.486241\n",
"Value SMA 0.857395 0.159222 16.518197 12.628268 4.673404 1021.574147 0.337055 14.389879 12.847359 24.042366 0.051072 4.673404 11215.741466\n",
"Technical SMA -1.141516 0.109234 -1.163120 -12.432710 -5.102461 -94.240220 0.307796 -15.226719 -13.299761 20.924733 -0.050313 -5.102461 57.597798"
]
}
],
"prompt_number": 22
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can make some comparisons. First we notice that the Technical SMA did quite poorly as compared to the other strategies. In almost all regards. It lost money. Next is the Value SMA. It made more money. And in fact it is less risky, there is less volitility. We can see this by looking at the sharp and sortino ratios. But then two questions arise... Did we choose the correct period, and did we choose the correct filter. Let's deal with the second question first. \n",
"\n",
"Let us deal with the first of these questions. We have done research, and the periods of 2 and 5 were recommended, but let us check a braoder range of periods. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"values = []\n",
"for short_period in range(1,5):\n",
" for long_period in range(short_period + 1, short_period + 5):\n",
" values.append([short_period, long_period,sp.dmac(prices.OPEN,prices.OPEN,sp.sma,short_period, long_period, 5, True,end_value=True)])\n",
" \n",
"X,Y,Z = zip(*values)\n",
"\n",
"print max(values,key=lambda x:x[2])\n",
"\n",
"fig = plt.figure()\n",
"ax = Axes3D(fig)\n",
"ax.plot_trisurf(X,Y,Z)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[2, 5, 1121.5741465850183]\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 23,
"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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MFj4AYDE0NBG33LIHTz3VjuuvH5mIK4oiBEEoy4hDM1k4WiQLpiHCl00wTSJ3\nqVm+D63rrtREDygD4SPko7QYad1CyEXwjNz7UFq+WpapzWaD3W5PK1k+XxGzK1dG8NprLDKL3EyE\nMfuSI2Hg97fh7ruP4z/+I4i///tJI9r5KG80jHChaaH8/FJb0DIlU8FJJ7pU3RU9Ue6hcu/QjF4A\n8p34fD44nc4Cz0ZfqPDlCBmPFGQGchM8gtGComWZmqHotfq4QyERCxZEceSIXnMKA4imfJWehMPj\n8Y//2Ie+Pj9++MP5cocQsvhlWtyZ1rI0H8pgGhIEouUuJdVmEgXTkH6H6s4W+SJRKkMudTrNSMkL\nn1GRnXq7NNUYLXwez+WqJbkInpHzPHMmirlzRVy8qKcQX9BxrPQRxWb89Kfn0dPzFn7725sBXI6Q\nBeIXSbXFkMqFlmm1EspljHQxZpJ7qA6mUYpivjwBZG5qSi2VASgD4SPoWVpMLXiEiooK3U5GvQWF\nWKTK8fQUar3ZsSOK22+XEArpbX26dR4vExrw8suD6O19Da+8sizuGeUiqdULL1k+mla1kkJZDOli\nlj2tQqCVauHz+SBJEmw22whhzCSYRi9BVI4xNDREha/Y0MviS2bhDQ8PGxIxSshlXCJ4atEjnbZz\nRU+BJu6fF1/k8OCDTkiSEUE1I29Y8ksdduzgcP31G/D2259Dqq2TZPloyQIstCwG6iY1P+Q3ImTq\nCVCOkU3uYTkkrwNlIHyEbBfodFyaRkSM5ro4SZJ2TzyyYJqpea0kXW5n9L/+lwW/+50L+gSxqPFD\nrzJluVGFkycnYt68Ddiy5QsYO7Yio3cnc6GpxTCZxQDEiouXcx88s1ieieaRyhOgDqgBkhfyVnsC\n0okupcJXxJBFQusOSYtM9vCMjBjN1JIkghcMBuN64pEWTV6vV9d2LrkcuyRJilJoUdx1lx2bN9tg\njOgBubQh0h8nPv64HbNnv4o337wFM2Y05DwiwzAjzs1kuWgA4tykZIx0FkiKfmRz7aRTmSZTd6nF\nYtGci9vtxujRozM/MBNT8sKXqaszm6CVfAhfKpRWUyGawGZ67Mranz4fsHSpK43GsbliRJmyXLBh\neHg6br75bTz33EJ86lNX6v4JiRZIn88HIBbYlO4CqWfpLjNYWmZOIcj2vekG06Ryl0ajUaxbtw5O\npxPnz5/H+PHjs56XGSl54SOkEqdcojSNzhFMNi6xmvx+v3wCJ+uJp/dcM71Q1aXQenpY3HKLC253\nPlyvQuqWogHVAAAgAElEQVSX5B0OodDVWLlyJ376Uw9Wr56R10+3Wq3yv9OJNlSizkUrZuvQDAJs\nZO5uokLeWq5x8tyaNWtw/vx5ALFtkvb2dnR0dGD69On4/Oc/j4kTJ474rDVr1uC5554Dy7Lo6OjA\n008/DZ/PhzvvvBOnTp1C6yd9+Uh6xJo1a/DUU0/BYrHgiSeewLJly0aMaQSMZMbbHh0hllA4HMbw\n8DA4jkNVVZX8vB5pCV6vF4IgwOVy6dKah+DxeBCJRFBZWanZrFPdEy+dJrA+nw+hUEi34BZRFDE0\nNASGYZK2LdGqDLNrlwMrVvAIh/NRGeYSgJ48fE62SGCYD/DNb47Bww8b29qIFFtgGCZlk+Nk7rNE\npBNcEQ6HEQqFwHGcLudhNigt34qKzPZZ9SST38NogsEgIpEIGIbBY489hiNHjmD//v3o7++Pu1n+\n4x//OKI7ek9PD2688UYcPXoUNpsNd955J2699VYcOXIEo0aNwve+9z08+uijuHTpEjo7O9HV1YW7\n7roLe/bsQV9fH26++WYcO3YsL5WiytbiSyR4drs94yrkRufcKcclkY9+vz+uCazD4YDNZjPd3bZW\nZRi73Y6nnuLx3e+ykKR8zXcwT5+TLQwkaSqeeOIEenpex3PPfbbQEwKQXS5aOqH3ZrjfNoO71Uzz\nUGK1WvGv//qvAID77rsPP/nJT+DxePD+++/j0KFDuO6660a8p6qqCjzPw+/3w2KxwO/3Y+zYsViz\nZg02b94MAFi1ahWWLFmCzs5ObNiwAStXrgTP82htbUVbWxt2796NefPmGX58ZSd85O4qFArFRTuS\nvbBcxjbK1UlI1BMvE8EzytWpHk/rxoKUQvvmNyU89RQD44JYtPDl8bNyoQ0bN/bihht+jz//+U5Y\nLOYscpxucAUJpEq2l1TukaVmIlFU59ixYzF16lTMnTs34Xvr6urw4IMPYty4cXA4HPjUpz6FpUuX\nYmBgAI2NjQCAxsZGDAwMAADOnj0bJ3ItLS3o6+sz4rBGUPLCp16YlaXFchW8RJ+hF2TcSCSCUCiU\nsCeeGeaqHFOdN8jz/Ce1/hgsXRrF9u35TqWIIN9lynLjCuzfz2PGjGewY8eXUVlpTf0WE5CudagM\nvScueyVq69CoAt5msbTMMg9Aey4+ny8tV/DJkyfxy1/+Ej09PaiursYXv/hFPPfcc3GvSbUHnK/v\noOSFj7jalJaHXoJHMLoOqHLuxMIzS7sT5YmqFjyO4+Q0ikuXRMyeHcWZM4XIH9S723o+aMLp0zyu\nvvppbNmyEuPGVaV+i0nRsg7JjRx5nIhhOiXaqHWYf9JZb/bu3YsFCxagvr4eAPCFL3wBO3bsQFNT\nE/r7+9HU1IRz586hoSGWutPc3Ize3l75/WfOnEFz88guJkZgjtXTQBiGGVG1RCtYJNfPAPQTvmg0\nCq/XO6IJbE1NTc5tgowohUYgyfIWiwWVlZWoqqoCx3E4ckTExIligUQPAIYK9Lm5Uo9Ll67G7Nkv\nYO/ec4WejK6Q85BlWblWrMvlgsvlkm/uOI6Tz3USgUiCYgKBAHw+n9wRhRR3NsPeYaaY2eLLpDDH\nlClTsHPnTnkdeOedd9De3o7Pfe5zWL9+PQBg/fr1clDM8uXL8eKLL0IQBHR3d+P48eOYM2eOAUc1\nkpK3+BiGkc10n88n303qWblELzHRinwEYntjerUF0WuuyqhSAsuycDqdcXmDGzdGsXJlro1jcyWQ\n+iWmpQqBwEx86lMb8PTTN2P58rZCT0gXklUqSdXlIFPrMFFRZ7MIjlnmAWjPJd0UlRkzZuCee+7B\nddddB5Zlce211+JrX/sahoeHsWLFCqxbt05OZwCA9vZ2rFixAu3t7eA4DmvXrs3bd1Dy6QxALChE\nFEW43W5Eo1HZEtFzfK1UiXRJ1BMPiLmEbDabbmHOgiDA6/WC53lUVlZmNYY6yIZQXV0dd0PR2RnB\nj36U7yAWNQEAHxTw8/UiBJbdj3/7t1n45jevzWkkM4TPE1en1WqNyyXMBK0alsnSLNRiKIoiQqGQ\nXOihUAiCAEEQwPO8rulQmaJM73C5XGAYBuFwGJ///OflqMxSoeQtPiWFTDTXQkvwlC2CtDpAFBJ1\n8jmJKlXWAyXcfXcEf/hDoUUPKM79PS1sEMVZ+Jd/OYieHjd+/vP/J+uRSuVeN1VkabpFnZUCWIgk\nfDNZfAQyF4/Hk9XNvNkpC+HLtGxZtuOnO65WqL9WTzwj5pvNmFouWIfDIUeVhkIhOWw9HBaxaFEU\nBw+apQi2J/VLigYewEz8n/9zCKdOvYY//OHvci5xVWqkKuqsZR0St30xtnfSk3IpUA2UifARCi18\n5M5SuS+WrEpMoYUvUfK53W7XDLDp75ewYEEU58+bRfQAIJT6JUWFBcB0vP32B1i48Dls3nwXeN5M\n33d65NvK0bIOiYtR6frMpL2TXtahWSw+rTWBCl8RU2iLj+QOqnPbUpVFM7oiTCLStUgJDMNg3z4G\nd9zBIBg0U6BwIZvOGgkLoB2HDx/HtGnrsGvXPaitLUzZr1LAYrHE7a0lqmGZrwLehUY591JsQguU\nifAR8iEkkqKFkCRp98RLN4cw3xZfIoF2Op1Jo2BfeYXF//yfToiimUQPMH+ZslyZiP5+G6ZNW4et\nW+/CVVclrpVKSR+Gyay9U7LI0nSsQ7NZfGpXJykoXUpQ4dNpXIaJbyGkFjxlT7xCnuBa30EigSbz\nTcYPfxjBf/yHA4UPYtHCbG2IjGAcvF4es2c/i40bb8fChflJAC4FMhGcRB0OtMQwU+vQLGh9H263\nm1p8xYra1ZluM9pMP4MISCgU0qUnXj6KX2v18CO5eKne+/nPR7BpEwtzip6IWKmycmAMwmEen/nM\nq/jd75ZhxYophZ5QSsxi5eSKlnhl2t6JQPYTzdTeyePxoLW1tdDT0J2yED6CsgqEnigtPRK4opXM\nnSlGuzo9Hk9cS6N05xsIiJg7N4pjx8wcVFEqaQzpMgqieC1Wr/7/cPq0B//0T/mpgEEZSboFvNUi\nGIlE4oJp0mnvpCdaNyNDQ0PU1VmsGBXcoqxeojxpnE5n0p546WKE8ClDtqPRaFo9/JT09IiYP1/E\npUtmFj0g1n+v3KgGMBs/+ckenDw5iF/8YklZheNnSj6tzmQFvEnSOMdxsosUSK+9k57uUq3vY3h4\nmLo6ix09y3Wpe+IRXC5X1pUoUn1mLheoOvkciM/FS4fNm0V87nMiBME8+xKJKeYyZbngAjAHzz+/\nD6dObcRLL90Sd+On1YWbCmLhUH73pL1Ypu2djCzgTYNbSgA9hC9RTzxSJFdPlCdutgtUovqfADLq\n4/e730XxrW8BklQMohdCbI+vXLEDmI2tW/djyZJX8c47XwDPs/ING4GULkunrqXemGGPzwxz0CKZ\ndajV3ilZIE0m7Z0SBbdQ4StS9HB1EgtPKXjKnnjkcSMiRrMZM1nyucfjkS+YdPjWtyL47W/NUH4s\nXS4UegImgAcwC8ePv4/rrvs9du78Murq7HJSNlkkUy2a1FVqLJlc2+nsHebS3ommM5QgyrtYcrKk\ncyFr1afUagJrZKpEJq1BMk0+T4YkSfjUp6L429+KwcpTUkplynLBAmAGPv64Cx0dT+Ovf12JKVPq\nwTCMvL9rt9uTLprqyiVaidpUEPUhm+8xHetQXbM00Y0OEUlBEODxeFBXVwdBEAzZuik0xbai5UQm\nJxbpiefxeGTRs9vtqK6uhsPhGDFWocuhSZKEQCAAt9stix7P86iurkZFRUXGNUDdbhGTJ0eKUPQA\nwFzFvQsLC2Aa/P4xWLDgOfzlL6flZ5Q1LbV64lmt1hE98SKRCARBQDAYhN/vh9/vlz0LpAtKOteA\nGQplm8HVadQcyE0Kz/Ow2+1wOp1wuVxwOp2w2+2wWq1xrk+lZXj06FG0trZi8uTJuHDhAn74wx/i\npZdewgcffDBCMJUMDQ3hjjvuwNSpU9He3o5du3ZhcHAQS5cuxaRJk7Bs2TIMDV3ujblmzRpMnDgR\nU6ZMwdtvv63r8aeiLNoSAZdbE126dAmSJKGmpkYzGkprTyxZfUpCIBBAIBCQTzK98Hg8iEQiCZvn\nZpN8nmrMDz8UsWiRiOHhYhS9YQAnCj0Jk3IKDHMcjz9+E+6446qM2vEky03TIpWr1OfzQZIkOJ3O\ngiVx+/1+iKKYlTdEL8zQIor8tiQV669//Su++tWvxtUUJlRVVeHixYuaa8uqVatwww034L777kMk\nEoHP58MjjzyCUaNG4Xvf+x4effRRXLp0CZ2dnejq6sJdd92FPXv2oK+vDzfffDOOHTuWt3OhbFyd\nBJZlZdNf+SVHo1EEg8ERPfHS7Xieb4svl+TzZPzf/yvii18UEYkUo+gB5Ze/lwnjIUk8HnjgHXz0\n0Sx8//vp5/plu7+UyFVKzudC3neXssWXLt3dDE6fZnHDDZc//zOf+Qz6+vpw8uRJfP3rX8ctt9yC\n999/HwcPHkR1dbWm6LndbmzZskXutM5xHKqrq7Fx40a5l9+qVauwZMkSdHZ2YsOGDVi5ciV4nkdr\nayva2tqwe/duzJs3Ly/HXXbCpxaSVD3xsh1Xb5QLBYkszSb5PNlcH3ssgh/8gEExe8A5zgudg2tL\njLEAePzyl/vR2+vF009/JuuRUu0vqQs9q6NKgZinRGkV5iuqtFw5eZLB1q0stmxhsW0bC4YB3nxT\nGLEWcByHcePGoba2Fg8//LD8eKIeod3d3Rg9ejTuvfdeHDx4ELNmzcIvf/lLDAwMoLGxEQDQ2NiI\ngYEBAMDZs2fjRK6lpQV9fX16H25Cykb4tMqW+f1+XYJAlOMaZfEBI1MpMk0+TzbXr341guefL6bI\nzZEwjIjKShGXyjF3PSNGA5iFV1/dj7NnX8amTV/UVWgSWYdKEVQXUihEVKkZdnmMtviOHWNkkdu2\nzYJz5y5/TnOziNdfF9DaKkH5VZC5aHVmsNu1u4BEIhHs27cPv/rVrzB79mx8+9vfRmdnZ9xrUt3Q\n5PNmp2yETw2plgCk1yIoFUYLn9KlSXIHM8nD0xozZj2KWLIkivfeM3slltRMmRLA0aOJ950oSmoA\nzMaOHfswc+Yz2LHjy3A4sneRp0IthkT4HA7HCAsx31GlpeLqlCTg6NGYRUeE7vx57XHHjJHw+usC\nrroq3uWcbSpDS0sLWlpaMHv2bADAHXfcgTVr1qCpqQn9/f1oamrCuXPn0NDQAABobm5Gb2+v/P4z\nZ86guTl/BdbLRvhI1KPyTlMPwSMYIXzRaFSeLxG9TKutJOPCBQmLFkXR31/8ogcAo0cP4+jRQs+i\nmKgAMAcfffQepk79f7Fz591oaqrI6wy0LLlMXKXqvLRycpVKEnD4MINt21hs3WrBtm0sLl5MfdyN\njRJefz2ECROSr1VDQ0OoqqpKay5NTU244oorcOzYMUyaNAnvvPMOpk2bhmnTpmH9+vX453/+Z6xf\nvx633XYbAGD58uW466678J3vfAd9fX04fvw45szJX33ZshE+n88XF6VktVpRUaHfRa6n8GntO1os\nFlRWVuoS9cQwDA4dYnDbbRwCgdIQPQBwu4cLPYUiJFblZXBwP6ZPfxrvvvv36OgYXdAZpeMqVZbx\nysZVagY3J5CZxSeKwPvvx4RuyxYLduxgcelSZgLf0BATvYkTRwbLqeeRaff1J598El/60pcgCAIm\nTJiAp59+GtFoFCtWrMC6devQ2tqKl19+GQDQ3t6OFStWoL29HRzHYe3atXm9WSmbdIZQKASPxwOW\nZSEIgu5pB6IoYmhoCAzDoLY2u4agWsnnFosF0WgUNptNt3DnF14IYPVq3oSNY7PH6YwiEjkEQSiL\n09kAIgDeh8VyCS+++Hf41KeuNOyTlIWZXS5X1gtesqhSLZSuUoZh5BtLPW+AM0UQBAiCAJ7n47rA\nA0A0Chw4wGDrVgu2bmWxcycLtzt7cRg1SsIbb4QwderI7ycSiSAYDMaluLzyyitwu9349re/nfVn\nmpWysfh4nkdVVRWCwSAEYWQUU67kYvFJUuLO5+FwGH6/X7d5/vjHEaxZY0UxB7FoMXWqF++9R0Uv\nezgA1yAa7cKKFX/Ez39+E1avnmH4p+Zyl69HVCkQ2z8vlKtUaWlFIsC+fay8R7dzJ4vhYX3mUV8v\n4U9/0hY95TyUZGrxFRNlI3wErUoFeo4LpF9QOp3kc71qgEqShDvvjGDjRrM2js0Nq3Uo9YsoKYhV\neZEkHt/5zrvo6fHg4YcXF3pSGZOOq5SIIlC4qFJBAHbutGDrVh67dlmxZw8Hn0//a7OuTsLGjSFM\nm5Z6DVG7OsePH6/7fMxA2Qgf+UGNakZLPiOdOqCZJJ/rsXcYComYPz+Krq7S2c9Tc+6ct9BTKBEY\nAJMBWPHEE3tw6pQbzz772UJPKmfUYkjSmQDI9UqNjioNBoG9ey9bdLt3swgEjL0Jra2VsGFDCB0d\nqUseAiM7M1CLr0QwMtE8VUHpbJLPc53vmTMi5s4VcfFi6Yre6NEh9PSMbLtESUb4kz9RxFo4kfOL\nRay49RgAjdiw4QJqa9/GuHE1GD3aijFjbBg3zoarrrJj8mQXOjpcqK7ObBkpdLUS5RxIrVL1c3pE\nlQYCwK5d7CdRlyz27mURCuXvmGtqJLz2WggzZqRfO7UcOjMAVPjyNna2yee5zHf7dhG33CIiFCqd\nIBYtJkzw4uOPCz0Lc+B0shg1yoLqagucThYsK6Gnx4OBgQBE0YLYJc8DsH7yJxE+AI0ARiEa7UV3\ndwDd3SHEaqHGwzAAzzNwuSyoquIwahSPpiYrrrjChgkTHJg0yYFp01xoaCiOKv/ZRpX6/cCePTx2\n7OCxcyePAwc4CEJhxL26WsIf/xjCzJnZr3PU4isB1JVb8iV8Wm2Nskk+z3S+Tz8dxf/4HyipyM1E\nMEzppzFYrUB9PYeaGhYulwU2W6zKTiQiIRAQ4fGIuHAhAq9XwunTEcSiNOV3I7nIaUGWBguAVsQ6\n2p9FTDTVeXeAIEgQhAguXYrg1KnE3TF4noHTyaKigkV9PYexYx1oabHhyivtmDTJifZ2J1pasivM\nkAmZXk9aYujxSNixg8XWrQy2bbPgwAELIpHC759XVkr47/8OYdas9I+RWnwlTLY9+TIZn4yt1eUh\nm+TzbOb3T/8Uwa9+Vdzlx9JHwokTxSt8LAvU11tQV8ehooKFzcaAYYBoNCZow8MiBgejGBoSce5c\nFOfORRFzURqJCECduOwAMAGxIuDZRxmHwxLc7ijc7ij6+sJ4//2RHQAAgOMYOBwsqqosqKvj0dho\nRUuLDa2tdkya5EB7uwtXXpl7IYdM3u924xOhiyWMHzzIIBo11zVWUSHhv/9bwOzZmQm7lvB5vd60\nE9iLjbISPsDYfQUydjAYjNsLyKTLQ6Ix0+1x9pnPRPDnP5dm5KYWbW1BnDhhzqrUNTUW1NVZUFXF\nwuFgYbEwEMVYsNHwcASXLom4eDGKjz8W8fHHqfYo8/l7BjBS+Aj1AGoRE0Dj+h5GIhKGh6MYHo6i\nr0/AoUM+zddZLIDDwaKigkNdHYeGBiuam61obbVj4kQnpk51YtIkByyWzK+9wcGY0G3ZEquKcugQ\nA1E073Xlckl45RUBc+fqE7EuSVLB2jUZTVkJHwk+STf6MhOU/cmI6OVS9Fo5ZyC18A0Pi5g7N4qP\nPirNEzURY8Z4cCLP7fdcrtg+WlVVbB8tFhvBQBBE+Hwxi+bChQiGhkQMDaVahMy4kKYSCRaxQtdh\nxATQaAs0MdEo4PWK8HoF9PcL6OrStkZZFrDbWVRUWFBby2H0aB6NjRaMH+/AlCkVmDrVidGjXdiz\nh5PLfx05wkCSzPj7jMTplPCHPwhYsCA70VNbfKVe16SshI+QKvoyE7SSz1mWRWVlpe53S4mE+sQJ\nEQsWiPB4ykv0AMDr1c/NabUyGDUqtjA6nQys1vh9NLc7iosXo/B6Jfh86n200oBhALu9Dho9SDXg\nATQhZiEOIuYiNSeiCPj9Ivx+EefPh/Hhh+QAtVp5kMhWEgRkR8zV60CsvmkFzLR0OhwSnnvOh7lz\nRYhidgn4Wq7OUq55ap5fL48ok9izFSet5HOWZSGKIqxWq26iR06+RBbqO++I+PznRYTDpR/EosZq\nFfHBB6nz95T7aC4XC7udBcNIEIQoBAHw+fCJhRbF2bOxP+XK5Ml2fPBBpueuA0AzADcAj/6Tyjvi\nJ3/CSL6fSQSSw2WBJCJZAaASMfE0DrtdwtNPuzFvXhiK0r4ZJ+CrhU8UxZIVPaDMhE+ZxE5CkTMl\nWfI5ieA0uhkt4Ve/iuJf/gVlKXoA0N7uQ08Pi+ZmDlVVFtjtDCwWBpIEBIMSvN4oBgcjuHAhYsJ9\nNHNSU2NF9pZbNWKLvbH7f+ZBKZABxIRfCwaXLUgbYsJYCaDuk+cl1d+xsa1WCTwvwmoVYbOxcLli\nrtqqKgtqaljU1VnwhS+IWLzYAlFksk7A18Lj8RS0hqnRlJXwEbLxY6eTfE6E0Ig6oOoxf/tbEY89\nBjQ0MGDZ2CY/w1z+GxDBMBJYFmBZ6ZNE3VjHZYYBRDHySf4VJz8WOybl546cR+z44h+XpNi+pihK\nsFi4T76L2HOiGHs+/m8J0aiESET65LGYS1GSYu+LPQf5udhj8X+mT2fhcg2AYazYvz/VIksFLV3O\nns31uyL7fwKAC4glyJc7EmJu8QhiAjkEhyOEmhoBdjtQUcGgpoZDba0FdXUsRo9mMWYMi7FjOYwf\nb0Vra8xToT0uA/Uynk0CPsHn88Fms8Hj8ZRsRCdQZsKXbS5fusnnRjejJeNeugR873upqkCkclfp\nvR+Yn+TksWMlNDdz6O4WcOlSHyIRYPHiRmzZUg4WhrFceaUN3d16CZUVwFgAXgBDiLdmypvZsyvx\nzjvtkCQJfr8fDMPo1nkFyC4Bn/Dkk0/iF7/4BSZNmgSO4/DrX/8a11xzDTo6OpJagNFoFNdddx1a\nWlrwpz/9CYODg7jzzjtx6tQpuR0RyQlcs2YNnnrqKVgsFjzxxBNYtmyZbseeLmXpI0tXoCKRCIaH\nhzE8PIxIJCInn1dXV2smoOdL+P7wB+S19JEZsFgkLF7Mwu22Ys8eCyZN6oEgSBBFCVu29GPu3ER3\nxZR0aW52GDBqBWICqF8LsGLGYgEee6wtzouTj700Ioak/ZHD4YDL5YLT6YTVevmm9ezZswgGg3j/\n/fexb98+3H///ViwYAGqqqrwwAMPJBz/8ccfR3t7u3wsnZ2dWLp0KY4dO4abbroJnZ2dAICuri68\n9NJL6OrqwqZNm3D//ffr3jAgHcpqpUjX4otGo/B6vfB4PHLFFbvdjpqaGjgcjpQnqtHC9/zzug5v\nejo6gCuv5LFlS6x6fUVFGAcPnol7za5dF9DUFMK4ccYGE5QyxpV9YxHL/xsDo4M9zM7q1WMwY4Y5\n9s6Im5NYhizL4sknn0RPTw8effRRfPazn8WqVaswY8YMWCwWNDU1aY5z5swZvPnmm1i9erW8Rm3c\nuBGrVq0CAKxatQqvvfYaAGDDhg1YuXIleJ5Ha2sr2trasHv37jwcbTxl5eokJBI+rc7nmSSfG3Xn\nppzv8ePArl3lYe3V1Ihob+exYwcbl081c+ZpbNkyMpXg5EkfqqtDmDVrFN57j7o+M6GpicOHHxqd\nnsHhcvrDRZSb+7OxkccPf9gq/98Mxbq15lFXV4eamhrccsstuP/++wHEGnkTI0DNP/7jP+JnP/sZ\nPJ7LEb0DAwNobGwEADQ2NmJgYABAzKKcN2+e/LqWlhb09fXpf1ApKCuLj6AWPtKiZGhoSBY9q9WK\n6upquFyutCuu5CP587/+qxwWCwmzZ0cBWLF9uyVO9CyWKE6ePJXwnW53BPv29WPxYvuI4BxKYiZM\n0G+PKTUOAC1obKzPuLNDMfPww1eZ8ni11iu3243a2lr5/zabTXOP7/XXX0dDQwNmzpyZcN1LlQ9Y\nCOE3369gIGpXJ7Hw1J3PHQ7HiFYlmYxvlKszGAzhhRdK21U0YQLgcHDYs0c7+Gb27HPYuTOk+RxB\nkoAtW/oxZ049urokeL3mTaw2C8PDLPIdgTkw4ITN5sSiRSG8994FBAKl+zstWlSNO+9siHvMLBYf\nQV2gOp3ODNu3b8fGjRvx5ptvIhgMwuPx4O6770ZjYyP6+/vR1NSEc+fOoaEhduzNzc3o7e2V33/m\nzBk0NzfrfzApKEuLj6DMu+M4DlVVVaisrMxK9IB44dNL/JRRV5s3A319pVmdxemMBa+cOsXj8OHE\nx3jpUk/aY+7efRH19X5ccUVpfmd6UV1tQVdXYcqOhULA1q02VFePxZw5pdkJgOcZPPbYhEJPIyG5\ndGb493//d/T29qK7uxsvvvgibrzxRjz77LNYvnw51q9fDwBYv349brvtNgDA8uXL8eKLL0IQBHR3\nd+P48eOYM2eOAUeVnLKy+ADI1VYIJPmc47i8VnpPhVZlmFdeses2vpm47joGZ8/y2LIl+fc3Y8bH\nOHgwsxJlp04FUVkZxsyZddi/v3A1Jc3MlCku7NpVWGurv59Bf38lOjpcCAQu4cSJ7DtAmI3772/G\nlCkjXclmsfj07L5OxnjooYewYsUKrFu3Tk5nAID29nasWLEC7e3t4DgOa9euLcjxM1KpVyNVEIlE\n8LEqdK22tlbXL/7SpUuQJAk1NTVZdWMgifJ+v18O82VZFl6viGuuqYPXaw63iB40N0sYOzaxW1PN\ntdfuxr59F7P+vAULRmHHjsiIBPxy57rrarF3r3luClhWwvz5ERw5cgFDQ8VdD7W52Yq9e6+DyzXy\nHBcEAYIgyCkGhYIErlitVjm1YdWqVXjyyScL4obMB2Xl6uQ4Dna7HU7n5Zwive82ctnnC4fDGB4e\nhtfrhSiKYFkWFRUVsNlseOMNa8mIHsfF3JqXLlnTFr22NndOogcA27dfwIwZIioqSuN71AO7ncGR\nIxg/f3gAACAASURBVOYSF1FksG0bD0lqwoIF9SjmzjidnRM0RQ8wt8Xn8XjigltKjbISPgBwuVxx\nd1dG59ylQzQaHZEo73Q6UV1dDavVCpZl8corhbsj1JOODmD8+FhOnt+f/gXf0NCty+cfOOBBbW0A\n48eXnZdfk2nTXAgEzGkCu90Mtm934sorW9DRUVno6WTMzTfX4u/+blTC583ibNMSvmAwCLu9NLdW\ngDLc4yOhtUb05CPjA+md1Fp5g1pd2vv6YnfAxUxdnYQpU7gROXnp0NQUwJ49/brNpbc3iIqKMGbP\nHo09e8o7389q5VHIfnrpcOIEA6AGc+ZU4vTpC+jvT1VsvPDYbAx+9rP0AloKbfElwqzz0oOys/gI\n+SovpoVW3qDNZktYGeallyym7vycHAkLFjCQpJE5eekycWIPwmF9fyevN4o9e/qxaJENWWzFlgQs\nC3zwQfEUkd692wK3uwGLFo2G3W7uH+3b327BhAnJS8CZ1dVpFkvUSMrS4lP+nU/h04rU5HkeTqcz\naf++3/++ODc5Yjl5PLZvz36R0ipPpidbtw7g2mtrcfIkA7e7dPPItGhvd+Dw4eI65kCAwdatdjQ3\nj8WYMcPYuzdRK6DCMX68FV//eh18Pp9mT7xCC52acmtCC5Sh8BHyKXxaPfw4jpPTKJKxezdw7Fhx\nnYBOp4RZsyzYscOCSCS3uV9zzSls3Wps8MW+fZcwbpwD9fWV+Ogj87vR9KKqyoZi7SLf18egr68K\n11xTAbd7EN3dabWMzwuPPDIOdjsr5+Aqux8AkIWwEMWZtVALnyAIWecyFwulfXRJIKkGep98auEj\nqQnk5LdYLHA4HHIPv1Q895yu0zOca68V0d9vS5mTlw4WSxTHj/fkPqk0OH06AJdLwJw5o7F7d3ns\n+/X0mGPhzYUDB1hYLPVYuDCCQ4c+hsdTWNftZz9bj+XLx8jxA8qeeGQNUIthMBgcYRmm6piuF4nK\nlWWTw1dMlJ3w5cvVGY1G4fF45B5+JFJT3cMvGYIAvPKKrtMzjLFjJTQ0APv26RcJNnNmb17zy3y+\nKHbv7seiRQ3Yvl2ASW7IDWHCBBtOniyNA4xGY8Ff9fVjMH++H7t2DRbkt3M6WTz66FUALrsKlbm8\nRAyJCCqLPhNxVKIUQSKKRoohGTvdcmXFTNkJH8Eo4SPjCYIgf47dbh8RqZkOb7wBDA6a283JcRIW\nLLBgzx6LDt2748mkPJmebN16HjNn1qC724KhoeIJ/siEhgYrTp4srSCGixcZ7NjhwuTJDlgsbnR1\nefP6+d/97jhccUXiGz+lGHIch0gkAkmS4HA44hrFkgaxWmJI+uopBTEXMdSzaksxUXbCZ5TFJ4oi\ngsEggsHLbrJMWhppYXY3Z0cH4Pfz+Nvf9I+wu/rqczh8uHD7Nvv3D6GlxYFRoypx4kTp7fv19zMo\n1bZAH37IAqjB3LmV6O6+gPPnjfcaTJrkwAMPZFblhKw9Wpac0jJUdk2XJEn2IhGImKotw2wF0e12\np1Wns5gpO+Ej6CV8kiTJgqcci+M4uFzZt3r5+GPg7bdzmpph5JKTly4WS48h42bCmTMBOBwhzJ3b\ngF27Smffb+xYHt3dpeHmTAyDXbs4VFQ0YtGiEHbvvgBBME7of/7zNvB8+jeAqdYdYtkpo72VVqBS\nFJVBNEr3qZZlqCWw5PMI5WDxmTsZxkByFT6SmuB2u+M6PCjLoeXCSy8B4bDZ3Jy55+Slw4QJbhw8\nOGTI2JkSCIjYtasfixZZi7p0lpJx40q3IocarzeW/tDY2Ixrr60y5DPuuGM0brghewspXcuMiCGp\n7el0OuFyueB0OmGz2cDzfJxQEiEMhULw+/3w+Xzw+/1ybU4inOo5UIuvBMnV1UmKSAcCgbhITafT\nCZ7nZTdErpbk88/n9HbdaWsD7PbccvLSpaHhI5w8afjHZMTWrecxY0YNenstGBws7n0/t7t03ZyJ\n6O1l0NtbjZkzK3Dx4kWcPp28p2O6VFVZ8O//flXG79MreT1VEI3aMtTaNwRiWzVvvfUWXC4XhoaG\nMHbs2JzmZXbKqjsDcDmnjhSEJn340iESicDv98vixrIsHA5HXKRmNBqF2+0Gy7JZ3zUdOQLMmmUO\na0/PnLx0aGz0Y3Dwb7pXatGLsWPtqKiowrFjxbnvV1fHYmjIWdIRq6ngeQmzZgVx6NAgfL7cvojO\nzqtw//2ZdzAg1ZsYhslpSyQTtNIrlMv/jTfeiA8++ABArGHswoULMXPmTMycORPz588fsU729vbi\nnnvuwfnz58EwDL72ta/hgQcewODgIO68806cOnVKbklE1sI1a9bgqaeegsViwRNPPIFly5bl5djV\nlJ2rU6sLeyqi0Si8Xq+cnsAwDBwOB6qrq2Gz2UZUPABys/jMEtQyezaD6mortmzh8iJ6AHDVVSdM\nK3oAcPZsEKdPX8Ds2cVZO3Xy5MqyFj0gtoWwc6cDDscYzJtXi2yNro4OF77+9ewso0KUK2MYBhzH\nwWq1wm63w+Vyged5+bm5c+eio6MDHMehr68PL7/8Mr7//e/j05/+NHbu3DliPJ7n8Ytf/AJHjhzB\nzp078Z//+Z84evQoOjs7sXTpUhw7dgw33XQTOjs7AQBdXV146aWX0NXVhU2bNuH+++8vWBJ/2bk6\nAcS5BlLV1FQXkSapCYkiNXMVvmgUePHFrN6qG83NEsaMSb9Pnl5UVAg4dOhcXj8zG4JBEXv2fIz5\n8+uxZ08UkSIqfiIIFgDF7arViwsXWFy4UIGpU50QxUv48MP0m98yDPDYY22wWMzhmckVnufx5JNP\nAgBWr16NL33pS7h48SL27duH/fv3Y+bMmSPe09TUhKamJgBARUUFpk6dir6+PmzcuBGbN28GEOvr\nt2TJEnR2dmLDhg1YuXIleJ5Ha2sr2trasHv3bsybNy9/B/oJZSl8QOqamsFgMK5Tu9VqhcPhSFpT\nU2ucTO/o3n0XOHeuMBcTx0mYP9+C996zoK8v/3Po6OjGjh3FY47s2HERHR3VOHeOw4UL5hcTl4vF\n4cPm7sRQCI4eZcEwdZg/vwrHjl3AxYup72S+9KVGzJ2bfbCMWQpUa+Hz+bBgwQKMGjUK9957b1rv\n6enpwf79+zF37lwMDAygsbERANDY2IiBgQEAwNmzZ+NErqWlBX19ffofQBqUnatTC3ISEsEbGhqS\nRY/neVRVVaGioiIt0VOGDGdj9RXKzTl9enZ98vSC46Lo7i7MRZALhw65wXE+TJli/n6J06ZVIBQy\nrxu5kEgSgx07eITDY7Bw4ShwXOJroLaWw7/925V5nJ1xJGpCm0k6g9frxe23347HH38clZXxfRNT\n5RMWSvjLUviUPfmAmEtTEAS43W74/X5IkgSLxYLKykpUVlZmXLA1W+HzeIA//Smjt+RMTY2I+fMt\neP99K06eLNzpMHv2WfT36xNpl2/6+4Po7j6PuXOthZ5KUhimbB08aePxANu2OXDFFc2YMUPbovvf\n/7sV9fW57fGaxeLTmocoimmveeFwGLfffjvuvvtu3HbbbQBiVl5/f6x/5rlz59DQ0AAgFjDT29sr\nv/fMmTNobs48MEgPylL4COTH9nq98Hq9EEURLMuioqICVVVV8sZvtuNmKnyvvhpru5IfJMydG4Uk\nWbFjR+ET1C5c6Cn0FHIiFJKwa9d5zJ3LIsvTxlA4jsHRo0W0GVlgursZHDxYjeuuG4vm5svW/KxZ\nlfjKV5oKODNjyWTNkiQJX/3qV9He3o5vf/vb8uPLly/H+vXrAQDr16+XBXH58uV48cUXIQgCuru7\ncfz4ccyZM0ffA0iTsrwFZBgmLnkzGo3KkZrqKM1sxwcyF758uTlJTt6uXea477nmmvM4cCC/dRWN\nYteuQbS3V2BgwIqLF82zX3n11S4cOGCe+RQLe/daYLM1YNGiEA4cuIjHHpsAls395tTMFp/W/7XY\ntm0bnnvuOUyfPl0OflmzZg0eeughrFixAuvWrZPTGQCgvb0dK1asQHt7OziOw9q1awt2/GWXxwcg\nbg8PiAWuuFwu3X4EkvZQUVEBqzU991d3N9DeDsOqoQD5z8lLl2uu2YkDBy4Vehq60thoQ11dNY4e\nNUe+38KFddi2zRxzKSZYFpg+3Yrrr7fjllvsWLhQn8pMpHqK1WpNe40wAp/PB0mS4HQ65R6Bn/vc\n5/C3v/2tYHPKB2Vr8QGQf+hMWgVlMn4m9xTPP2+s6M2ezeDMGV6XPnl60tY2VHKiBwADAyEMDn6M\nBQsasX174et8njhh/qhTszBpkgWLFlmxeLENixfbUV/P560/Xr5Rr1FerxcOh6NAs8kfZSl8JHEz\nEAhAEATDm9GmQpKMK1FWqJy8dKmtPV7oKRhGOCxh+/Z+LFgwGnv3RgwtkpyMqVOdOHqUCl8irryS\nw6JFVixcyGPhQh719cpnIwgELvfU1KslkBlcncr1SdmLr9TrdAJlKnzKExgwrhltOuNGo1H8+c8h\ndHfrW7aI9Mnbu7cwOXnp0Njow4EDFws9DcPZvv1jtLdX4cIFK86fz3+ASX29DQDN3yOMGcNi4UIe\n119vxw032NHSElsGle181HUuU7UEIutJrv3xCgWZczl0ZgDKWPiUfxslfMlQVoV54QV9RW/6dMDr\nNaZPnp5MnNiDrVvLY4u5q8uDUaOsuPrqWhw+nN+0jTNnyuM7TkR9PYMFC/hPLDorJkyIeT+UN7+A\ndvlCnudHiGGilkAEtRiSP0rMZPGVW0sioEyFj2C08KVTFSYQAF5/XZ/k5/p6CZMnc9i+3ZxuTSWV\nlWEcPFh8Ceu5cOGCgKGh81i4sBHbtuVn32/cOCt6esorjaG6msXChXbccIMDixZZceWVl61d5bWp\nFiwAIxq5aokhx3HgeV6+vjMRQyKIZo0ppMJXBuRT+EhXiEAgIF9MPM/jrbdcGB7O9a5PwsKFLLq6\neGzfXhxulhkzTmHr1vLbd4pEJGzb1o8FC0bhvfeihldSaWmx4/Tp0k5jcDoZzJ9vx5IlDlx/vQMz\nZ9rAskAwGIQgxCJZSScVkphNhEr5J1sxJL04iRgq06WUXRC0msUKgoBoNKpL5/RMSVS1he7xlSj5\ncnWSccPhMPx+v2b/vhdeyO2zSE7etm3mdmsq4bgoTpw4XehpFJTt2y9g6tRKDA5aMTBg3A3A4KAF\nQGkJn9UKzJkTs+huuMGB2bPtsFovL97hcBg+X0C+/kg3AuUCT6wvZZEKpRgqLTgtMVR3NdcSQ9I0\nloihekzymaIoZtw5XQ8SCR+ptFLKlKXwEYwWPlEUMTw8LJ/U6v59584Bf/5zdp/hckm49lrz5eSl\nw3XX9WHnzuIsT6YnR48Oo66OR3t7Nbq69HdHNjby+PDD4g9qsViAmTNtstAtWGCHwzHyRk8URQSD\nwbjrzel0pl1YXksMlZaaUhS1GrqqhYq8N/5YYmLo98c6QVit1rgGsYmsTq09w1zFUGvdc7vdaGtr\ny2ncYqAshc9oi4+Mp4wAczgcI+46f/97IBrN/OSdM4dBb6/5cvLSpdjLk+nJ4GAYbvdFQ/b92tpc\nGBgovv09hgGmTbNiyRLHJ/t0DlRVJfZoSJKEcDiMYDAoX3t2u12X/FzSw05ZuzJTMVQKldq6Ay6L\nISHdzul6iaHa4qutrc14jGKjLIUPyL2LghZa7YxsNhscDodm/75MS5SNGSOisZHB7t3mLoacjGuu\nGcCBA75CT8NURKOxfb9580bhwIEogkF9zkevt3hujCZN4mWLbvFiB0aNSs9KI9HR5CaT47iE15te\n5CqGBKVQJXOlApmJoVoQE4mhHp0ZipWyFT4A8sWRawK7VuAKEDuhXC7tVIX9+4GurvQWJtInb+9e\nDufOFc9enhaS1F3oKZiWnTsvYNKkCni9dpw9m5ulVl1tQVeXed2c48ZxstAtWeLAmDGZLUXkmgsG\nY1YywzCw2+1y+kG+SSWGWoUyRFGUm1xrWW2pXKlaATTk/0pvk3JsZRBNIuGjFl8ZkU3TWEA7cMVu\nt8PnS27VpGvtkZy8LVuKR/BYVkJTk4RRoyRUVEiorhYxfbqEBQsk1NdfiZ6eMTh1Koje3iBOnQri\n9OkQTp8OYni4/KI81Rw75kVdXQjTp9fh/fez3wedOtWFnTvNE9TS0MBgwQIrFi3icf31Nlx1lQ0W\ni2VELl06RKNRBAIB+ZrjeR52u91QKy8byHqiFD2e52G1WrNykwKJxZC4ddUBNMksQ2U6hs/ng8vl\noukMpY6yJ58kSRkLXzQahd/vl/31DMPA6XTKBWdJ8VetccNh4JOC5Qkxe06e0ylhzBgRtbUS7PbY\ncfp8EgYHJZw7J6GiArj5ZuCzn5UwZ05s3yZGJWbOrNQc8+LFsCyGRBBjf8f+eDzlIYyDg2EMDQ1g\n0aImbN2a3b5fNMoBKFxR6ro6FosW2bF4sQ0LF1oxcSIb1xGFpBkQiAgqxVB93UiShFAoJFtJpKNK\ntu3DjIRseyRKp1BbhlrpFVqCpaw6pVy7lGMlE0MtkfV4PJg8eTJaW1tRWVmJ3/zmN5g9ezZmzpyZ\nVWrDpv+/vTOPjqLK/vi3ekknTRYEIUBAQoCRsGcPEAKEfcdBQVxgRlFxgzjMiAujoIiCDAIKiM6R\n0XFG5jjjOIgh44JhwNCJCZu/EFECWdiCQBaSdJJe6vdHfEV1pXpLV3VV0u9zjkdJQvdLWV333fu+\n93uzs5GZmQmbzYalS5di1apVXr+G3ATkdAagJVOz2+2orq6G3W5HRESER+ovvuMKQUy4cv36dQDA\nLbfc0uoDvG8fcOedzoIs6cnToapKuTMahmHRrRuL7t1ZdOpkg1Zrh8XC4sYNFleuANeva1r9fEKC\nHTNm2DFnDjBokDSmvsQmymw2o6rKgoqKZly6ZMfly3ZUVDTxgmQjamo6XmBMTe2KEyfsMJs9/5ga\nDAy02lA0NPjvox0WxmD06July2HDgkTH9zg7CxODHwgBOIhXxFoU1AK5X8nv1Za1OguGYgiDIb+M\nSV6L/z0SDMn1LCoqwowZM1qJbgBg4MCBKCoq8nhzYbPZcPvtt+Orr75CVFQUkpKS8NFHHyE2Ntbj\n390fBHTGx/+3u/hPdnD8D58r4YqrTNJZmXPAAMBg8F9PXlAQi549bejSpaU9AmBhNrOoqmJx8SKL\nK1cYXLnC/xvML/+0YDCwSEuzYsqUZkyZYkFk5M1rWFvb8uDS6XTcw8vbfiRhSatLlyBERUU4nQ5d\nU2NFefnNjFEYGKuq2p/C0WS6hgEDOqGx0Yjz5z07sxs6NBSFhfIGveBgBqmpN3vpEhIM0Onc/7/1\nRhji7GFP7ikyOFotwc9dlucNJJjxN+POgqEzD1Fh5kzmjpLXIsTHx+PChQsoKirC7373O6SmpqKw\nsBAnTpyAXq/3KqPOz8/HgAEDEB0dDQC4++678Z///IcGPrXhLvA5c1xxd0OLlSEA4Pp1ICvL8Wfl\n7Mnr0oVFZKQd4eEstForrFY76uqAa9cYVFYCZWUMyspEfwPR14uIYDF1aksJc8oUICxMC5YNhtWq\nc+uCwf8wuzrfET5AGIaBwWBwK0+PiNBh2LBQDBsWKvr92lrrL2XTmyVUfin12jV1BsYzZ+rRuXMT\nRo68FcePuy99Ggx6SF3m1OuBhISbgS41NRgGgzT3qlgwJMIPYUkUaMmo+A96T8qkcmO1WtHQ0OCw\nKZZiqDUfqYIhWa/dbueeU1qtFrGxsbBYLNixYweAlqpYZWWlV2u8cOEC+vTpw/25d+/eyMvLa+uv\nLBs08LkIfK4cV9r6uh9/DDQ33/wwJCczKC9ve0+eTsciMtKGLl3sCA0FdDoGjY12VFezuHyZxfXr\nDH6puv6C99lkVBSLmTNbgl16estDkA/DMK12hq4+jPwPJPkw6nQ6bj5iU1OTQ0nLYDBIIlwID9dh\n6NBQDB0qHhjr6mwOgfBmcGwR31y9qpxKsrraipMnW0Yc5eY6X4dGA/zwg+8BnAxgbSldGjF6dDBC\nQ/1TiRC2KGi1WoSEhDicV9lsNlitVpc2Y/4IhmJZnjdN877iSzA8dOgQHnvsMYwYMQIxMTH49ttv\nER8fz1Wp9Ho9evfu7fV62gMBG/hclTpdCVc8/R/rLPCRMmdUFIsePXTIz3f/AQkLY9GrF4uwMBv0\neitYlkF9vR3XrgGVlQwuXGBwQdTvue034eDBLGbNAmbPZhEXxxeneIbQBcPdh1Fsd0qCqb8+TKGh\nWgwZ0glDhoi3oNTX21Be3ojSUjNKSm6grKwR5883o6KiGefPW/Dzz/IGRru9ZcRRQkJnFBczomd4\nQ4Z0wvfft03NOXhw0C+jelp66W65xb/CKmGLAtC6EV2j0bTKDIl83xPPTSmDocVigdlsljXLawti\nwVB47sgwDIqLi1FVVYWcnBzk5OQAAE6fPo3s7Gzce++9ePPNN71+76ioKFRUVHB/rqio8Dp4+oOA\nDXwEYYOoJ8IVb16XH/h+/BE4fhxIT9fgu+9uzsnTaFhERgLdurEIC7NDo2FhsbCoqWnJ2qqqgNOn\nuVf+5d/S7r41GhapqcDMmSxmzwb695f05Z3uTK1WK5qamlo9pMhDkL+T5p8XKlHOMho16NdPi169\n9Bg9ugsAxwez2WwTPVskCtUrV5ohhZSssLAa/fqFoLnZiAsXHK9bp06ee3PGxNzspUtPD0FkpHKP\nA+F5rqeN6GSDJQyG3hhQexsMWZaF2WzmNsYkI/VXlucNYv2ORqMROp0Od9xxB7777jvcfvvtCA4O\nxvHjx1FYWIiff/651UbUUxITE/HTTz+htLQUvXr1wj/+8Q989NFHUv5KkhCwgY+/gwTQyvLIlXDF\nm9fnB77PP2eRnq5DUxOQkGBFQ0OL/P/iRRaXLgGXLvnyG3lPcDCLjIyWEub06YA/vWnFdvfkHE/4\n4CKbkrZI4KVCuGMW6x0LCdFi0KBOGDRIPGNsbLQLyqhNDmKcykrPA+O5c2ZERFgQF9cVx47d3KiV\nlzt/gZ49NUhPD8b48UaMH2/Ebbcp3wYgR4uCOwNqX4KhMMuTyhpNDsT6HUNCQmC327Fr1y588skn\n2L59O4YPH879HZZlceHChTabeuh0Orz11luYOnUqbDYbHnzwQdUJW4AAbmcgD9L6+nqHB6onwhVP\nqK+vR1NTE4xGI4KDg/H22yxWrgScKJL9RpcuLeKU2bNZTJoEODGWkRVhENHpdAgODna6Y/ZGAs/P\nCqVwthczPiYOIVLT1GT/pY+xqZXwpqysEZcvN0P4azMMkJYWicOHm9C/fzDOnLl537YMYA3CmDE6\nhwGsBKVFIVLI/n3BWTAUg8zQI2v191meN4hleWQzUVFRgSeffBKpqalYvXo113ccaARs4GtubkZ1\ndTW3G2IYBqGhoZI90BoaGtDY2AiDIQRr1wZj2zZJXrZN3HZby3ndrFksxowBfIzpbUYoWvAliHj6\n0PJUSSrEWUaq5BlOc3NL76KY+CYszACbLRgajQ5jxuiRnh6MhIQwTvbf1mslx0gcKWX/UuNtMFRa\nTSpE+BkjlQkA+Nvf/oa//OUv2LJlC1JSUpRcpuIof6cpCOlr4c/OkoqWMx/goYf0+PxzyV7WY4YN\nazmrmz2bBa+SoQjCchbgexDxppwlpiQVywwJYhmp3MbHnhAUpEH//iHo3z+E+5pY64ewVOjrtWrL\nxsEZahWEEPjXShhEGIbhlMdKq0mFkAkVxCCffx9UVlZixYoVGDBgAA4cOICQkBA3r9bxCdiMj2VZ\n1NXVAQDq6uqg0+kQHh4u2euXlzdiwQItjh/3z95Cq2WRkmLFtGkWTJ1qQZ8+dsV3pHzXFXKb+dNX\n0Rv3C/LA49s5yVnW9BWxUTy+lApJz6lcWbSwZKx2QYi7MUdqygydTahgGAaffPIJ3nrrLWzcuBHp\n6emq2WAoTcBmfAzDICgoiLtZpIz/p06xmDcvCOXl8t5kRiPL+WFOnmxFRIQNNpsdNluL9L2tDeRS\nIDxYV6Kc5U2Pk7PxMaRXTC2lLMB5n5svQYSUNIUtKCQYCtsFXGWGJJsm1RR+JgKoWxDi6ZgjOQU0\n3kDK8eT5RbK869ev4/e//z06d+6Mr776CmFh4v64gUrAZnxAy01jtVpRU1MDjUbTJkNWIQcOsFi0\nCKipkWCBInTtasfUqVbMmaPBpEkaOKtaeHOu46rs5y1tdV1RCqHjBt/LUAwls2ixkjF50PlzDd54\nSJK/A9w0gFC6ZCyGWICW4trKlRkKM2h+lpednY0NGzZg7dq1mDZtmio/d0oTsBkfwVOvTk94/30W\nTzzRMn1BSqKjbZg2zYJp06xIT9f/YknlGrEGcme7d4vF4mBQS9zd+Y4qnvQ2iZXepHJdkRrhg4Oc\nieh0Oi5T4T+snLmE+CuL9qSdwh946xTCx2azob6+XlRAoyRyDrOVIzMUHh+QAH3jxg08++yzsFqt\nyM7ORpcuXXxef0cl4DM+u92OqqoqAOKTFDyBZVmsWQNs2CDd2kaOtGHKlGZMm9aM2FhWlqxJ+MAi\n/n1iuNqNWq1WNDY2ch9atZ/fNDc3O9iieSqwkFtJ6uw9he0UalFAiiEM0OR3J9dODP5Gy5/BUEz2\nr9QwW28yQwC4ePEiCgoKkJqaytmNvfDCC3j66acxf/58xTcTakednx4/QcpariYpuKOpicVDD7mf\nr+cOvZ5FWhowfboFGRkN6NVL/qzJ2e5d7PxLLNMhwyz5NkhKTsF2hzBAu+sfFOIqi+Zn0mJnYN4+\n3MUyaLUpIPl4oi51dm+Rf/hVB38IQvg+vEord91lhuTeIhw8eBArV64EABiNRnTq1AkLFiyA3W5H\nWVkZon+ZjiA1r776Kj788ENoNBoMGzYMu3fvhsFgkOW95CSgM762zuQjXLvG4q67gNzctr1/WBiL\nSZNa2g4mTrTAYGj0uKnbnyh1XigVQqd/YVlTSrxVkooFQ6EwSM0ZNNC6RcEbdak35gRSBEM1c7Z9\nKQAAIABJREFUZXmeINbzGBQUhOzsbLzzzjv4/vvvce3aNYe/M2nSJHz55ZeSr6W0tBQZGRkoLi6G\nwWDAwoULMWPGDCxZskTy95KbgM/4+P/2Zg9w5gyLuXOBkhLv3jMyksWMGSxmzWIxYQIDnc6GxsbG\nX8qM6pTQ83ejQgEAyfykPC+UCqkl/57gyRkYKSmLZTqk+kBQuwLS1zIs2Sy1dT6fN8FQuKFQ6pzU\nU5yNOmpubsaxY8dgNBpx7NgxMAyDo0ePoqCgAIWFhUhPT5dlPeHh4dDr9WhoaIBWq0VDQwOioqJk\neS+5CeiMj5QPamtrYbVaERYW5lHA+fZbFgsWAIKNllMGDmQxZw6DmTNtSExkodEwnEKPb5em9oec\nK9cVqc4LpULtWZMz8YwYSvdjCvGkz02O9xQrKYvBv1YkoJL1AtL4gcqJWJZH7NFOnjyJ3/3ud7j/\n/vvxyCOP+D1ov/POO1i5ciVCQkIwdepU/PWvf/Xr+0tFQAc+8iG6ceMGLBYLQkND3XrX/eMfLB5+\nGOApylvBMCzi422YNq0ZU6daEBfX6ZevtzwUhFZYalY/iknoPX3IeVrGklIMInbWpOZSlpi6VKfT\ncddObvFMW9YrdQ+hL2vxRhACtKyXHCGo8X4QioNIlme1WrFlyxYcOnQIb7/9NgYMGOD3tZWUlGD2\n7Nk4dOgQIiIicNddd+HOO+/Evffe6/e1+EpAlzoJnpY6X3uNxdq1EHXQNxhYjBljxdSpzZgzR4O+\nfYNRU9MMlmVx48aNVnZHgLrO8YRI4boiVsaSylZMbL3+Lmv6gqfiFaWsxcTWK9yw+buHUIgrQQi5\nPsKNFmmpUHLzIIZwg8kvG58+fRqZmZmYPXs2/vvf/yr2vCgoKMDo0aPRtWtXAMCvf/1r5Obm0sDX\nXnEX+CwWFo8/DnzwgePXIyJYZGRYMHVqMzIyLLjlFj3XRGqz2WAwGGCxWBz6dPiQCRFqKWERhGVC\nKSX0cvQXqr2sKUS4XleKQn8qST1dr5rPxojSmB/0dDod572p5ObBGTZby+Br4ZQKu92O7du347PP\nPsPOnTsxZMgQ2dfiikGDBuHll1+G2WxGcHAwvvrqKyQnJyu6prYS0IHPE3FLTQ2Lu+8Gvvmm5c+9\newPTp9sxeXIjUlKaoNcTR4ow6HQ6rpzHMIzDh42g1d4cbyKcMaf0LlQ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"text": [
""
]
}
],
"prompt_number": 23
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So yes, our research worked out, in fact the 2 and 5 periods lead to the best overall gain. So the final question we will ask is: Is our filter right? We will focus on four different types of filters (all described and coded in signal_processing.py). The filters are \n",
"\n",
"* SMA (simple moving average): This is the coarsest method of finding a trend. It weights past events the same as current events, which means it is relativly unresponsive\n",
"* EMA (exponential moving average): This uses exponential weighting. Thus more recent events are weighted more heavily.\n",
"* Gaussian Filter: This is a n order exponential moving average and is better able to capture price displacment because of events\n",
"* Butterworth Filter: More sophisticated infinite impulse response filter. It is a higher oder gaussian with two poles.\n",
"\n",
"Let us then do a naive optimization over all of these filters to find their optimal periods, and then veiw some statistics. \n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"for filt,name in [(sp.ema,'EMA'),(sp.gaussian,'Gaussian'),(sp.butterworth,'Butterworth')]:\n",
" values = []\n",
" for short_period in range(1,5):\n",
" for long_period in range(short_period + 1, short_period + 5):\n",
" values.append([short_period, long_period,sp.dmac(prices.OPEN,prices.OPEN,filt,short_period, long_period, 5, True,end_value=True)])\n",
"\n",
" optimal = max(values,key=lambda x:x[2])\n",
" \n",
" print \"%s Value, Returns: %d, Periods: %d, %d\" % (name, optimal[2], optimal[0], optimal[1])\n",
" \n",
" values = []\n",
" for short_period in range(1,5):\n",
" for long_period in range(short_period + 1, short_period + 5):\n",
" values.append([short_period, long_period,sp.dmac(prices.OPEN,prices.OPEN,filt,short_period, long_period, 5, False,end_value=True)])\n",
"\n",
" optimal = max(values,key=lambda x:x[2])\n",
" \n",
" print \"%s Technical, Returns: %d, Periods: %d, %d\" % (name, optimal[2], optimal[0], optimal[1])\n",
" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"EMA Value, Returns: 499, Periods: 1, 5\n",
"EMA Technical, Returns: 59, Periods: 4, 8"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Gaussian Value, Returns: 457, Periods: 2, 3"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Gaussian Technical, Returns: 42, Periods: 2, 6"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Butterworth Value, Returns: 101, Periods: 1, 2"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Butterworth Technical, Returns: 98, Periods: 1, 2"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So we are done right? Not quite yet. So it may seem like SMA preforms the best out of all of the filters above. But we have not looked at their statistics. Let us veiw the best of the best, and compare SMA, EMA, and the baseline. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" equity_curves['Value EMA'] = sp.dmac(prices.OPEN,prices.OPEN,sp.ema,1, 5, 5, True)\n",
"equity_curves['Value Gaussian'] = sp.dmac(prices.OPEN,prices.OPEN,sp.gaussian,2, 3, 5, True)\n",
"del equity_curves['Technical SMA']\n",
"equity_curves.plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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TJzN37tyHdywnSvs+lZZvCjpUhPy2v37KmcRYAGwtLJnR/Nly6xCfkVrsmKKM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\naS2cFg0s0/PNjjkvn6JZ6rxZr63103UYMqxZqec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8/f11jZFCNCV4uE5GIQrbuihTNZNj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\nLGLSMFXr18kyM8G6HOVQ9eWAl4WytgWK5FwS6pmT4GWF5cyOuDo6Epe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"text": [
""
]
}
],
"prompt_number": 25
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before we move on to the stats, let's take a look at what we have here. The most curious thing to note is that the EMA did not do too much better than the baseline. Oddly enough the EMA seemed to do best in times of economic downturn. Well, lets move onto the statistics, and comparative statistics. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"stats = []\n",
"for strategy in ['Baseline','Value SMA','Value EMA','Value Gaussian']:\n",
" stats.append( sp.performance(equity_curves[strategy], time_frame= 251))\n",
" \n",
"pd.DataFrame([stat.values() for stat in stats],columns = stats[0].keys(),index=['Baseline','Value SMA','Value EMA','Value Gaussian'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" sharp | \n",
" std | \n",
" sortino | \n",
" car3 | \n",
" car1 | \n",
" cret | \n",
" pos | \n",
" car5 | \n",
" aret | \n",
" max | \n",
" ave | \n",
" ytd | \n",
" 1000 | \n",
"
\n",
" \n",
" \n",
" \n",
" Baseline | \n",
" 0.450600 | \n",
" 0.169088 | \n",
" 0.868786 | \n",
" 14.479322 | \n",
" 17.134151 | \n",
" 284.648624 | \n",
" 0.526083 | \n",
" 5.947035 | \n",
" 6.967836 | \n",
" 56.700440 | \n",
" 0.033569 | \n",
" 17.134151 | \n",
" 3846.486241 | \n",
"
\n",
" \n",
" Value SMA | \n",
" 0.857395 | \n",
" 0.159222 | \n",
" 16.518197 | \n",
" 12.628268 | \n",
" 4.673404 | \n",
" 1021.574147 | \n",
" 0.337055 | \n",
" 14.389879 | \n",
" 12.847359 | \n",
" 24.042366 | \n",
" 0.051072 | \n",
" 4.673404 | \n",
" 11215.741466 | \n",
"
\n",
" \n",
" Value EMA | \n",
" 0.509205 | \n",
" 0.185759 | \n",
" 1.388655 | \n",
" 8.647352 | \n",
" 8.518586 | \n",
" 399.564057 | \n",
" 0.327045 | \n",
" 11.128043 | \n",
" 8.375112 | \n",
" 48.362182 | \n",
" 0.035617 | \n",
" 8.518586 | \n",
" 4995.640570 | \n",
"
\n",
" \n",
" Value Gaussian | \n",
" 0.537531 | \n",
" 0.168085 | \n",
" 1.455399 | \n",
" 4.046805 | \n",
" 4.218977 | \n",
" 357.432135 | \n",
" 0.300866 | \n",
" 6.198407 | \n",
" 7.898730 | \n",
" 30.130000 | \n",
" 0.033532 | \n",
" 4.218977 | \n",
" 4574.321353 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 26,
"text": [
" sharp std sortino car3 car1 cret pos car5 aret max ave ytd 1000\n",
"Baseline 0.450600 0.169088 0.868786 14.479322 17.134151 284.648624 0.526083 5.947035 6.967836 56.700440 0.033569 17.134151 3846.486241\n",
"Value SMA 0.857395 0.159222 16.518197 12.628268 4.673404 1021.574147 0.337055 14.389879 12.847359 24.042366 0.051072 4.673404 11215.741466\n",
"Value EMA 0.509205 0.185759 1.388655 8.647352 8.518586 399.564057 0.327045 11.128043 8.375112 48.362182 0.035617 8.518586 4995.640570\n",
"Value Gaussian 0.537531 0.168085 1.455399 4.046805 4.218977 357.432135 0.300866 6.198407 7.898730 30.130000 0.033532 4.218977 4574.321353"
]
}
],
"prompt_number": 26
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"stats = []\n",
"for strategy in ['Value SMA','Value EMA','Value Gaussian']:\n",
" stats.append( sp.stats(equity_curves[strategy], equity_curves['Baseline'],time_frame= 251))\n",
" \n",
"pd.DataFrame([stat.values() for stat in stats],columns = stats[0].keys(),index=['Value SMA','Value EMA','Value Gaussian'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" alpha | \n",
" beta | \n",
" r | \n",
" return | \n",
" correlation | \n",
"
\n",
" \n",
" \n",
" \n",
" Value SMA | \n",
" 12.124887 | \n",
" 0.021216 | \n",
" 0.000268 | \n",
" 1021.574147 | \n",
" 0.016368 | \n",
"
\n",
" \n",
" Value EMA | \n",
" 6.986131 | \n",
" 0.019568 | \n",
" 0.000234 | \n",
" 399.564057 | \n",
" 0.015300 | \n",
"
\n",
" \n",
" Value Gaussian | \n",
" 6.260903 | \n",
" 0.038330 | \n",
" 0.000822 | \n",
" 357.432135 | \n",
" 0.028669 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 27,
"text": [
" alpha beta r return correlation\n",
"Value SMA 12.124887 0.021216 0.000268 1021.574147 0.016368\n",
"Value EMA 6.986131 0.019568 0.000234 399.564057 0.015300\n",
"Value Gaussian 6.260903 0.038330 0.000822 357.432135 0.028669"
]
}
],
"prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So this tells the story. The Value SMA has lower varience (meaning high sharp and sortino, and low maximum drawdown and standard deviation). And it has higher in terms of return. All of the strategies yeild positive alpha and have very low beta. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### DMAC Further Work\n",
"\n",
"One can much more thruoghouly examine different filters and different periods in order to find the optimal. But we should be wary of overfitting. There are other statistical test that we could preform to judge the value of a strategy. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"###RSI \n",
"\n",
"RSI or relative strength index is a measure of a certain stock being overbought or oversold. Thus if the RSI (implemented and explained further in signal_processing.py) breaches upper and lower bounds of 70 and 30, we should assume that the stock will revert to the mean. But what does this look like?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"equity_curves = pd.DataFrame(sp.rsi(prices.OPEN,50),columns =['RSI'],index=prices.index)\n",
"equity_curves.plot(); remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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CAO7rMYJ7fW5uLo4HX0I634CeEz7rjw6EUrSKjAlaZqf8sOm8C3bzp2YnoISc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"text": [
""
]
}
],
"prompt_number": 28
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Well this does not tell us much. First the principal of RSI is: Sell wehn above 70 and buy when below 30. So lets add some more graphics to the chart."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"equity_curves['Upper Bound'] = [70]*len(equity_curves.RSI)\n",
"equity_curves['Lower Bound'] = [30]*len(equity_curves.RSI)\n",
"# normalize the original s&p\n",
"equity_curves['Baseline'] = 100*prices.OPEN/prices.OPEN[-1]\n",
"equity_curves.plot(); remove_border(); plt.legend(loc='upper left')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 29,
"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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b2c4qDowfrooKFCz3nNIHqihKgLMWvrUlQMiZxxzGGuE69X9kMH97TOoDAFCo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\nyJEMuYSEhEQj5/8Bp3pP6pndWdsAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 29
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Ah, now we can see the strength of RSI. Notice that when RSI breaks the bounds of 70/30, the morket will then move in the other direction. RSI tells us if the stock is overbought or oversold. Thus we can see that it works, to an extent. Let's try to find the best implementation of this strategy. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"values = []\n",
"for period in range(1,101):\n",
" values.append([period,sp.equity_curve(sp.rsi(prices.OPEN,period), prices.OPEN, [70]*len(prices.OPEN), [30]*len(prices.OPEN), 5,end_value=True)])\n",
" \n",
"print max(values,key=lambda x:x[1])\n",
"\n",
"periods, returns = zip(*values)\n",
"\n",
"plt.plot(returns)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[13, 114.08440469332842]\n"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 30,
"text": [
"[]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Za10vfWxeYtS3S7ANyJFbfTVMG+HKvt2PjaPGH4Op7Bv7HfNeQ6WWsU/3YeMA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\nVfYW6YsjCIIQNCMi9rNSM0N6nd6zHy9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"text": [
""
]
}
],
"prompt_number": 30
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So as one can see, there is a trend to RSI such that by increasing or decreasing the period can lead to consistantly better results. Notice that as the period increases, we get less volitility, because we get fewer trades. But we have found a generally optimal strategy. Let us view some statistics on this curve vs. the baseline and finish off with our conclusions on RSI."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"equity_curves = pd.DataFrame(sp.equity_curve(sp.rsi(prices.OPEN,13), prices.OPEN, [70]*len(prices.OPEN), [30]*len(prices.OPEN), 5),columns =['RSI'],index=prices.index)\n",
"# normalize the original s&p\n",
"equity_curves['Baseline'] = 100*prices.OPEN/prices.OPEN[1]\n",
"equity_curves.plot(); remove_border();# plt.legend(loc='upper left')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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mbPsqrUEHpuUHvnta6zHnDv01tjdWB/sA9dwuxtDUnoEpUH3W1GIRqmgqisAE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\ndXWYmJjAxMSkST2MGDGC82BmZgYzM7MG6VdWVsLPzw8ymQxOTk4oKir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"text": [
""
]
}
],
"prompt_number": 31
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So RSI might not be what we are looking for. RSI is a naive approach to handle the stock market from the 1970s and it is not surprising that such a naive strategy might not work. Further implemntations might be to change the holding period, to set stops, or in short develop a more comprehensive RSI tool. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"###Conclusions \n",
"\n",
"Signal processing can get us far. It can make us money, ensure low volitility, and even beat the stock market. But sometimes it just does not work. Our naive approach to signal processing has given us insight on how traders might look at the market and how to evaluate a strategy, however there exist problems with overfitting and a potentially limitless supply of different signals. \n",
"\n",
"Extensions and future work for signal processing include: run more advanced statistics, to try a wider range of techniques, and develop a more in depth trading system (including stops, limits, commissions, and slippage). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Portfolio Construction and Analysis\n",
"\n",
"This is the most classice way to go about making money on the market: buying some stocks and putting them in your portfolio. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate returns from price data.\n",
"---------------------------------\n",
"\n",
"Returns defined as: \n",
"$$ $$\n",
"$$r_t = \\frac{p_t-p_{t-1}}{p_{t-1}} $$\n",
"\n",
"We define the iterative return index:\n",
"\n",
"$$i_t = (1 + r_t) \\cdot i_{t-1}, \\quad i_0 = 1$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"RR = close_px/close_px.shift(1) - 1\n",
"daily_index = (1 + RR).cumprod()\n",
"daily_index['MSFT'].plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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aK92V1lPU21S3/NiG66cx8dhGjWdG5sotUJ36wkhmPMvDiQcJCo+5n/8ELbYv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\nIAjCzPk/tb+YuVXV+DwAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 32
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Let's sample and plot monthly returns...\n",
"monthly_index = daily_index.asfreq('EOM', method='ffill')\n",
"monthly_RR = monthly_index / monthly_index.shift(1) - 1\n",
"monthly_RR.plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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LjAeo/8jzmLkm9/u8mUPfV9ReUvB28263fqJNgoq3nUuXbb+zFx/NfvsaUplu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\nAABJRU5ErkJggg==\n",
"text": [
""
]
}
],
"prompt_number": 33
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can plot multiple timeseries in a dataframe using matplotlib:\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"subRR = RR.ix[:, ['AAPL', 'IBM', 'XOM', 'MSFT']]\n",
"(1 + subRR).cumprod().plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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hKZebvG4LrBC1agp8ib/R5x388WDtAYfbqzq3HEWvbqNdWX16xej7eb9mKSG9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\n+9mqVStyc3NRFIWYmBjatGnDzp07CQoKIjY2lmeffZb09HS2b99uL8d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"text": [
""
]
}
],
"prompt_number": 34
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can look at the distributions of stock and ETF (Exchange Traded Fund) returns:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"RR[-250:].hist(bins=50)\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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6FtDVv/r166ex3oMHD4anpye8vb1x69YtLF68GO7u7pg6dapaeADYvHkzfHx8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\n25e9t0/ZXDQrff8tj7Mq3OUpWL8A+GrH9nCpr1xsuGjFtU1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"text": [
""
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"RR.ix[-1].plot(kind='bar')\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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4s2l88tpllv/ABiZIB9ogZ2r8aPj9mDj+dGIqCE1NTXi9Xvx+PwDLly8nISGB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\njzVr1th6bSUTHT16lD/+8Y8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"text": [
""
]
}
],
"prompt_number": 36
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use a sliding window of price to calculate certain functions of timeseries, such as rolling volatility and moving averages."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# We have the following plot for Apple:\n",
"px = close_px['AAPL']\n",
"close_px['AAPL'].plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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8fDx4PB7Mzc2xbVt1eEgbGxt4eXnBxsYGWlpaCA0NBY/Ha0JBeTTlc+qI2urY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\ny7l6gOoFgmPGjJHbv4KGtP/880/07t0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"text": [
""
]
}
],
"prompt_number": 37
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And the corresponding rolling volatility:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"vol = rolling_std(px / px.shift(1) - 1, 250) * np.sqrt(250)\n",
"vol.plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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/D54MLoeL0CGBcG5mx1T8uZ//jM621CAVPEGkiLmx8vVNhe92dPHrarLG+/rz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\nAAAjhMUbAGCEPgBW0zeLNJBKVwAAAABJRU5ErkJggg==\n",
"text": [
""
]
}
],
"prompt_number": 38
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We calculated the rolling volatility using a sliding window of price; similarly we can calculate a smoothed exponential moving average of the rolling volatility to more easily recognize changes in trend."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"evol = ewmstd(RR, span=250) * np.sqrt(250)\n",
"vol.plot()\n",
"evol.plot()\n",
"plt.xlim([datetime.datetime(1991, 1, 1), datetime.datetime(2012, 1, 1)])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 39,
"text": [
"(726833.0, 734503.0)"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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AqLY+MBMKFR45uY7zNjZmduyHn98aD6FAiLABQXBp5MBW/LmT84TOttQhpSJJ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\na9cutGzZEvv37wcgeXIdN24ckpOTcfr0aV5+Z1x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"text": [
""
]
},
{
"metadata": {},
"output_type": "display_data",
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QPszKpwuo6pWNORunQF3ykD3WZuYOuI/7DG4j32P3tf/sFu98u9DneG3tSUyn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\nt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O3bt2FkZITa2lrk5+ejq6sLNjY2mDp1Kt577z2sWbMGxsbGMDAwwIsvvjjk1vdJ/e3t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\n",
"text": [
""
]
}
],
"prompt_number": 39
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Correlation of Equity Returns\n",
"-----------------------------"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the variable $RR$, we have the returns of the various $SPX Equities. These returns may be correlated. We can look at the correlation in a grid:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"RR.corr()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" AA | \n",
" AAPL | \n",
" GE | \n",
" IBM | \n",
" JNJ | \n",
" MSFT | \n",
" PEP | \n",
" SPX | \n",
" XOM | \n",
"
\n",
" \n",
" \n",
" \n",
" AA | \n",
" 1.000000 | \n",
" 0.216917 | \n",
" 0.454180 | \n",
" 0.320836 | \n",
" 0.239261 | \n",
" 0.332316 | \n",
" 0.231136 | \n",
" 0.599806 | \n",
" 0.433569 | \n",
"
\n",
" \n",
" AAPL | \n",
" 0.216917 | \n",
" 1.000000 | \n",
" 0.309258 | \n",
" 0.353119 | \n",
" 0.153393 | \n",
" 0.365921 | \n",
" 0.129998 | \n",
" 0.439518 | \n",
" 0.189228 | \n",
"
\n",
" \n",
" GE | \n",
" 0.454180 | \n",
" 0.309258 | \n",
" 1.000000 | \n",
" 0.413646 | \n",
" 0.374792 | \n",
" 0.414954 | \n",
" 0.332428 | \n",
" 0.744141 | \n",
" 0.392965 | \n",
"
\n",
" \n",
" IBM | \n",
" 0.320836 | \n",
" 0.353119 | \n",
" 0.413646 | \n",
" 1.000000 | \n",
" 0.247022 | \n",
" 0.426098 | \n",
" 0.215850 | \n",
" 0.575682 | \n",
" 0.278011 | \n",
"
\n",
" \n",
" JNJ | \n",
" 0.239261 | \n",
" 0.153393 | \n",
" 0.374792 | \n",
" 0.247022 | \n",
" 1.000000 | \n",
" 0.292051 | \n",
" 0.372419 | \n",
" 0.506015 | \n",
" 0.351107 | \n",
"
\n",
" \n",
" MSFT | \n",
" 0.332316 | \n",
" 0.365921 | \n",
" 0.414954 | \n",
" 0.426098 | \n",
" 0.292051 | \n",
" 1.000000 | \n",
" 0.249435 | \n",
" 0.618319 | \n",
" 0.314164 | \n",
"
\n",
" \n",
" PEP | \n",
" 0.231136 | \n",
" 0.129998 | \n",
" 0.332428 | \n",
" 0.215850 | \n",
" 0.372419 | \n",
" 0.249435 | \n",
" 1.000000 | \n",
" 0.450798 | \n",
" 0.306896 | \n",
"
\n",
" \n",
" SPX | \n",
" 0.599806 | \n",
" 0.439518 | \n",
" 0.744141 | \n",
" 0.575682 | \n",
" 0.506015 | \n",
" 0.618319 | \n",
" 0.450798 | \n",
" 1.000000 | \n",
" 0.601648 | \n",
"
\n",
" \n",
" XOM | \n",
" 0.433569 | \n",
" 0.189228 | \n",
" 0.392965 | \n",
" 0.278011 | \n",
" 0.351107 | \n",
" 0.314164 | \n",
" 0.306896 | \n",
" 0.601648 | \n",
" 1.000000 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 40,
"text": [
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"AA 1.000000 0.216917 0.454180 0.320836 0.239261 0.332316 0.231136 0.599806 0.433569\n",
"AAPL 0.216917 1.000000 0.309258 0.353119 0.153393 0.365921 0.129998 0.439518 0.189228\n",
"GE 0.454180 0.309258 1.000000 0.413646 0.374792 0.414954 0.332428 0.744141 0.392965\n",
"IBM 0.320836 0.353119 0.413646 1.000000 0.247022 0.426098 0.215850 0.575682 0.278011\n",
"JNJ 0.239261 0.153393 0.374792 0.247022 1.000000 0.292051 0.372419 0.506015 0.351107\n",
"MSFT 0.332316 0.365921 0.414954 0.426098 0.292051 1.000000 0.249435 0.618319 0.314164\n",
"PEP 0.231136 0.129998 0.332428 0.215850 0.372419 0.249435 1.000000 0.450798 0.306896\n",
"SPX 0.599806 0.439518 0.744141 0.575682 0.506015 0.618319 0.450798 1.000000 0.601648\n",
"XOM 0.433569 0.189228 0.392965 0.278011 0.351107 0.314164 0.306896 0.601648 1.000000"
]
}
],
"prompt_number": 40
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Or preferably, we can use a colorful visualization to see at a glance which equities exhibit stronger correlation with each other:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_corr(RR.corr())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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EsBDFLNfQVUREBBEREUX2aQtmixcvLrU8g3pqoaGhxMbGkpiYyIQJEwgICGDn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\nkaAmhLAo/w96NNnYAykvAAAAAABJRU5ErkJggg==\n",
"text": [
""
]
}
],
"prompt_number": 41
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also plot the correlation of the monthly returns."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_corr(monthly_RR.corr())"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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cevToUeLR30IIC2EpSzrCw8NJSEhg3759TJw4kaZNm7J9+/YS56hUKhITE6le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\nBDUhhEX5f0d6q9vlZSHYAAAAAElFTkSuQmCC\n",
"text": [
""
]
}
],
"prompt_number": 42
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Leave-One-Out Regression (LOOCV):"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Note: the function leave_one_out is included in the helper file.\n",
"leave_one_out(RR)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 43,
"text": [
"{'ex-AA': GE -0.056442\n",
"IBM 0.196518\n",
"JNJ -0.138967\n",
"MSFT 0.175767\n",
"PEP -0.113942\n",
"SPX 1.142164\n",
"XOM -0.178632\n",
"intercept 0.000844\n",
"dtype: float64,\n",
" 'ex-GE': AA -0.079250\n",
"IBM 0.194958\n",
"JNJ -0.150925\n",
"MSFT 0.174841\n",
"PEP -0.118740\n",
"SPX 1.170754\n",
"XOM -0.157575\n",
"intercept 0.000841\n",
"dtype: float64,\n",
" 'ex-IBM': AA -0.082702\n",
"GE -0.060464\n",
"JNJ -0.162179\n",
"MSFT 0.187395\n",
"PEP -0.127989\n",
"SPX 1.445041\n",
"XOM -0.185627\n",
"intercept 0.000924\n",
"dtype: float64,\n",
" 'ex-JNJ': AA -0.069560\n",
"GE -0.054263\n",
"IBM 0.199524\n",
"MSFT 0.173160\n",
"PEP -0.141957\n",
"SPX 1.153692\n",
"XOM -0.173623\n",
"intercept 0.000799\n",
"dtype: float64,\n",
" 'ex-MSFT': AA -0.086019\n",
"GE -0.075172\n",
"IBM 0.211504\n",
"JNJ -0.155034\n",
"PEP -0.125363\n",
"SPX 1.479190\n",
"XOM -0.183643\n",
"intercept 0.000965\n",
"dtype: float64,\n",
" 'ex-PEP': AA -0.074750\n",
"GE -0.054790\n",
"IBM 0.199032\n",
"JNJ -0.175586\n",
"MSFT 0.174323\n",
"SPX 1.175799\n",
"XOM -0.168719\n",
"intercept 0.000829\n",
"dtype: float64,\n",
" 'ex-SPX': AA 0.026372\n",
"GE 0.214939\n",
"IBM 0.332856\n",
"JNJ -0.028252\n",
"MSFT 0.319514\n",
"PEP -0.031255\n",
"XOM 0.026058\n",
"intercept 0.000598\n",
"dtype: float64,\n",
" 'ex-XOM': AA -0.090336\n",
"GE -0.035589\n",
"IBM 0.205419\n",
"JNJ -0.161027\n",
"MSFT 0.180873\n",
"PEP -0.123881\n",
"SPX 1.095649\n",
"intercept 0.000791\n",
"dtype: float64}"
]
}
],
"prompt_number": 43
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can organize this output into a dataframe."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"DataFrame(leave_one_out(RR))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" ex-AA | \n",
" ex-GE | \n",
" ex-IBM | \n",
" ex-JNJ | \n",
" ex-MSFT | \n",
" ex-PEP | \n",
" ex-SPX | \n",
" ex-XOM | \n",
"
\n",
" \n",
" \n",
" \n",
" AA | \n",
" NaN | \n",
" -0.079250 | \n",
" -0.082702 | \n",
" -0.069560 | \n",
" -0.086019 | \n",
" -0.074750 | \n",
" 0.026372 | \n",
" -0.090336 | \n",
"
\n",
" \n",
" GE | \n",
" -0.056442 | \n",
" NaN | \n",
" -0.060464 | \n",
" -0.054263 | \n",
" -0.075172 | \n",
" -0.054790 | \n",
" 0.214939 | \n",
" -0.035589 | \n",
"
\n",
" \n",
" IBM | \n",
" 0.196518 | \n",
" 0.194958 | \n",
" NaN | \n",
" 0.199524 | \n",
" 0.211504 | \n",
" 0.199032 | \n",
" 0.332856 | \n",
" 0.205419 | \n",
"
\n",
" \n",
" JNJ | \n",
" -0.138967 | \n",
" -0.150925 | \n",
" -0.162179 | \n",
" NaN | \n",
" -0.155034 | \n",
" -0.175586 | \n",
" -0.028252 | \n",
" -0.161027 | \n",
"
\n",
" \n",
" MSFT | \n",
" 0.175767 | \n",
" 0.174841 | \n",
" 0.187395 | \n",
" 0.173160 | \n",
" NaN | \n",
" 0.174323 | \n",
" 0.319514 | \n",
" 0.180873 | \n",
"
\n",
" \n",
" PEP | \n",
" -0.113942 | \n",
" -0.118740 | \n",
" -0.127989 | \n",
" -0.141957 | \n",
" -0.125363 | \n",
" NaN | \n",
" -0.031255 | \n",
" -0.123881 | \n",
"
\n",
" \n",
" SPX | \n",
" 1.142164 | \n",
" 1.170754 | \n",
" 1.445041 | \n",
" 1.153692 | \n",
" 1.479190 | \n",
" 1.175799 | \n",
" NaN | \n",
" 1.095649 | \n",
"
\n",
" \n",
" XOM | \n",
" -0.178632 | \n",
" -0.157575 | \n",
" -0.185627 | \n",
" -0.173623 | \n",
" -0.183643 | \n",
" -0.168719 | \n",
" 0.026058 | \n",
" NaN | \n",
"
\n",
" \n",
" intercept | \n",
" 0.000844 | \n",
" 0.000841 | \n",
" 0.000924 | \n",
" 0.000799 | \n",
" 0.000965 | \n",
" 0.000829 | \n",
" 0.000598 | \n",
" 0.000791 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 44,
"text": [
" ex-AA ex-GE ex-IBM ex-JNJ ex-MSFT ex-PEP ex-SPX ex-XOM\n",
"AA NaN -0.079250 -0.082702 -0.069560 -0.086019 -0.074750 0.026372 -0.090336\n",
"GE -0.056442 NaN -0.060464 -0.054263 -0.075172 -0.054790 0.214939 -0.035589\n",
"IBM 0.196518 0.194958 NaN 0.199524 0.211504 0.199032 0.332856 0.205419\n",
"JNJ -0.138967 -0.150925 -0.162179 NaN -0.155034 -0.175586 -0.028252 -0.161027\n",
"MSFT 0.175767 0.174841 0.187395 0.173160 NaN 0.174323 0.319514 0.180873\n",
"PEP -0.113942 -0.118740 -0.127989 -0.141957 -0.125363 NaN -0.031255 -0.123881\n",
"SPX 1.142164 1.170754 1.445041 1.153692 1.479190 1.175799 NaN 1.095649\n",
"XOM -0.178632 -0.157575 -0.185627 -0.173623 -0.183643 -0.168719 0.026058 NaN\n",
"intercept 0.000844 0.000841 0.000924 0.000799 0.000965 0.000829 0.000598 0.000791"
]
}
],
"prompt_number": 44
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can conveniently use the function 'groupby' to group the data by year."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"grouped = RR.groupby(lambda x: x.year)\n",
"for year, group in grouped:\n",
" print year\n",
" print group[:5]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"1990\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1990-02-01 NaN NaN NaN NaN NaN NaN NaN NaN NaN\n",
"1990-02-02 0.012048 0.017812 0.000000 0.005956 0.023419 0 0.008278 0.006478 0.019608\n",
"1990-02-05 0.005952 0.022500 0.000000 0.025459 -0.006865 0 -0.006568 0.002810 0.001603\n",
"1990-02-06 -0.011834 -0.007335 0.003484 0.013857 -0.004608 0 0.016529 -0.006599 -0.003200\n",
"1990-02-07 0.005988 -0.043103 0.010417 0.021071 0.013889 0 0.003252 0.012407 0.016051\n",
"1991\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1991-01-02 0.006250 0.011799 -0.014545 -0.007874 -0.025554 0.000000 -0.008526 -0.011417 -0.019746\n",
"1991-01-03 -0.006211 -0.011662 -0.022140 0.003472 -0.010490 0.000000 -0.029484 -0.013907 0.005755\n",
"1991-01-04 -0.022917 0.005900 -0.011321 -0.003460 -0.007067 0.012195 -0.005063 -0.002827 0.010014\n",
"1991-01-07 -0.006397 0.000000 -0.015267 -0.016865 -0.030249 -0.012048 -0.025445 -0.017321 -0.012748\n",
"1991-01-08 -0.015021 0.000000 0.007752 -0.011100 0.009174 -0.024390 0.005222 -0.001712 -0.002869"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"1992\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1992-01-02 -0.005445 0.054978 0.000000 0.014328 -0.019958 0.027473 0.000000 0.000408 -0.014874\n",
"1992-01-03 0.010949 -0.008451 -0.002646 0.001177 -0.004287 -0.010695 0.015654 0.004985 0.002323\n",
"1992-01-06 -0.009025 -0.017045 -0.005305 0.020576 0.009688 0.032432 -0.015413 -0.003291 -0.008111\n",
"1992-01-07 0.000000 0.019509 -0.005333 0.025922 0.012793 0.026178 0.000000 -0.001340 -0.005841\n",
"1992-01-08 0.001821 0.023388 -0.002681 -0.023582 0.018947 0.035714 0.041436 0.001677 -0.012926\n",
"1993\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1993-01-04 0.019108 -0.025017 0.000000 -0.004980 -0.019883 -0.004762 -0.008889 -0.000757 0.004348\n",
"1993-01-05 0.001562 0.017106 0.011494 -0.024024 -0.022673 0.014354 -0.009716 -0.002389 0.009740\n",
"1993-01-06 -0.006240 0.042046 -0.004545 -0.018462 -0.030525 0.033019 -0.015094 0.000414 -0.004287\n",
"1993-01-07 -0.001570 -0.012105 -0.002283 -0.020899 -0.026448 -0.022831 -0.028352 -0.008722 -0.002153\n",
"1993-01-08 -0.028302 0.020422 -0.002288 -0.010672 0.024580 0.000000 0.016562 -0.003900 -0.016181\n",
"1994\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1994-01-03 0.019293 0.021038 -0.007299 0.020636 0.007702 -0.005051 -0.006662 -0.002165 0.009054\n",
"1994-01-04 -0.001577 0.054945 -0.003676 0.023589 -0.002548 0.005076 -0.011923 0.003115 0.007976\n",
"1994-01-05 0.023697 0.071615 -0.007380 0.008230 -0.002554 0.020202 -0.009804 0.001414 0.005935\n",
"1994-01-06 -0.004630 -0.030377 0.009294 -0.017143 -0.020487 0.029703 -0.012186 -0.000920 -0.005900\n",
"1994-01-07 0.004651 0.012531 0.005525 0.006645 0.011765 0.004808 0.022359 0.005951 -0.007913"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"1995\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1995-01-03 -0.013854 -0.015560 0.000000 0.003251 -0.004111 -0.013333 -0.006552 -0.000348 -0.001996\n",
"1995-01-04 0.003831 0.025290 0.000000 0.008425 0.009288 0.006757 -0.014015 0.003485 0.004000\n",
"1995-01-05 -0.007634 -0.012333 0.003643 -0.004499 -0.005112 -0.016779 -0.020903 -0.000803 0.001992\n",
"1995-01-06 0.029487 0.080125 -0.005445 0.014848 -0.006166 0.017065 0.000000 0.000739 0.000000\n",
"1995-01-09 0.009963 -0.019268 -0.009124 0.005089 -0.011375 -0.006711 0.003416 0.000326 -0.007952\n",
"1996\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1996-01-02 0.028340 0.007528 0.021330 -0.005691 -0.014848 0.023202 -0.002611 0.007793 -0.006442\n",
"1996-01-03 0.015748 0.000000 0.001229 -0.017690 0.039974 -0.031746 0.002618 0.000950 0.002882\n",
"1996-01-04 0.008721 -0.017435 -0.011043 -0.026483 -0.009452 0.004684 -0.002611 -0.005826 0.006466\n",
"1996-01-05 -0.006724 0.084918 0.001241 0.020131 0.000000 -0.011655 -0.002094 -0.001603 0.024982\n",
"1996-01-08 -0.054159 0.011682 0.007435 0.005333 0.012723 0.000000 0.000000 0.002838 0.011838"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"1997\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1997-01-02 0.021470 0.005747 -0.013405 0.011413 0.000000 -0.012315 0.008358 -0.005036 0.003425\n",
"1997-01-03 0.044462 0.036190 0.015399 0.038426 0.010388 0.036160 0.008289 0.014952 0.002844\n",
"1997-01-06 -0.002322 -0.178309 -0.000892 0.013216 0.007576 -0.002407 -0.016441 -0.000508 0.013613\n",
"1997-01-07 -0.005431 -0.020134 0.020536 0.013333 0.002148 0.007238 0.008358 0.007463 0.002798\n",
"1997-01-08 -0.001560 0.006849 -0.013998 -0.021453 0.007503 -0.019162 0.004388 -0.006399 -0.007812\n",
"1998\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1998-01-02 0.012546 0.237805 0.008289 0.009545 -0.012215 0.014173 -0.006844 0.004750 0.011111\n",
"1998-01-05 0.017493 -0.022167 0.018203 0.007696 -0.000824 -0.005435 0.013783 0.002082 -0.010989\n",
"1998-01-06 -0.022923 0.193955 -0.013264 -0.011128 -0.015264 0.005464 -0.036136 -0.010736 -0.036000\n",
"1998-01-07 0.002199 -0.075949 0.008182 -0.009488 0.009636 -0.011646 0.019673 -0.002669 0.031812\n",
"1998-01-08 -0.042429 0.038813 -0.009275 -0.000668 0.011618 0.007070 0.000000 -0.008247 -0.021448\n",
"1999\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"1999-01-04 -0.010981 0.007820 -0.014274 -0.007505 -0.013889 0.016514 -0.004727 -0.000919 -0.006899\n",
"1999-01-05 0.020819 0.050436 0.021295 0.036295 0.003841 0.038989 0.001583 0.013582 -0.008775\n",
"1999-01-06 0.039429 -0.036011 0.019600 -0.004621 0.011798 0.032662 0.026241 0.022140 0.039838\n",
"1999-01-07 -0.012426 0.077586 -0.016769 0.007575 -0.009455 -0.005047 -0.025570 -0.002051 -0.001419\n",
"1999-01-08 0.101987 0.000000 -0.005824 -0.013823 0.000636 -0.004058 0.015492 0.004221 -0.006039"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"2000\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2000-01-03 -0.024605 0.089105 -0.030891 0.075319 -0.011504 -0.001526 0.046093 -0.009549 -0.027742\n",
"2000-01-04 0.004360 -0.084673 -0.039774 -0.033934 -0.036617 -0.033843 -0.025473 -0.038345 -0.019244\n",
"2000-01-05 0.057674 0.014832 -0.001763 0.035125 0.010607 0.010621 -0.024373 0.001922 0.054465\n",
"2000-01-06 -0.013193 -0.086538 0.013243 -0.017214 0.031487 -0.033542 0.044895 0.000956 0.051652\n",
"2000-01-07 -0.002971 0.047579 0.038629 -0.004429 0.042397 0.013188 0.027027 0.027090 -0.002746\n",
"2001\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2001-01-02 -0.037407 0.000000 -0.087551 -0.002150 -0.029224 0.000000 -0.003787 -0.028032 0.025161\n",
"2001-01-03 0.013467 0.100806 0.092764 0.115690 -0.031875 0.104985 -0.058287 0.050099 -0.043664\n",
"2001-01-04 0.032650 0.041514 0.005251 -0.015210 -0.021688 0.010085 -0.045748 -0.010552 -0.027753\n",
"2001-01-05 -0.018382 -0.039859 -0.015670 0.008703 0.013088 0.014188 0.021151 -0.026242 0.004604\n",
"2001-01-08 0.014981 0.010989 -0.036851 -0.004618 -0.001318 -0.003627 0.016570 -0.001918 -0.004583\n",
"2002\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2002-01-02 0.003434 0.063927 0.021575 0.004416 -0.006894 0.011909 0.009647 0.005740 0.007600\n",
"2002-01-03 0.013005 0.012017 -0.008381 0.017775 -0.000217 0.032650 -0.007292 0.009180 0.001571\n",
"2002-01-04 0.032095 0.005089 0.008452 0.015718 -0.009330 -0.004779 -0.008865 0.006213 0.008472\n",
"2002-01-07 0.023241 -0.033755 -0.038887 -0.012398 -0.004599 -0.004802 -0.005878 -0.006499 -0.008712\n",
"2002-01-08 -0.021753 -0.012227 -0.010464 0.005315 -0.006601 0.011878 -0.005913 -0.003588 0.001255"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"2003\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2003-01-02 0.033578 0.033520 0.046729 0.039604 0.030168 0.039389 0.021092 0.033200 0.015288\n",
"2003-01-03 0.010660 0.006757 -0.003151 0.013445 0.026788 0.001421 0.006791 -0.000484 0.000684\n",
"2003-01-06 0.024611 0.000000 0.025817 0.023770 0.009507 0.017975 -0.010118 0.022474 0.024624\n",
"2003-01-07 0.000000 -0.002685 -0.006163 0.028888 -0.022558 0.019052 -0.018171 -0.006545 -0.033712\n",
"2003-01-08 -0.103922 -0.020188 -0.015504 -0.021123 -0.005826 -0.028272 0.012435 -0.014086 -0.004145\n",
"2004\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2004-01-02 -0.011967 -0.004677 0.004203 -0.012204 0.000000 0.002765 -0.003352 -0.003094 -0.008929\n",
"2004-01-05 0.032609 0.042293 0.015069 0.016391 0.005971 0.025276 0.017076 0.012395 0.023249\n",
"2004-01-06 -0.007218 -0.003607 -0.006598 0.000120 -0.004511 0.003586 0.006360 0.001292 -0.006816\n",
"2004-01-07 -0.007573 0.022624 0.009548 -0.003008 0.000477 -0.001340 -0.012892 0.002367 -0.007149\n",
"2004-01-08 0.011905 0.033628 0.018092 0.002776 0.004529 -0.001342 -0.019974 0.004963 -0.002592"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"2005\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2005-01-03 -0.013120 -0.017081 0.002787 -0.008455 -0.008205 0.000845 -0.004984 -0.008119 -0.022717\n",
"2005-01-04 -0.018095 0.010111 -0.012161 -0.010687 -0.003078 0.003797 -0.007058 -0.011671 -0.006904\n",
"2005-01-05 -0.006017 0.008758 -0.005980 -0.002068 -0.000772 -0.002522 0.001147 -0.003628 -0.005098\n",
"2005-01-06 0.004162 0.000930 0.007785 -0.003109 0.002897 -0.000843 0.007100 0.003506 0.012579\n",
"2005-01-07 0.010173 0.072491 -0.005969 -0.004390 -0.003659 -0.002952 0.008642 -0.001431 -0.006441\n",
"2006\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2006-01-03 0.010985 0.039783 0.009191 -0.001741 0.025469 0.026428 0.011600 0.016430 0.041046\n",
"2006-01-04 0.005620 0.002943 -0.001401 -0.001342 0.015402 0.004568 -0.000583 0.003673 0.001739\n",
"2006-01-05 0.008197 -0.007870 -0.002455 0.006717 -0.004171 0.000827 -0.005834 0.000016 -0.005016\n",
"2006-01-06 -0.003326 0.025813 0.006681 0.029624 0.004570 -0.002891 0.003717 0.009399 0.019779\n",
"2006-01-09 0.011865 -0.003277 -0.002445 -0.014256 0.006255 -0.002071 -0.005067 0.003656 -0.000570\n",
"2007\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2007-01-03 -0.022661 -0.012258 0.020692 0.001230 0.005795 0.000000 0.002734 -0.001199 -0.032981\n",
"2007-01-04 -0.007479 0.022196 -0.006018 0.010721 0.012395 -0.001472 0.006908 0.001228 -0.018699\n",
"2007-01-05 -0.012057 -0.007121 -0.004780 -0.009061 -0.008967 -0.005898 -0.003069 -0.006085 0.007165\n",
"2007-01-08 -0.009535 0.004938 -0.000320 0.015165 -0.001740 0.010011 0.002173 0.002220 -0.008022\n",
"2007-01-09 0.001540 0.083070 0.000000 0.011863 -0.003660 0.000734 0.004156 -0.000517 -0.007782"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"2008\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2008-01-02 -0.011481 -0.016357 -0.008186 -0.031513 -0.011862 -0.010658 -0.008092 -0.014438 -0.001862\n",
"2008-01-03 0.001489 0.000462 0.000952 0.001944 0.000171 0.004001 0.006526 0.000000 0.003382\n",
"2008-01-04 -0.036574 -0.076335 -0.020615 -0.035948 -0.001372 -0.027897 -0.003095 -0.024552 -0.018596\n",
"2008-01-07 -0.050309 -0.013385 0.003886 -0.010699 0.015625 0.006623 0.023503 0.003223 -0.009356\n",
"2008-01-08 -0.063698 -0.035972 -0.021613 -0.024521 0.001183 -0.033521 0.007943 -0.018352 -0.012791\n",
"2009\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2009-01-02 0.076137 0.063269 0.053999 0.038154 0.013774 0.046002 0.021860 0.031608 0.022773\n",
"2009-01-05 -0.020708 0.042204 -0.025940 -0.006386 -0.009964 0.009424 -0.006418 -0.004668 -0.000131\n",
"2009-01-06 0.022026 -0.016494 0.013981 0.027771 -0.006038 0.011411 0.001762 0.007817 -0.016374\n",
"2009-01-07 -0.101724 -0.021608 -0.044649 -0.016047 -0.009389 -0.060000 -0.032630 -0.030010 -0.025436\n",
"2009-01-08 0.043186 0.018569 0.002062 -0.006955 -0.001858 0.031097 -0.011715 0.003397 0.010659\n",
"2010\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2010-01-04 0.032746 0.015565 0.020891 0.011908 0.004126 0.015700 0.007282 0.016043 0.014102\n",
"2010-01-05 -0.031098 0.001729 0.005457 -0.012079 -0.011506 0.000336 0.012048 0.003116 0.003930\n",
"2010-01-06 0.052234 -0.015906 -0.005427 -0.006547 0.008148 -0.006382 -0.010034 0.000546 0.008582\n",
"2010-01-07 -0.021531 -0.001849 0.051842 -0.003414 -0.007257 -0.010142 -0.006356 0.004001 -0.003135\n",
"2010-01-08 0.025061 0.006648 0.021401 0.010039 0.003489 0.006831 -0.003285 0.002882 -0.003893"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"2011\n",
" AA AAPL GE IBM JNJ MSFT PEP SPX XOM\n",
"2011-01-03 0.026797 0.021732 0.000000 0.004900 0.015773 0.002556 0.006421 0.011315 0.019624\n",
"2011-01-04 0.045831 0.005219 0.017937 0.001099 0.008336 0.004006 -0.005135 -0.001313 0.004641\n",
"2011-01-05 0.002435 0.008180 0.001652 -0.003979 -0.000648 -0.003264 0.017988 0.005007 -0.002717\n",
"2011-01-06 -0.012143 -0.000808 -0.004398 0.010951 -0.001460 0.029476 0.003841 -0.002123 0.006540\n",
"2011-01-07 0.003688 0.007161 -0.007178 -0.004973 -0.009747 -0.007777 -0.006735 -0.001845 0.005414\n"
]
}
],
"prompt_number": 45
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Further, we can use groupby to do a linear regression, calculating beta.\n",
"-------------------------------------------------------------------------"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def get_beta(RR):\n",
" RR = RR.dropna()\n",
" RR['intercept'] = 1.\n",
" model = sm.OLS(RR['MSFT'], RR.ix[:, ['AAPL', 'intercept']]).fit()\n",
" return model.params\n",
"\n",
"#get_beta(RR), for AAPL\n",
"\n",
"grouped = RR.groupby([lambda x: x.year, lambda x: x.month])\n",
"beta_by_ym = grouped.apply(get_beta)\n",
"beta_by_ym.unstack(0)['AAPL']"
],
"language": "python",
"metadata": {},
"outputs": [
{
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" 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011\n",
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"3 0.205730 0.604625 0.229554 0.467642 0.157241 -0.130381 0.234062 0.161575 0.127244 0.330306 0.215007 0.625861 0.562043 1.137488 0.227146 0.020839 0.093893 0.550877 0.505030 0.998851 0.070641 0.466862\n",
"4 0.406723 -0.055939 0.766337 0.645863 0.337084 -0.097639 -0.166418 -0.092456 0.015637 0.124685 0.445522 0.421632 0.598160 0.468462 0.044444 0.272978 -0.009106 0.059114 0.463362 0.321722 0.061764 -0.232956\n",
"5 0.185421 0.034390 -0.118079 0.700196 0.287318 0.097011 0.110495 0.474461 0.117327 0.193558 0.406288 0.305603 0.927363 0.160195 0.242406 0.115821 0.227492 0.144143 0.415390 0.229804 0.548791 0.517262\n",
"6 0.173833 0.124975 0.218792 0.117013 0.386103 0.221485 0.266115 0.464815 0.500223 0.319529 0.422132 0.227274 0.232655 0.315496 0.106455 0.032854 0.126484 0.054197 0.275618 0.171693 0.743858 0.465253\n",
"7 0.130995 -0.022488 0.507049 0.156466 0.475714 0.886968 0.098349 0.223480 0.260195 0.274491 0.259399 0.216299 0.486249 0.380805 0.019886 0.241723 0.007129 0.037335 0.492093 0.512913 0.207223 0.380265\n",
"8 0.902234 0.307631 0.345300 0.214452 0.278754 0.673664 0.054254 0.054791 0.389318 0.113426 -0.037612 0.708398 0.919043 0.061068 0.295398 0.241400 -0.019745 0.338582 0.562713 0.589150 0.382959 0.847749\n",
"9 0.904113 0.422216 0.399828 0.161215 0.382306 0.229729 0.074385 -0.009814 0.482903 0.287425 0.024519 0.528889 0.766441 0.725022 0.215218 -0.022490 -0.007107 0.219036 0.480952 0.453823 0.514019 0.678709\n",
"10 0.362579 -0.027998 0.159585 -0.069302 0.109282 0.280408 -0.004444 0.142951 0.349357 0.186547 -0.122512 0.348552 0.804821 0.299456 0.035525 0.146915 0.091303 0.234525 0.592720 0.249662 0.405615 0.232681\n",
"11 0.569319 0.233042 0.781442 0.219592 0.502614 0.075520 0.183464 0.153227 0.212188 0.005807 0.466090 0.337734 0.519945 0.348925 -0.057999 0.009591 0.126967 0.320820 0.763112 0.493005 0.473650 NaN\n",
"12 0.204879 0.179746 0.305322 0.035841 0.194147 0.255704 0.067983 0.244797 0.316726 0.138289 0.425003 0.308701 0.435298 0.047410 0.102319 0.053251 0.109467 0.705481 0.711442 0.158556 0.903940 NaN"
]
}
],
"prompt_number": 46
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can emply the statistical Ordinary Least Squares (OLS) technique to do a moving window regression:\n",
"-----------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"RR = close_px / close_px.shift(1) - 1\n",
"y = RR['AAPL']\n",
"x = RR.ix[:, ['MSFT']]\n",
"model = ols(y=y, x=x) # OLS\n",
"model"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 47,
"text": [
"\n",
"-------------------------Summary of Regression Analysis-------------------------\n",
"\n",
"Formula: Y ~ + \n",
"\n",
"Number of Observations: 5471\n",
"Number of Degrees of Freedom: 2\n",
"\n",
"R-squared: 0.1339\n",
"Adj R-squared: 0.1337\n",
"\n",
"Rmse: 0.0289\n",
"\n",
"F-stat (1, 5469): 845.4989, p-value: 0.0000\n",
"\n",
"Degrees of Freedom: model 1, resid 5469\n",
"\n",
"-----------------------Summary of Estimated Coefficients------------------------\n",
" Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%\n",
"--------------------------------------------------------------------------------\n",
" MSFT 0.5227 0.0180 29.08 0.0000 0.4874 0.5579\n",
" intercept 0.0007 0.0004 1.84 0.0665 -0.0000 0.0015\n",
"---------------------------------End of Summary---------------------------------\n"
]
}
],
"prompt_number": 47
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# more least squares\n",
"model = ols(y=y, x=x, window=250)\n",
"model.beta.info()\n",
"model.beta['MSFT'].plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"DatetimeIndex: 5222 entries, 1991-01-29 00:00:00 to 2011-10-14 00:00:00\n",
"Data columns (total 2 columns):\n",
"MSFT 5222 non-null values\n",
"intercept 5222 non-null values\n",
"dtypes: float64(2)"
]
},
{
"metadata": {},
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V6ghubxka5tDxGLP1FsTHyxsxpth5/guDzgR55g53jEwMjzDej5u/V44YW3fj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\n3xDu4M3BwcHxG/InCJ8xUwO4NRAAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 48
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Beta of Microsoft relative to the S&P 500 as a function of time."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def RB(returns, benchmark, window=250):\n",
" betas = {}\n",
" for col, ts in returns.iteritems():\n",
" betas[col] = _r_b(ts, spx, window=250)\n",
" return DataFrame(betas)\n",
"def _r_b(returns, benchmark, window=250):\n",
" model = ols(y=returns, x={'bmk' : benchmark}, window=window,min_periods=100)\n",
" return model.beta['bmk']\n",
"def GMR(daily_returns):\n",
" daily_index = T(daily_returns)\n",
" monthly_index = daily_index.asfreq('EOM', method='pad')\n",
" return TR(monthly_index)\n",
"def T(returns):\n",
" return (1 + returns).cumprod()\n",
"def TR(prices):\n",
" return prices / prices.shift(1) - 1\n",
"\n",
"\n",
"\n",
"rets = GMR(TR(close_px))\n",
"spx = rets.pop('SPX')\n",
"betas =RB(rets, spx, window=36)\n",
"betas['MSFT'].plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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0aluoamqgsK6K149sMwzgivMJxEljx762ieoAVKhYHn8Tt4fEc8e3/6GwvpoZ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\n",
"text": [
""
]
}
],
"prompt_number": 49
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And finally the most important application: discover the portfolio of S&P 500 stocks that minimizes tracking error; (the 'Minimum Variance Portfolio') and visualize this portfolio's performance relative to the benchmark.\n",
"-----"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"tracking error:\n",
"\n",
"$TE = \\omega =\\sqrt{\\operatorname{Var}(r_p - r_b)} = \\sqrt{{E}[(r_p-r_b)^2]-({E}[r_p - r_b])^2}$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# benchmark is the S&P 500\n",
"\n",
"px = close_px.ix[datetime.datetime(1992, 1, 1):]\n",
"RR = px / px.shift(1) - 1\n",
"annualizer = np.sqrt(250)\n",
"bmk = RR.pop('SPX')\n",
"\n",
"tickers = RR.columns\n",
"weights = Series(1. / len(tickers), index=tickers)\n",
"weights\n",
"\n",
"# plot weighted portfolio versus the benchmark\n",
"port_returns = (RR * weights).sum(1)\n",
"plot_returns(port_returns, bmk)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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l5OgFODH6g3r7SJYB9nZXnfmFw6ozY6pm9OpwJOOWyvNtea6Y3lZ1GFVni4av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\nQC9YBmj2osp97h45A1yavF1h25qsG8jbMhnll/9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eXh4GDhyI6dOnw8/PD1OmTJG2LuTd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\n0GYwGIweBAvaDAaD0YNgQZvBYDB6EP8PAcZ5ouB3DxIAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 50
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Annualized:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"calc_te(weights, RR, bmk) * annualizer"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 51,
"text": [
"0.092509298588231245"
]
}
],
"prompt_number": 51
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's minimize tracking error for the entire sample of data, which uses hindsight:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"clean_RR = RR.fillna(0)\n",
"clean_bmk = bmk.fillna(0)\n",
"opt_weights = get_opt_holdings_opt(clean_RR, clean_bmk)\n",
"calc_te(opt_weights, RR, bmk) * annualizer"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 52,
"text": [
"0.077470788727965992"
]
}
],
"prompt_number": 52
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can even use convex optimization to minimize tracking error over a rolling two year period. \n",
"----"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def rolling_min_te_portfolio(UNIRET, TRARET, window=250,T_intervals=100):\n",
" \n",
" ports = {}\n",
" for i, cur_date in enumerate(UNIRET.index):\n",
" if i < T_intervals:\n",
" continue\n",
" if i % 100 == 0:\n",
" print >> sys.stdout, '*',\n",
" UNI = UNIRET[max(0,i-window+1):i]\n",
" TRA = TRARET[max(0,i-window+1):i]\n",
" UNI = UNI.ix[:, UNI.count() > 0]\n",
" UNI = UNI.fillna(0)\n",
" TRA = TRA.fillna(0)\n",
" ports[cur_date] = get_opt_holdings_opt(UNI,TRA)\n",
" return DataFrame(ports).T\n",
"ports = rolling_min_te_portfolio(RR, bmk)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"* "
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"*\n"
]
}
],
"prompt_number": 53
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ports"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"<class 'pandas.core.frame.DataFrame'>\n",
"DatetimeIndex: 4888 entries, 1992-05-26 00:00:00 to 2011-10-14 00:00:00\n",
"Data columns (total 8 columns):\n",
"AA 4888 non-null values\n",
"AAPL 4888 non-null values\n",
"GE 4888 non-null values\n",
"IBM 4888 non-null values\n",
"JNJ 4888 non-null values\n",
"MSFT 4888 non-null values\n",
"PEP 4888 non-null values\n",
"XOM 4888 non-null values\n",
"dtypes: float64(8)\n",
"
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 54,
"text": [
"\n",
"DatetimeIndex: 4888 entries, 1992-05-26 00:00:00 to 2011-10-14 00:00:00\n",
"Data columns (total 8 columns):\n",
"AA 4888 non-null values\n",
"AAPL 4888 non-null values\n",
"GE 4888 non-null values\n",
"IBM 4888 non-null values\n",
"JNJ 4888 non-null values\n",
"MSFT 4888 non-null values\n",
"PEP 4888 non-null values\n",
"XOM 4888 non-null values\n",
"dtypes: float64(8)"
]
}
],
"prompt_number": 54
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ports['JNJ'].plot()\n",
"remove_border()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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IX5dKEAUAfms+qNbnL4zdiSXn90ruO5ldVeR66/U4fHS6qkqbJTHODMOkCB6o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\nhAr6CoVCMYtQQV+hUChmEX8AddkBZ7YmD8AAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 55
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"port_return = (ports.shift(1) * RR).sum(1)\n",
"plot_returns(port_return, bmk)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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z58LPXjLqtTWzpMvFlOFXGVm288etQkl45scqvhSqhQLEPkiizz9XMVlqCPQ2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\nouMAAAAASUVORK5CYII=\n",
"text": [
""
]
}
],
"prompt_number": 56
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Sharpe ratio of this portfolio is quite high!"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def sharpe(RR, ann=250):\n",
" return np.sqrt(ann) * RR.mean() / RR.std()\n",
"sharpe(port_return)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 57,
"text": [
"0.66534966791660943"
]
}
],
"prompt_number": 57
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Particularly in relation to the benchmark..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sharpe(bmk)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 58,
"text": [
"0.37931166467025773"
]
}
],
"prompt_number": 58
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Conclusion\n",
"---------\n",
"This reflects the concept that the lowest risk stocks in an index actually deliver the highest performance, as opposed to the common perception that one must take on more risk to attain a chance at higher reward.\n",
"\n",
"This also worked very well. But let's do some sentiment analysis to round out our analysis. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 58
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Bayesian Tweets: Twitter Sentiment Analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we load in some standard packages and a couple of packages we wrote ourselves."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#ours\n",
"import twitter3 as tw3\n",
"import performance1 as perf1\n",
"import performance2 as perf2\n",
"import sentiment1 as sent\n",
"#standard\n",
"import pandas as pd\n",
"import numpy as np\n",
"import datetime\n",
"from pattern.web import Element\n",
"import requests\n",
"from sklearn.cross_validation import train_test_split\n",
"from sklearn.naive_bayes import MultinomialNB\n",
"from scipy import sparse\n",
"from sklearn.feature_extraction.text import CountVectorizer\n",
"#import ystockquote as ysq"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 59
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Load the Data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The next two cells scrape wikipedia for the ticker symbols of the S&P 500 companies, our stock data set we'll be using, and also prepare the list of dates we'll try to use for our analysis. Notably, the Twitter API only allows us to go back about a week. We've commented out the first cell and just loaded the symbols from a csv file in the second cell"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"# spy = requests.get('http://en.wikipedia.org/wiki/List_of_S&P_500_companies').text\n",
"# tickers = []\n",
"# dom = Element(spy)\n",
"# for a in dom('tr td:first-child a'):\n",
"# ticker = a.content\n",
"# if len(ticker) < 5:\n",
"# tickers.append(str(ticker))\n",
"# tickers.append('BRK.B')\n",
"# tickers.append('CMCSA')\n",
"# tickers.append('DISCA')\n",
"# tickers = np.sort(tickers)\n",
"#tickerlist = tickers\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 60
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"spx = pd.read_csv('SPXSymbolsPD.csv', delimiter=',')\n",
"tickerlist = list(spx['Ticker'])\n",
"datelist = [datetime.date(2013,12,5),datetime.date(2013,12,6),datetime.date(2013,12,7),datetime.date(2013,12,8),datetime.date(2013,12,9),datetime.date(2013,12,10)]\n",
"weekdays_datetime = [datetime.date(2013,12,5),datetime.date(2013,12,6),datetime.date(2013,12,9),datetime.date(2013,12,10)]\n",
"weekdays_str = [str(day) for day in weekdays_datetime]\n",
"weekend_datetime = [datetime.date(2013,12,7),datetime.date(2013,12,8)]\n",
"weekend_str = [str(day) for day in weekend_datetime]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 61
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we need to use the Twitter API to search for the tweets including each stock ticker symbol on each day. We take all the tweets we can find, or 100 tweets, whichever is smaller. We wrote all of the functions in tw3, although we do use other packages (twython and twitter) designed to interface with the Twitter API. We initially made extensive use of twitter and then switched to twython as it gave us better error handling. As we want to do build this entire data set in one call, we have to be able to handle a wide variety of errors, such as dealing with our rate limits and many of the small issues that could crop up during a single API call. We also make use of extensive printing so we can monitor the function as it runs. We've commented it out and loaded the data from csv so as to avoid the 1.5 hour process of performing the searches."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#loadfull = tw3.safemultisearch(tickerlist,datelist)\n",
"#loadfull.to_csv('data.csv')\n",
"data = pd.read_csv('data.csv')\n",
"#remove weekend days as the market is closed\n",
"data = data[data['date']!=weekend_str[0]]\n",
"data = data[data['date']!=weekend_str[1]]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 62
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we need to check the stock performance on each day, so we wrote another function to add a 0 wherever the stock went down and a 1 wherever it went up. We use the ystockquote package to assist in gathering the stock data. Again, we comment this out to limit ourselves to a single round of data collection and load the results from csv."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#data,performance = perf1.check_performance(data)\n",
"#data = data[data['performance']>-1]#only keep if performance is 0 or 1, not NaN\n",
"#data.to_csv('data_perf.csv')\n",
"data = pd.read_csv('data_perf.csv')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 63
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have a data set! We can go ahead and print part of our dataframe to see what sort of information we've stored, namely the symbol of the company, the date in question, text from the twitter searches, and a performance indicator. We made the choice to treat the entire twitter corpus for each stock from each day as a single bag of words, so the text here is the concatenated tweets (converted to ascii and without punctuation) of the entire result of each particular search. We'll turn it into a proper bag of words a bit later on.\n",
"\n",
"This differs from rotten tomatos where we kept each review separate, but in that case we also had a \"fresh\" or \"rotten\" indicator for each review. Here we only have the stock performance, which is obviously doesn't change depending on which tweet we're looking at, so we just combine all of the tweets into a single bag of words."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print data.irow(0)\n",
"print data.irow(0)['text']"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Unnamed: 0 0\n",
"Unnamed: 0.1 MMM\n",
"company MMM\n",
"date 2013-12-05\n",
"text MMM Could 3M Dare Trump GE on Dividend Hikes h...\n",
"performance 0\n",
"Name: 0, dtype: object\n",
"MMM Could 3M Dare Trump GE on Dividend Hikes httptcoG7ukoGT5kECould 3M Dare Trump GE on Dividend Hikes MMM httptco4QBxAilSRDRT MScharts TSN MAT MMM LH Portfolios Pops amp Drops httptco9hMj9HZuCGBarclays has estimated MMM target price at 121 defensive on 3Ms ability to maintain margins httptcofvmByxwClFLaMonicaBuzz MMM Buy on the dip httptcoxVMwKU07SsGeoffrey2313819 Ha Did 3M sponsor that tweet MMMSampP100 Stocks Performance INTC BA SPG NSC EBAY DVN UNP EMC MA GILD F MMM LMT ABBV AAPL more httptcon4QZIDxy7wTSN MAT MMM LH Portfolios Pops amp Drops httptco9hMj9HZuCGOne more small order filled Sold 1 Dec13 MMM 120 put for 37 centsTSN MAT MMM LH Portfolios Pops amp Drops httptcoeB1gLFQgbDTSN MAT MMM LH Portfolios Pops amp Drops httptcokqZTxc7ofATSN MAT MMM LH Portfolios Pops amp Drops httptco2z5afpz5SrAnalyst estimate MMM EPS at 672 which is 2 above second quarter estimates httptcofvmByxwClF httptco5wqB2bnXnFMMM mean target price is 127 as Barclays Credit Suisse and Citi gave stock neutral ratings httptcoDtPqdKgHjrOptionSniper1 On my list to look at GOGO SLW P AAPL IBM OXY MMM IYR TWTR Didnt get to any yday Wanted to sell MSFT callsMMM breaking out3M Co The stock is testing its highs MMM httptcodS64sIMoSi httptcoZE6oMDONO0Pennystock Research on DCIN MMM GFIG XPO SHOR AIN View now httptcotCMpiAEdzGLooking for winners like ENV STXS RNIN BPZ MMM Got to see httptcoxeMnQv7YcRMMM above 12760 can gain steam Volume not impressing meTSN MAT QQQ XLE XLV XOP MS MMM ChartsinPlay Portfolio changes in stops and sell advice article later httptcoCW4YD3lpfBTSN MAT QQQ XLE XLV XOP MS MMM ChartsinPlay Portfolio changes in stops and sell advice article later httptco70ZRkrIBhJTSN MAT QQQ XLE XLV XOP MS MMM ChartsinPlay Portfolio changes in stops and sell advice article later httptcofyoFkbgRZcTSN MAT QQQ XLE XLV XOP MS MMM ChartsinPlay Portfolio changes in stops and sell advice article later httptcoWy7KgCw9YzMMM 3M Analyst Is Right Limited Short To MediumTerm Appeal gt httptcoTuJoiXQMAf stock stocks MMMMMM 3M Co MMM 3M Analyst Is Right Limited Short To MediumTerm Appeal httptcotT8fZdmp0O3M Co MMM 3 Reasons To Buy 3M E I Du Pont De Nemours And Co MMM httptcox9HB2qh8Xs3M Co MMM 3M Analyst Is Right Limited Short To MediumTerm Appeal MMM httptco0ZrdXLtIZB3M Analyst Is Right Limited Short To MediumTerm Appeal httptcoeu5vDkFlui MMM3M Analyst Is Right Limited Short To MediumTerm Appeal httptcoW8SwGHrC3E MMM\n"
]
}
],
"prompt_number": 64
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Naive Bayesian Classifier"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can begin making a proper bag of words and performing sentiment analysis. Many of the functions for this are contained in the file sentiment1.py, which we wrote and which we imported at the top. We start with a make_xy function, where X is a matrix where each row represents a (stock,date) combination and each column represents a particular word, with the elements representing the frequency of that word in the bag of words. The Y is just are performance indicator (1 for up for the day, 0 for down) which we made and attached to our dataframe earlier."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X, Y = sent.make_xy(data,vectorizer=None)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 65
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we use a Naive Bayes classifier as we did in the Bayesian Tomatoes problem set, split our data into a traininig set and a testing set, and check our accuracy on the training set and on the testing set."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X_train,X_test,Y_train,Y_test = train_test_split(X,Y,test_size=0.33,random_state=22)\n",
"clf = MultinomialNB()\n",
"clf.fit(X_train,Y_train)\n",
"clf.predict(X_test)\n",
"print \"accuracy on testing set\",1-float(sum(abs(Y_test-clf.predict(X_test))))/float(len(Y_test))\n",
"print \"accuracy on training set\",1-float(sum(abs(Y_train-clf.predict(X_train))))/float(len(Y_train))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"accuracy on testing set 0.516279069767\n",
"accuracy on training set 0.973221117062\n"
]
}
],
"prompt_number": 66
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So how did we do? At first glance, 51.6% is not very good. On the other hand, even a small edge in finance can be useful. But do we have an edge?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"fraction that are positive on the day\",float(len(Y_test[Y_test==1]))/float(len(Y_test))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"fraction that are positive on the day 0.517829457364\n"
]
}
],
"prompt_number": 67
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We actually did worse than just assuming every stock went up! It turns out that we didn't gain any edge at all. Particularly considering how high our accuracy was on the training set and how poor it is on the testing set, it looks like we have serious over-fitting issues, likely due to the smaller size of our data set, the sparsity of our word frequency, and a potentially weak underlying connnection from tweets to stock performance. For example, people sometimes might tweet \"$GOOG is doing great today!\", but not all tweets are necessarily as clear. Unlike movie reviews, the explicit purpose of a tweet is not to determine whether a stock is doing well or poorly, the way the movie reviews are explicit about whether a movie is good or bad.\n",
"\n",
"We'll try fitting for the best alpha and min_df parameters as we did in the problem set to see if this resolves these issues, although if the underlying problems are in the data we wouldn't expect this to work."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"alphas = [0, .1, 1, 5, 10, 50, 100, 150, 200]\n",
"min_dfs = [1e-6, 1e-7, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1]\n",
"\n",
"#Find the best value for alpha and min_df, and the best classifier\n",
"best_alpha = None\n",
"best_min_df = None\n",
"max_loglike = -np.inf\n",
"\n",
"#for alpha in alphas:\n",
"for alpha in alphas:\n",
" print alpha#I print alpha as this takes a bit to run and I like to be able to see the progress\n",
" for min_df in min_dfs: \n",
" vectorizer = CountVectorizer(min_df = min_df) \n",
" X, Y = sent.make_xy(data, vectorizer)\n",
" clf = MultinomialNB(alpha=alpha)#should move outside of inner for loop\n",
" loglike=sent.cv_score(clf,X,Y,sent.log_likelihood)\n",
" #print loglike\n",
" if loglike>max_loglike:\n",
" max_loglike=loglike\n",
" print \"max_loglike\",max_loglike,\"alpha\",alpha,\"min_df\",min_df\n",
" best_alpha = alpha\n",
" best_min_df = min_df\n",
"print \"best max_loglike\",max_loglike,\"best alpha\",best_alpha,\"best min_df\",best_min_df"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"0\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -701.863599147 alpha 0 min_df 0.1\n",
"0.1\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -701.698320488 alpha 0.1 min_df 0.1\n",
"1\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -700.218818186 alpha 1 min_df 0.1\n",
"5\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -693.812946439 alpha 5 min_df 0.1\n",
"10\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -686.175301985 alpha 10 min_df 0.1\n",
"50\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -636.827815439 alpha 50 min_df 0.1\n",
"100\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -595.120648905 alpha 100 min_df 0.1\n",
"150\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -566.893075242 alpha 150 min_df 0.1\n",
"200\n",
"max_loglike"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" -547.192426876 alpha 200 min_df 0.1\n",
"best max_loglike -547.192426876 best alpha 200 best min_df 0.1\n"
]
}
],
"prompt_number": 68
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see that the maximal parameters are absurd, particularly the very high best_min_df, so it looks like we can't salvage our model this way. But is there anything else we can do?"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Beyond Binary Classification"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the case of movie reviews, Rotten Tomatoes compresses down \"thumbs up\", \"four out of five stars\", and other such positive reviews to just \"fresh\". Similarly, we took all positive days and just converted them to \"up\", and all negative days and converting them to \"down\". Seeing as how we're up against a shortage of data, it's sensible for us to avoid this strategy (which is what allowed us to do binary classification earlier) and instead keep more detailed performance information.\n",
"\n",
"We rebuild the performance indicator portion of our data set, instead looking at the fractional gain, clipping it from -1 to 1, then transforming it to the range 0 to 1. So now a gain of 3% would be .56. Again, we comment out the code to build the data set and just read it in from our previuos efforts."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#data = pd.read_csv('data.csv')\n",
"#data = data[data['date']!=weekend_str[0]]\n",
"#data = data[data['date']!=weekend_str[1]]\n",
"#data,performance = perf2.check_performance_scaled(data)\n",
"#data = data[data['performance']>=0]#only keep if performance is 0 to 1, not NaN\n",
"##data.to_csv('data_perf_scaled.csv')\n",
"data = pd.read_csv('data_perf_scaled.csv')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 69
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As in our previous model, we now run make_xy. Again, the X will be our bag of words results in matrix form, and our Y will be our performance indicators (which, recall, are continuous and based on the gain/loss.)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X, Y = sent.make_xy(data,vectorizer=None)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 70
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the binary classification model, we then ran this through a multinomial naive Bayes model to predict the probability of up/down for each stock. Since we aren't giving our model a binary classification anymore, this will no longer work. However, we can still use a MultinomialNB model. Now, instead of predicting the probability of 1/0, this will actually build a prediction of performance (such as, say, .52 for a 1% gain) based on the elements of our bag of words."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X_train,X_test,Y_train,Y_test = train_test_split(X,Y,test_size=0.33,random_state=22)\n",
"clf = MultinomialNB()\n",
"clf.fit(X_train,Y_train)\n",
"#clf.predict(X_test)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 71,
"text": [
"MultinomialNB(alpha=1.0, class_prior=None, fit_prior=True)"
]
}
],
"prompt_number": 71
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To check the accuracy of our model, we see which stocks it predicts a nontrivial gain for (using a tolerance of .2% movement) and then see if the direction predicted is correct."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"predvec = clf.predict(X_test)\n",
"indexpred = np.abs(predvec-.5)>0\n",
"actual = np.divide(Y_test[indexpred]-.5,np.abs(Y_test[indexpred]-.5))*.5+.5\n",
"predict = np.divide(clf.predict(X_test)[indexpred]-.5,np.abs(clf.predict(X_test)[indexpred]-.5))*.5+.5\n",
"print \"accuracy on testing set\",1-float(sum(abs(actual-predict)))/float(len(actual))\n",
"print \"portion of stocks with motion going up in testing set\",float(len(predict[predict>0]))/float(len(predict))\n",
"predvec = clf.predict(X_train)\n",
"indexpred = np.abs(predvec-.5)>0\n",
"actual = np.divide(Y_train[indexpred]-.5,np.abs(Y_train[indexpred]-.5))*.5+.5\n",
"predict = np.divide(clf.predict(X_train)[indexpred]-.5,np.abs(clf.predict(X_train)[indexpred]-.5))*.5+.5\n",
"print \"accuracy on training set\",1-float(sum(abs(actual-predict)))/float(len(actual))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"accuracy on testing set 0.646341463415\n",
"portion of stocks with motion going up in testing set 0.40243902439\n",
"accuracy on training set"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
" 0.981389578164\n"
]
}
],
"prompt_number": 72
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we've succeeded! We still have a very high probability on our training set indicating over fitting issues, but it works out to give us accurate results on our testing set, enabling us to gain an edge. The edge is not massive, as we are getting our predictions right about 65% of the time and the actual split between up stocks and downs tocks (among the stocks with sufficient movement) is 40/60, we have gained a several percent edge, which is considered very significant in the realm of finance.\n",
"\n",
"In our binary classification models, we could from here check the level of overfitting of our model by binning up predictions (10%-20% up, 20%-30% up, and so on) and seeing if our accuracy matches our predictions. Unfortunately, one cost of using our Multinomial Naive Bayes model in this way is that we no longer have probability predictions, just direction predictions. In essense, we've lost our error term, which is always something we'd like to avoid when possible in data analysis. This also makes it difficult to tune our model, such as by carefully adjusting min_df or alpha parameters. Still, if the benefit of losing tunability and error analysis is going from just noise to a useful prediction, we'll take it.\n",
"\n",
"One way we can check the reasonableness of our model, though, is by checking some words with strong negative and positive indications, as we did with Rotten Tomatoes."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"vec = CountVectorizer(min_df = 1e-3)\n",
"#vec = CountVectorizer()\n",
"text = [words for i,words in data.text.iteritems()]\n",
"vec.fit(text)\n",
"words = np.array(vec.get_feature_names())\n",
"singles = np.eye(len(words))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 73
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"X_df, Y_df = sent.make_xy(data,vectorizer=vec)\n",
"X_train_df,X_test_df,Y_train_df,Y_test_df = train_test_split(X_df,Y_df,test_size=0.33,random_state=22)\n",
"clf_df = MultinomialNB()\n",
"clf_df.fit(X_train_df,Y_train_df)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 74,
"text": [
"MultinomialNB(alpha=1.0, class_prior=None, fit_prior=True)"
]
}
],
"prompt_number": 74
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#clf_df = clf\n",
"negativeindices = clf_df.predict_proba(sparse.csc_matrix(singles))[:,0].argsort()\n",
"positiveindices = clf_df.predict_proba(sparse.csc_matrix(singles))[:,1].argsort()\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 75
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"badwords=words[negativeindices]\n",
"badprobs = clf_df.predict_proba(singles)[negativeindices,1]\n",
"badprobs=badprobs[::-1]\n",
"badwords=badwords[::-1]\n",
"goodwords=words[positiveindices]\n",
"goodwords=goodwords[::-1]\n",
"goodprobs = clf_df.predict_proba(singles)[positiveindices,1]\n",
"goodprobs = goodprobs[::-1]\n",
"print \"negative words\",[(badwords[i],badprobs[i]) for i in range(10)]\n",
"print \"positive words\",[(goodwords[i],goodprobs[i]) for i in range(10)]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
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"negative words [(u'dva', 0.00065429865287221971), (u'davita', 0.00070301231619910383), (u'healthcare', 0.0006835894031860572), (u'partners', 0.0013194339424065626), (u'dialysis', 0.00072809514936371226), (u'dvadva', 0.00072592477320190742), (u'scan', 0.00072375005946349695), (u'rated', 0.00071782864597029678), (u'patients', 0.00071095170136868311), (u'health', 0.00066552469716559491)]\n",
"positive words [(u'cpb', 0.032144008476641339), (u'soup', 0.013377734519007296), (u'options', 0.011244340670651403), (u'campbell', 0.010575715690765052), (u'day', 0.008966277117938088), (u'today', 0.0081946750241469728), (u'keeneonmarket', 0.007881447433107246), (u'over', 0.0078077819981858913), (u'iv', 0.00693413576281382), (u'up', 0.0068814076007903853)]\n"
]
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"On both sides, it looks like there are a lot of words that were specific to just one or two stocks in our set. We again have to recall that we're not predicting probabilities of going up or down but a magnitude in the direction, so one stock that really tanked on one day could easily have a large effect on our most extreme words. This seems to be the case with so many pharmaceutical and health related words in our negative category. On the positive side, in addition to a few that seem stock specific, we do seem some general terms we might have suspected such as \"options\" and \"up\".\n",
"\n",
"This is a long way from a predictive tool that could make money in real time, and it's not clear how good of a choice it is up against some of our other options we explored. We did have the advantage of compiling all of the tweets for each day, including tweets that were about stock behavior that already happened, but this does in its current form provide a several percent edge and shows potential to be honed into a more realtime tool should one desire."
]
},
{
"cell_type": "markdown",
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"source": [
"#Complete Conclusion\n",
"\n",
"We looked at an array of different solutions. We showed how we collected data, we showed some of our tried and failed attempts, we used a slew of statistical analysis on each, and we showed three great ways to make money (and one not so good one). \n",
"\n",
"In sum, each of our solutions can be expanded. But it seems that we stumbled upon a few good solutions, and are happy with our results. "
]
},
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