ml-finance-python

python scripts for finance machine learning

git clone https://9o.is/git/ml-finance-python.git

bayesian_risk_perf_v3.ipynb

(734942B)


      1 {
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     16     "<center><h1>Probabilistic Programming in Quantitative Finance</h1><br>\n",
     17     "<h3>Thomas Wiecki</h3><br>\n",
     18     "<h3>@twiecki</h3><br>\n",
     19     "<img width=40% src=\"http://i2.wp.com/stuffled.com/wp-content/uploads/2014/09/Quantopian-Logo-EPS-vector-image.png?resize=1020%2C680\">\n",
     20     "</center>"
     21    ]
     22   },
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     24    "cell_type": "markdown",
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     35    "source": [
     36     "# About me\n",
     37     "\n",
     38     "* Lead Data Scientist at [Quantopian Inc](https://www.quantopian.com): Building a crowd sourced hedge fund.\n",
     39     "* Previous: PhD from Brown University -- research on computational neuroscience and machine learning using Bayesian modeling."
     40    ]
     41   },
     42   {
     43    "cell_type": "code",
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     53    "source": [
     54     "%pyplot inline\n",
     55     "\n",
     56     "figsize(12, 12)\n",
     57     "import pandas as pd\n",
     58     "import seaborn as sns\n",
     59     "import matplotlib.pyplot as plt\n",
     60     "import numpy as np\n",
     61     "import itertools\n",
     62     "import scipy as sp\n",
     63     "import pymc3 as pm\n",
     64     "import theano.tensor as T\n",
     65     "\n",
     66     "from scipy import stats\n",
     67     "import scipy\n",
     68     "\n",
     69     "data_0 = pd.read_csv('data0.csv', index_col=0, parse_dates=True, header=None)[1]\n",
     70     "data_1 = pd.read_csv('data1.csv', index_col=0, parse_dates=True, header=None)[1]\n",
     71     "\n",
     72     "def var_cov_var_t(P, c, nu=1, mu=0, sigma=1, **kwargs):\n",
     73     "    \"\"\"\n",
     74     "    Variance-Covariance calculation of daily Value-at-Risk\n",
     75     "    using confidence level c, with mean of returns mu\n",
     76     "    and standard deviation of returns sigma, on a portfolio\n",
     77     "    of value P.\n",
     78     "    \"\"\"\n",
     79     "    alpha = stats.t.ppf(1-c, nu, mu, sigma)\n",
     80     "    return P - P*(alpha + 1)\n",
     81     "\n",
     82     "def var_cov_var_normal(P, c, mu=0, sigma=1, **kwargs):\n",
     83     "    \"\"\"\n",
     84     "    Variance-Covariance calculation of daily Value-at-Risk\n",
     85     "    using confidence level c, with mean of returns mu\n",
     86     "    and standard deviation of returns sigma, on a portfolio\n",
     87     "    of value P.\n",
     88     "    \"\"\"\n",
     89     "    alpha = stats.norm.ppf(1-c, mu, sigma)\n",
     90     "    return P - P*(alpha + 1)\n",
     91     "\n",
     92     "def sample_normal(mu=0, sigma=1, **kwargs):\n",
     93     "    samples = stats.norm.rvs(mu, sigma, kwargs.get('size', 100))\n",
     94     "    return samples\n",
     95     "\n",
     96     "def sample_t(nu=1, mu=0, sigma=1, **kwargs):\n",
     97     "    samples = stats.t.rvs(nu, mu, sigma, kwargs.get('size', 100))\n",
     98     "    return samples\n",
     99     "\n",
    100     "def eval_normal(mu=0, sigma=1, **kwargs):\n",
    101     "    pdf = stats.norm(mu, sigma).pdf(kwargs.get('x', np.linspace(-0.05, 0.05, 500)))\n",
    102     "    return pdf\n",
    103     "\n",
    104     "def eval_t(nu=1, mu=0, sigma=1, **kwargs):\n",
    105     "    samples = stats.t(nu, mu, sigma).pdf(kwargs.get('x', np.linspace(-0.05, 0.05, 500)))\n",
    106     "    return samples\n",
    107     "\n",
    108     "def logp_normal(mu=0, sigma=1, **kwargs):\n",
    109     "    logp = np.sum(stats.norm(mu, sigma).logpdf(kwargs['data']))\n",
    110     "    return logp\n",
    111     "\n",
    112     "def logp_t(nu=1, mu=0, sigma=1, **kwargs):\n",
    113     "    logp = np.sum(stats.t(nu, mu, sigma).logpdf(kwargs['data']))\n",
    114     "    return logp\n",
    115     "\n",
    116     "# generate posterior predictive\n",
    117     "def post_pred(func, trace, *args, **kwargs):\n",
    118     "    samples = kwargs.pop('samples', 50)\n",
    119     "    ppc = []\n",
    120     "    for i, idx in enumerate(np.linspace(0, len(trace), samples)):\n",
    121     "        t = trace[int(i)]\n",
    122     "        try:\n",
    123     "            kwargs['nu'] = t['nu_minus_one']+1\n",
    124     "        except KeyError:\n",
    125     "            pass\n",
    126     "        mu = t['mean returns']\n",
    127     "        sigma = t['volatility']\n",
    128     "        ppc.append(func(*args, mu=mu, sigma=sigma, **kwargs))\n",
    129     "\n",
    130     "    return ppc\n",
    131     "\n",
    132     "def plot_strats(sharpe=False):\n",
    133     "    figsize(12, 6)\n",
    134     "    f, (ax1, ax2) = plt.subplots(1, 2)\n",
    135     "    if sharpe:\n",
    136     "        label = 'etrade\\nn=%i\\nSharpe=%.2f' % (len(data_0), (data_0.mean() / data_0.std() * np.sqrt(252)))\n",
    137     "    else:\n",
    138     "        label = 'etrade\\nn=%i\\n' % (len(data_0))\n",
    139     "    sns.distplot(data_0, kde=False, ax=ax1, label=label, color='b')\n",
    140     "    ax1.set_xlabel('daily returns'); ax1.legend(loc=0)\n",
    141     "    if sharpe:\n",
    142     "        label = 'IB\\nn=%i\\nSharpe=%.2f' % (len(data_1), (data_1.mean() / data_1.std() * np.sqrt(252)))\n",
    143     "    else:\n",
    144     "        label = 'IB\\nn=%i\\n' % (len(data_1))\n",
    145     "    sns.distplot(data_1, kde=False, ax=ax2, label=label, color='g')\n",
    146     "    ax2.set_xlabel('daily returns'); ax2.legend(loc=0);"
    147    ]
    148   },
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    160      "name": "stdout",
    161      "output_type": "stream",
    162      "text": [
    163       "Cannot compute test value: input 0 (<TensorType(float32, matrix)>) of Op Dot22(<TensorType(float32, matrix)>, <TensorType(float32, matrix)>) missing default value\n",
    164       " [-----------------100%-----------------] 5000 of 5000 complete in 12.1 sec"
    165      ]
    166     },
    167     {
    168      "name": "stderr",
    169      "output_type": "stream",
    170      "text": [
    171       "/home/wiecki/envs/pymc3/local/lib/python2.7/site-packages/theano/gof/cmodule.py:293: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n",
    172       "  rval = __import__(module_name, {}, {}, [module_name])\n"
    173      ]
    174     }
    175    ],
    176    "source": [
    177     "def model_returns_normal(data):\n",
    178     "    with pm.Model() as model:\n",
    179     "        mu = pm.Normal('mean returns', mu=0, sd=.01, testval=data.mean())\n",
    180     "        sigma, log_sigma = model.TransformedVar('volatility', \n",
    181     "                                                pm.HalfCauchy.dist(beta=1, testval=data.std()), \n",
    182     "                                                pm.transforms.logtransform)\n",
    183     "        #sigma = pm.HalfCauchy('volatility', beta=.1, testval=data.std())\n",
    184     "        returns = pm.Normal('returns', mu=mu, sd=sigma, observed=data)\n",
    185     "        ann_vol = pm.Deterministic('annual volatility', returns.distribution.variance**.5 * np.sqrt(252))\n",
    186     "        sharpe = pm.Deterministic('sharpe', \n",
    187     "                                  returns.distribution.mean / returns.distribution.variance**.5 * np.sqrt(252))\n",
    188     "        start = pm.find_MAP(fmin=scipy.optimize.fmin_powell)\n",
    189     "        step = pm.NUTS(scaling=start)\n",
    190     "        trace_normal = pm.sample(5000, step, start=start)\n",
    191     "    return trace_normal\n",
    192     "\n",
    193     "def model_returns_t(data):\n",
    194     "    with pm.Model() as model:\n",
    195     "        mu = pm.Normal('mean returns', mu=0, sd=.01, testval=data.mean())\n",
    196     "        sigma, log_sigma = model.TransformedVar('volatility', \n",
    197     "                                                pm.HalfCauchy.dist(beta=1, testval=data.std()), \n",
    198     "                                                pm.transforms.logtransform)\n",
    199     "        nu, log_nu = model.TransformedVar('nu_minus_one',\n",
    200     "                                          pm.Exponential.dist(1./10., testval=3.),\n",
    201     "                                          pm.transforms.logtransform)\n",
    202     "\n",
    203     "        returns = pm.T('returns', nu=nu+2, mu=mu, sd=sigma, observed=data)\n",
    204     "        ann_vol = pm.Deterministic('annual volatility', returns.distribution.variance**.5 * np.sqrt(252))\n",
    205     "        sharpe = pm.Deterministic('sharpe', \n",
    206     "                                  returns.distribution.mean / returns.distribution.variance**.5 * np.sqrt(252))\n",
    207     "\n",
    208     "        start = pm.find_MAP(fmin=scipy.optimize.fmin_powell)\n",
    209     "        step = pm.NUTS(scaling=start)\n",
    210     "        trace = pm.sample(5000, step, start=start)\n",
    211     "\n",
    212     "    return trace\n",
    213     "\n",
    214     "def model_returns_t_stoch_vol(data):\n",
    215     "    from pymc3.distributions.timeseries import GaussianRandomWalk\n",
    216     "\n",
    217     "    with pm.Model() as model:\n",
    218     "        mu = pm.Normal('mean returns', mu=0, sd=.01, testval=data.mean())\n",
    219     "        step_size, log_step_size = model.TransformedVar('step size', \n",
    220     "                                                pm.Exponential.dist(1./.02, testval=.06), \n",
    221     "                                                pm.transforms.logtransform)\n",
    222     "        \n",
    223     "        vol = GaussianRandomWalk('volatility', step_size**-2, shape=len(data))\n",
    224     "        \n",
    225     "        nu, log_nu = model.TransformedVar('nu_minus_one',\n",
    226     "                                          pm.Exponential.dist(1./10., testval=3.),\n",
    227     "                                          pm.transforms.logtransform)\n",
    228     "\n",
    229     "        returns = pm.T('returns', nu=nu+2, mu=mu, lam=pm.exp(-2*vol), observed=data)\n",
    230     "        #ann_vol = pm.Deterministic('annual volatility', returns.distribution.variance**.5 * np.sqrt(252))\n",
    231     "        #sharpe = pm.Deterministic('sharpe', \n",
    232     "        #                          returns.distribution.mean / ann_vol)\n",
    233     "\n",
    234     "        start = pm.find_MAP(vars=[vol], fmin=sp.optimize.fmin_l_bfgs_b)\n",
    235     "        #start = pm.find_MAP(fmin=scipy.optimize.fmin_powell, start=start)\n",
    236     "        step = pm.NUTS(scaling=start)\n",
    237     "        trace = pm.sample(5000, step, start=start)\n",
    238     "\n",
    239     "    return trace\n",
    240     "\n",
    241     "results_normal = {0: model_returns_normal(data_0),\n",
    242     "                  1: model_returns_normal(data_1)}\n",
    243     "results_t = {0: model_returns_t(data_0),\n",
    244     "             1: model_returns_t(data_1)}"
    245    ]
    246   },
    247   {
    248    "cell_type": "code",
    249    "execution_count": 11,
    250    "metadata": {
    251     "collapsed": false,
    252     "slideshow": {
    253      "slide_type": "skip"
    254     }
    255    },
    256    "outputs": [],
    257    "source": [
    258     "from IPython.display import Image\n",
    259     "sns.set_context('talk', font_scale=1.5)\n",
    260     "sns.set_context(rc={'lines.markeredgewidth': 0.1})\n",
    261     "from matplotlib import rc\n",
    262     "rc('xtick', labelsize=14) \n",
    263     "rc('ytick', labelsize=14)\n",
    264     "figsize(10, 6)"
    265    ]
    266   },
    267   {
    268    "cell_type": "markdown",
    269    "metadata": {
    270     "slideshow": {
    271      "slide_type": "slide"
    272     }
    273    },
    274    "source": [
    275     "# Data Science Motivation"
    276    ]
    277   },
    278   {
    279    "cell_type": "markdown",
    280    "metadata": {
    281     "slideshow": {
    282      "slide_type": "slide"
    283     }
    284    },
    285    "source": [
    286     "<center><img src=\"model-inference1.svg\">"
    287    ]
    288   },
    289   {
    290    "cell_type": "markdown",
    291    "metadata": {
    292     "slideshow": {
    293      "slide_type": "fragment"
    294     }
    295    },
    296    "source": [
    297     "<center><img src=\"model-inference2.svg\">"
    298    ]
    299   },
    300   {
    301    "cell_type": "markdown",
    302    "metadata": {
    303     "slideshow": {
    304      "slide_type": "slide"
    305     }
    306    },
    307    "source": [
    308     "# What's wrong with statistics\n",
    309     "\n",
    310     "* Models should not be built for mathematical convenience (e.g. normality assumption), but to most accurately model the data.\n",
    311     "* Pre-specified models, like frequentist statistics, make many assumptions that are all to easily violated."
    312    ]
    313   },
    314   {
    315    "cell_type": "markdown",
    316    "metadata": {
    317     "slideshow": {
    318      "slide_type": "slide"
    319     }
    320    },
    321    "source": [
    322     "<center><img src=\"general_vs_insight_wo_pp.svg\">"
    323    ]
    324   },
    325   {
    326    "cell_type": "markdown",
    327    "metadata": {
    328     "slideshow": {
    329      "slide_type": "slide"
    330     }
    331    },
    332    "source": [
    333     "<center><img src=\"general_vs_insight.svg\">"
    334    ]
    335   },
    336   {
    337    "cell_type": "markdown",
    338    "metadata": {
    339     "slideshow": {
    340      "slide_type": "slide"
    341     }
    342    },
    343    "source": [
    344     "# \"The purpose of computation is insight, not numbers.\" -- Richard Hamming\n",
    345     "<center><img src=\"http://upload.wikimedia.org/wikipedia/en/0/08/Richard_Hamming.jpg\">"
    346    ]
    347   },
    348   {
    349    "cell_type": "markdown",
    350    "metadata": {
    351     "slideshow": {
    352      "slide_type": "slide"
    353     }
    354    },
    355    "source": [
    356     "# Quantitative Finance motivation"
    357    ]
    358   },
    359   {
    360    "cell_type": "markdown",
    361    "metadata": {
    362     "slideshow": {
    363      "slide_type": "slide"
    364     }
    365    },
    366    "source": [
    367     "# <center>Types of risk</center>\n",
    368     "\n",
    369     "<center><img src=\"risk_first.svg\"></center>"
    370    ]
    371   },
    372   {
    373    "cell_type": "markdown",
    374    "metadata": {
    375     "slideshow": {
    376      "slide_type": "slide"
    377     }
    378    },
    379    "source": [
    380     "# <center>Types of risk</center>\n",
    381     "\n",
    382     "<center><img src=\"risk_full.svg\"></center>"
    383    ]
    384   },
    385   {
    386    "cell_type": "markdown",
    387    "metadata": {
    388     "internals": {
    389      "frag_helper": "fragment_end",
    390      "frag_number": 23,
    391      "slide_type": "subslide"
    392     },
    393     "slideshow": {
    394      "slide_type": "slide"
    395     }
    396    },
    397    "source": [
    398     "# Probabilistic Programming\n",
    399     "\n",
    400     "* Model **unknown causes** of a phenomenon as **random variables**.\n",
    401     "* Write a **programmatic story** in **code** of how **unknown causes** result in **observable data** -> **generative framework**\n",
    402     "* Use **Bayes formula** to invert generative model to infer **unknown causes**.\n",
    403     "* Inference is **completely automatic** (when things go well)!\n",
    404     "* -> No math, great flexibility and freedom when building models.\n",
    405     "* The catch: At the cost of increased computational demands. "
    406    ]
    407   },
    408   {
    409    "cell_type": "markdown",
    410    "metadata": {
    411     "slideshow": {
    412      "slide_type": "slide"
    413     }
    414    },
    415    "source": [
    416     "# Motivating the problem we face at Quantopian"
    417    ]
    418   },
    419   {
    420    "cell_type": "markdown",
    421    "metadata": {
    422     "slideshow": {
    423      "slide_type": "slide"
    424     }
    425    },
    426    "source": [
    427     "# Web based backtester for trading algorithms & live trading\n",
    428     "<center><img src='quantopian.png' width=85%>"
    429    ]
    430   },
    431   {
    432    "cell_type": "markdown",
    433    "metadata": {
    434     "slideshow": {
    435      "slide_type": "slide"
    436     }
    437    },
    438    "source": [
    439     "# Crowd sourced hedge fund\n",
    440     "\n",
    441     "* \"15 uncorrelated return streams are the holy grail of investing\"\n",
    442     "* -> Search for diverse trading strategies.\n",
    443     "* Perfect problem for crowd sourcing!\n",
    444     "\n",
    445     "# Our problem today\n",
    446     "\n",
    447     "* How do we identify the best trading algorithms?"
    448    ]
    449   },
    450   {
    451    "cell_type": "markdown",
    452    "metadata": {
    453     "slideshow": {
    454      "slide_type": "slide"
    455     }
    456    },
    457    "source": [
    458     "## Monthly trading competitions -- win, and we'll invest $100k, you keep all the profits\n",
    459     "<center><img src='contest.png'>"
    460    ]
    461   },
    462   {
    463    "cell_type": "markdown",
    464    "metadata": {
    465     "slideshow": {
    466      "slide_type": "slide"
    467     }
    468    },
    469    "source": [
    470     "# Let's take just two strategies and try to pick the better one"
    471    ]
    472   },
    473   {
    474    "cell_type": "code",
    475    "execution_count": 90,
    476    "metadata": {
    477     "collapsed": false
    478    },
    479    "outputs": [
    480     {
    481      "data": {
    482       "image/png": 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YXEuSJEkpMbmWJEmSUmJyLUmSJKXE5FqSJElKicm1JEmSlJJZlQ5AklQeIYR3\nAH9fVPyVGONbQwgrgDuAc4HtwPUxxgfLHaMk1Tp7riVp5ngNcD+wdNjXb4cQMkAnsBc4A7gLuC+E\nkKtQnJJUs+y5lqSZ4xTgJzHGPcMLQwgXAScB58UY9wObQwgXA9cAN5c/TEmqXfZcS9LMcTIQRyk/\nG3g0n1gXbADOKUtUkjSN2HMtSTNACOEY4ETg10MIfwZkgC8CHwSWAbuK3rIHaC5rkJI0DZhcS9LM\n8EvA0UAv8FaSRPs2oB44Fhgsaj8IZCd4jFxpIZZFrmhb7XJF26rS0dHRsGbrmqbskmxd3Qt1DQDN\n85ubBpcM9q/uWH0C0FjhEA8nV7StZrmibTXLFW2rXQ54PM0dmlxL0gwQY/zPEMKCGONz+aJ/zz/I\neC/JLCHHFb0lC/RP8DBfLzHMcqqlWKFK421paWHvY3uZt2Aeu7ftBqA1tK7qW9JHy2ktN1Y4vPGq\nyp/tGIx1amTS3JnJtSTNEMMS64LNwGxgJ3BaUd3SfPlEXAJ0Tyq48smR/NGvhVihyuPt6upqWLt1\nbWt2Sba/bmfdiS2nt1zVGTtv2/LTLf2Ldi7qbGtre6bSMR5Gjir+2RbJYaxTJZf2DktKrkMIs4GP\nAm0kWf8/AH8QY/yFc6ZKUvUIIbwV+DTwyhjj8/niXwaeAb4P3BhCqIsxFnqrzwcenuBhukn59uoU\n6qZ2YoUqjbe9vb2J6+gB+o5/9viFADue29ETn4z97be0b2lra+upcIjj0U0V/mzH0I2xVr1Se67/\nAmgF3pJ/fQ/wNPD/kcyZ+p8kc6a2ksyZ+poYY3eJx5QkTdw/Ay8Aa0MIHyKZeu/PSa7j3wa2AXeG\nEG4FLgXOBK6uTKiSVLsmPRVfCGEB8DvAu2OMj8QYHwFuAc4YNmfqe2OMm2OMHyXpAbkmhZglSRMU\nY3yG5DbtCuBR4DPA38QYPxJjPETSCbIY+BGwErgsxri9UvFKUq0qpef6fKA/xvhQoSDGeBdwVwjh\nJkafM/WCEo4nSSpBjHEjcNEYdVuAC8sakCRNQ6Uk1ycA20IIVwKrgbkkc6behHOmSpIkaQYqJbmu\nB44Hfg94DzAf+Jv8PueQzpypkiRJUs0oJbk+SJJQr4wxPgEQQrgBWAfcSelzpuZKiK1a5Iq2tSxX\ntK2Ijo6OhjVrsk3ZLHXFdb29dY1wbKa+nqHD1TU30wRQ2I73fcV1g4PZutWrO0ZdJGHXrl1Hr1+/\nfv5Y53HwGuY7AAAgAElEQVTxxRc/t2zZsheOeMKHlyva1rJc0baW5ZihT8hLkkpLrncCBwuJdd7j\nJCt97QZOLWo/0TlTa2ny8SPxXFLS0tLC3r0wb97Iut27lwNZli4dX11rK6sm876Cvr5GWlpGXyRh\n9uzZbNt2DnV1C0bU9ffvY/bs2aO9bbL8fFWfVBckkCTVjlKS60eAWSGE18YY/yNfdgrJ0rqPAO8r\ncc7UWpl8/HBy1NZE6oeTowrOpaurq2Ht2rNas9mmEXdBenu3L4T6TH19bsS8qsPrmptpam1lVWcn\nt+3YQc9431dcNzj4dN2iRT8YdZGErq6uhrvvHj3OwcGn61as6EpjcYUcVfA7SUmO6XUukqQZatLJ\ndYzxpyGETuBzIYRrSR5o/DCwFniI0udM7Wb63FrtxnNJRXt7exNs7AH6Rtb2Z5LF5tgznrodO+jZ\nuJE9E33fSwbntbePvkjC4eMc+32T1I2fL0mSqsKk57nOawM2At8CvgzcD9zonKmSJEmaiUpaoTHG\n2EeyMMyIxWGcM1WSJEkzTak915IkSZLyTK4lSZKklJhcS5IkSSkxuZYkSZJSYnItSZIkpcTkWpIk\nSUpJSVPxSZKkmSWTycwCFuRfNnKITCXjkaqNybUkSZqIBVzJtRzHAX7GQgYYAHorHZRULRwWIkmS\nJuY4DrCEPuYxUOlQpGpjci1JkiSlxGEh0qQNHAU0ZjKjDjdshIOOQ5QkaYYxuZYmbeccuOcqeO1T\nI+seWQjPOg5RkqQZxuRaKsmyATi1b2T51rnlj0WSJFWaY64lSZKklNhzrapTNIdqMccyS5KkqmVy\nrWq0AL52LSw/MLLKscySJKl6mVyrSi0/4FhmSZJUaxxzLUmSJKXE5FqSJElKicm1JEmSlBKTa0mS\nJCklJteSJElSSpwtRJJmoBDCHcCJMcY35l+vAO4AzgW2A9fHGB+sYIiSVJPsuZakGSaE8GvANcBQ\n/nUG6AT2AmcAdwH3hRBylYpRkmqVPdeSNIOEEOYCa4HvAYXVTt8InAScF2PcD2wOIVxMkoDfXJFA\nJalG2XMtSTPLGuBbwLeHlZ0NPJpPrAs2AOeUMS5JmhZMriVphgghnANcAdzAS73WAMuAXUXN9wDN\nZQpNkqYNh4VI0gwQQsgCnwVWxRifDSFAfsw1UAcMFr1lEMhO8DC5UmIsk1zRttrlirYV19HR0bBm\n65qm7JJsXe/TvY1kydQvqR+qe6GuAaB5fnPT4JLB/tUdq08AGisc7uHkirbVLFe0rWa5om21ywGP\np7lDk2tJmhk+APw0xnjfsLJC7/UAML+ofRbon+Axvj7J2CqhlmKFKoq3paWFvY/tZd6CeexevBuO\nhqXNS9m9bTcAraF1Vd+SPlpOa7mxwqGOV9X8bMfBWKdG5shNxs/kWpJmhncAy0IIvfnXxwBH519/\nCHhdUfulwM4JHuMSoLuUIMsgR/JHvxZihSqMt6urq2Ht1rWt2SXZ/t5NvQvJkql/dX1P3c66E1tO\nb7mqM3betuWnW/oX7VzU2dbW9kyl4z2MHFX2sz2MHMY6VXJp79DkWpJmhgt56ZqfAf4QOB14J7AC\nuCmEUBdjLPRWnw88PMFjdJPy7dUp1E3txApVFG97e3sT19ED9LGHDFlgLnuOf/b4hQA7ntvRE5+M\n/e23tG9pa2vrqWy049JNlfxsx6EbY616JteSNAPEGLcPfx1C2AcMxBi3hhC2AduAO0MItwKXAmcC\nV5c/Uk03mUxmFrAg/3Lf0NDQwUrGI001ZwuRpJlpKP9FjPEFoBVYDPwIWAlcVpyQS5O0gCu5liu5\nlpeSbGnasudakmagGOPNRa+3kAwdkdJ3HAcqHYJULvZcS5IkSSkxuZYkSZJSYnItSZIkpcTkWpIk\nSUqJybUkSZKUEpNrSZIkKSVOxSdJktJ1kKOAxkwmA9DIITIclcyrLk13JteSJCldvczhcq5iMU/x\nMxYywAB17K90WFI5OCxEkiSlbx4DLKGPeQxUOhSpnEyuJUmSpJQ4LEQVkclkZgELxqhuhIOZcsYj\nSZKUBpNrVcoC+Nq1sPzAyKpHFsKzA0Bv2aOSJEkqgcm1Kmj5ATi1b2T51rnlj0WSJKl0jrmWJEmS\nUmJyLUmSJKXE5FqSJElKicm1JEmSlBKTa0mSJCklJteSJElSSkyuJUmSpJSYXEuSJEkpSW0RmRDC\nHcCJMcY35l+vAO4AzgW2A9fHGB9M63iSJElStUml5zqE8GvANcBQ/nUG6AT2AmcAdwH3hRByaRxP\nkiRJqkYl91yHEOYCa4HvAZl88RuBk4DzYoz7gc0hhItJEvCbSz2mJEmSVI3S6LleA3wL+PawsrOB\nR/OJdcEG4JwUjidJkiRVpZKS6xDCOcAVwA281GsNsAzYVdR8D9BcyvEkSZKkajbp5DqEkAU+C6yK\nMT6bLx7Kb+uAwaK3DALZyR5PkiRJqnaljLn+APDTGON9w8oKvdcDwPyi9lmgfwL7z00+tKqRK9rW\nslzRtiQdHR0Na9Zkm7JZ6orrenvrGuHYTH39i/9ZS7WuuZkmgMJ2qo9XXDc4mK1bvbrjBKCxuG6C\nckXbWpYr2tayHPB4pYOQJFVGKcn1O4BlIYTe/OtjgKPzrz8EvK6o/VJg5wT2//USYqs2nkuRlpYW\n9u6FefNG1u3evRzIsnTp1Na1trKqnMcr6OtrpKWl5caRNZPm56v6ZI7cRJI0HZWSXF847P0Z4A+B\n04F3AiuAm0IIdTHGQm/1+cDDE9j/JUB3CfFVgxxJsuC5FOnq6mpYu/as1my2acTdjN7e7QuhPlNf\nn+uZirrmZppaW1nV2cltO3bQM9XHK64bHHy6btGiH3S2tbU9M/InMyE5/HxVo1ylAxhLCOH/Af4K\nOAt4CvirGOPH8nWuTSBJKZh0ch1j3D78dQhhHzAQY9waQtgGbAPuDCHcClwKnAlcPYFDdDN9bq12\n47m8THt7exNs7AH6Rtb2Z2A2JA/BTlndjh30bNzInnId7yWD89rb27e0tbWNSLwnqRs/XzqCEMJs\noAt4CHgvcDJwTwhhJ3AvydoE/0myNkErydoEr4kxdlcmYkmqTWkufz6U/yLG+ALJxXkx8CNgJXBZ\ncUIuSSqbVwLfB34vxrg1xviPwHrgV3lpbYL3xhg3xxg/SnKn8ZqKRStJNSq15c9jjDcXvd5CMnRE\nklRh+R7od8CLq+ieC7wB+F3GXpvggjKHKUk1L82ea0lSbdgB/AtJ7/R9uDaBJKXG5FqSZp5fJxm6\ndzrwCWAOrk0gSalIbViIJKk2xBgfBR4NIdQBdwF/BxxX1GyiaxNAFc+UMkyuaFvtckXbiuvo6GhY\ns3VNU3ZJtq736d5GsmTql9QP1b1Q1wDQPL+5qXdx71ChvNDmmLnHzFndsTqNOf7TkivaVrNc0baa\n5Yq21S5Hyg/Sm1xL0gwQQngFcEaM8avDijeRrFGwCzi16C0TXZsAamue8lqKFaoo3paWFvY+tpd5\nC+axe/FuOBqWNi9l97bdALSG1lVnHXvWS+X5NvPmzaPltFTn+E9L1fxsx8FYp0aqaxOYXEvSzHAK\nyfR6r4gx7s2XnU4ytnoD8P4S1yaA2pinPEdtzameo8ri7erqali7dW1rdkm2v3dT70KyZOpfXd9T\nt7PuxJbTW67qjJ23bfrBpqFCeaHNMXOP6V+0c1Eac/ynJUeV/WwPI4exTpVc2js0uZakmeHbwH+R\nrD/wR8CJwIeBNcB3KH1tAqitecq7qZ1YoYribW9vb+I6knUK9pAhC8xlz/HPHr8QYMdzO3qe2PPE\ni+Uvtqljf/stqc7xn5ZuquRnOw7dGGvV84FGSZoBYowHgf8JHAR+AHwa+ESM8VMxxkO4NoEkpcKe\na0maIWKMO0iS6NHqXJtAklJgz7UkSZKUEpNrSZIkKSUm15IkSVJKTK4lSZKklJhcS5IkSSkxuZYk\nSZJSYnItSZIkpcTkWpIkSUqJybUkSZKUEpNrSZIkKSUm15IkSVJKTK4lSZKklJhcS5IkSSkxuZYk\nSZJSYnItSZIkpcTkWpIkSUqJybUkSZKUEpNrSZIkKSUm15IkSVJKZlU6AGnmGTgKaMxkMmM12Dc0\nNHSwjAFJkqSUmFxLZbdzDtxzFbz2qZF12+fApZ8BesoeliRJKpnJtVQRywbg1L5KRyFJktLlmGtJ\nkiQpJfZcS5Kkw8pkMrOABfmXjRxizIdGxnSQ4udNfL5E05LJtSRJOpIFXMm1HMcBfsZCBhgAeie0\nh17mcDlXsZineJY53IPPl2haMrmWJElHdhwHWEIfzzB30vuYxwBL8HkTTWuOuZYkSZJSYnItSZIk\npcTkWpIkSUqJybUkSZKUEh9olKQZIoRwAvBJ4DxgP/AFYHWMcTCEsAK4AzgX2A5cH2N8sGLBSlKN\nsudakmaAEMIxwAPAAeAc4J3AbwBr8k06gb3AGcBdwH0hhFz5I5Wk2mbPtSTNDGcCrwbOiDH2AzGE\ncDPw8RDCPwInAefFGPcDm0MIFwPXADdXLGJJqkH2XEvSzLAZeHM+sR5uAXA28ON8Yl2wgaSHW5I0\nAfZcS9IMEGPsAb5VeB1COAr4feCbwDJgZ9Fb9gDNZQtQkqYJe64laWb6OHAa8MfAXGCwqH4QyJY7\nKEmqdfZcS1Vl4CigMZPJjNVg39DQ0MEyBqRpJoSQIZkx5Drg8hjjphDCADC/qGkWKB5CciS50iOc\ncrmibbXLFW0roqOjo2HN1jVN2SXZut6nexvJkqlfUj80/Pu6F+oaAJrnNzf1Lu4dKm7DIC+WDTJY\nt7pj9QlAYwVPK1e0rWa5om01yxVtq10OeDzNHZpcS1Vl5xy45yp47VMj67bPgUs/A/SUPSxNC/mh\nIH8LXAm8Lcb4QL5qB/C6ouZLGTlU5Ei+XlqEZVVLsUKF421paWHvY3uZt2AeuxfvhqNhafPSl3+/\nbTcAraF11VnHnjWiDS/wYlnfvj5aTmu5sZLnNEwtfRaMdWqM2aM1GSbXUtVZNgCn9lU6Ck1Lfwm8\nHbgsxvhPw8q/D9wUQqgb9sDj+cDDE9z/JUB3yVFOrRzJH/1aiBWqJN6urq6GtVvXtmaXZPt7N/Uu\nJEum/tX1PcO/r9tZd2LL6S1XdcbO2zb9YNNQcZsXe65fXd8z+ORg3aKdizrb2tqeqdQ5USU/23HK\nYaxTJZf2Dk2uJWkGCCGcDawC/gR4NISwdFj1d4BtwJ0hhFuBS0mm7rt6gofpJuXbq1Oom9qJFSoc\nb3t7exPX0QP0sYcMWWAue4Z/f/yzxy8E2PHcjp4n9jwxsk1hFP9c9vAk89pvad/S1tZWDXfiuqmd\nz0I3xlr1fKBRkmaGy/Pbj5AM9yh8/Txf3gosBn4ErCTp3d5e7iBVPTKZzKxMJtOUyWSagEYOpXvr\nXJqu7LmWpBkgxvg+4H2HabIFuLA80ahGLOBKruU4DvAzFjLAANBb6aCkamfPtSRJGt1xHGAJfcxj\noNKhSLXC5FqSJElKicm1JEmSlBKTa0mSJCklPtCoKZPJZGYBC8aoboSDPnkuSZKmlZKS6xDCCSTL\n6J4H7Ae+AKyOMQ6GEFYAdwDnAtuB62OMD5YYr2rLAvjatbD8wMiqRxbCsz55LkmSppVJJ9chhGOA\nB4D/AM4BlgB/l6++AegE/hM4g2T+1PtCCK+JMXaXErBqzfIDo682uHVu+WORJEmaWqX0XJ8JvBo4\nI79cbgwh3Ax8PITwj8BJwHkxxv3A5hDCxcA1wM2lBi1JkiRVo1IeaNwMvDmfWA+3ADgb+HE+sS7Y\nQNLDLUmSJE1Lk+65jjH2AN8qvA4hHAX8PvBNYBnJsrrD7QGaJ3s8SZIkqdqlORXfx4HTgD8G5gKD\nRfWDQDbF40mSJElVpeSp+EIIGZIZQ64DLo8xbgohDADzi5pmgeIhJIeTKzW2KpAr2tayXNH2iDo6\nOhrWrMk2ZbPUFdf19tY1wrGZ+nqGyl3X3EwTQGFbyVgmUjc4mK1bvbrjBKAxX5Qr2tayXNG2luWA\nxysdhCSpMkqdiu8o4G+BK4G3xRgfyFftAF5X1HwpI4eKHM7XS4mtyszIc2lpaWHvXpg3b2Td7t3L\ngSxLl1aurrWVVdUSy3jq+voaaWlpuXFkzcz8fFU553CXpBmq1J7rvwTeDlwWY/ynYeXfB24KIdQN\ne+DxfODhCez7EqC7xPgqLUeSLMzIc+nq6mpYu/as1my2acQdi97e7QuhPlNfn+spd11zM02trazq\n7OS2HTvoqWQsE6kbHHy6btGiH3S2tbU9ky/KMYM/X1UsV+kAJEmVU8o812cDq4A/AR4NIQzva/sO\nsA24M4RwK3ApydR9V0/gEN1Mn1ur3czAc2lvb2+CjT3AKPNc92dgNiQPulakbscOejZuZE81xDK+\nusF57e3tW9ra2ooT725m4OdLkqRqVMoDjZfntx8hGe5R+Pp5vrwVWAz8CFhJ0ru9vYTjSZIkSVWt\nlKn43ge87zBNtgAXTnb/kiRJUq1Jcyo+SZIkaUYzuZYkSZJSYnItSZIkpcTkWpIkSUqJybUkSZKU\nEpNrSZIkKSUm15IkSVJKTK4lSZKklJhcS5IkSSkxuZYkSZJSMunlzyWATCYzC1gwRnUjHMyUMx5J\nkqRKMrlWqRbA166F5QdGVj2yEJ4dAHrLHpUkSVIFmFwrBcsPwKl9I8u3zi1/LJIkSZVjci1JM0wI\nIQv8G7AqxvhQvmwFcAdwLrAduD7G+GDlopSk2uQDjZI0g4QQjgXuBU4BhvJlGaAT2AucAdwF3BdC\nyFUoTEmqWfZcS9IMEUI4BbhnlKo3AicB58UY9wObQwgXA9cAN5cxREmqefZcS9LM8QbgIeCcovKz\ngUfziXXBhlHaSZKOwJ5rSZohYoyfLnwfQhhetQzYVdR8D9BchrAkaVqx51qSVAcMFpUNAtkKxCJJ\nNc2ea0nSAWB+UVkW6J/gfnKpRDO1ckXbapcr2pZNR0dHw5qta5qyS7J1vU/3NpIlU7+kfmis7+te\nqGsAaJ7f3NS7uHeouA2DvFg2yGDd6o7VJwCN5T6vYXJF22qWK9pWs1zRttrlgMfT3KHJtSTp58Bp\nRWVLgZ0T3M/X0wmnLGopVqhAvC0tLex9bC/zFsxj9+LdcDQsbV469vfbdgPQGlpXnXXsWSPa8AIv\nlvXt66PltJYby31OY6ilz4KxTo1UV5M2uZYk/QC4KYRQF2Ms9FafDzw8wf1cAnSnGdgUyJH80a+F\nWKGC8XZ1dTWs3bq2Nbsk29+7qXchWTL1r67vGev7up11J7ac3nJVZ+y8bdMPNg0Vt3mx5/rV9T2D\nTw7WLdq5qLOtre2Zcp5TkRy181nIYaxTJZf2Dk2uJUnfBrYBd4YQbgUuBc4Erp7gfrpJ+fbqFOqm\ndmKFCsTb3t7exHX0AH3sIUMWmMuesb4//tnjFwLseG5HzxN7nhjZpjCKfy57eJJ57be0b2lra+sp\n5zmNoZva+Sx0Y6xVzwcaJWmGizEeAlqBxcCPgJXAZTHG7RUNTNPXQY4CGjOZTFP+y84+TRt+mCVp\nBooxHlX0egtwYWWi0YzTyxwu5yoW8xTPMod7+AxQDb3YUslMriVJUvnNY4Al9FU6DCltDguRJEmS\nUmLPtQDIj3dbMFb9zp07j162bFkZI5IkSao9JtcqWABfuxaWHxhZtX3O+vXr17e1tZU/KkmSpBpi\ncq1hlh+AU8cY//Z0eUORJEmqQY65liRJklJiz7UkSTPQKM/a7BsaGjpY9kBemvMakoXSIVksvXIx\nSSUwuZYkaWZawJVcy3EcqOhc08PnvP4ZC8mC81+rlplcS5I0Ux3HgaqYa7ow5/UzzCULVRGTNEmO\nudY4DBy1cePG43p6eli3bl3DsOVqm4BGOJipdIQzw8DLlgtet25dQ9HvxP8sS5JUYf4x1jjsnPOF\nL1zw1mXLYO3as1ph47BbdI8shGcHgN6KhTdj7JwD91wFr30KYM2abNPevYXfydf2w6XePpU0OaOP\nez6OQ9h5Ik2QybXGZdasxQPz5jWRzTb1w/DbdVvnViyoGWnZQGG6xGyWunnzyP9OBkeZn1ySxmm0\ncc+DwAB2nkgTZHItSZJGjnueXemApNrkmGtJkiQpJSbXkiRJUkpMriVJkqSUmFxLkiRJKTG5liRJ\nklJici1JkiSlxKn4ppn8Kn0LxqguLAzwwih1rrQoSdNc0d+IRheJkdJncj39LICvXQvLR1lU5JGF\nUE9hhb+Rda60KEnT3AKu5FqO4wA/Y6GLxEjpM7melpYfKKzi93Jb58JxjF0nSZr2juPAi4vFSEqd\nyXWVcniHJmbgKKAxkxnzV79vaGjoYBkDkiRpRjK5rl4O79AE7JwD91w1+mdi+xy49DNAT9nDklQ2\no3TK1PZ/qg9S3Gkw5vlMu3NXTTO5rmoO79BELBsY/TMhaYZ4aTz1s8zhHmr7P9W9zOFyrmIxT43j\nfKbXuaummVxLkjRdFMZTTxfzGBj3+Uy3c1fNMrmWNEIJY/7B27GSpBnM5FrSaCY55t/x3VKadu3a\ndfTs2bPp6upqaG9vb2KU/7wO+8/wqPNWT9e5rcdzXhMZiz1WW8dza6JMriWNYTJj/iWlaf369fO3\n1W/j7q13t3Il+8cYS5yMN36OujHmrZ6uc1uP57wmMhZ7rLaO59aEmFxL057T9Em1rK6+juySbD9P\nMsqdpLzjOMAhjjps/XSc23o85zWRsdhjtXU8tyZgSpPrEEIW+BRwBTAIfDzG+BdTeUxJxZymT+Pj\nNVuSSjfVPdd/AZwF/BrwKmBdCGF7jPELU3xcSS/jNH0aF6/ZU2S0cbv5rWN5x+Plc14XHqo+btTx\n4y9v+9JY7KJ9/PVf//XC3/zN3yyMZ6/InfzJjuee6Puqfdx4tcc3UVP2YQohzAXeDVwaY/wx8OMQ\nwp8Dvw9U7YX6CLMkwAR/4QcPHuTee+8tPIhSzJUWVWFjDhkp6+dvlIe2iqV6oZ3sv/Nxvq/U8Cqi\n2q/ZmTMy72Qhh3ie2fyYrqFnhvZWOqYJGm3cLo7lHafhc17/jIVkSe6tjDbOurhtoU1R+Ycf+/DC\nAycd4PZHb/8tYEv5TwqY/Hjuib6v2seNV3t8EzKV/1M7DcgCG4aVfQ+4OYSQiTGW/Bcok/mN8+At\np45e+8MDQ0N/c9ckdnuYWRImfgt937593HJL82/Bxh0ja11pUZU21pCR8n7+1q9fP3/btnO4++6z\nWmFj0b+vKRm6Mtl/5+N5X62a8mt2SZbTyGkM8jRz2MixFY1lskYbt+tY3vErzHn9DHPJArPH2XaM\n8lnzZw3MWzCP2QtmD0xp3Ecy2c/ARN9X7Z+1ao9vAqYyuV4GPB1j/MWwsieBY4DF+e9LtGg2vOvQ\n6HWDYz/YcURjzZIwObNnv3IATnKlRVWp0YaMlP/zV1e3gGy2qR/KdXGd7L/zdK8PVaQM12xJmv5K\nSECPqI7kps1whdfZKTyuJGnivGZLUgqmsud6gJEX5MLr/nG8P3ekBm1tpzRs2vT5+tHqjjnm2cF1\n69adNY7jvMwNN9xw3P339zTPnv34iNtEzz/fc+xb33rDr6xbt+7Z8ewrl8u9avHixTQ2PrUshJH1\n/f19CyBzVF3d43Oqva6hIbugr6+HxsbnmkM4WFetcY6nrrFxVmNf3/wXz6Va4zxS3fDzeNWr+g6l\nebzJxjjRfyMFAwMDp/T37xvx+Spln4cz2X/nR3rfLf9/e3ceLkdV5nH8G7YkBEiISxJMJCz6EqJG\nloxsQcABAUEHZgYHI5sSZBRESBBZRgIoxoFxQ824sCQ44PgggyyCCBogkIBMQLb4IoMhGhYdASUJ\nNwuJf7ynSKVvd7h976m+fcPv8zx5+qbqdPd7qrrfqj51zqmpM7cjLkc9nivWFuppzoYu5O3u2mXQ\nLgP6Pd9vk1eWvbLRhKMn7HjllVdu1Z3XGT169KgxY8Ywf/78dy1YsGDL3HE2MmXKlMHXrrx25MZs\n3LGi/4oBh085fGeA2mW1n7uOjo4dl760lKEdQ0du23/bpfXKFK+9YuCKAWzCBpuy6cDy65Xfe+nA\npUOKMq/1NxuwqqtlN2XTgYP6DRrWsbiDoR1DR44aOKrTc5t9vdzx1f695eothyx+cTFDVw8dMWXK\nlIb7o96+y5WPuvratZ/bZmOqsg6vFWtXnlMb39SZU7cDhlYRXx2jyZyz+1U1+MbM9gDuBAa4+8q0\nbF/gp8Agd2/QnUNERFpNOVtEJI8qu4U8CCwH9iwt2wu4X0laRKTtKGeLiGRQWcs1gJlNB/YGjiUG\ny8wEjnf3ayp7UxER6RblbBGRnqt60vTTgOnAL4C/AOcpSYuItC3lbBGRHqq05VpERERE5PWkyj7X\nIiIiIiKvKzq5FhERERHJRCfXIiIiIiKZ6ORaRERERCSTqmcLqcvMvggcD2wMXAqc0WgeVTPbGvge\nsAewEDjN3W8prd8d+AYwFnDgFHe/s9oarBVftrqUym0PPAQc2FfrYmafBk4GhgMPA5PdfU6FsfcH\nLgH+ibhl81fc/aIGZccB/wm8C5gPnOju95fWHwFcSExF9nNgkrv/qarYa2LLUg8z2xA4FziKuMvV\nfcDJ7v6byiuxJr5s+6RUbgJwBzDa3RdWFXud9835+ToU+DKwNfBAWv9ItTXoucz54XPAJ4E3EDeu\nOdndn2jTWFuSyyo6lkwkPl8TehBXn8utFeWes4Ed3P2odouzVfk+Y7wbETnwI8Ag4OYU7x/bLdaa\ncl0+/rS85drMTgOOBv4ROAw4Eji9Qdl+wE+APwG7AjOAH5vZ6LR+FHArcBvwDmIHXWdmb6y2Fq/G\nl60uNeW+DwyoLPD68eXcLx8FzgfOAMYBs4BbzKxbtyvuoouA9wDvAz4BnGNmH64Te/FFvgfYGbgL\nuMnMNkvrxwNXpPh3A7Yg5vptlSz1AM4EjgMmAeOBPxD7YNPa16pQrroU5QYQ343emOIo1+drV+Aa\nYsh1c4AAABA9SURBVLq7ccBvgevNbONWVKK7MueH44HJxInkOOAF4Mb0vHaLtSW5rKJjyb7Ad+n5\n96Uv5tbcuedIYCr5c09fy/e54p0KfJD4vO9G/Mj+QZvGWpRr6vjTG91CPgOc6+6z3f0OIml9qkHZ\nfYG3Aye4+2/c/cvEBvh4Wn8y8IC7n+nuT7r7WcDviITTCjnrUjiRvr9fjgG+5e7XlvbLs8ChVQSe\nvhzHA6e6+wPufj3w78BJdYp/GFjm7pM9nErM51t86U4GrnH3me7+MHHAe7+ZbVtF7BXW4xjgfHe/\nzd0fB04gEli3W7CakbkuhfOA54AsJ2FdlbkunwV+5O6XpJbak4BVwA6VV6RncuaHzYAp7n5r2gbT\nUvlhbRhrq3JZ1mOJmZ1L3Lb+/3oSVF/MrTljNrMN042VLqWH27LKOGlBvs8c7wbAp939Hnd/jOh9\nsHebxlpo6vjT0pO49Gt/JHEZsHA3MNLM3lLnKbsB89x9SWnZbGD39Pd+wI/LT3D3XbzO5bHcKqhL\n0RI/lfhitEwFdTmHuGRZa3CGcOsZB/RPMRTuBsbXaQ3bLa2jpuzupfWvbgd3/wPwFHH5tWo563EC\n0bpVWE0khar2Qa2cdSlafD8KTMkf6mvKWZd9iZZrANx9ibtvn0422lLu/ODuX3P3Gem1BxMnkY+4\n+7PtFistyGVVHEuAvwcOII6PPfkx2hdza86YNwfeCfwdMIe8P+z7Wr7PFq+7n+XuNwOY2TDiRPj2\ndow1xdj08afVfa5HpMenS8ueS48jgUV1yj9Ts+yPqSzAtsASM7uaOGg9QfSHuzdbxI3lrgvAd4Cv\nEPVopax1qd3+ZnYg8Dai+04VRgDPu/vy0rLngE2AN7OmLhD9Jmv7of2R6GtVrH+6Zv1zQL2DXG45\n6jEOwN1/WbOu6MvZqj782eqSukxcStw98PmqAl6HLJ8vM9uCaE3awMxuAnYBfk30NXy8quAzqCLX\nYWYnEP0clwHvzxJp38xl2bevpz7WZva+DLH1tdyaM4++COwFr3bHadc4W5Hvs8VbsBhncCaR1/dq\nx1i7e/zJfnKdOpGParC66P+zrLSs+Lt/g/LLapYtK5XdgrikeEF6PBq4zcx2cPfahNS0VtbFzI4m\ndvJFVHBFocX7pfy+byf61c1w93ldDrg5jeKhTkyvFXuX61aBnPV4lZntCVwMXJijdbCLctblTOAp\nd/9vi8G+rZajLgOIVjCIS6BnE62ik4HbU85aQi/ppfxwC9HHcRLwEzPbyd0XtGmsPcplvRVzBn0x\nt1aSRyvQ1/J9FfFeDlxL5PhbzWysu7/UZrF26/hTRcv1eOr/WlpN9CODCHpp6W9K/y97mTiBLusP\nFAehlcBN7v719P/JZrY/MWJ2WvOhd9KKuiw1szcTX4aD3H2VxchfyHsJqiV1KS8ws3cQA04fIwYU\nVKWDzl+YRvF30HmwaDn2Rq9VbzvklrMeAJjZPsD1wPXufl6eMLskR12WmNlYoq/mTjXrW9nvOktd\niHwFcJm7zwQws48RLZOHAj/MFXA3tDw/eIy2Xwh8Kg2+O4bo19h2sWbIZS2POZO+mFuz59GK9LV8\nnz3eNOYCMzuKGIR5ODFAtx1i7dHxJ/vJtbvPpkHLq5mNIDqVDweeTIuHp8fay1wQB51xNcuGl8ou\nonNz/uM0biFoSgvrciBxuXiWmZXX32xm57t7j38otKgur17yS32UfkZc9j6k5vJMbouALc1sI3cv\nTmCGE78+ay/jLGJN3SiVfaaL66uUox7lfXAw0efyf4j+Yq2Uoy7PEqPJhwDz03ejSGqPmtkkd7+6\niuDrxJfj8/X/wApKOcvdl5vZU2TKWd3VyvyQGkCedPfyALH5RA5sq1jTa/Y4l7U65oz6Ym7Nmkcr\n1NfyfZZ4U/eaDwJzPE295+4vm9kCupgDWhRrj44/LR3Q6O7PEC0V5RGsewGLGnTjmAu8u2Y6mb3S\ncogBBrsUK9JO2xFYkDHsujLWZQ5xWeRtRMIcx5o6fZzoh12p3Psljf6+BbgfONjdq24FeBBYDuxZ\nE8/93nme2LmUBtCkz8yerPlMzaW0HdIg07eW1lcpWz3M7D1Eov0hMLHO86uWoy5ziHlKjTXfjWKW\nhoOAGyqJvLMs+8XdXwF+xdo5awCwDS3IWd1VQd4+F/h0scJiztt3EyfYbRVrK3JZBds3p76YW3PG\nXJZ7Gr6+lu9z5cHVwDeBiaX1g4HtyZADMsbao+NPb9xEZjrwJTNbSExBdSFQdOvAzN4ELE39D+8g\nRhNfYWbnAYcQo3aPS8W/BtxtZqcANxF997Yi/3yJldbF3RcDi0vPK/bLInd/oSU1ybtfvkXU50Rg\nSKk1/qUq+pW6+1IzmwF828yOJQYzFPPoYmbDgRfdvYOYqWGamV2S6jyJmMS+uCQ/HbjDzO4G7k3b\n4Kc1rWyVyFWPlBwuAx4BzgKGlfZB8fw+UZf0eXn1O2BmRYPAU+l7U7nMn6+LgavM7AHiRPsc4CXg\nxlbUpQdy5odvADPM7B6iNfh04liU43Jw7lhblctyxpxNX8ytmWMuy9oVra/l+8zb9RLgLDN7jGg5\nnhZvETOItEusPTn+9MZ8yhcBVxG/sq5Jf/9Haf19xEYg/cL4EDG6837iUsdhqa8eHnfQOYzYYA8D\n+xB3NWzFJXzIWJc2kKUuZrY5MfJ/FDEv6NOlf2dQndOIk5VfAN8GznP3Ysqzp4EjUuwvAR8gfqn+\nLzHdzsHFgdLd5xJfrnOIuWNfIPqCtkqOeowFxhCDxRax9j74SMtqkmmf1NEbN5HJ9fm6jrgz4XlE\n68pI4AB3f7l1VemWnHn7R8ApwBeAeUTr5QEZW4X7Yi6r6liymp5/X/pibq0i9+TYllXE2cp8n2u7\nXkz8uPoe0XK8jOgq0o6x1urSZ6Df6tW9cZwSEREREVn/9EbLtYiIiIjIekkn1yIiIiIimejkWkRE\nREQkE51ci4iIiIhkopNrEREREZFMdHItIiIiIpKJTq5FRERERDLRybU0xcymmdkqM+v25P9mNiu9\nxrjSslVm1qq7UXaLmY03s9t7Ow4Rka5SzlbOltbrjdufy/qhJ3cfWk39u121+x2N5gJ/6e0gRES6\nQTlbpEV0ci294WhgILCgl+NoVr/eDkBEpBcoZ4s0QSfX0nLu/vvejkFERLpGOVukOTq5lrrMbBBw\nBjAR2Ar4DXDBOspvA0wB9gdGpsULgWuBC919cansLGBvYCd3/3Wd1xoAPEu0lAx39xdq1g9J63/n\n7mPWEdOxwGXAJGBX4CigA5jm7henMu8GzgHeC2xGtMz8ALjY3ZfVvA7AEDNbBdzh7vua2VTg88Cp\n7v71Bu//dXc/NS0ryh8KHAscQly2PBXon8ofBzwD/BuwE7ACuB0429295j0mAJ8DxgFvBBYBtwBf\ndPenG20bEVm/KGcrZ0v70IBG6SQlyluJBLYRcD2wIXAN8ME65ccBDwD/CrwA3ED0dduGSCI31Hmb\nev33AHD3DuCHwMbAP9cpcgSwCTCzi1X6LHFZ8+dEAnw4xf0h4F7gH4AngBuJZH0BcFvaDqR1/5X+\nXkEk8lvr1KeReuu+AuwL/BRYAswrrTscuBl4A5F0X0jLZpvZm4pCZrZ7qtP+gBP7aSWxH+amA5qI\nrOeUs5Wzpb2o5VrqORXYnfjiH+Huy2GtX/C1LgK2ACa6+9XFQjPbHvgVsLeZjXH3+aXnvFZfuBnA\nCcBHgO/WrPsosIpImF2xPbCnu88txTacSPTLgA+4+11p+SbApUTrz/nAZ919NpEkJwJL3P3oLr7v\nuowExrr7glJMu6c/D03vW7TUbEwcGN4LfAz4cip3AXHA2s/dZ6Wy/YjtciTRyvK1DLGKSHtTzlbO\nljailmupZxLxa/rEIkkDuPtU4NE65Z8EflBO0qn8E8AsIim/tZkA3H0O8Ftggpm9pVhuZlsDewF3\nNtEP8NflJJ18HNgc+FKRpNP7LidaEV4EPmFm/ZuJuwk/KyfpGvOLJJ1iWgF8P/13x1K5txAtLE+X\nyq4mLk2eCNyWM2ARaVvK2crZ0kbUci1rMbORwGjgQXd/tk6RG4Gx5QXufmLNa/QDRgG7EJcZIX6t\nN2sm8Uv/SKBIXBNL67rq4TrL3pse76xd4e6Lzew+4ABgZ2BOE+/Vk5gK99ZZ9lx6HFRadidgwC/M\n7HJi39zn7k/SueVIRNZDytnK2dJ+dHIttUakx0YDKxbWW2hmuwKfJAahvI0Y6AFr+q51Z0qkmcRl\nvomsnaiXEn0Ju6rejQ6KATx3mdm6nrtVE+/TjHXdfKHevKwr02P5atMZRKLeGzg7/fuzmV0HTHf3\neYjI+k45e23K2dLrdHIttV7rpgAraxeY2dlEa8Uq4EFiIMmjwN3ASUR/u6a5++/N7JfAfma2AzAA\nGANcXR7J3gWr6izbMD1eQ4xGb6ReS1BXbbiOdfViKnTpxgzu/iKwj5ntARxGtNq8g7h8epyZTXL3\ny7sarIj0ScrZa1POll6nk2upVbR+NOpvN6L8nzSd0/lEQtvf3R+tWT+4h/HMAPYjRocXI8GbubzY\nyLNEa80X3P2hHrxOkXDrJeWWjPx293uAe4DTzWwE8BngdOBLgBK1yPpNObs5ytlSOQ1olLWkeTYd\nGGtm29UpcmDN/8cTlw9vqJOkBwF7pP92905ZPwYWE4n6ECLB1k6p1B3FgJja+mBmG5jZbWY2Kw3G\nWZel6XFYnXW79STAdTGzLcxsnpmtNeesuz/j7mcQlynfZGb6AS2yHlPOVs6W9qOTa6nnEiKxXm5m\nmxcLzewzdE4+xejvfcxss1LZwcBVxLyfsKY/X1PcfSmRrMcTk/NflUZX99T3iUuL55jZfsVCM9uA\nuFy6HzDE3Z8qPWc5MLAm+RWDXP7FzLYsvc6hxGW/Srj7X4nLve80s0+U15nZAcBg4CF373RJWETW\nO8rZytnSRvQLSeqZDryfmLvzCTO7ixiNvjMxKvo9pbL3Ejcf2C2VnUNcCpxATLR/FTHvab1Wgq66\nAjiG6NeW4/Ii7r4gJbjLgJ+b2Txi4M+7gO2A54m4y54gplW628xmu/tkYuqkh9Lz3MxmE9MtjSf6\nMU6kOicBdwDTzeyTxDRYw4A9iYPKKRW+t4i0D+Vs5WxpI2q5lk5SK8PhRB+wPwMHA5sSgy6uoDR4\nw91XEZf+vk1cCjyQGA39PWKgxjdT0UNKb9HwTl8N3J/KP9xkX7t1voe7X0nMv3odsDVwENEf7zvE\nbX4fq3nKCcAjRFL+QHqNV4D3peesJOq/EZGgpzWIqVFcTbXuuPt9wD7EjSOGEQfW7YAfAePdvdOU\nVSKy/lHOVs6W9tJv9eocV2tEqpPusnUlMNndv9rb8YiISGPK2fJ6p24h0pbSLW1XEJfrPg+8TIxC\nFxGRNqOcLbKGuoVIuzqISM4LiemXvuruz/duSCIi0oBytkiilmtpVw78lfiMziBaQkREpD0pZ4sk\n6nMtIiIiIpKJuoWIiIiIiGSik2sRERERkUx0ci0iIiIikolOrkVEREREMtHJtYiIiIhIJjq5FhER\nERHJ5G86UCOGHdpsPgAAAABJRU5ErkJggg==\n",
    483       "text/plain": [
    484        "<matplotlib.figure.Figure at 0x7fd8d56fe890>"
    485       ]
    486      },
    487      "metadata": {},
    488      "output_type": "display_data"
    489     }
    490    ],
    491    "source": [
    492     "plot_strats()"
    493    ]
    494   },
    495   {
    496    "cell_type": "markdown",
    497    "metadata": {
    498     "internals": {
    499      "slide_type": "subslide"
    500     },
    501     "slideshow": {
    502      "slide_type": "slide"
    503     }
    504    },
    505    "source": [
    506     "# Sharpe Ratio\n",
    507     "\n",
    508     "$$\\text{Sharpe} = \\frac{\\text{mean returns}}{\\text{volatility}}$$"
    509    ]
    510   },
    511   {
    512    "cell_type": "code",
    513    "execution_count": 12,
    514    "metadata": {
    515     "collapsed": false
    516    },
    517    "outputs": [
    518     {
    519      "name": "stdout",
    520      "output_type": "stream",
    521      "text": [
    522       "Sharpe ratio strategy etrade = 0.627893606355\n",
    523       "Sharpe ratio strategy IB = 1.43720181575\n"
    524      ]
    525     }
    526    ],
    527    "source": [
    528     "print \"Sharpe ratio strategy etrade =\", data_0.mean() / data_0.std() * np.sqrt(252)\n",
    529     "print \"Sharpe ratio strategy IB =\", data_1.mean() / data_1.std() * np.sqrt(252)"
    530    ]
    531   },
    532   {
    533    "cell_type": "code",
    534    "execution_count": 16,
    535    "metadata": {
    536     "collapsed": false
    537    },
    538    "outputs": [
    539     {
    540      "data": {
    541       "text/plain": [
    542        "(-2, 5)"
    543       ]
    544      },
    545      "execution_count": 16,
    546      "metadata": {},
    547      "output_type": "execute_result"
    548     },
    549     {
    550      "data": {
    551       "image/png": 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pW13LWbFq/1VL1ly0pv25xcy2wWS1upaamFbXUhPT6lpqYlrAVf0UHBoZGRl1Y0TsC1wI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\nFwAAAABJRU5ErkJggg==\n",
    552       "text/plain": [
    553        "<matplotlib.figure.Figure at 0x7f7a5ffc0a90>"
    554       ]
    555      },
    556      "metadata": {},
    557      "output_type": "display_data"
    558     }
    559    ],
    560    "source": [
    561     "plt.title('Sharpe ratio'); plt.xlabel('Sharpe ratio');\n",
    562     "plt.axvline(data_0.mean() / data_0.std() * np.sqrt(252), color='b');\n",
    563     "plt.axvline(data_1.mean() / data_1.std() * np.sqrt(252), color='g');\n",
    564     "plt.xlim((-2, 5))"
    565    ]
    566   },
    567   {
    568    "cell_type": "markdown",
    569    "metadata": {
    570     "slideshow": {
    571      "slide_type": "slide"
    572     }
    573    },
    574    "source": [
    575     "# Detour ahead"
    576    ]
    577   },
    578   {
    579    "cell_type": "markdown",
    580    "metadata": {
    581     "internals": {
    582      "frag_helper": "fragment_end",
    583      "frag_number": 10,
    584      "slide_helper": "subslide_end",
    585      "slide_type": "subslide"
    586     },
    587     "slide_helper": "slide_end",
    588     "slideshow": {
    589      "slide_type": "slide"
    590     }
    591    },
    592    "source": [
    593     "# Short primer on random variables\n",
    594     "\n",
    595     "* Represents our beliefs about an unknown state.\n",
    596     "* Probability distribution assigns a probability to each possible state.\n",
    597     "* **Not** a single number (e.g. most likely state)."
    598    ]
    599   },
    600   {
    601    "cell_type": "markdown",
    602    "metadata": {
    603     "internals": {
    604      "frag_helper": "fragment_end",
    605      "frag_number": 10,
    606      "slide_type": "subslide"
    607     },
    608     "slideshow": {
    609      "slide_type": "slide"
    610     }
    611    },
    612    "source": [
    613     "## You already know what a variable is..."
    614    ]
    615   },
    616   {
    617    "cell_type": "code",
    618    "execution_count": 92,
    619    "metadata": {
    620     "collapsed": false,
    621     "internals": {
    622      "frag_helper": "fragment_end",
    623      "frag_number": 14,
    624      "slide_helper": "subslide_end"
    625     },
    626     "slide_helper": "slide_end",
    627     "slideshow": {
    628      "slide_type": "fragment"
    629     }
    630    },
    631    "outputs": [],
    632    "source": [
    633     "coin = 0 # 0 for tails\n",
    634     "coin = 1 # 1 for heads"
    635    ]
    636   },
    637   {
    638    "cell_type": "markdown",
    639    "metadata": {
    640     "internals": {
    641      "frag_helper": "fragment_end",
    642      "frag_number": 14,
    643      "slide_type": "subslide"
    644     },
    645     "slideshow": {
    646      "slide_type": "slide"
    647     }
    648    },
    649    "source": [
    650     "## A random variable assigns all possible values a certain probability"
    651    ]
    652   },
    653   {
    654    "cell_type": "code",
    655    "execution_count": 93,
    656    "metadata": {
    657     "collapsed": false,
    658     "internals": {
    659      "frag_helper": "fragment_end",
    660      "frag_number": 16
    661     },
    662     "slideshow": {
    663      "slide_type": "fragment"
    664     }
    665    },
    666    "outputs": [],
    667    "source": [
    668     "#coin = {0: 50%,\n",
    669     "#        1: 50%}"
    670    ]
    671   },
    672   {
    673    "cell_type": "markdown",
    674    "metadata": {
    675     "internals": {
    676      "frag_helper": "fragment_end",
    677      "frag_number": 18
    678     },
    679     "slideshow": {
    680      "slide_type": "fragment"
    681     }
    682    },
    683    "source": [
    684     "### Alternatively:\n",
    685     "\n",
    686     "coin ~ Bernoulli(p=0.5)\n",
    687     "\n",
    688     "* `coin` is a random variable\n",
    689     "* `Bernoulli` is a probability distribution\n",
    690     "* `~` reads as \"is distributed as\""
    691    ]
    692   },
    693   {
    694    "cell_type": "markdown",
    695    "metadata": {
    696     "internals": {
    697      "frag_helper": "fragment_end",
    698      "frag_number": 18,
    699      "slide_type": "subslide"
    700     },
    701     "slideshow": {
    702      "slide_type": "slide"
    703     }
    704    },
    705    "source": [
    706     "## This was discrete (binary), what about the continuous case?\n",
    707     "\n",
    708     "returns ~ Normal($\\mu$, $\\sigma^2$)"
    709    ]
    710   },
    711   {
    712    "cell_type": "code",
    713    "execution_count": 94,
    714    "metadata": {
    715     "collapsed": false,
    716     "internals": {
    717      "frag_helper": "fragment_end",
    718      "frag_number": 21,
    719      "slide_helper": "subslide_end"
    720     },
    721     "slide_helper": "slide_end",
    722     "slideshow": {
    723      "slide_type": "fragment"
    724     }
    725    },
    726    "outputs": [
    727     {
    728      "data": {
    729       "text/plain": [
    730        "<matplotlib.text.Text at 0x7fd8d553b290>"
    731       ]
    732      },
    733      "execution_count": 94,
    734      "metadata": {},
    735      "output_type": "execute_result"
    736     },
    737     {
    738      "data": {
    739       "image/png": 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AeBfJ3TbWAj8Gvus4zg8cx3kW+ADJkwhfBD4BfMBxnD+NXmQRkcK3f/PvTxro3j8XoHrG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\nB1F9s/uHQVtrAAAAAElFTkSuQmCC\n",
    740       "text/plain": [
    741        "<matplotlib.figure.Figure at 0x7fd8d52b2850>"
    742       ]
    743      },
    744      "metadata": {},
    745      "output_type": "display_data"
    746     }
    747    ],
    748    "source": [
    749     "from scipy import stats\n",
    750     "sns.distplot(data_0, kde=False, fit=stats.norm)\n",
    751     "plt.xlabel('returns')"
    752    ]
    753   },
    754   {
    755    "cell_type": "markdown",
    756    "metadata": {
    757     "internals": {
    758      "frag_helper": "fragment_end",
    759      "frag_number": 21,
    760      "slide_type": "subslide"
    761     },
    762     "slideshow": {
    763      "slide_type": "slide"
    764     }
    765    },
    766    "source": [
    767     "# How to estimate $\\mu$ and $\\sigma$?\n",
    768     "\n",
    769     "* Naive: point estimate\n",
    770     "* Set `mu = mean(data)` and `sigma = std(data)`\n",
    771     "* Maximum Likelihood Estimate\n",
    772     "* Correct answer as $n \\rightarrow \\infty$"
    773    ]
    774   },
    775   {
    776    "cell_type": "markdown",
    777    "metadata": {
    778     "internals": {
    779      "frag_helper": "fragment_end",
    780      "frag_number": 23,
    781      "slide_helper": "subslide_end"
    782     },
    783     "slide_helper": "slide_end",
    784     "slideshow": {
    785      "slide_type": "fragment"
    786     }
    787    },
    788    "source": [
    789     "# Bayesian analysis\n",
    790     "* Most of the time $n \\neq \\infty$...\n",
    791     "* *Uncertainty* about $\\mu$ and $\\sigma$\n",
    792     "* Turn $\\mu$ and $\\sigma$ into random variables\n",
    793     "* How to estimate?"
    794    ]
    795   },
    796   {
    797    "cell_type": "markdown",
    798    "metadata": {
    799     "internals": {
    800      "frag_helper": "fragment_end",
    801      "frag_number": 23,
    802      "slide_type": "subslide"
    803     },
    804     "slideshow": {
    805      "slide_type": "slide"
    806     }
    807    },
    808    "source": [
    809     "# Bayes Formula!\n",
    810     "\n",
    811     "<img src=\"bayes_formula.svg\">\n",
    812     "\n",
    813     "Use prior knowledge and data to update our *beliefs*."
    814    ]
    815   },
    816   {
    817    "cell_type": "code",
    818    "execution_count": 95,
    819    "metadata": {
    820     "collapsed": false,
    821     "internals": {
    822      "frag_helper": "fragment_end",
    823      "frag_number": 23,
    824      "slide_helper": "subslide_end"
    825     },
    826     "slide_helper": "slide_end",
    827     "slideshow": {
    828      "slide_type": "skip"
    829     }
    830    },
    831    "outputs": [],
    832    "source": [
    833     "figsize(7, 7)\n",
    834     "from IPython.html.widgets import interact, interactive\n",
    835     "from scipy import stats\n",
    836     "def gen_plot(n=0, bayes=False):\n",
    837     "    np.random.seed(3)\n",
    838     "    x = np.random.randn(n)\n",
    839     "    ax1 = plt.subplot(221)\n",
    840     "    ax2 = plt.subplot(222)\n",
    841     "    ax3 = plt.subplot(223)\n",
    842     "    #fig, (ax1, ax2, ax3, _) = plt.subplots(2, 2)\n",
    843     "    if n > 1:\n",
    844     "        sns.distplot(x, kde=False, ax=ax3, rug=True, hist=False)\n",
    845     "    \n",
    846     "    def gen_post_mu(x, mu0=0, sigma0=5):\n",
    847     "        mu = np.mean(x)\n",
    848     "        sigma = 1\n",
    849     "        n = len(x)\n",
    850     "        \n",
    851     "        if n == 0:\n",
    852     "            post_mu = mu0\n",
    853     "            post_sigma = sigma0\n",
    854     "        else:\n",
    855     "            post_mu = (mu0 / sigma0**2 + np.sum(x) / sigma0**2) / (1/sigma0**2 + n/sigma**2)\n",
    856     "            post_sigma = (1 / sigma0**2 + n / sigma**2)**-1\n",
    857     "        return stats.norm(post_mu, post_sigma**2)\n",
    858     "    \n",
    859     "    def gen_post_var(x, alpha0, beta0):\n",
    860     "        mu = 0\n",
    861     "        sigma = np.std(x)\n",
    862     "        n = len(x)\n",
    863     "        post_alpha = alpha0 + n / 2\n",
    864     "        post_beta = beta0 + np.sum((x - mu)**2) / 2\n",
    865     "        return stats.invgamma(post_alpha, post_beta)\n",
    866     "    \n",
    867     "    \n",
    868     "    mu_lower = -.3\n",
    869     "    mu_upper = .3\n",
    870     "    \n",
    871     "    sigma_lower = 0\n",
    872     "    sigma_upper = 3\n",
    873     "    ax2.set_xlim((2, n+1))#(sigma_lower, sigma_upper))\n",
    874     "    ax1.axvline(0, lw=.5, color='k')\n",
    875     "    #ax2.axvline(1, lw=.5, color='k')\n",
    876     "    ax2.axhline(0, lw=0.5, color='k')\n",
    877     "    if bayes:\n",
    878     "        post_mu = gen_post_mu(x, 0, 5)\n",
    879     "        #post_var = gen_post_var(x, 1, 1)\n",
    880     "        if post_mu.ppf(.05) < mu_lower:\n",
    881     "            mu_lower = post_mu.ppf(.01)\n",
    882     "        if post_mu.ppf(.95) > mu_upper:\n",
    883     "            mu_upper = post_mu.ppf(.99)\n",
    884     "        x_mu = np.linspace(mu_lower, mu_upper, 500)\n",
    885     "        ax1.plot(x_mu, post_mu.pdf(x_mu))\n",
    886     "        #x_sigma = np.linspace(sigma_lower, sigma_upper, 100)\n",
    887     "        l = []\n",
    888     "        u = []\n",
    889     "        for i in range(1, n):\n",
    890     "            norm = gen_post_mu(x[:i])\n",
    891     "            l.append(norm.ppf(.05))\n",
    892     "            u.append(norm.ppf(.95))\n",
    893     "        ax2.fill_between(np.arange(2, n+1), l, u, alpha=.3)\n",
    894     "        ax1.set_ylabel('belief')\n",
    895     "        #ax2.plot(x_sigma, post_var.pdf(x_sigma))\n",
    896     "    else:\n",
    897     "        mu = np.mean(x)\n",
    898     "        sd = np.std(x)\n",
    899     "        ax1.axvline(mu)\n",
    900     "        ax2.plot(np.arange(2, n+1), [np.mean(x[:i]) for i in range(1, n)])\n",
    901     "        #ax2.axvline(sd)\n",
    902     "        \n",
    903     "    ax1.set_xlim((mu_lower, mu_upper))\n",
    904     "    ax1.set_title('current mu estimate')\n",
    905     "    ax2.set_title('history of mu estimates')\n",
    906     "    \n",
    907     "    ax2.set_xlabel('n')\n",
    908     "    ax2.set_ylabel('mu')\n",
    909     "    ax3.set_title('data (returns)')\n",
    910     "    plt.tight_layout()"
    911    ]
    912   },
    913   {
    914    "cell_type": "code",
    915    "execution_count": 96,
    916    "metadata": {
    917     "collapsed": false,
    918     "internals": {
    919      "frag_helper": "fragment_end",
    920      "frag_number": 23,
    921      "slide_helper": "subslide_end",
    922      "slide_type": "subslide"
    923     },
    924     "slide_helper": "slide_end",
    925     "slideshow": {
    926      "slide_type": "slide"
    927     }
    928    },
    929    "outputs": [
    930     {
    931      "data": {
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0+rTN/V+caUkuKnMTV2I53fsAJ5T52I7jOE4RuALg5OJE7N74CLi+3AcPVoDL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\n",
    933       "text/plain": [
    934        "<matplotlib.figure.Figure at 0x7fd8d52ed050>"
    935       ]
    936      },
    937      "metadata": {},
    938      "output_type": "display_data"
    939     }
    940    ],
    941    "source": [
    942     "interactive(gen_plot, n=(0, 600), bayes=True)"
    943    ]
    944   },
    945   {
    946    "cell_type": "markdown",
    947    "metadata": {
    948     "internals": {
    949      "frag_helper": "fragment_end",
    950      "frag_number": 23
    951     },
    952     "slideshow": {
    953      "slide_type": "skip"
    954     }
    955    },
    956    "source": [
    957     "## Approximating the posterior with MCMC sampling"
    958    ]
    959   },
    960   {
    961    "cell_type": "code",
    962    "execution_count": 97,
    963    "metadata": {
    964     "collapsed": false,
    965     "internals": {
    966      "frag_helper": "fragment_end",
    967      "frag_number": 23,
    968      "slide_helper": "subslide_end"
    969     },
    970     "slide_helper": "slide_end",
    971     "slideshow": {
    972      "slide_type": "skip"
    973     }
    974    },
    975    "outputs": [],
    976    "source": [
    977     "def plot_want_get():\n",
    978     "    from scipy import stats\n",
    979     "    fig = plt.figure(figsize=(14, 6))\n",
    980     "    ax1 = fig.add_subplot(121, title='What we want', ylim=(0, .5), xlabel='', ylabel='')\n",
    981     "    ax1.plot(np.linspace(-4, 4, 100), stats.norm.pdf(np.linspace(-3, 3, 100)), lw=4.)\n",
    982     "    ax2 = fig.add_subplot(122, title='What we get')#, xlim=(-4, 4), ylim=(0, 1800), xlabel='', ylabel='\\# of samples')\n",
    983     "    sns.distplot(np.random.randn(50000), ax=ax2, kde=False, norm_hist=True);\n",
    984     "    ax2.set_xlim((-4, 4));\n",
    985     "    ax2.set_ylim((0, .5));"
    986    ]
    987   },
    988   {
    989    "cell_type": "markdown",
    990    "metadata": {
    991     "internals": {
    992      "frag_helper": "fragment_end",
    993      "frag_number": 23,
    994      "slide_type": "subslide"
    995     },
    996     "slideshow": {
    997      "slide_type": "slide"
    998     }
    999    },
   1000    "source": [
   1001     "## Approximating the posterior with MCMC sampling"
   1002    ]
   1003   },
   1004   {
   1005    "cell_type": "code",
   1006    "execution_count": 98,
   1007    "metadata": {
   1008     "collapsed": false,
   1009     "internals": {
   1010      "frag_helper": "fragment_end",
   1011      "frag_number": 31,
   1012      "slide_helper": "subslide_end"
   1013     },
   1014     "slide_helper": "slide_end",
   1015     "slideshow": {
   1016      "slide_type": "fragment"
   1017     }
   1018    },
   1019    "outputs": [
   1020     {
   1021      "data": {
   1022       "image/png": 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POsoyIf6kCecBOwPdBwIfd5NIRESmQm19S299c2v3rLqGPtdZRKJGhY5UpEQq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\n",
   1023       "text/plain": [
   1024        "<matplotlib.figure.Figure at 0x7fd8d6dfefd0>"
   1025       ]
   1026      },
   1027      "metadata": {},
   1028      "output_type": "display_data"
   1029     }
   1030    ],
   1031    "source": [
   1032     "plot_want_get()"
   1033    ]
   1034   },
   1035   {
   1036    "cell_type": "markdown",
   1037    "metadata": {
   1038     "internals": {
   1039      "frag_helper": "fragment_end",
   1040      "frag_number": 31,
   1041      "slide_helper": "subslide_end",
   1042      "slide_type": "subslide"
   1043     },
   1044     "slide_helper": "slide_end",
   1045     "slideshow": {
   1046      "slide_type": "slide"
   1047     }
   1048    },
   1049    "source": [
   1050     "PyMC3\n",
   1051     "=====\n",
   1052     "\n",
   1053     "* Probabilistic Programming framework written in Python.\n",
   1054     "* Allows for construction of probabilistic models using intuitive syntax.\n",
   1055     "* Features advanced MCMC samplers.\n",
   1056     "* Fast: Just-in-time compiled by Theano.\n",
   1057     "* **Extensible**: easily incorporates custom MCMC algorithms and unusual probability distributions.\n",
   1058     "* Authors: John Salvatier, Chris Fonnesbeck, Thomas Wiecki\n",
   1059     "* Upcoming *beta* release!"
   1060    ]
   1061   },
   1062   {
   1063    "cell_type": "markdown",
   1064    "metadata": {
   1065     "slideshow": {
   1066      "slide_type": "slide"
   1067     }
   1068    },
   1069    "source": [
   1070     "<center><img src=\"http://www.iskonline.org/media/news/end_detour.gif\"></center>"
   1071    ]
   1072   },
   1073   {
   1074    "cell_type": "markdown",
   1075    "metadata": {
   1076     "slideshow": {
   1077      "slide_type": "slide"
   1078     }
   1079    },
   1080    "source": [
   1081     "# Model returns distribution: Specifying our priors"
   1082    ]
   1083   },
   1084   {
   1085    "cell_type": "code",
   1086    "execution_count": 99,
   1087    "metadata": {
   1088     "collapsed": false,
   1089     "slideshow": {
   1090      "slide_type": "slide"
   1091     }
   1092    },
   1093    "outputs": [
   1094     {
   1095      "data": {
   1096       "image/png": 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kmK+n7t5iOrHWK3RfY2pnFZ+DN9/5kCVdbsroyUeOPRE4sdZBNVjTvg/232UD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\nNEGFVEREpAn/D+XB0B/ZaHqzAAAAAElFTkSuQmCC\n",
   1097       "text/plain": [
   1098        "<matplotlib.figure.Figure at 0x7fd8d7450450>"
   1099       ]
   1100      },
   1101      "metadata": {},
   1102      "output_type": "display_data"
   1103     }
   1104    ],
   1105    "source": [
   1106     "import theano.tensor as T\n",
   1107     "x = np.linspace(-.3, .3, 500)\n",
   1108     "plt.plot(x, T.exp(pm.Normal.dist(mu=0, sd=.1).logp(x)).eval())\n",
   1109     "plt.title(u'Prior: mu ~ Normal(0, $.1^2$)'); plt.xlabel('mu'); plt.ylabel('Probability Density'); plt.xlim((-.3, .3));"
   1110    ]
   1111   },
   1112   {
   1113    "cell_type": "code",
   1114    "execution_count": 100,
   1115    "metadata": {
   1116     "collapsed": false,
   1117     "slideshow": {
   1118      "slide_type": "slide"
   1119     }
   1120    },
   1121    "outputs": [
   1122     {
   1123      "data": {
   1124       "image/png": 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OjJH7CKPyr0r14Yniz+4xKpVKnHz2nTzS9xrLLTWRD6+6JJusvTzrr7kMo0eNqOuZiEgn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\n",
   1125       "text/plain": [
   1126        "<matplotlib.figure.Figure at 0x7fd8d7fc4450>"
   1127       ]
   1128      },
   1129      "metadata": {},
   1130      "output_type": "display_data"
   1131     }
   1132    ],
   1133    "source": [
   1134     "x = np.linspace(-.1, .5, 500)\n",
   1135     "plt.plot(x, T.exp(pm.HalfNormal.dist(sd=.1).logp(x)).eval())\n",
   1136     "plt.title(u'Prior: sigma ~ HalfNormal($.1^2$)'); plt.xlabel('sigma'); plt.ylabel('Probability Density');"
   1137    ]
   1138   },
   1139   {
   1140    "cell_type": "markdown",
   1141    "metadata": {
   1142     "internals": {
   1143      "frag_helper": "fragment_end",
   1144      "frag_number": 31,
   1145      "slide_type": "subslide"
   1146     },
   1147     "slideshow": {
   1148      "slide_type": "slide"
   1149     }
   1150    },
   1151    "source": [
   1152     "## Bayesian Sharpe ratio\n",
   1153     "\n",
   1154     "$\\mu \\sim \\text{Normal}(0, .1^2)$ $\\leftarrow \\text{Prior}$\n",
   1155     "\n",
   1156     "$\\sigma \\sim \\text{HalfNormal}(.1^2)$ $\\leftarrow \\text{Prior}$\n",
   1157     "\n",
   1158     "$\\text{returns} \\sim \\text{Normal}(\\mu, \\sigma^2)$ $\\leftarrow \\text{Observed!}$\n",
   1159     "\n",
   1160     "$\\text{Sharpe} = \\frac{\\mu}{\\sigma}$"
   1161    ]
   1162   },
   1163   {
   1164    "cell_type": "markdown",
   1165    "metadata": {
   1166     "internals": {
   1167      "frag_helper": "fragment_end",
   1168      "frag_number": 31,
   1169      "slide_type": "subslide"
   1170     },
   1171     "slideshow": {
   1172      "slide_type": "slide"
   1173     }
   1174    },
   1175    "source": [
   1176     "## Graphical model of returns\n",
   1177     "<img width=80% src='bayes_formula_mu2.svg'>"
   1178    ]
   1179   },
   1180   {
   1181    "cell_type": "markdown",
   1182    "metadata": {
   1183     "internals": {
   1184      "frag_helper": "fragment_end",
   1185      "frag_number": 31,
   1186      "slide_type": "subslide"
   1187     },
   1188     "slideshow": {
   1189      "slide_type": "slide"
   1190     }
   1191    },
   1192    "source": [
   1193     "## This is what the data looks like"
   1194    ]
   1195   },
   1196   {
   1197    "cell_type": "code",
   1198    "execution_count": 101,
   1199    "metadata": {
   1200     "collapsed": false,
   1201     "internals": {
   1202      "frag_helper": "fragment_end",
   1203      "frag_number": 31,
   1204      "slide_helper": "subslide_end"
   1205     },
   1206     "slide_helper": "slide_end",
   1207     "slideshow": {
   1208      "slide_type": "-"
   1209     }
   1210    },
   1211    "outputs": [
   1212     {
   1213      "name": "stdout",
   1214      "output_type": "stream",
   1215      "text": [
   1216       "0\n",
   1217       "2011-10-18 20:00:00   -0.011876\n",
   1218       "2011-10-19 20:00:00   -0.000422\n",
   1219       "2011-10-20 20:00:00   -0.017066\n",
   1220       "2011-10-21 20:00:00   -0.012890\n",
   1221       "2011-10-24 20:00:00   -0.005419\n",
   1222       "Name: 1, dtype: float64\n"
   1223      ]
   1224     }
   1225    ],
   1226    "source": [
   1227     "print data_0.head()"
   1228    ]
   1229   },
   1230   {
   1231    "cell_type": "code",
   1232    "execution_count": 102,
   1233    "metadata": {
   1234     "collapsed": false,
   1235     "internals": {
   1236      "frag_helper": "fragment_end",
   1237      "frag_number": 31,
   1238      "slide_helper": "subslide_end",
   1239      "slide_type": "subslide"
   1240     },
   1241     "slide_helper": "slide_end",
   1242     "slideshow": {
   1243      "slide_type": "slide"
   1244     }
   1245    },
   1246    "outputs": [],
   1247    "source": [
   1248     "from pymc3 import *\n",
   1249     "\n",
   1250     "with Model() as model:\n",
   1251     "    # Priors on parameters\n",
   1252     "    mean_return = Normal('mean return', mu=0, sd=.1)\n",
   1253     "    volatility = HalfNormal('volatility', sd=.1)\n",
   1254     "\n",
   1255     "    # Model observed returns as Normal\n",
   1256     "    obs = Normal('returns', \n",
   1257     "                 mu=mean_return, \n",
   1258     "                 sd=volatility,\n",
   1259     "                 observed=data) # data is a list of daily returns, e.g. [0.01, -.05, ...]\n",
   1260     "    \n",
   1261     "    sharpe = Deterministic('sharpe ratio', \n",
   1262     "                           mean_return / volatility)"
   1263    ]
   1264   },
   1265   {
   1266    "cell_type": "code",
   1267    "execution_count": 103,
   1268    "metadata": {
   1269     "collapsed": false,
   1270     "internals": {
   1271      "frag_helper": "fragment_end",
   1272      "frag_number": 31,
   1273      "slide_helper": "subslide_end",
   1274      "slide_type": "subslide"
   1275     },
   1276     "slide_helper": "slide_end",
   1277     "slideshow": {
   1278      "slide_type": "slide"
   1279     }
   1280    },
   1281    "outputs": [
   1282     {
   1283      "name": "stdout",
   1284      "output_type": "stream",
   1285      "text": [
   1286       " [-----------------100%-----------------] 500 of 500 complete in 0.7 sec"
   1287      ]
   1288     }
   1289    ],
   1290    "source": [
   1291     "with model:\n",
   1292     "    # Instantiate MCMC sampler\n",
   1293     "    step = NUTS()\n",
   1294     "    # Draw 500 samples from the posterior\n",
   1295     "    trace = sample(500, step)"
   1296    ]
   1297   },
   1298   {
   1299    "cell_type": "markdown",
   1300    "metadata": {
   1301     "slideshow": {
   1302      "slide_type": "slide"
   1303     }
   1304    },
   1305    "source": [
   1306     "# Analyzing the posterior"
   1307    ]
   1308   },
   1309   {
   1310    "cell_type": "code",
   1311    "execution_count": 104,
   1312    "metadata": {
   1313     "collapsed": false
   1314    },
   1315    "outputs": [
   1316     {
   1317      "data": {
   1318       "text/plain": [
   1319        "<matplotlib.text.Text at 0x7fd8d62f9f50>"
   1320       ]
   1321      },
   1322      "execution_count": 104,
   1323      "metadata": {},
   1324      "output_type": "execute_result"
   1325     },
   1326     {
   1327      "data": {
   1328       "image/png": 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YyzjcYPf34W4TlfWbXiR3K6rAPHITTr+Ea+bN3/4wrql2vV9/3J9nPK53W7GTbav3moiI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\nHMdxyuD/A2eMcDdlEjRoAAAAAElFTkSuQmCC\n",
   1329       "text/plain": [
   1330        "<matplotlib.figure.Figure at 0x7fd8d62f9350>"
   1331       ]
   1332      },
   1333      "metadata": {},
   1334      "output_type": "display_data"
   1335     }
   1336    ],
   1337    "source": [
   1338     "sns.distplot(results_normal[0]['mean returns'], hist=False, label='etrade')\n",
   1339     "sns.distplot(results_normal[1]['mean returns'], hist=False, label='IB')\n",
   1340     "plt.title('Posterior of the mean'); plt.xlabel('mean returns')"
   1341    ]
   1342   },
   1343   {
   1344    "cell_type": "code",
   1345    "execution_count": 105,
   1346    "metadata": {
   1347     "collapsed": false,
   1348     "slideshow": {
   1349      "slide_type": "slide"
   1350     }
   1351    },
   1352    "outputs": [
   1353     {
   1354      "data": {
   1355       "text/plain": [
   1356        "<matplotlib.text.Text at 0x7fd8d67b89d0>"
   1357       ]
   1358      },
   1359      "execution_count": 105,
   1360      "metadata": {},
   1361      "output_type": "execute_result"
   1362     },
   1363     {
   1364      "data": {
   1365       "image/png": 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OteB7as4GPmpmjwGPOeeuMLPFYbNHnHO7hG2uxH/4537YT8RPbBoFQ+76CUCp\n1++m4Xt3Zm5c67iNVg+tZpsNp21ImLB2UvvEtuWrV7DJxI22BGZkWsDG0ZGzlNJ05CylNB05SylN\nR86y3ox2ma2kYQmt+Nrbx/GzbQ9E62JhF5kPvC88fg7YKmf9NOAhfNPl8vD80XCcccDm+B6bpRik\nTmpPm07amJeXvMrRMw4/BzgHYJfNdzjw7mcfZN+t3/5JfE9UKd11WRegQem8JaPzlky9nreW0VaU\nUsPrBY4HPmJmv4tedM59G5hhZh+MbbsP8Fh4fCdwWGz7ycDewHlhWMI9wLvwPTbBD3tYDTxQQpnA\nf7uoixreq0tf/xOwxY1P3f6l9+387vuB655+fdEfgSPufvaBa/5l/0+cnXERG0UH/j/RUfgvNFKa\nDnTekuhA5y2JDhr0vBUbh3cQfrLRLwL3O+emxVZfDfwxDB7/HXA0cALwnrD+x8BZzrlzgGuAc4Fn\nzOzGsP4HwKXOuYeAReH5ZWUMSXgh/GRuaHioHeDp1xc9Q/gDWLF6xesAi1cuWUmBKrbkNYjOWRKD\n6LwlMYjOWxKDNNh5K9Zp5aNheSG+R2X08xxwB77mdyr+XkunAceb2R0AZvYMcCw+BO8BpgJd0Y7N\nrA84H5iD7/V5N9CTxi+VgbxTi4WHddHsKiLS7ArW8MzsLOCsAptcFX5Ge/88YF6B9RcBFxUpY13r\n7pvdQp5emq0treqlKSJSRzQVTeXGMXIe19bwWmlVDU9EpI4o8CoXn0klVsPT7YFEROqJAq9y8Rrc\nSOC1qoYnIlJPFHiVi9fgRpo0WxR4IiL1RIFXubw1vLaWNgWeiEgdUeBVLm8Nr61VgSciUk8UeJXL\n22mlTU2aIiJ1RYFXubxNmuNGanjqpSkiUgcUeJUbpUlznGp4IiJ1RIFXuSjwhoHoLue0x67hhdlY\nREQkQwq8ykU1uBVzZ80Zjl5sb2uP39y2vbZFEhGRXAq8ykU1vOXxF8e3ta+MPVWzpohIxhR4lRsf\nlivXebFtfPy5Oq6IiGRMgVe5KPDiTZhMGDdeNTwRkTqiwKtc3hrepHETFXgiInVEgVe5vIE3uX2S\nAk9EpI4o8CqXN/A2nrhhvIlTgScikjEFXuVGCbyN1GlFRKSOKPAqFwXeqviLb5u8mZo0RUTqiAKv\ncnlreFtM2TwegAo8EZGMKfAql7+XZvvE+FRjCjwRkYwp8CqXN/CCaPYVBZ6ISMYUeJWL5snMF3hR\nT00FnojRWmxlAAAgAElEQVRIxhR4lStUw4sCT700RUQypsCrXCmBpxqeiEjGFHiVU+CJiDQABV7l\nFHgiIg1AgVc59dIUEWkACrzK5Z1pJVCnFRGROqHAq5yaNEVEGoACr3IKPBGRBqDAq5wGnouINAAF\nXuXUaUVEpAEo8CqnmVZERBqAAq9yuoYnItIAFHiVU+CJiDQABV7lFHgiIg1AgVc5BZ6ISANQ4FWu\nlF6a6rQiIpIxBV4Fuvtmt1Da1GKq4YmIZEyBV5m22GM1aYqI1DEFXmXGxx4r8ERE6pgCrzIKPBGR\nBqHAq0yxwNPUYiIidUKBV5lSa3jqpSkikjEFXmVKDbxx3X2zda5FRDKkD+HKlBp4oGZNEZFMKfAq\no8ATEWkQCrzKKPBERBqEAq8y7bHH+WZaWR57rI4rIiIZUuBVRjU8EZEGocCrTDzwCs2lCQo8EZFM\nKfAqEwXemrmz5qzJs16BJyJSJ8YV28A5txPwXeCdwBKgD/iyma1wzm0PXAocAiwEzjSzebH3HgFc\nDOwE3A2cYmYLYus/A5wNbARcCZxhZktT+t1qodCtgUCBJyJSNwrW8Jxz44EBYBlwMPAJ4MPAv4dN\n+oGXgf2AnwJXOec6wnunA9cCVwD7Ai8A/c65lrD+WOAbwGnAEcD+QG96v1pNFAs8dVoREakTxZo0\nDwB2BE4071bgXOATofY2A/hnM5tvZv8J3AGcHN57KvCAmX3LzOYDJwHT8eEG8Dnge2b2WzO7Dx98\nJzrnJqf5C1ZZscBbDQyHx6rhiYhkqFjgzQeOydPMuAlwED7QlsRevw1fEySsvzVaYWbLgPuBg51z\nbfha4a2x996Fb2Ldp9xfIkMFA2/urDnD6I4JIiJ1oWDgmdkrZnZT9Nw51wqcAVwPbAX8LectLwHb\nhsfT8qx/MazfGN/Et3a9ma0GXo29vxEUq+GBAk9EpC6U20vz28Be+I4mU1i3UwbhefTBPrnA+smx\n56O9vxEo8EREGkTRXpoAoaPJd4HZwEfN7DHn3HJ878q4CfienOA7bOR+yE/Ed3IZ7T5xE4BSe2lO\ny3P8mtpqwy22en7xS7S3jmvBX88E6Igv21pa16wZHmK7jbfZLraN5NeRs5TSdOQspTQdOUspTUfO\nst48PtqKUoYltAKXAR8Hus1sIKx6Fnh7zubTgOfD4+fwzZ656x/CN10uD88fDccZB2wee38xg2Rc\na3p3x0H86uFr2XbjrWYAlrP6OoAtpryN5996iffseMh5wHk1L2Rjui7rAjQonbdkdN6Sqdfz1jLa\nilJqeL3A8cBHzOx3sdfvBM5xzk2OdWo5FN9TM1p/WLRx6H25N3CemQ075+4B3gVE1wgPxvdqfKCE\nMoH/dpFpDe/Gp27/DHDGc2+++CAwK7zcgf9DOAoYfGXpawPAjOuevOWiY2a857JsStowOoidu0xL\n0lg60HlLogOdtyQ6aNDzVjDwnHMHAZ8Fvgjc75ybFlt9C/AMcLlz7uvAB/HDGD4d1v8YOMs5dw5w\nDX44wzNmdmNY/wPgUufcQ8Ci8PyyMgaevxB+MvPyklcXA6xcs/JN1q9GDwKPrxpavRjg+cUvLc6z\njeQ3iM5VEoPovCUxiM5bEoM02Hkr1mnlo2F5Ib5HZfTzXHi9C9gCuBf4JL4WuBDAzJ4BjgVOAO4B\npobtCev7gPOBOfhen3cDPRX/RrWlTisiIg2iYA3PzM4CziqwyQLg8ALvnwfMK7D+IuCiwkWsawo8\nEZEGocmjK1NK4EU9UjW1mIhIhhR4lVENT0SkQSjwKqPAExFpEAq8yrSHpQJPRKTOKfAqE9Xw8t3t\nPKLAExGpAwq8ypTTpKlOKyIiGVLgVaacXpqq4YmIZEiBVxl1WhERaRAKvMoo8EREGoQCrzIKPBGR\nBqHAq4w6rYiINAgFXmXUaUVEpEEo8CqjgeciIg1CgVeZUmp40brxBbYREZEqU+BVppxreAo8EZEM\nKfAqU8rUYqrhiYjUAQVeZcpp0mzv7put8y0ikhF9AFemnMCDkU4uIiJSYwq8hLr7ZrcBbeFpKdfw\nQM2aIiKZUeAlF6+tlVrDU+CJiGREgZdcPLxKDTyNxRMRyYgCLznV8EREGogCL7lSa3i6hiciUgcU\neMkladJU4ImIZESBl5yu4YmINBAFXnLxwCs004qaNEVE6oACLzk1aYqINBAFXnKlBl689qfAExHJ\niAIvuZICb+6sOWuANeGpruGJiGREgZdcqTU80C2CREQyp8BLLhp4PsxIDW40ukWQiEjGFHjJrb1T\nwtxZc4aLbKvAExHJmAIvuVJuDRSJttE1PBGRjCjwkisn8HQNT0QkYwq85JLU8BR4IiIZUeAlF4VX\noVlWIgo8EZGMKfCS0zU8EZEGosBLTtfwREQaiAIvOV3DExFpIAq85BR4IiINRIGXXDTTSjlNmrqG\nJyKSEQVecuqlKSLSQBR4yUW1tRUFt/IUeCIiGVPgJReFlwJPRKQBKPCSi2p4uoYnItIAFHjJqZem\niEgDUeAlp2t4IiINRIGXnGp4IiINRIGXXDmdVnQNT0QkYwq85MrptKIanohIxhR4yWlYgohIA1Hg\nJacanohIA1HgJZfk9kC6hicikpFxpW7onJsA3Ad81sxuDK9dApyas+nnzOx7Yf0RwMXATsDdwClm\ntiC2z88AZwMbAVcCZ5jZ0uS/Tk1pWIKISAMpqYbnnJsI/BKYCQzHVs0EPg9Mi/1cGt4zHbgWuALY\nF3gB6HfOtYT1xwLfAE4DjgD2B3or/o1qR8MSREQaSNEannNuJvCLUVbvBnzZzF7Ks+5U4AEz+1bY\nz0n40DsCuAn4HPA9M/ttWH8acINzrqdBankaliAi0kBKqeEdBtwIHBx/0Tk3DdgMeHyU9x0E3Bo9\nMbNlwP3Awc65NmC/+HrgLnwA71Nq4TOmTisiIg2kaOCZ2Q/NrCcEVtxMYDXwDefcs865B51z/xRb\nPw34W857XgS2BTYGJsbXm9lq4NWwvhEkGZYwrrtvtjoKiYhkoJIP392AIeBB4P3AZcAlzrnjwvrJ\nrB8GK/A1o8mx5/nWN4IkNTwYuVO6iIjUUMm9NHOZ2X87564ws8XhpUecc7sAs/E9LpezfnhNBF4O\n68izfgJQ6vW7afjenVkZD7DnlrtOBWbEXu/IWXLI9H23uGPRfQCcc9gZM4ElNSlh4+nIWUppOnKW\nUpqOnKWUpiNnWW9Gu8yWPPAAYmEXmQ+8Lzx+DtgqZ/004CF80+Xy8PxRAOfcOGBz4PkSDz9IRrXB\nNUNr1j7+8G5H/WiUza6LHnxo138gCrwdN9v+/qoWbmy4rvgmkofOWzI6b8nU63lrGW1F4sBzzn0b\nmGFmH4y9vA/wWHh8J77DS7T9ZGBv4DwzG3bO3QO8C99jE3ynmNXAAyUWoYOManhPvb5wIvAXgOue\nuOXje26563055boOOAofytz41O0zgAGA2565+13HzHhPvl6tkufcSUk60HlLogOdtyQ6aNDzVkkN\n72rgj2Hw+O+Ao4ETgPeE9T8GznLOnQNcA5wLPBMNWgd+AFzqnHsIWBSeX1bGkIQXwk/NffmGizaJ\nHt/93IMLyF+FHoxev37Bn9Z+47j8gV8/e8yM9wxWuYiNbpACzRIyqkF03pIYROctiUEa7Lwl7rRi\nZrcBx+PH2z2MH0B+vJndEdY/AxyLD8F7gKlAV+z9fcD5wBzgevxMLD1Jy1Nj8abUcqYWy32viIjU\nSFk1PDNrzXl+FXBVge3nAfMKrL8IuKicMtSJ+Hi6coYl5L5XRERqpKJOK02s3BqeAk9EStLZ038k\nvj/DLQO9XcPFtpfSaRB0MvHQKrdJU4EnInl19vR/DH+J54/A9zMuzpijwEsmXsMrt0lT1/BEZD2d\nPf0TgP+KvXR6Z0//DlmVZyxS4CVTbg1v1SjvFRGJHIafnzjSAvxLRmUZkxR4yZRVw5s7a84Qvk0e\nFHgikt8HwvJBRm6V9v6MyjImKfCSKbeGByPBqMATkXzeG5a/x9+hBmCvzp7+zTMqz5ijwEsmCq01\nc2fNWVNwyxFRMOoanoisI1y/2zU8vQu4DYg+W96dSaHGIAVeMuXcKSGim8CKyGh2ZWSY2EMDvV2L\nGZlmcf9sijT2KPCSiWp45QRedD/BiSmXRUQa355h+RbwTHj8YFjuVfvijE0KvGSiWlopQxIi0S2R\nJqVcFhFpfG8Py0cGeruGwuO/hKUCLyUKvGSS1PCiwFMNT0Ry7RKWj8VeiwJv686e/rfVuDxjkgIv\nmUpqeAo8EckVDTB/KvbaQ7HHquWlQIGXTCXX8NSkKSJrdfb0tzASeE9Hrw/0dv2dkfvNKfBSoMBL\nJgo81fBEpFKbMnIz66dz1uk6XooUeMkkGZagwBORfDpijxV4VaTAS0bDEkQkLVFz5nLghZx10XW8\nmZ09/e21K9LYpMBLRsMSRCQt24Xlwjz3v3s4LNsZ6ckpCSnwktGwBBFJy1Zh+bc86xYw8sV6Zm2K\nM3Yp8JLRsAQRScvWYfl87oqB3q41wPzwdPealWiMUuAlo2EJIpKWQjU8gEfDUjW8CinwkolqacsL\nbrUu1fBEJJ8o8Nar4QV/DUvV8CqkwEtGgSciaSkWeFENb4Z6alZGgZdMksDTsAQRWUdnT/8kYJPw\ndLQmzaiG1w7sXPVCjWEKvGSi63DLCm61Lg1LEJFcW8Uej1bDe4qRDnJq1qyAAi8ZNWmKSBqKBt5A\nb9dqwMJTBV4FFHjJVFLDU+CJSCQakrAUWFxgu6hZUz01K6DAS6aSa3iTuvtmt6RcHhFpTGuHJOSZ\nZSUu6riiGl4FFHjJVNKk2YK/+CwiUqyHZiSq4amnZgUUeMlU0qQJatYUEW/UWVZyRDU89dSsgAIv\nmUqaNOPvF5HmVmyWlcgCRmZ2UrNmQgq8ZCqt4WlogohAiU2aoadmNKemOq4kpMArU3ff7DZGrsEl\nuYYHquGJiFfqNTxQx5WKKfDKNyH2WIEnIol09vRPADYPT0sJPA1NqJACr3zx5shymjTj26pJU0Sm\nxR4Xu4YHIzU8p56aySjwyhevnamGJyJJlTKtWJzm1KyQAq98SWt48XvnKfBEJBqSsAJ4o4TtFwBr\nwuMdq1KiMU6BV75ENby5s+YMo+nFRGREqbOsAGt7aj4XnnZUq1BjmQKvfEmbNEF3PReREeX00IwM\nhmVHqiVpEgq88iVt0gTV8ERkhAKvxhR45aukhqfAE5FIqdOKxQ2G5fbpFqU5KPDKF9XwVs6dNWeo\nzPeqSVNEIqVOKxY3GJYdqZakSSjwypdkHs3I0rCcklJZRKRxVdKkObWzp1+fI2VS4JUvyTyakSVh\nOTmlsohIAwoDx7cIT5MEHqhZs2wKvPKphicildoy9ricJs1ngehSSkdqpWkSCrzyVRJ4UQ1PgSfS\n3MqdZQWAgd6uVfjQAwVe2RR45UujSVOBJ9LcosBbBbxa5nsHw1JNmmVS4JVPNTwRqVQ0JOGFUmZZ\nyTEYlh2plaZJKPDKp04rIlKpJEMSIs+EZUc6RWkeCrzyqdOKiFQqyZCEyMKw3DalsjQNBV751KQp\nIpVKMstKJOq0spXui1ceBV751GlFRCpVSZNmdMeEFta9iawUocArn2p4IlKpSpo0n409VrNmGRR4\n5VOnFRFJrLOnv42RgedJAu8NRvoDKPDKoMArXyqdVrr7ZrekVB4RaSxbMPLZW3bghWEMUS1vm7QK\n1QzGlbqhc24CcB/wWTO7Mby2PXApcAi+59CZZjYv9p4jgIuBnYC7gVPMbEFs/WeAs4GNgCuBM8ws\nCoV6lUaTZkvYT5Jaoog0tvgsK0mu4YEPvBmohleWkmp4zrmJwC+BmcBweK0F6AdeBvYDfgpc5Zzr\nCOunA9cCVwD7Ai8A/eF9OOeOBb4BnAYcAewP9Kb0e1VTGk2aoOt4Is0qCrw1+M/PJKIangKvDEUD\nzzk3E7gT2DFn1RH4bxj/bGbzzew/gTuAk8P6U4EHzOxbZjYfOAmYHt4H8Dnge2b2WzO7Dx98Jzrn\n6v36Vho1PNB1PJFmFQ1JeHGgt6vce2pGop6aCrwylFLDOwy4ETg45/WDgPvNLP4hfltsu4OAW6MV\nZrYMuB842DnXhq8V3hp77134JtZ9yvkFMlBJDS/eXKsankhzqqSHZkQ1vASKBp6Z/dDMekJgxW3F\n+v9gLzHyDzCN9dunXwzrN8bXlNauN7PV+ElU6/0fMK0angJPpDlVMgYvEgXe1p09/ep8WKKSO63k\nMRlYkfPaCmBCCesnx56P9v5ipuE7u9RUS0vL5OHhYXberGMTfJNuro6c5VoX/sOXJnzx+gsA2H+b\nvRzwZpWK2ag6cpZSmo6cpZSmI2dZE1MmjttlyfLVbLLBhKXk/wwp6r37T2+98Z5FAO3/etxeB1L+\nHRcq0ZGzrDePj7aiksBbxvqBM4GRWsxy1g+vifiLtMtj2+e+v9RemoN53l917a3jWLlmFR/e7ahe\nCneyuS73hR02nU4LLQwzzHt3PPRn1Stlw1vv3ElJdN6Sqel523rqBjyx6A2OPqRjFjAryT5O/MDu\nhMBj5203uSPN8pWhXv/eRh3yVUngPQfslfPaNEaaOZ9j3e630fqH8N9GlofnjwI458YBm1N6u3YH\nNa7hrVqzmpVrVs0HWv7w5C2nHrDt3rfm2awD/4dwFCO38QCgpaUF/HXMKb95bN7/946t96jXP5is\ndDDKuZOCOtB5S6KDDM7bU8/9/RZg2p8ffv7cjx+169wk+xjf3tYCPAy0XzbwyOkXnH7ojakWsrAO\nGvTvrZLAuws4xzk3OTZ27lB8T03wPTsPizYOvS/3Bs4zs2Hn3D3Au4CbwiYHA6uBB0o8/gvhp2Y+\nceVnJhC+PTz04vwnKVB1xv8hrLd+mOElwBR7ZcGbRd7fzAbRuUliEJ23JAap0XkL19veBjD4/Jt/\nSXrcyRPHga9UdDyy4NXWpPup0GBGx02sksC7GX9fpsudc18HPggcAHw6rP8xcJZz7hzgGuBc4Jlo\n0DrwA+BS59xDwKLw/LI6H3g+MfY4SacV0HyaIs3sbYx87lbSSxN8x5UO6r+jX91I3LvHzIaALvw0\nOfcCnwQ+YmYLw/pngGOBE4B7gKlh++j9fcD5wBzgevxMLD1Jy1Mjk2KPFXgiUq74ZZ40Ag80vVjJ\nyqrhmVlrzvMFwOEFtp8HzCuw/iLgonLKkLF44CWdFkyBJ9K8osAbxg/TqoTG4pVJ4zfKE2/SVOCJ\nSLmiWVZeGujtWl3hvhR4ZVLglSeNGt5bYblBhWURkcaTxiwrkbXTi3X29OvuKyVQ4JUnjWt4i8Ny\nwwrLIiKNJ41ZViJRDW8SsGkK+xvzFHjlUQ1PRCqRZg0vfudzdVwpgQKvPNE1vNVzZ81J2v6uGp5I\n84qu4aUReC8A0d0WdB2vBAq88lRyp4SIangizSu1Gl7o9BLtR4FXAgVeedIIPNXwRJpQ6FiS5jU8\nUE/NsijwyhMFXtIOKzASeKrhiTSXzYDx4XEaTZqgG8GWRYFXnjSbNFXDE2kuac6yElENrwwKvPJE\nnVbSaNLcoLtvtsbOiDSPeOClNfG9phcrgwKvPGnW8MaRwf38RCQzUeC9MtDbtTKlfaqGVwYFXnnS\nvIYHatYUaSZpDkmIRIG3cWdPvz5PilDglSfNGh6o44pIM0lz0HnkudhjNWsWocArT5rX8EA1PJFm\nkvaQhNx9qVmzCAVeeVTDE5GkUm/SHOjtWg68HJ6qhleEAq88aVzDWxJ7rBqeSPOIAi/NGh6o40rJ\nFHjlqbiGN3fWnDXA0vBUNTyRJhBmWYkC77lC2yagwCuRAq88aVzDA00vJtJsNmNkGJICLyMKvPKk\ncQ0PNL2YSLOJX19Lu0lT04uVSIFXnrQCT9OLiTSXKPCGSW+WlYhqeCVS4JUnjU4roBqeSLOJrt+9\nGG7rk6Yo8N7W2dM/seCWTU6BVx7V8EQkiaiGl/b1O1j3zudbj7qVKPDKpE4rIpJENQMvvk81axag\nwCtP2jU8NWmKNIdqjcFjoLfrLeCN8FSBV4ACrzxpX8NTDU+kOVSzhhffrwKvAAVeibr7ZrcDbeGp\nangiUo5qB150HW96lfY/JijwShfv/aRreCJSks6e/nZgi/A09SbNYGFYKvAKUOCVblLssQaei0ip\n4nc6r1YNLwq87au0/zFBgVe6eOBVeg1PwxJEmkd8lpVqBd4zYbldlfY/JijwSqcanogkEfXQXM5I\nb8q0RYG3WWdPvz5XRqHAK12a1/CiGt6k7r7Z4yrcl4jUt7UdVgZ6u4ardIyFscdq1hyFAq901ajh\ngWp5ImNdtXtoRvseCo/VrDkKBV7p0gw83fVcpHlUbdB5ZKC3a1Vs/6rhjUKBV7oo8IaASid/jdfw\n1HFFZGyrRQ0P1HGlKAVe6dZOKzZ31pxK2+FVwxNpHrUOPNXwRqHAK11aE0eDangizaTqTZqBxuIV\nocArXVoTRzN31pyVwKrwVDU8kTGqs6d/I0b+j6tJM2MKvNKlNXF0RNOLiYx9tRh0HolqeNuE6cwk\nhwKvdKnV8IIlYTk5pf2JSP2J35D1+SofK6rhtbJu0EqgwCtdmtfwAJaG5ZSU9ici9ScKnlcHervS\nah0aTXzwuZo181Dgla5aNTwFnsjYFQVetTusMNDbtRh4PTxVx5U8FHilS/sanpo0Rca+qEmz2tfv\nIuq4UoACr3Rp1/DUpCky9tVqDF5EY/EKUOCVLu1reGrSFBn7atakGWgsXgEKvNKpl6aIlEtNmnVE\ngVc6NWmKSMk6e/rbGLnbea0Cb20Nr7Onv6VGx2wYCrzSVavTigJPZGyaCrSFx7Vq0nwqLCcB02p0\nzIahwCudmjRFpBy1nGUlsiD2eKcaHbNhKPBKp4HnIlKOKPBWAy/X4oADvV1vAK+Fpwq8HAq80mng\nuYiUI+qw8vxAb9dQwS3TFTVrKvByKPBKp4HnIlKOWo/Bi0TNmjvW+Lh1T4FXOvXSFJFyZB14quHl\nUOCVLqqJLSm4VenUpCkyttXqxq+5FHijGFfpDpxzHwN+nvPyNWZ2rHNue+BS4BD8+JAzzWxe7L1H\nABfj/2HuBk4xswXUme6+2S2MBNPSQtuWIQq8cd19s9vnzpqzquDWItJosq7hTe3s6d8wTCotpFPD\n2x24Gj/mI/o50TnXAvTjeyftB/wUuMo51wHgnJsOXAtcAewLvAD0h/fVmwlAVK60anjx4FQtT2Ts\nyTrwQLW8dVRcwwNmAg+a2UvxF51z7wFmAO80syXAfOfckcDJwLnAqcADZvatsP1J+NB7D3BjCuVK\nU7xjSdo1PPCB90ZK+xWRjHX29E8CNg1Pa92k+TdgBf6L+k7AgzU+ft1Ko4a3G2B5Xj8IuD+EXeQ2\n4ODY+lujFWa2DLg/tr6exGtg1Qg89dQUGVvidzqvaQ0vDIF4OjxVDS+mohqec248sDPQ6Zw7H9/s\n92vgq/g55HJvaf8SsG14PI31v/m8GFtfT+KBpCZNESkmPstKrWt4AE8CuwK7ZHDsulVpk+Yu+Lni\nFgPH4sPvYmBD/MwkK3K2j6rZ4EOk0Pp6Uu0mTdXwRMaWqIa3OKNOI/OBD+JDT4KKAs/M/uqc28TM\n3gwvPRw6nfwS3ztz45y3TGDkg34564fbBOCVEg8/Ddio/FKX78Bt99n1rmcfAOCrR/zb1sAmBTbv\nyFnmddmHv9l68jVnAbD3tN1nUPrvPZZ15CylNB05SylNR84yNdtM3WCv515+i3FtrS/j+zLU1I5b\nb/z6U3/7O60tLbtX4fgdOct68/hoKyrutBILu8h8oB1fjd8rZ900Rpo5n2Pk1hmRrYCHSzz0IDWq\nDR6506FEgbfb1J0fKPFt1xVaueGEDWhva2fVmlUcudOhP6m0jGNMwXMno9J5Syb187bfblvy3Mtv\nMXOHzXYkfx+Hqjrt2Lfzhf/6E0PDw5v+/a0VtvEGVfmorNe/t1F7+ld6De9Y4IfANmYWjSPbB3gd\nuBP4knNusplFzYCHAneEx3cCh8X2NRnYGzivxMN3UKMa3tWPzjsS+G9gRWtL69uLbN6B/0M4Ch/K\no1o9tPouYJNrHruu54Bt9/5tCkVtdB2UeO5kHR3ovCXRQZXO2433LvwOcMzg829eA5yd5r5L8crf\nl22MH9vMD676y8e/9E8H3Jfi7jto0L+3Smt4fwTWAD9yzv0Hvup8EfBN4Gb83Xcvd859Hd+efADw\n6fDeHwNnOefOAa7BD1V4xsxKHZLwQvipusdefmL/8HAJBarLOQaLbTs8PLwY2OTJ1wYXl7HfZjCI\nzkcSg+i8JTFIyuftraWrNgJ4c8nK+WnvuxTv2nsbLvrfe18CtrjjoeenVKkMg1Xab9VUNCzBzF7H\np/z2+CEFlwBzzOxCMxsCuoAtgHuBTwIfMbOF4b3P4Du6nADcg79ZYlcl5amitKcVi2h6MZGxKeql\nmUUPzcj8sNwtwzLUlTSu4T2EHyyeb90C4PAC750HzBttfR2JAi+tHpqRaH/qpSkyRnT29Lcw0kuz\n1rOsxM3HXzZST81Ak0eXJqqBqYYnIsVsxkiHuiwD77GwVA0vUOCVplo1PAWeyNiT9aDzSNSk2RGm\nOmt6CrzSpH2nhIiaNEXGnqg5c5gadawbRVTDa0EzrgAKvFKp04qIlCqaHvHFgd6uLG/7tYiRG1ar\nWRMFXqnUpCkipdouLBdmWYgwiXQ06F0dV1DglUpNmiJSqroIvEAdV2IUeKVRk6aIlKqeAi/quKIa\nHgq8UlWrSfOtsKzJFGkiUhP1FHhRDc919vS3ZVqSOqDAK021mjRfC8tNC24lIg2hs6e/FZgentZD\n4EU1vImMBHHTUuCVplpNmq+G5eYp71dEsrEFMD48fibLggRPAEPhcdM3ayrwSlOtJs2ohjexu2+2\nBoaKNL54LSrzGt5Ab9dy4OnwtOk7rijwSlOtJs1XY49VyxNpfFHgLWPd/99ZUseVQIFXmmo1ab4W\nezezfj4AABUDSURBVKzAE2l8azusDPR2DWdakhFRx5WZmZaiDijwiujum90GRM2N1WrSBD/hrIg0\ntnrqoRl5NCxnhjs5NC0FXnHxMXKL09zx3FlzljMSoqrhiTS+eg68TYEtsyxI1hR4xW0Ye5xq4AVR\nLU81PJHGV4+B91jscVM3ayrwiqt24GlogsjYEQXeokxLETPQ2/UmI+XZPcuyZE2BV1ytAm9qFfYt\nIjXS2dO/ESP/j5/Ksix5rL2Ol2kpMqbAK67agfd8WE6rwr5FpHbi95x7IrNS5KfAQ4FXiijwVs6d\nNWdlFfYf3SByqyrsW0RqJwq8JYx8ka0XUeDt3sw9NRV4xUWBV43aHYz8x1DgiTS2GWH5RB2NwYv8\nNSw3p4kvnyjwilPgiUgpohpevTVnwro9NZu244oCr7haBd5G3X2zdSNYkcblwrLuAm+gt+sN4Nnw\n9O1ZliVLCrziahV4oI4rIg0p3BYoqjk9kmVZCnggLPfJtBQZUuAVV8vAU7OmSGPqYGTO3b8W2C5L\nCrysC9AAqh14b+JnVgcFnkijimp3awDLsiAFRIE3s7Onf2KmJcmIAq+4DcKyKoE3d9acYdRxRaTR\n7RGWjw/0dq3ItCSjuz8sxzFS3qaiwCtuo7CsVg0PFHgije4dYflwpqUobBEjc/c2ZbOmAq+4aFLn\n1wpuVRkFnkhj2y8s78m0FAWEsYFNfR1PgVdcNKlzLQJPvTRFGkxnT//b8J1WAO7NsCiliJo1FXiS\nV1TDe7XgVpVRDU+kce0blsOMBEq9isq3d2dP//hMS5IBBV4B4W7nm4SnatIUkXz2D0sLt+KpZ38O\ny4k0YS1PgVfYJkA00WotanhTu/tmj6vicUQkfdH1u3pvzgR/Y9rnwuN3ZlmQLCjwCovflLWaNbwX\nw7KFJp7YVaRBNUzghY4rt4WnCjxZx2axx9Ws4b0Qe7xlFY8jIinq7OnfCtgmPK37wAtuD8tDm+1W\nQQq8wqIa3hB+RpRqeQV/wRvUU1OkkUS1pFWMdPmvd1HgbQHslGVBak2BV1gUeK/PnTVnqFoHmTtr\nzmp86IFqeCKN5NCwvG+gt2tppiUp3UPAW+HxoYU2HGsUeIVFgVfN5sxI1KypGp5I44gC47aCW9WR\ngd6u1Yz01jwiy7LUmgKvsKht/m81OFbUcUU1PJEG0NnTvyEjXfsbJvCC68PyqHBro6bQNL9oQlHg\nPVdwq3SohifSWA5k5DP0jiwLksC8sNySJrohrAKvsG3D8tmCW6VDNTyRxhI1Z84f6O16OdOSlO8R\nRlqujsqyILWkwCusloGnGp5IYzksLButOTMaj/eH8FSB1+y6+2a3AluHp7Vo0lQNT6RBdPb0T2Fk\nSMJNWZalAteF5aHheuSYp8Ab3duAaHLVWjZpbt7dN7u9BscTkeQOY+Tz4cYsC1KBPwCrgXagM+Oy\n1IQCb3TbxR7XIvDix9i+BscTkeT+ISwfGOjteinTkiQ00Nv1GnBDeNqdZVlqRYE3uh3DchnrTv1V\nLU8Ca8Lj3WpwPBFJ7n1heX3Brerf3LA8urOnf6NMS1IDCrzRRYH31NxZc4YLbpmCubPmrAQWhKe7\nVvt4IpJMZ0//1sDu4ekfCm3bAK7BT4s2HujKuCxVp8AbXTTH3FM1POZjYakankj9OiYslzMyL2VD\nGujtep2R0P5ElmWpBQXe6KIa3oKCW6UrCrymGQgq0oD+MSx/N9DbtTzTkqTjirB8X2dP/w6ZlqTK\nFHijW9ukWcNjRvPb7dPdN3uzgluKSM119vRvAbw3PP11lmVJ0TXAS/j7cf5zxmWpKgVeHt19s8cz\n0kuzljW8P+K7CbcCR9bwuCJSmpOBNmAx8NuMy5KKgd6ulcBl4enJnT394wtt38gUePltx8i5qVkN\nb+6sOYuBP4WnH63VcUWkuM6e/gnA7PD0fwd6u94qtH2D+RH+npxTgU9mXJaqUeDlNyMsh4DBGh/7\nl2HZ1d03e9MaH1tERncaMB3/ufD9jMuSqoHerkHgyvD03M6e/okZFqdqMg8859wE59yPnHOvOeee\nd86dlXWZgL3C8vG5s+bU+qL0XHzvrwnArBofW0TyCJ05zg9PfzrQ2zU/y/JUydfxYd4BfCXbolRH\n5oEHfBN/m433Av8C/D/nXNYf9HuH5V9qfeC5s+b8HfhNeHpGd9/sllqXQURGdPb0bwZcC2wAvAJ8\nMdsSVcdAb9dfge+Gp1/q7On/dJblqYZMA885NwU4Bfg3M3vAzK4FLgLOyLJcjNTwah54wcVhuTtw\ndEZlEGl6nT39uwK3AnvgZ0L6ZKNOJVai/wfcFR7/uLOnv6+zp3/MTHWYdQ1vL3zTXfz2GrcD+zvn\nMqnZdPfN3oKRa3gPZFGGubPm3MVI55VvdPfNbsuiHCLNqrOnf4POnv4vAPfhv3gOAScO9HZdV/id\njW2gt2sZ8AHg5vBSN/BEZ0//JWNhjN64jI+/FfCama2MvfYifpqbLRi5g0BNhObDT+PHoyzHf7PL\nylfwwxTeAVzY3Tf7q/gB6SuBv8ydNWdNoTeLSGkefPzlKedecsce+EnbZwAH4e8Rt3HY5AXgEwO9\nXY16G6CyDPR2vdrZ038kcBL+uuUW+PF5J3f29P9q5g6b/fmzx+/D868smfK1S+9sG+jtapjPopbh\n4apPEzkq59wJwAVmtm3stR3xEyl3mNnCapehu2/2+/C3xtgG/4e+VVj1k7mz5pyUYJczAAMc8HiF\nZfsRcGqeVX8D5gH3ApfOnTVndSXHqSOpnbsmo/NWRGdP/8eB/YGJ4Wfz9nGtu4xvb9t1ybJVo71t\nJfBj4KtjvBlzVOG+f6cBZzH6vTqXAW8BrwOvhZ838LVi8BWIyBCwIvysBG4f6O26Kv2S55d1DS/q\njRgXPV9a5L3TgIpm91684q3WFlquHmZ4Svz19tb2+afu97FLGGnaLEdHzjKx7x3z9YvPueGiaW+t\nXJJ7r6qt8d++Tjp4+jteI6Om1yroyFlKaTpylhJz1U1PTAN+nvv6qtVDrFo9FH9paFxby7MT2tue\n2HyTSbcfddD213/oXTu9BGwSfprOQG8XwMCTz77xh+/88v7jXnxt6QdWrFyzD+teDpsUfqYmOMTn\n7njobwcc8vat30yhuJFRv/RlXcM7BN9sONHMVofXjgB+B0wxs6FC7xcRESlV1p1WHsRXa98Ze+1Q\n4F6FnYiIpCnTGh6Ac24OcBhwIv762RXAKWZ2ZaH3iYiIlCPra3gAZwJzgJuAvwNfV9iJiEjaMq/h\niYiI1ELW1/BERERqQoEnIiJNQYEnIiJNQYEnIiJNoR56adYl59wE/E0ej8NPg/NtM/vmKNvuBfwQ\nP9flY8BpZnZvbH03/3975x5813TF8Y+EKuJVLWklBh0W2lL1aImY6ghtQqJeHYJiRlBDQuoxtPWY\n8QrTSKnEqyQIHSFthbTaBpHUo9TQenynqUZItEqbByFDm/6x9s3v5Dr398t9nfu77vrMZM7vnn3u\nfqycc9fZa+29FlyGb7v4LXCSpH/l1HMBviWjbYO0Fik3Mzsf+B6etmUmcKqkxc0YV7MpSm5mtiGe\nAmY4nuF6OnCWpHebNLSm0ki5Za67ANhB0rFl5y/Fs7usA9wCnNuu+4WLkpuZbQ6MB4bg99sM/H5b\n0tgRrRkxw6vMGuXpSymOZgJ/wAM9PwY8YGb9UvkewG3AJXiszo3wvYbl9ewI/BC/KdqZQuRmZmOA\nsXiItX3xMHDXNWtQBVDU/TYOjyn5TWAoHujhyqaMqBgaIrfMdUcBF1H2HJrZWcBxwGHAt4Gj8PiS\n7UohcgOm4qEQ98fvty/hLwstIRReDlXm6fsOsELSWDln4vsJSzfP6cA0SVMk/Rl/aA5MQbJL7fXB\nb4KnWD3QaltRlNySvM4FzpH0kKTn8R+fnVuVVqoeCr7fBgM3S3omvaVPAr7RvNE1j0bKzcz6piAY\ntwB/y/n+GOBCSXMkPYrff6c1flTNpyi5mdkA/N4aJel5Sc8Ao4FDzOyTzRpfd4TCy6eaPH1fS2WU\nXbtXpnxVmiFJrwOvAntnrj8DjzY+ue6et5Yi5LYXsBOesuTeTPksSTtLascZclFyA/gjcLiZbWpm\nmwCH4lk32pFGym1DfPaxJ/A4mRdPM/scMIDV04XNBQaY2ZZ1jqEVFCI3PGPCUDz7TZY+1Bn4v1bC\nh5dPNXn6+gMvl33/TdzeXSpfVFb+TzwdUSkd0vl0mRfamSLkNhB/OVgK7G5mV6Rrf42/sS5rwDiK\npgi5lVJwnYHnWXwrfX4BGFFP51tII+S2C0Dy/e4DkPOjX0oZlpVrqe4BwMIa+98qCpGbpHfw5zLL\naOAvklqSbilmePmsjztys5Q+l6czqnTtumtYfhNwpaS/19zb3kNRcuuXjlcD5+H+lK+Q4xttE4q8\n367FU7kMAfbDg7e3q2WhkXLrqZ1s3d210w4UJbfVMLMz8UUyY6r9bqMIhZdPNXn63scTSpZfuzxT\nnlfXe2Z2Ep5VeXxdve09FCG3d4EP03fPlPQ7SY/hiXJHmFmlJJW9mSLktjyZ347FVwLPkjQb/wEa\nYWa71dH/VtFIufXUTrbu7tppB4qS2yrMbCz+gnq6pJZljg+Fl89CYFMzy5p8++NvNv/OubZ/2bn+\nwBtrUH4U8EVgiZktw9++tzKzZcnh224UJbeSaSlraiklfdyq+m63nKLktiXuY3muVCBpPp6puh23\nwjRCbuXm30rtlK6n7O83aD+KkhsAZnYJvir0DEkTq+9u4wiFl081efqeILMAJdmxB6XzpfLBmfKB\n+I/y48Ax+AKMXdK/i/EbaRfa80EqQm5PpHZWANlZyU74kuhXGzGQgilKbq+k01/IlPfHs3nnrUzs\n7TRSbllWW/gkaRGwgIxcUzsLJbWb/w4Kklu6fjRwAb4X9Kd19rtuYtFKDpKWm9lk4HozOx538o7F\nl/KWfiQWS3ofmAZcYWbX4mmOTgI2AO5O1U0EHjWzucCTwATgQUkf+YExs7eADyW9Ul7WDhQpNzOb\nBEwws8W4eWUicF+rnOH1ULDc7gRuNLOT8ZeG8cBsSc8WMtgG0mC5Zcnb2jIRuNzMFgD/wzf2T2js\niIqhKLmZ2Vb4Hs/rgRmp3hJvtmLTfszwKnMWvoR7Fv4fls3Ttwg4EiCtChyGvwU9gy/XHVqKXCHp\nCfwm+QG+efM/wHcrtLmS9t94XpTczgbuwyOFPIyb6U5o5sCaTFFyG4VvHp6OR2F5Dd9I3a40RG5l\n5D2HV+GbqO/FlcBUSVc3diiFUoTchuMrP0+jyxWxCDeTbt3Y4awZkQ8vCIIg6AhihhcEQRB0BKHw\ngiAIgo4gFF4QBEHQEYTCC4IgCDqCUHhBEARBRxAKLwiCIOgIQuEFQRAEHUFEWgmCXoKZzcfDgG0i\naWmNdWwMXI5HV5mRzm2NhxV7TtKu6dzxwM+ACSmpJ2Z2EfAjPCj3hHSuD54YdDNJF9Y4tCDoFcQM\nLwh6F/VGgvgxcAr5z3Ze3SvL/i6PljESuAZP9BkEbU3M8ILg40XfnHOvAzvQleamEtcBd+EJPrur\nLwjaklB4QfDxZFUgX0kf0pU+qSKS3gbe7qm+IGhXQuEFQRWY2XhgNDBa0rU55bfjZsBhkmYmn9q5\nwGF4wNylwFzgcklPrmGb+6Q29wI+g2c5eBG4VdINmeuy0eenmxmpzT6U+fAqtHMR7sMbI+knZvYI\nsG8qHp1SvZyA53E8ABhe8hOW1fMUnoF+oKR2THMVfEwJH14QVMed6XhEeYGZrQuMAN4CHkrpUJ4G\nzgPWA34JvAQcDMwxs+N6aiwtLpmdvvNSqkPAnsDEpKSyfSullnoEuAN4J1NerX/wITxvI6ntO4B5\nwG3p3NE5/d0e2B34fSi7oLcRCi8IqkDS0/iP/iAz+2xZ8beAfsA9kv4L3Ax8HlcQ20o6UtK+wP74\nLO0GM9uuUltmtj6+YGQp8GVJQ1Ide5DStwCnZvp2LDAnfbxG0nGSyjNYVzPWy4Ab08ffpPrmAr8A\nlgEHpz5mOSYdp9TabhA0i1B4QVA9d+I+rcPKzpeU0F1mti0wFF8wcnLyowEg6WHgUmBdfMl/JTYH\nHgAuk/RytiDlLlsCfDrNLJvFR3x3KTHoz/FEoIeUFY/EZ5X3NbFPQVATofCCoHqmpuMqs6aZrYeb\nHRdImgPsk4rul/RBTh33pOPgSo1Imi9ppKRxmXbWNrMdzewEup7fT9Q4jnqYnI6rzJpmtjewDZ55\n/r0W9CkIuiUUXhBUiaS/4r65QclPBz6b2wC4O30umTvnV6hmQTr2r1AO+MZvMzvUzKab2TxgOfAC\ncAtuPoUWrKBMps15wAFmtlk6HebMoFcTCi8IamMq/vwcnj6vMmemY09KqPTsrah0gZn1BR4EpgFD\ngNeAScAoYHvcXNpKpuArvY8ws7VxGbwuaVZruxUE+cS2hCCojbuBq4FDzOxmYBjwkqTnUvnCdNym\nwvdL59+sUA4+YzoAeAwYIWlxttDMNqml4w3kduBi3I/3MvAp4KaW9igIuiFmeEFQA5L+ATyM++CO\nBNany7cHvtcO4CAzWyenitLMcHY3zXw1HSflKLs96Qr3lZ1N1huarJyK9Ul6FXgU+DpdvrzbG9x+\nEDSMUHhBUDtTgXXwFZcr6TJnIukV3Bw5AN8vt8qaYmb74XvzVuC+uEq8lo7DsifNd5Rn/WTZVZol\nE+nG1QykG3qqbzK+aOZE4E+SXmxQu0HQcMKkGQS1cy9wPbAl8FRScllG4TOgE/HFHU8CW+ArOD8A\nTinfbsDqs7UpwPeBo81sN3yxyhZ4xJVncVPn4HSuZBqdl47jzGw4cHadYyzVN9LMNsWju9yfKZ+G\nx+DcgFisEvRyYoYXBDWSUvg8gM/upuaULwL2AMbhM6WD8I3o9wCDJN1a9pXVMhVIWogrtF8BG9G1\nsf0cYG9gZrr+oEwdE1P9/fCFLtvRc5aE3PZTH57G/XRLgAOBXcvK38XDnH1AZoYbBL2RtVaubLTJ\nPwiCTsHMBuJbL2ZIGtHi7gRBt4RJMwiCqjCztXDfZV889NlawA3dfikIegGh8IIgqJaN8DRCK3Gl\nN0fSg63tUhD0TPjwgiCoCklL8IwNK/CVqOUxRYOgVxI+vCAIgqAjiBleEARB0BGEwguCIAg6glB4\nQRAEQUcQCi8IgiDoCELhBUEQBB1BKLwgCIKgI/g/aXAJmIul7aoAAAAASUVORK5CYII=\n",
   1366       "text/plain": [
   1367        "<matplotlib.figure.Figure at 0x7fd8d6236790>"
   1368       ]
   1369      },
   1370      "metadata": {},
   1371      "output_type": "display_data"
   1372     }
   1373    ],
   1374    "source": [
   1375     "sns.distplot(results_normal[0]['volatility'], hist=False, label='etrade')\n",
   1376     "sns.distplot(results_normal[1]['volatility'], hist=False, label='IB')\n",
   1377     "plt.title('Posterior of the volatility')\n",
   1378     "plt.xlabel('volatility')"
   1379    ]
   1380   },
   1381   {
   1382    "cell_type": "code",
   1383    "execution_count": 106,
   1384    "metadata": {
   1385     "collapsed": false,
   1386     "slideshow": {
   1387      "slide_type": "slide"
   1388     }
   1389    },
   1390    "outputs": [
   1391     {
   1392      "data": {
   1393       "image/png": 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QcW4pNvOmWG4dQNs4kCR7k2QrFGFvf38/I0ZUwRb4wOnzTiK951jZ+OR7D8OJ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\nKmaKoihK4FExUxRFUQLP/wPjl55O9FHYuAAAAABJRU5ErkJggg==\n",
   1394       "text/plain": [
   1395        "<matplotlib.figure.Figure at 0x7fd8d6dccd90>"
   1396       ]
   1397      },
   1398      "metadata": {},
   1399      "output_type": "display_data"
   1400     }
   1401    ],
   1402    "source": [
   1403     "sns.distplot(results_normal[0]['sharpe'], hist=False, label='etrade')\n",
   1404     "sns.distplot(results_normal[1]['sharpe'], hist=False, label='IB')\n",
   1405     "plt.title('Bayesian Sharpe ratio'); plt.xlabel('Sharpe ratio');"
   1406    ]
   1407   },
   1408   {
   1409    "cell_type": "code",
   1410    "execution_count": 107,
   1411    "metadata": {
   1412     "collapsed": false,
   1413     "internals": {
   1414      "frag_helper": "fragment_end",
   1415      "frag_number": 31,
   1416      "slide_type": "subslide"
   1417     },
   1418     "slideshow": {
   1419      "slide_type": "slide"
   1420     }
   1421    },
   1422    "outputs": [
   1423     {
   1424      "name": "stdout",
   1425      "output_type": "stream",
   1426      "text": [
   1427       "P(Sharpe ratio IB > 0) = 96.52%\n"
   1428      ]
   1429     }
   1430    ],
   1431    "source": [
   1432     "print 'P(Sharpe ratio IB > 0) = %.2f%%' % \\\n",
   1433     "    (np.mean(results_normal[1]['sharpe'] > 0) * 100)"
   1434    ]
   1435   },
   1436   {
   1437    "cell_type": "code",
   1438    "execution_count": 108,
   1439    "metadata": {
   1440     "collapsed": false
   1441    },
   1442    "outputs": [
   1443     {
   1444      "name": "stdout",
   1445      "output_type": "stream",
   1446      "text": [
   1447       "P(Sharpe ratio IB > Sharpe ratio etrade) = 85.10%\n"
   1448      ]
   1449     }
   1450    ],
   1451    "source": [
   1452     "print 'P(Sharpe ratio IB > Sharpe ratio etrade) = %.2f%%' % \\\n",
   1453     "    (np.mean(results_normal[1]['sharpe'] > results_normal[0][0]['sharpe']) * 100)"
   1454    ]
   1455   },
   1456   {
   1457    "cell_type": "markdown",
   1458    "metadata": {
   1459     "slideshow": {
   1460      "slide_type": "slide"
   1461     }
   1462    },
   1463    "source": [
   1464     "# Value at Risk with uncertainty"
   1465    ]
   1466   },
   1467   {
   1468    "cell_type": "code",
   1469    "execution_count": 109,
   1470    "metadata": {
   1471     "collapsed": false
   1472    },
   1473    "outputs": [
   1474     {
   1475      "data": {
   1476       "text/plain": [
   1477        "<MultiTrace: 1 chains, 5000 iterations, 5 variables>"
   1478       ]
   1479      },
   1480      "execution_count": 109,
   1481      "metadata": {},
   1482      "output_type": "execute_result"
   1483     }
   1484    ],
   1485    "source": [
   1486     "results_normal[0]"
   1487    ]
   1488   },
   1489   {
   1490    "cell_type": "code",
   1491    "execution_count": 111,
   1492    "metadata": {
   1493     "collapsed": false
   1494    },
   1495    "outputs": [
   1496     {
   1497      "data": {
   1498       "image/png": 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d1D1ywJ3ADe5+eeL65sB5wObAu8Dvgd+4e/qvb6m9fwDMmjVrw3o3RES6pViQoUxGG2mY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\nSUVORK5CYII=\n",
   1499       "text/plain": [
   1500        "<matplotlib.figure.Figure at 0x7fd8d57ab550>"
   1501       ]
   1502      },
   1503      "metadata": {},
   1504      "output_type": "display_data"
   1505     }
   1506    ],
   1507    "source": [
   1508     "import scipy.stats as stats\n",
   1509     "ppc_etrade = post_pred(var_cov_var_normal, results_normal[0], 1e6, .05, samples=800)\n",
   1510     "ppc_ib = post_pred(var_cov_var_normal, results_normal[1], 1e6, .05, samples=800)\n",
   1511     "sns.distplot(ppc_etrade, label='etrade', norm_hist=True, hist=False, color='b')\n",
   1512     "sns.distplot(ppc_ib, label='IB', norm_hist=True, hist=False, color='g')\n",
   1513     "plt.title('VaR'); plt.legend(loc=0); plt.xlabel('5% daily Value at Risk (VaR) with \\$1MM capital (in \\$)'); plt.ylabel('Probability density'); plt.xticks(rotation=15);"
   1514    ]
   1515   },
   1516   {
   1517    "cell_type": "markdown",
   1518    "metadata": {
   1519     "slideshow": {
   1520      "slide_type": "slide"
   1521     }
   1522    },
   1523    "source": [
   1524     "# Interim summary\n",
   1525     "* **Bayesian stats** allows us to **reformulate common risk metrics**, use **priors** and **quantify uncertainty**.\n",
   1526     "* IB strategy seems better in almost every regard. Is it though?"
   1527    ]
   1528   },
   1529   {
   1530    "cell_type": "markdown",
   1531    "metadata": {
   1532     "slideshow": {
   1533      "slide_type": "slide"
   1534     }
   1535    },
   1536    "source": [
   1537     "# So far, only added confidence"
   1538    ]
   1539   },
   1540   {
   1541    "cell_type": "code",
   1542    "execution_count": 112,
   1543    "metadata": {
   1544     "collapsed": false
   1545    },
   1546    "outputs": [
   1547     {
   1548      "data": {
   1549       "image/png": 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wCeA/c7QnlmO7oIkllWEmllSGnVhSmZGRwwZdvG1XO0Mqy59s/ta7ck6XX7SI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\nbFwNsDFf50a/Y4UkllSGmRjwUi4Ns4nZKmC0MaZ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oWKmUPbHrCwGe6GljsXRiA+wie4Cu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\nUTFTFEVRQo+KmaIoihJ6/h8dfb0Jm/h/OAAAAABJRU5ErkJggg==\n",
   1550       "text/plain": [
   1551        "<matplotlib.figure.Figure at 0x7fd8dbcbef50>"
   1552       ]
   1553      },
   1554      "metadata": {},
   1555      "output_type": "display_data"
   1556     }
   1557    ],
   1558    "source": [
   1559     "sns.distplot(results_normal[0]['sharpe'], hist=False, label='etrade')\n",
   1560     "sns.distplot(results_normal[1]['sharpe'], hist=False, label='IB')\n",
   1561     "plt.title('Bayesian Sharpe ratio'); plt.xlabel('Sharpe ratio');\n",
   1562     "plt.axvline(data_0.mean() / data_0.std() * np.sqrt(252), color='b');\n",
   1563     "plt.axvline(data_1.mean() / data_1.std() * np.sqrt(252), color='g');"
   1564    ]
   1565   },
   1566   {
   1567    "cell_type": "code",
   1568    "execution_count": 113,
   1569    "metadata": {
   1570     "collapsed": false,
   1571     "slideshow": {
   1572      "slide_type": "skip"
   1573     }
   1574    },
   1575    "outputs": [],
   1576    "source": [
   1577     "x = np.linspace(-.03, .03, 500)\n",
   1578     "ppc_dist_normal = post_pred(eval_normal, results_normal[1], x=x)\n",
   1579     "ppc_dist_t = post_pred(eval_t, results_t[1], x=x)"
   1580    ]
   1581   },
   1582   {
   1583    "cell_type": "markdown",
   1584    "metadata": {
   1585     "slideshow": {
   1586      "slide_type": "slide"
   1587     }
   1588    },
   1589    "source": [
   1590     "# Is this a good model?"
   1591    ]
   1592   },
   1593   {
   1594    "cell_type": "code",
   1595    "execution_count": 114,
   1596    "metadata": {
   1597     "collapsed": false,
   1598     "slideshow": {
   1599      "slide_type": "-"
   1600     }
   1601    },
   1602    "outputs": [
   1603     {
   1604      "data": {
   1605       "image/png": 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5aQV/UnJ6YU3TZ4vvNMacjetq9Dn5TX42f9wD6O/vL3rZkwKwDvij/Jdz1Ui4OX/733P0\n/DIFE/6QjTFrgL/DdTMMAV8D/tRamzLG3IUbTlzsfdbav88/9lXAnbi+/seBdxXm7ojI9PT395+q\nu3A21fX19dHd3V3X3d3dMNkHzVK53gV8D3jMGPNZoA/YiLteV2wrblrDHcaYDtwozwtwUw+ex40M\nbSk6/zBuxObH3/3ud//ic5/7HNFodF86nf5dY8wwsB03heFtuKkSlDx+qrx8i7J48EszbvrGy4H/\ntNYqBCvAaUMw3+/+Ldy7rSuABPDl/OEPAOfnb/+l6GED+ceeiZvv83HgP3GTX+8zxrzEWjut9f9E\nhL78ItVzZsuWLWvWr1//ka6urvtuv/32qb5p7ZvJa1trf2KMuRL4BG4SexgXeB/CXQMsnLfTGPN6\n3P+XD+B6tX6KGy26DegEXot70w5umbLzgA898cQTj0UiEW655ZZ3fv7zn9+MC6bfAyzw2fzHLuDV\nkyjyeOuG+sDdRfflcP8bd+JatZ+dxHPLPJioJfgyYDVwqbV2GLDGmNtww5U/AJwL/NRae+QUj70F\neNpa+yn4ZT/9YeBaYNZXYhAJgvw2RbO+S0OJVoBNmzb1btq0aa5f60Wstds59eCUUMl5D1IUjBOc\nuw24MP/lWsDeeuutL9x6661vHOfxq8e5v7SsqyZzn1Suia4J7gR+LR+AxZqNMQncH8uphjODWxz2\n4cIX+bk4T+FalCIiImV32pagtbaHondaxpgQ8Ie4dfzOBzLAnxtjNuDenX66aK+vpUBXyVN2Aytm\np+giIiIzM9XRoXfgLjh/CNe/ngN+hlsN4UvAXcaYwhJGdbh1/4qlmJv9vERERKZsUkOA88OK/w63\nVt9N1todwA5jzBZrbWEk1bPGmHPy53wdSPLiwIsz9esZHVM8fyHoKLmtNh0lt1Wlo6PjzNHRURob\nG9sSicTwli1b1pC/jlYlOkpuq01HyW016Si5rTYdjH8JblomM0UihGvlbQTeZK39VuFYUQAW7ARe\nk//8ILCs5Pgy4JkplvE7Uzx/IanmukGV1u+8885j27ZtGGNuTSQSrF+//iPlLtMcqcqfX5Fqrl81\n121W11ydTEvwb4G3ADdYa79duNMYcwew1lr7hqJzLwZ25D//CW5Fh8L5dbgFcj8xxTK+FjfcuZp0\n4H5Jq7FuUOX127Fjx4XAv1tr79y9e/dwV1fXfZs2beotd7lmUQdV/POjuuvXQfXWDeaghTvRPMHL\ncXN1Pgw8ZYxZWnT4G8APjDHvBb4NbMDN0bk2f/zLwAeNMR/FbYp5G7BvGhtVdjLLzd8K0kn11g2q\ntH6dnZ0ty5cv58SJEz3d3d3Dt99++55yTCWYB51U4c+vSCfVW79Oqrdus2qigTE35W8/iRvpWfg4\nCDyKayHeguvi/H3gLdbaRwGstfuAG3HB+ASwBLh+lssvIiIybRNNkfgg8MHTnHJv/mO8x29Fm0eK\niEiF0gLaIiISWApBEREJLIWgiIgElkJQREQCSyEoIiKBpRAUEZHAUgiKiEhgKQRFRCSwFIIiIhJY\nCkEREQkshaCIiASWQlBERAJLISgiIoGlEBQRkcBSCIqISGApBEVEJLAUgiIiElgKQRERCSyFoIiI\nBJZCUEREAkshKCIigaUQFBGRwFIIikzA87yI53lthY/t27c3ZbPZchdLRGZBpNwFEFkAmjdu3Pju\npqamEYBjx46dPTIyUu4yicgsUAiKTEJTU9NIIpEYBDh+/Hiq3OURkdmh7lAREQkshaCIiASWQlBE\nRAJLISgiIoGlEBQRkcBSCIqISGApBEVEJLAUgiIiElgKQRERCSyFoIiIBJZCUEREAkshKCIigaUQ\nFBGRwFIIiohIYCkERUQksBSCIiISWApBEREJLIWgiIgElkJQREQCSyEoIiKBpRAUEZHAUgiKiEhg\nKQRFRCSwFIIiIhJYCkEREQkshaCIiASWQlBERAJLISgiIoEVmegEY8wa4O+AlwNDwNeAP7XWpowx\nK4EvAlcC+4H3W2u3Fj32VcCdwBrgceBd1to9s14LERGRaThtS9AYEwO+BYwAVwC/A/wm8H/yp9wH\nHAUuBb4C3GuM6cg/9kzgfmALcAlwGLjPGOPNei1ERESmYaKW4MuA1cCl1tphwBpjbgPuMMb8F7AW\neLm1dgjYaYy5DngncBtwC/C0tfZTAMaYd+CC8Frg+3NSGxERkSmY6JrgTuDX8gFYrBm4HBdyQ0X3\nP4JrMZI//nDhgLV2BHiq6LiIiEhZnbYlaK3tAR4sfG2MCQF/CHwXWAZ0lTzkCLAi//nSUxzvLjou\nIiJSVlMdHXoHsB74EFAPpEqOp4B4/vO6CY6LiIiU1YSjQwHyg1n+DtgM3GSt3WGMSQKNJafGcSNI\nAZK8OPDiQM8Uy9gxxfMXgo6S22rTUXK7oG3ZsqVl7969bYlEog4gm822ADQ2NrYlEonhLVu2rAFa\ny1rI2dVRclttOkpuq0lHyW216QB2zeYTTmaKRAj4ErAReJO19lv5Qy8AF5acvhQ4lP/8IK7LtNgy\n4JkplvE7Uzx/IanmukGV1G/Dhg1s27aN5uZmAPbt2weAMebWRCLB+vXrP1LO8s2hqvj5nUY116+a\n6zarMwwm0xL8W+AtwA3W2m8X3f8T4KPGmLqigTNXAY8WHb+6cLIxpg64CPjEFMv4WqBzio+pdB24\nX9JqrBtUWf0eeOCBlr17916fSCSGAbq6us6+5JJL3matvXP37t3DXV1d923atKm33OWcRR1U0c/v\nFDqo3vp1UL11gzlo4Z42BI0xlwO3Ah8GnjLGLC06/ENgH/DPxpiPA2/ATal4e/74l4EPGmM+CnwT\nN21in7V2qtMjOpnl5m8F6aR66wZVUr+bb765bfPmzT3AIEB/f/9igBMnTvR0d3cP33777Xs2bdo0\n1W7+haCTKvj5nUYn1Vu/Tqq3brNqooExN+VvP4kb6Vn4OJi//3qgHfgp8FZca3E/gLV2H3AjsAl4\nAliSP19ERKQiTDRF4oPAB09zyh7gmtM8fiuwdbzjIiIi5aQFtEVEJLAUgiIiElgKQRERCSyFoIiI\nBJZCUEREAkshKCIigaUQFBGRwFIIiohIYCkERUQksBSCIiISWApBEREJLIWgiIgElkJQREQCSyEo\nIiKBpRAUEZHAUgiKiEhgKQRFRCSwFIIiIhJYCkEREQkshaCIiASWQlBERAJLISgiIoGlEBQRkcBS\nCIqISGApBEVEJLAUgiIiElgKQRERCSyFoIiIBJZCUEREAkshKCIigaUQFBGRwFIIiohIYEXKXQCR\nSuN5XgRoLrqrNZfLeeUqj4jMHYWgyIs1b9y48d1NTU0jAAcOHFicTCaTwECZyyUis0whKHIKTU1N\nI4lEYhCgt7e3vtzlEZG5oWuCIiISWApBEREJLIWgiIgElkJQREQCSyEoIiKBpRAUEZHAUgiKiEhg\nKQRFRCSwFIIiIhJYCkEREQkshaCIiASWQlBERAJLISgiIoGlEBQRkcBSCIqISGApBEVEJLAUgiIi\nElgKQRERCazIZE80xsSBJ4FbrbXfz993F3BLyanvs9b+ff74q4A7gTXA48C7rLV7ZqPgIiIiMzWp\nlqAxpgb4KrAO8IsOrQM+ACwt+vhi/jFnAvcDW4BLgMPAfcYYb7YKLyIiMhMTtgSNMeuAe8Y5fB7w\np9baI6c4dgvwtLX2U/nneQcuCK8Fvj+94oqIiMyeybQEr8aF1hXFdxpjlgKtwK5xHnc58HDhC2vt\nCPBU6fOIiIiUy4QtQWvtFwqfG2OKD60DMsCfG2M2AD3Ap621X8kfXwp0lTxdN7BiJgUWERGZLTMZ\nHXoekAN+BrwO+BJwlzHmt/LH64BUyWNSQHwGrykiIjJrJj06tJS19nPGmC3W2oH8Xc8aY84BNgNf\nB5K8OPDiuBbjVHRMt4wVrKPkttp0lNwuKFu2bGnZu3dvWyKRqAM4fvx4azwe9xKJhA+QzWZbABob\nG9sSicTwli1b1uAuDVSLjpLbatNRcltNOkpuq00H41+Cm5ZphyBAUQAW7ARek//8ILCs5Pgy4Jkp\nvsx3plG0haKa6wYLtH4bNmxg27ZtNDc3A9De3k44HGbFCteTv2/fPgCMMbcmEgnWr1//kbIVdm4t\nyJ/fFFRz/aq5brM6w2DaIWiMuQNYa619Q9HdFwM78p//BDeopnB+HXAR8IkpvtRrgc7plrNCdeB+\nSauxbrDA6/fAAw+07N279/pEIjEMsGPHjsXxeNxbvXp1D0BXV9fZl1xyydustXfu3r17uKur675N\nmzb1Ahw6dCj8ve99r7H4+a677roTy5Yty85/TaatgwX885uEDqq3fh1Ub91gDlq4M2kJfgP4gTHm\nvcC3gQ3AJtwUCIAvAx80xnwU+CZwG7CvMNF+CjqZ5eZvBemkeusGC7R+N998c9vmzZt7gEGAI0eO\nePF4nPr6+iMA/f39iwFOnDjR093dPXz77bfv2bRpUw/A8uXL2zZu3HhjU1PTSP7c2ptvvvku3/en\nehmgEnSyAH9+U9BJ9davk+qt26ya9sAYa+0jwFtw8wGfAX4feIu19tH88X3AjbhgfAJYAlw/0wKL\nVLqmpqaRRCIxmEgkBgthKCKVaUotQWttqOTre4F7T3P+VmDr9IomIiIyt7SAtoiIBJZCUEREAksh\nKCIigaUQFBGRwFIIiohIYCkERUQksGa0bJpI0GUymRDQ6nm/XMmpNZfLaeNokQVCISgyAwMDA7U3\n3XTT29rb248BHDhwYHEymUwCpevqikgFUgiKzFBDQ0MykUgMAvT29taXuzwiMnm6JigiIoGlEBQR\nkcBSCIqISGApBEVEJLAUgiIiElgKQRERCSyFoIiIBJZCUEREAkshKCIigaUQFBGRwFIIiohIYCkE\nRUQksBSCIiISWApBEREJLIWgiIgElkJQREQCSyEoIiKBpRAUEZHAUgiKiEhgKQRFRCSwFIIiIhJY\nCkEREQkshaCIiASWQlBERAJLISgiIoGlEBQRkcBSCIqISGApBEVEJLAUgiIiElgKQRERCSyFoIiI\nBJZCUEREAkshKCIigaUQFBGRwFIIiohIYCkERUQksBSCIiISWApBEREJLIWgiIgElkJQREQCK1Lu\nAogsSLkcNYOD0SWDg5GaVIr6gYHoSF1dptzFEpGpUQiKTFHdyEikpqeHM37+8/ZMV1c0Gol47cPD\nkd7W1hNdIyOxkXh8tNxlFJHJUQiKTEFzb29Npq+vtnH/fsJHjjQuSqWIZLN+3dBQbWx0NLYqkwl3\nRyID5S6niEyOQlBkkhoGBmKLjxypbzh4sD20ahWpurrk/paWYb+mJlvveaM1yWQ8MTCwKBKNEu7t\nrelraUmWu8wicnoaGCMyCdFsNtRy7Fj9yv37l3u+72diMYYbG0c8oHZ0NHpi0aKBkfr6ZDiXCy8Z\nGFjU2tNTXzMyojeZIhVu0n+kxpg48CRwq7X2+/n7VgJfBK4E9gPvt9ZuLXrMq4A7gTXA48C7rLV7\nZq/4IvOjdXCwZsXAQEN0dDQay2ZjpNM0d3c3dvT0RIjHc+3pdI5QyD/iebnaTCbcePRoc7K2Nr0/\nEsmVu+wiMr5JtQSNMTXAV4F1gJ+/zwPuA44ClwJfAe41xnTkj58J3A9sAS4BDgP35R8nsmDUp1KR\nRH9/fUtvb2tDf39zbSoVbzx8mMYjR9qaUqn65uHhhkVDQ4viqVRNczJZFxkdDdeMjNS0HD/e0DQ0\nFC93+UVkfBO2BI0x64B7TnHoVcBa4OXW2iFgpzHmOuCdwG3ALcDT1tpP5Z/nHbggvBb4/uwUX2Tu\nLR4aquk4frytfng4HE2na6OhkEc2SyiX82pSqbiXy+VCkUgknsmEoplMpD6Xi8WSyYHGEycamsBL\ngN74iVSoybQEr8aF1hUl918OPJUPwIJHis67HHi4cMBaOwI8dYrnEalY9YODsZW9vU2tJ0401CaT\nTdlQaDQ6OhoNj4yQ8bzRkWg0mQuFcvHR0bpYKlVfl0rFPN+nfmiooX5wsG5xf3/dG6G+3PUQkVOb\nsCVorf1C4XNjTPGhZcChktOPACvyny8FukqOdxcdF6l4bUeO1Lf29rY2J5NNOc8bWDQ83B4KhZpj\nBw8S6+43Bv75AAAgAElEQVRewcBAJhOLpWrC4SE/FPJq0ukInpcNRaMjtUND9U2el7sIGvE8D9/3\ny10fETnZTEav1QGpkvtSQHySxyerY8olq3wdJbfVpqPkdkHZsmVLy969e9tWNDYu6kilVsRCoWXx\nUKihIZ1uDXlemHS6nv5+Iun0ojrI4vtEwuEawuFsczZbNxoKpWpiMS8ci6WXRCKNZ9944/n88R97\nwEi56zZJHSW31aaj5LaadJTcVpsOYNdsPuFMQnAEaCy5Lw4UukeTvDjw4kDPFF/nO1Mv2oJRzXWD\nBVq/DRs2sG3bNtqGh2no6yPb3U1dby/xZBIvmYR0mmwySaSl5ZzawUG8aJRwSwvE42SyWeKeR82y\nZWTa2iASYdmv/upvsmZNuas1HQvy5zcF1Vy/aq7brF5jn0kIHgTWl9y3lLEu0oO4LtNiy4Bnpvg6\nrwU6p1q4CteB+yWtxrrBAq/fAw880PL87t3XX717d1vd9u2rYgcPnlWTTC4KZ7NhPC9HLBbyli5t\n5/jxzuzwsB+GSOTIET8XCo2GPM/3o9Gct3//sF9TM5KsqxsZ+tGPHmp59asf45ZbujjvvHS56zcJ\nHSzgn98kdFC99eugeusGc9DCnUkIPgZ81BhTZ60dzt93FfBo/vOf4AbVAGCMqQMuAj4xxdfpZJab\nvxWkk+qtGyzQ+t18881tf/7GNyYj+/enFx061OgNDsZj2Ww8BJlMLDY0GIlksh0d7d6hQ3sHcrlo\nSyrVEk+n45FcLhLJ5XKZWCwdSqXC4ZERLzY8nAsfPpzh2WeH+PSnu/D93nLXbwo6WYA/vynopHrr\n10n11m1WzSQEHwL2Af9sjPk48AbgZcDb88e/DHzQGPNR4Ju4aRP7ChPtRSpVA7Cip6cpcfjwiujI\nyKKabLYpB+RCodFUTU1vf3OzT0cHpNO9B1Ip/1gud/zcgYG2hsHBpdFsNhJKpwl7XsZLp2sbcrlo\nFGqABHAQz+vTABmRyjHtZdOstTngeqAd+CnwVuAGa+3+/PF9wI3AJuAJYEn+fJGKthkWNQ4M1DX1\n9a2IJ5OtHoR8yI3E40eHGxqOj8TjyUwsxnBT01BvXd1wKhZL9zc2HhypqTke8rxoJJeLeblcOAzx\nWDodi7i/kQTQBNSWuXoiUmRKLUFrbajk6z3ANac5fyuwdbzjIpXoFbBk2ZEjy2ODg81hqM1CLgmD\n2bq6EQ883/NyoUyGRX19TUuHhrzh2tqhgdraoZrR0WM1yWRrPJ2uDY2O1mbi8WTY92MROAN4HvdG\n8AVg+PQlEJH5ogV+RYp5XjwBrUuOHz8jns02A54PmVRNzaDnedmRmpoTJxoa6mI1NWRDoUz96Oii\nFQMD7Q3R6EgqGh0eiEb745lMbTiXi/jpdNgPh8MhWAQsxwVgU75LVGuKilQAhaDIyZrPAFM/PNwO\nRIFMEpKjsViG2trBE01Nx0fD4Visp4fl1p6bOXGi3vM8ajwvlQuFcslsNuZBzguFIuFstjbteaOe\nuya4AtcaXIxbNEKtQZEKoBAUKfC8MLC4AS6K5XKLcK1AP1lbOzAajY6MNDV158Jh/5yurrNak0nC\nuVx8NBTK+J6X833fi6TTtSHw/XA4FE2na9O5XCqUTqdDEAbacFOI2nDXBRWCIhVAISgyphZYHXNT\neaJALuN5A6lIJHW8rq4/Hgr5K/fvvyCbzTZm6upILl586JH29s5YOOxdMDRU23DiRJs3OHhGyPMy\nvuflop5Xn/H9XM5N7o0Dq4AdQCue16suUZHyUwiKjGkALg7B0pwbOZ1O19ScGI5GU8lYLLnyyJFV\nkWy2bjgWS564+GKeXLv2e99/7DG/Nhr1MqlU7qKnn77Yz2TqFo2ONtTkcqF4LhevgUW+awn6uFGi\ny4FmXBepWoMiZaad5UUAPC8KrASu8l2L0MvAYDYaHT0Ri/W3DQ621IyONmUikZE9y5fv3/+a15Cp\nqckB5EIhf9e6dUd+9IpXPDoQiw2OxGJDqWi0z/e8tAfhsAs/D7ee7tm4LlHtMyhSARSCIk4tsAYX\nUh6QycZiwyPxeF8sl4s0p1ItmWg02dfc3PWdyy7biffi5QsPnXXWwEOrV29PRaOpTDw+lAyH+wFC\nbo3dOK5FeCZuzmDrfFVMRManEBRx6oBX4ia0h7MwnI7FkplYLN2UTrdkwuFsKhYb/uE11zyaiUTG\nXfFl25lnHtvd1rY/HYmkUvH4cR8Ka4UmcCG4CNfibMHz1BoUKTOFoIjnxXAtwEtxA2L8UbdEWn84\nl4vFcrloJhwe3b127bbuZcsGT/dUvufxsDF7hhYtOpaLRjPDoVBf/lAc1yKMAufgpkooBEXKTCEo\n4rpC1+N2OYkAw5lodDgbCqVr0+mG0Ugkfbyuru8nV1wxqQWJ+xYtGn1+1apdozU1g6ORyFDObSsW\nwrUyY7gVZJaiLlGRslMIikBjGq5NQl1+F+iRZCw2FPX9uAdeOhwe/fHq1Tuzp+kGLfXzl7zkQH9T\n09HRmprRNPRngAzEMm5kaC1gcF2iGqEtUkYKQQk2Nyp0VRbW+RDPgX8CwiPhsB/OZmOZSCTV3dDQ\n88yKFUen8rRDTU3p/StXdvZGIsO9oVAkDV7WdX824FqDa3EtQ3WJipSRQlCCrhZ4BW7aAkB6NB4f\nDgNeKORlotHRJ848c49/itGgE9mxbt2BYw0Nvdna2mEfkvk/tjCuNdiG636tn4U6iMg0KQQl6FqB\ny3EtslwaUslYLBXL5eLpaDR5orGxZ/vSpT3TeeKhpqb0862th4dqagazoVAyBxnGRog2AOsYC18R\nKQOFoASXux63GjdaMwKQ87wRz/dzhEJeNhIZ3XnuuTum0wos2L5s2eFj9fV9o9HoiawLQS//Wi35\n123Oj04VkTJQCEqQxYGrcK3BnA/pbG1tMgzRZCSSHKqv733u/PO7ZvICRxsbU90tLUeTDQ19Wcjm\nW4MhXEswkf/QRrsiZaIQlCBrBi7DhaGfgWQmHB4Me15kNBod7ezo2OuHZvYn4nseNpE4MlRffyzt\necM5N3k+hJsv2Aacny+HiJSBQlCCbB1uZ4cIkMvCaCgUCo+GwyOpSCS1/cILn5+NF9nb3t7f39ra\nk4rF+oBs/iOE6xJdAyzGm0Gfq4hMm0JQgsldh3sprivU92A0HY2ORHK5eDIaTe5rbe1K1tVlZ+Ol\nsuGw351IdPc1NBzHBWChS7SwXmkCTZUQKQuFoARVPa4rtAZ3PTCZjUQyuUgknQ6Hs493dOybzRfr\nXL36yEBjY38OjgOFfQQ9XACuwY0YFZF5phCUoLoANzI0itvrbzgcCoVTsdhQT3398cPNzbO619/x\nJUuGjzQ39+TgIC4Ec7jpEi24blktoSZSBgpBCR7PCwFXMjZHLwP0hiCcjsVGdixZ8sJsv6QfCnFw\nyZKjadiFGxyTZWy6xLnAGXheeLZfV0ROTyEoQVQLvIx8VyiQ9iE7Go2OZCOR0SfPOOPwXLzoL5Yt\nOz4CB4BjnNwlehZuUe2auXhdERmfQlCCqDAqNIwLo+EQRJOx2NCR9vYXUtFo7vQPn56hurpMH+wD\n9uRf18+XoRF4Sf5WROaRQlCC6DLcNbgILoxOAJnRSCS1a+3aWZkWMZ5dLgQtrks0k787wthWTiIy\njxSCEixu14grcKNDCwNUkjnoHa6pGepcterYXL78P8F+4Hmgt7hUuN3mV+m6oMj8UghK0KzKf8Rw\ng1OGgUgOjh1oazs40xViJvJfrvW3BxeGpaNEzwPq5rQAInIShaAEzeW4UaER8lMjgFQGhp5duXLW\nR4WOoxN4DtclmsO1BKO4blotoSYyjxSCEhxuabLLcRPTfVxLMAn0JqHrYFvb4DyVZD+wExjIl6PQ\nGiy0UkVknigEJUiacV2ONWnIJiGbhsgQ9D8B+3K53Pys3+n7hS7RFxjrEvXy5bs0P49RROZBpNwF\nEJlHVwJLcNcAc2mIjNTU1B9paVnx9fPOewnJ5Alc62w+7MdNnF+H+zv0cOuHXoJrqfbPUzlEAk3v\nOCUYXFfolbh9/MKATzic9uPxwdHFiw+m2ttPzHOJDgDbcNckwXXNRnEb7S6f57KIBJZCUIIijpuL\ntwjI+pDzPM8fjcUGX1ixYr4GxIzx/TSwFziK6w4N5T8W48JaROaBQlCC4nzcZPQIkPUgnQ2HM5lo\ndHjnueceKFOZngd2MzZpHtwUiZdpvqDI/FAISlC8ArcsWQTAg3Q6EhnpbW3tPtHcnCpTmQ4A24ER\nxgbI1OAG7ywuU5lEAkUhKNXPrRLzK4xNjch5kE5Fo8OHli2b/67QAt9P4qZK9HHyWqKtwMvLVi6R\nAFEIShAsAc7GXRfM4AInlYpGR3atXVu+EHR+gesWzTI2WrsBuLpsJRIJEIWgBMHVQBNjq8RkfBg4\nvmhR97ElS0bKWzQO4FaPSeLK5uPWNb0g34IVkTmkEJTq5gaYFFaJCZEPwRz07Wtv7ypr2QB8fxD4\nGTDE2HXBOG4tUY0SFZljCkGpdotwE9LrcV2OOWAoC33PnXVW+UPQ+QVwiLEuUQ/XJXpVOQslEgQK\nQal2FwEJxjbQBRgchc5DixcPla9YJ3ket8fgaP7rHG4k66X5Sf4iMkcUglK9XIC8nOJVYlxrq/8I\nPFnOopU4gesSHWZsQe1aoB1YU8ZyiVQ9haBUs1rgQlxXKLiAGQH6HoFny1aqUr6fw80X7MWFtIcL\n7Xrg1WUsmUjVUwhKNXO7tY9toOvhFsg+8D44XM6CncIe3LXBNGOjWBcBLy1noUSqnUJQqtmVuGtr\nha7QHC4EH5mvjQOn4BjwDCd3iS4CVuJ5beUsmEg1UwhKdfK8GGOrxBQGxYzirr/9tIwlOzW3x+BT\nwCBjC2rHcNczrylfwUSqm0JQqtUy3BqcxV2hg8BBoLN8xTqtZ4EuxsoLLgQ1X1BkjigEpVpdgBtd\nGWVs53bXCvR9v5wFO41u3FqiScYm9jcCa/G8ReUsmEi1UghK9fG8CG5ASQNjYZLFtQQfKl/BJuD7\no7ipG4Vd5T3cCNFG4GXlKpZINVMISjVqAV6CmyJR6FYcxm1gu6tchZqkx3BTJQp7DBZWj9GuEiJz\nQCEo1ehsoAPXFZrGDYwZAH6G72fLWK7J2I+bLpFibAm1RtyC2jXlLJhINVIISnXxvBBwCdDMWFeo\njwvBh8pXsEkbwU2VGMQFYGG+YDNu4r+IzCKFoFSbRcB6oA73+x3Gtap6cV2Nlc0N2vkJ7rpgFlf+\nCK41eEUZSyZSlSITn3J6xpjfBv615O5vWmtvNMasBL6IG+K9H3i/tXbrTF9T5DRWAmtxUyNgbJWY\n5/D9dNlKNTXbcFMlOnBduoXrghfhedEFVA+RijcbLcHzgW8AS4s+ftcY4wH34QYjXAp8BbjXGNMx\nC68pMp61uKkRIVxLClzX4iNlK9HUDQI/xw3mCeNCcBHQBpxbxnKJVJ0ZtwRxe7X9zFp7pPhOY8y1\nuH9IL7fWDgE7jTHXAe8EbpuF1xU5mefV4a4H1uOCI4cbZdkPPFzGkk2N72fxvMeB1+NGuoZwG+26\n7ZXcNUMRmQWz0RI8D7cXWqnLgafyAVjwCLquIXNnBa6lFMe1oEK41tRu4HgZyzUdj+LKnMYFehQX\ngpfkB/+IyCyYUUvQGBPDDUf/dWPMX+D+WP8d+Bhu2apDJQ85gvtHJTIXzsbtGlGYGhEBhoDHKniV\nmPH04MLbMNaybQCW4OpZ6fMdRRaEmXaHnsPYHKwbcX+cd+KuX9TgRuUVS+HepYvMLs+L4lqBzYx1\nhWZxv5sPlrFk0+P7aTzvKeCVjC0CHgdagYtRCIrMihmFoLX258aYZmvtifxdz+QHxHwVNyq0qeQh\ncVz31FR0zKSMFaqj5LbadJTczr2PfWw5d9xxBQMDY1MjPC9FY2M3W7fW4a5P/9KWLVta9u7d25ZI\nJOoAjh8/3hqPx71EIuEXf156DCCbzbYANDY2trW3t/unO7fk67otW7aswQXZxN70phe4995hstnC\nrhI11NQsobX11aRSTxOfs/eTHSW31aaj5LaadJTcVpsOZvkN4IwHxhQFYMFOXHdUF26+VrGl+fun\n4jvTLNpCUM11g/ms3yteAd/8JuzaBSMjEItBe/sibrnl9Vx22etLT9+wYQPbtm2jubkZgPb2dsLh\nMCtWrDjp89JjAPv27QPAGHNrTU3Nac8t/rqvr4/169d/ZNJ1+tKXoL8fHnoIUimIRhs466wlXHrp\neg4ceCdnnz3979fk6Pdz4armunkTnzJ5M70meCPwBeAMa21h7tLFuInJPwE+Yoyps9YWWn9X4S74\nT8Vrqdytb6arA/dLWo11g/muX0+Px3vecwO7dr0bN5oSRkdDdHd38eSTf4bn/az0IQ888EDL3r17\nr08kEsMAO3bsWByPx73Vq1f3FH9eegygq6vr7EsuueRt1to7H3vsMf905xZ/3d3dXdfV1XXfpk2b\neidVr2gUnnnmj0ilbgRaSKdT/OIXfXR1PU9n59f5n//57sy/eafUgX4/F6oOqrduMAct3Jm2BH+A\nu+7yj8aY/4vrcvpr4G9wS1TtA/7ZGPNx4A24lfDfPsXX6KR6r390Ur11g/mq35IlCWA5rrvdx71T\nTJFO7+H++x/EDTI5yc0339y2efPmHtycPI4cOeLF43Hq6+uPFH9eegygv79/McCJEyd6Jjq3+Ovu\n7u6G22+/fc+mTZteVJ5Tisehq+tbuOuCTYBHLhdicDDCo48uw/N2z/GAn070+7lQdVK9dZtVMxpq\nba3txb3jWInbFfsu4B+stZ+01uaA63ETl38KvBW4wVq7f2ZFFnmRDtxUnSjud9rD7SK/DbeH4EL2\nJG7BieKpEg24Swsd5SuWSHWYjWuC24Frxzm2B7hmpq8hMi7P84A1wBm4EZSF9TYHcV3yC32JsX5g\nB25lpgbccnAxXLfvRcDz5SuayMKnSbey0LXiVi1ahGspFZZLOwxsX4DzA0/m1gl9EjfVI4R74xrF\nheD6/JsAEZkmhaAsdCtxraQa3PXAEK4rdDvQV8ZyzaYfA8cY6xKtxa0esxQ4q4zlElnwFIKy0BVW\niSn8LvtAErdt0mC5CjXL9uE22k3j6lmLaw0247pERWSaFIKycHleC27VohZO7go9Avwc38+UsXSz\nx/eHgadxoR7Of0SBxcBL1CUqMn0KQVnIVgEX4LpCwf0+p3EDSUrXrV3oHsbNv80ytqvEIlyXqNbj\nFZkmhaAsZKtxI0MLe+6BC8GHWfhTI0rtAF5grEu0HnWJisyYQlAWJtcVupKxDXRDuL0Dj+AmCSfL\nV7g5MYibizuCGyEawwV/GxolKjJtCkFZqFYCL+HkrtAsLgAP4vu5chVsTrj6PIQb8ZrDtX7rcaNE\n23GtYhGZIoWgLFSrcXvtRXC/xznc1IgfsfA20J2sn3Fyl2gDLgxbgF8pY7lEFiyFoCw8nteEawkm\nGLsWmMXNpdvF1LfrWigGcBPnUxS2VnIKo0TD5SqYyEKlEJSFaDVwIW6+XPHUiN24rtDRMpZt7rjV\nYx7BLaVWWEe0Djc4pgm3fqqITIFCUBYWNwDkbNz8wMLatz6uK/RRTrFjRJV5krEuUXABmMMtH3dJ\nuQolslApBGWhWYLbPWE5Y6NCs7g5dDtwXYbVrBd4AtclGsZ1iXq4LtFz8bw5225epBopBGWhWYVb\nK7SWsW2TxkaFVt/UiJP5foqT50FGcZPmm3Bdo+vLVDKRBUkhKAuH54Vwk+PX4rpCC4NiUrhFpnsq\nedeITCYTAlo9z2sr+pjOdmY/Bfbj5kWGcKNDM7hWskaJikzBjPcTFJlHy3GDYpYx1hWaxl0H3EmF\n7xoxMDBQe9NNN72tvb39GEB/f3/tPffccxdTv47Zj+sSvQA3VzCO+1teDJyN5zXh+/2zWHSRqqWW\noCwkq3AjIOtw18N83KCQHUAXC6ArtKGhIZlIJAYTicRgU1PTyDSfJgV8HxeGMLaOaB2um/jymZdU\nJBgUgrIweF4UNyL0PNzvbSEAh3GTyHvw/Wz5CjiPXJfvNqAT1w0axl0TTOFWj7lUy6iJTI5CUBaK\n1bhrgW28eNuk56jeVWLGcwL4H1zwFTbajeGuDy7GvWEQkQkoBGWhWAuci+v6K6yMkgV+zgLpCp1l\nSeAHjIV/HPcGIYxbT/SyMpVLZEFRCErl87zFuBBcy8lzAwdxIXg8v5pKcLgu0WdwU0PSuIExTbjv\nyxLgAjyvvnwFFFkYFIKyEJyDmxrRyNjegTncyinPUv2rxIxnGHgQt71SYS3RWtwqMjXApeUrmsjC\noBCUyuYWhT4bWIebGB7BtXaSuGuB3bgQCB7fT+K2V+rGfU+iuFZgEjdA5goNkBE5PYWgVLrVuJbg\nCsYmx+dwO0ZsB47h+5kyla0SPI/bbDeNayU34P6uF+MC8dzyFU2k8mmyvFQu14o5F9cKrMf9vuZw\n0wL2A7+gaFRofvWV5pJn6fMrNCSLVpAp3FU84AcmV/YR4DvAdbiBMbW4EaK9uGuEV+HmUYrIKSgE\npZK14TbOXYsLiAguAAdwXaFHObkrtHnjxo3vLkxCn8GKLPOidAWZAwcOLI7H47S3tx+bdNl9fxTP\newzYiwu/KG5HiUO4LtFz8bwl+P7ROa2MyAKlEJRKtg53PXAxYyvEFOYGbgcOl3aFNjU1jSQSicH5\nLuh0FVaQAejt7a2Px+NMo/w9uAEy5+NWjWnADSJK4wbIXA3cO3ulFqkeuiYolcnzanGrw5yLmwRe\nGBAzDOwB9jG2k0LQDQP/jWsZg5sz2IqbSL8EuERbLImcmkJQKtU63KCYlbgBMYUtk45RWCYtqKNC\nS/l+Djdf8KeMDZBZjHvj0IK7nvryspVPpIIpBKXyuAEu5+N2SajBXefK4naP348b6NE90bZJJVsX\nJfIfbZ7ntQGtuVyumqYPDAPfxi2qHcINkGnDtQbbgKuZ3rZNIlVNfxRSic7FDYhZw9jk+AxuxOMu\n3KCPoYmepHjgSfGgE3CDUJLJZJJq2Yne95N43qO4LaVaGOsSPYjrEj2K213ikbKVUaQCqSUolcVN\njr8AF4QNuOuBOVw332FcV+hRfH90Mk9XGHjS0NCQLN7GqKGhoRrXGj2Gaw0O579uwgVgCheI1+S/\nvyKSpxCUSnM2YwNiorjf0RyuFbgbt31Qb7kKV+GGcfsM7sF1H8dxIZjDTZdoA15WttKJVCCFoFQO\n10q5GDcoppmxVuAobmkw1woca+lIMXeN9ABupGgS143cjBskk8F1k16na4MiYxSCUknOxQ2IOY+x\nVmAG6MMNiNkDHJloQEzADQEP4MIwhxtYtBjXnZzAtQavKlvpRCqMQlAqg2udXIoLwWZcV15hROgR\n4AncII8JB8QEmls8YDeuNVjYcLcNF4SFa4PXat6giKMQlEpxIa4bdC0uAAt7Bh7HTYzfzSlWiJFT\nGgC+xVhrsA5Ymv98Ca5b9NVlK51IBVEISvm5zV9fhusGbcWFYAY3Gf4YbhL4C7hNdGUi7o3CDly3\n6CiuNdiCGxxTWEXmFXjekrKVUaRCKASlElyOmxZhcAEIY6vDdFKYGxi03eNnptAafB73vazFtQZ9\n3NSJZuAG7TcoQacQlPLyvOXAS3FdoU24EaEZ3Lqgx4Enca3AF01q9zwvUlgBpkpXgZk+94ZhJ/Af\njO0834wLwmFcq3AdrhtaJLA0VFrKx02JuAb3j3g1rrXi40Yy9uD+ie8ADo7TCjxp66SqWwVm5vpx\new1ei3ujUQMsw82z9HFdzzfgebvwfa3DKoGklqCU02XAJYxtmluYEtGD6wp9Ejc1YtxQK2ydVMWr\nwEyf72dxXclfw00z8XHXBlfgWoNLcC3Cm8pVRJFyUwhKeXjeUtx8tXW4f8Q1uNGLA7gWzJO4neM1\nInRmBnB7DT6Ma2FHcPMFE7gJ9QngUjzvorKVUKSMFIIy/9wctdcBv4KbElGPa6UkcSvCvIDbNPd5\n1LU5M25hgReAf8VNmSgMkjkLNwipHjeP8E2466oigaIQlPnlRiNehxsRej7uulRhTuCxNJw4DNse\ngaM3Qs5zWyEF7tp1yTZQhY9JfR9KBwx50LAHngbuxr2pKCynthI37aQ9//E2LakmQaNfeJlvlwBX\n4wJwGW55tBzuGmDvEDz73YsuWrPXGG9pa+vFG/v7a++55567cNcJA6N4GyiA/ql9H04aMNTf31/7\n8nvu+cfDboeJS4DX4rqfCyNF9wPLcddjf5tU6jHiWlBGgkEhKPPH89YCbwAuwu0WUYPrBi1Mh3i+\nF545euaZZ4XPOedoIhIJ9Bqhha2fpvPYwoChwtfd7vv8C+DLwCrcwgR1uG7RJG7gzHLgcjZsqOPB\nB2dafJEFQd2hMj8870zgt3DXAc8HFuFagCO4fQK7gYefhx1dbW0D2YAH4Jzw/RRuDdbP477nGdw1\nwcL0lCiwjOeeu4qHHipXKUXmlUJQ5p7nnQW8Fbc02sW4SfGF+YBduNGgPwKe/Q94YbimRqNB54rv\n9+JGi/4LrvXn4d6QrMX1DDUyMtLOv/0b/MZvaO9BqXoKQZkTmUyGu+++u+VbnnfpUdichitwu0S0\n4P7xZnC7QvSl4dFn4Rd/AUc/C7HTrfpSPOgDrRADTG3lHM/zIotg5L9gay98KwkDaQjjfi4GCJFO\nN3LgADz++AY8b0NhabUXDbgpGqxzumMilUy/pDIn+vr6SN1zz3tXLV2aGDl27MzGdHoxrsvNw7UA\nD+JagI/ugWf+5XWvu3Sgo6PjDS+8MNGqL78c9KEVYn5pKivnNP/Gxo3v3trQkDy4Z8/g1Y89tr9j\ncHBV1F0fbAHOZXT0IMeOwdDQcuAGYDGe9/9KX6dksM7pjolULIWgzL6f/SwSefJJXvnss6btyJGm\n+lzujJALPx+3q8FBXFfcj4D/eRA6B1euPLN96dLB43199RM9fWHQR29v74TnBkXxQJiJvi9NTU0j\nbRGBZjYAABW7SURBVInE4JH29sEf5XIs/8EPfl7j5m02Ak1ks3F6eiCTaQDW4NZzPeOz8K2flwy4\nGa8MIguFukNldnleBzfc8Lb4177G0hdeWNWQy53lue42Dzcc/yBuOsSDwA+BJz8BR3KhkAbCzLNs\nJOJvW7u2+6fwReCruDVFAerYvRuSySW4gTMGeNkmeN+vPv30OeFMJvBd0FI95rwlaIyJA5/BjQxM\nAXdYa/9mrl9X5pnnNeKmP7yKzs7LwocOEXEtCx8gC30RtxrMfuAh4HHgWeB4t9v1XMogFwr518Ou\nAfh73CCldwJn5g8vARpwI0nXxCHx0l27ai/s6Vn+/9s79zir6mqBf888QVAHE3kIhkKuDBUxURTT\n1B4+MLK6muCrm698YCndwuyada/lzW5pKdW9Vgx9tLpYkZFgLy0fiCAg+FimhCgg+GCAmWGY17l/\nrN9hNpszwxlmn9kjs76fz3z2md/+7d9e6+yz99q/32/91lp+xBFLNwwatCklsR0nMbpjOPTbWKDk\n07Cba5aIrFbVX3bDuXeLTCZTduSRR57at2/fVoDa2lpWrFjxp7TlKjbBkaEqVlyTDbE78+yvydo8\n0hnABMzzcxSwV6axESCTheZtUFthD9LlWO9vEfAPstm6cOLiKbWHEIkgkysqDdsWduEgFDt2h7rN\nzc0ltbBfBt7+Jsw5B94aWlLyubKysnGZxsaSUuhXbusK6zOwpWrLlsqWpqZ+E2pqBo/s3//tKbCM\nTOaRoihdAHl/k7sRa3ZXv/3ukKEn0JXv4Z1KUY2giPQDLgUmquoSYImI/BdwDRbZvqdSOnr06PeK\nSAPAsmXLyoE93giya+eGqsmTJ18xrKSkedSzzx7y8SVL3sCS4Y7Beg1l2LBnJpvN0gz1rSUltfWV\nlTVNW7c+WGk9wOXABg+K3TniEWReffXVd1VWVnLAAQe8tSsHoeix8brRfauB6f/85/4ntraunNSn\nz7iBDzxQX5HNVpTbde2fhf7lTU2tFU1N/Svr6/er2LJlUB/4InDOKnjm/jVrBtTtv39da2lpdw5t\nb//NdtEZpyuOPUnJ0BPodQ5Oxe4JjsGC9D4aKXsM+KqIZFTV54F6GHmdGzKZvYBRq+D4hrlzzxi8\nefPgsmz2XRXmMFHGjnPLLUBty6BB+9XW1b1Z27//P14cOHBd6/Llvz0TnvG8dbtPNILMxo0b+1VW\nVlKog1Du2Hx14+2+Pnz465snTmTZtm2/P3X+/NY+cDIWZLscKMlCRUlLS2W/lpZ9Smwo+4ihcMoF\nf/5zWcuCBW++td9+q7WqquYkOJBMZmNI6VQ0knLI6Uo7e5JT0J6kSyEU2wgOAd5W1cZI2Xrs4XlA\n+OykiY2RVQBVj8GhNX/5y2EjNm2q6l9bO6hPbe2Q78K12LxQxVCoZNOm0u2HtrWSxeZ764D17LXX\nG43nnnvakhUrFr8xePDSZZWVzbcvX/5y1g3gO4bWfv1Yfvzxa+bOnz/jHuvlf7IVJmFBt8uykG0B\nWqGszAzkwAF1dRnq6kbsv2HD0aOguRTOBt4mk1kFrMLCtq3C7vs3MUeczT4q4KRJsY3gXtjDMUru\n/11H6K2ogKamJ7HwWrtLpyectkGm6b77ynIHZgEymVu7IEOcEkpLoaVlMW265ZMz0055Z8lEtpk8\nZQCZYyGTVc17YO5zruuehWzWrmU9sA5L17McWMTkyQ1NU6eetrC6+uXW0tI369av75+ADk4K/AS2\n3pPNPk0ms+RuqD5k7NipY1euPHTApk1SDlXB85cW7LdRAiUZKC2FsozFhh2ExSnNh/2cMpnIz4rW\nsM2yw89th8/bt/VA64wZ259j34GvRtrLEX9+lFJRAY2NT2JBG6iHkpYZM8qj9/ztcGOetnYavaqD\nktYZMypy/4fjuvLM6gol7LMPHHxwOUuXpiTCO4tiG8EGdjZ2uf/rd3l0UxNYL6RbyfnzR0n6VTXb\n0kJ4SPRoWiHbaDd+cys0NkDztvLyLXV7711HScnCkqFDn9s0bNi6t0aNeuutkSO3NAwY0DJixIjh\nB7S00FJSMjgD2crKyj7Tpk07etasWXm9CadNm7Zvc3PzMKChb9++VRUVFSXYwnrix3ZUt6P/k6yb\nyWQG1dbW0tDQMKxv376tachQzLrZbLaqpqaGbDY7ZPt3X13N6888s+9rzc3bnpk06anyhobFZStX\nDjj56adfGbl27WGl9fWHZ2B4BVRkwtxwBmixrUWciXwOxF/EoM3hpyDK2dEq5UIR7YpsYyOZyLOl\nnJ0fhhnoW0hbFTvLUNBxxSK7eTNbly2bN2fWrE919tjo/QV2/1VXV4/EUp71BEYALybZYMZybhYH\nETkBy2jdR1WbQ9kpWEqXfqqa1tuS4ziO4xR9sfxSLELIhEjZicAiN4CO4zhO2hS1JwggIjOwJKqX\nYI4y1cClqjq7qCd2HMdxnF3QHYvlrwdmYGGyNgG3uAF0HMdxegJF7wk6juM4Tk/FA2g7juM4vRY3\ngo7jOE6vxY2g4ziO02txI+g4juP0WlLNLC8i/4llmSgH7gG+1N76QRF5N5b88wQsJ931qjovsv/L\nwFVYQN+/Adeq6kvF1aBjEtZvKhbHczAWnuwGVX2iuBp0TJL6RepNAa5U1Q8UTfD88hWc91JExgA/\nBI4EnsfkXRTZfy5wK7Yk6I/AZar6RnE12DVJ6hip9xXgvap6YdEEL4CkdBORUuBm4EIsSspC7Fny\nQtGVaIcEdSsDbgMmY8mSH8R021B0JTqgSL/LD2Bp20ao6uqOzp9aT1BErgcuAj4JnAOcj6VlyVc3\nA8zBkrIeA8wE7heREWH/pcAN2AN5DBaY9/fhuFRIWL8LgK8DX8L0exiYJyJDi6pEBySpX6TeKcCP\nyROfsRuI5r28ArhJRM6LVwrpwR4EHgeOBv4OzBWR/mH/OOBn2PUajyUWru4G+QshER0j9c4HvkY6\n1ytOUrpNBz4DXAaMw2LizhORvYquQfskpdvXgI9h9+x4rMPw82ILXwBJ/y77AP9Lgb/LNIdDPw/c\nrKqPquoj2AP+6nbqngIcClyuqi+o6m3YF/HZsL8/ME1VHwq9v2+F+oOKqkHHJKnfxcBdqvprVV2p\nqjdiSWrPLq4KHZKkfojIzVg4vZeLK/bORPJefkFVl6jq74Bc3ss45wHbVPUGNb6ArX/N3bTXArNV\ntVpVl2MvCh8VkUOKr0n7JKmjiJSGIBj3kML1ipPw9bsY+Lqq/klVXwQux4xFt45M5EhYtxJgqqo+\nrqrPAXdigUxSI2H9ctyCZSopqBOUihEMPZhh2LBljseAYSJyYJ5DxgNPq2pdpOxR4HgAVf2eqs4M\nbe+LPYxXqOrrxZB/VyStH3ATNpQYZ98ExO00RdAP4EPAR4D7SSZzRmdoL+/luDyjCePDPmJ1j4/s\n3/69qOprwCvYMHCaJKnj3sARwLHAE3T/9YqTpG6XY6MWObKYfqncaySom6reqKoPAojIIMz4/LkY\nQneCJK8dInIMcAEwrVAB0poTHBK2ayNludyCw4A1eeqvi5VtCHW3IyKXY+PF24CPJiLp7pGofqr6\nZHSHiJwOvIf0st0nfv1yc4AiclpyYhZMZ/JeDgbi80MbsDmK3P61sf3rgXwvB91JEjqOAVDVGiwG\nMHkeVGmQpG5/je3LzXn/jXRITLccYS5/OvA24TqmSGL6iUjON+F6TLeCKJoRDJOdw9vZnRtfj+Ya\n7CjPYHt5CeN152FjxZcBc0RkrKquKlTmzpCSfojIodgc00xVfbpggTtJWvqlRGfyXu5Kl56qa5I6\n9jSKopuITABuB25Na1SJ4uj2U+DXmCF8SERGq+qWBGTdHZLUbzrwiqr+UkRGFSpAMXuC48j/9pTF\n5o/AhK+PfIb8eQa3Yg4GUSrjdYMX0Grg6uBkcTE2PlwMul0/ETkceAh4DptALibdrl+KdCbvZQM7\n54GM6tJeW2nrmqSOPY3EdRORDwK/A36nqsV6hhRC4rrlvOZF5ELM8ecTmLNaGiShX52IjMbm48fG\n9u9ypKJoRlBVH6WdOUcRGYJNfg4GVobiwWEbHzYDG14bEyvbPuwkIh8GVqpqdJL+eWxCuyh0p36h\nzWOA+cAyYGJs+CBxulu/lFkDDBCRslzeS0y+bew8rLKGNl2J1F1X4P60SELHnnK94iSqm4icic1N\n/wabX0qTRHQLw9YfA57ILYlQ1a0isooiPicLIAn9Xsc8XquA50UE2ozfsyJymare154AqTjGqOo6\nrMcW9bg6EVijqvH5JIAFwFExN+UTQznYup6puR1hPcxRmCHsdpLWL3gWzgMWAWeqaqpv5EW4fmnT\nmbyXC4g4uYSHywTadFlA5HsRkeHAQaSva5I6RukJyyMS001EjsMM4C+AKXmO724S0U1Vs8APgCmR\n/fsCo0jpORlIQr8nsHWGgr1sj6HNc/4M4IGOBEhzsfwM4JsishpoxRYX35HbKSIDgfrgUfgI5mH3\nMxG5BZiIeaZ9JlS/E5gpIo9jPaUvYrql1cWHZPW7C6gFrgSqwpsOwJaYx2V3kqR+qaKq9SIyE7hb\nRC7BJutz604RkcFAjao2ALOBb4nI97Hv4DJs4fEvQnMzgEdE5DHgSew7+UNslKLbSVjHKKk7xiSl\nW3io/gRYAdwIDIrca7nju5WEr9v3gRtF5DmsV/UtO4V5jKZBUvqF58zGXLsikuvgvaKqtR3JkOY6\nwW8D92JvXbPD5+9E9i/EvgzCG8EkzFtoETZEcU6YA0RVfwVcB/wH8DT25v2RlHtMiegnIntjnq7D\nsTVZayN/XyI9Ert+MbKk07u4HngKy3t5NzvmvVwLnAsQHAjOwt5IF2Pu2WfmXkZUdQF2c96ErYXc\niM1N9wQS0TFGWtcrThK6jQYOw5zr1rDjvTa52zTZmaSu2+3YS9n/YL2qbdgQadoU43cJBf4uPZ+g\n4ziO02vxANqO4zhOr8WNoOM4jtNrcSPoOI7j9FrcCDqO4zi9FjeCjuM4Tq/FjaDjOI7Ta3Ej6DiO\n4/Ra0owY4zhdIkSY+EmeXU3AFuAlLP7jXbuKGlHAuUZgcVKXqerY2PnvCAk+exwhcsY1wLtU9ea0\n5XGcnoYbQWdP4GUsfmCOciw6zTgsPNuVIvKhhEKX5Ysu0ZMjTkwBvhf+HMeJ4UbQ2RP4u6r+a7xQ\nRAZgIaI+AfxBRI7uQqzV14D3Yulc3kmUpi2A4/Rk3Ag6eyyqulFEzgceA44BrsJinu5OW83AiwmK\n192kHujacXoibgSdPRpVbRKRr2C5GK8gZgRF5OxQPg4YANRh6V1+oKr3R+qNIDYnGEdEPo0FEv+1\nqn4qz/6rsHQ201X1tvZkFpGHgZOwnue9wBHAq8BZqqphnu+zWKDu0UAzFpj8NlV9KE87ANeJyHXA\nJapaHfLIHQRUqermds5/lKo+E8pWYcO+U7B50BHYMPQE4LehfiWWfeEi4EAsCPXPsczs2yLtlwJf\nAD4NHBrafR6oBn7YA9IXOb0I9w51egN/xbLbHxzy+wEgIjcDc7AH+OLweQ1wMvB/wfElTkfzf78B\nNgFnhOwfcS4AWjDDUAgPAPsAc7Fh2BdDup97gR8BI4GHsWwVJwDzROTayPEP0TZX+nw4b3RetCNd\n4vuyQZY5QZb5wHpVrYnUmY0ZwVfC/iHAV7Eh6SjfxZIyH4hlDngEeB/2gnBnBzI5TuK4EXT2eMJQ\n5kpsSPA9ACJyEJbuaDXwHlU9U1X/RVUPB/4tHPq5Tp5nG/AroC+W6Xo7ITHyeODhdhIP56MeOFxV\nP6Gqh4fEqFdiqWUeDnKfpapnYIlE1wDfEZEjgzy3Aj8Obc1X1YtU9bECzx0fPs1gPeWFqnqUqk5S\n1VNjdY4F3q+qp6rqpPB/IzAl5IXLJRm+BjPKh6jqx1X1Y5gRfBO4QkTSzHTu9DLcCDq9hU1hm3vA\nDsRyIf67qq6P1c31XA7ajfPkEjnH889dELazOtHWT1W1MVZ2PdabvEhV384VquqLwHRsiuOaSP2k\n5wJ/1MG+/1bVFRGZVgCPBhkOC8VDw3ajqm6N1H0NG+K9CBvedZxuwecEnd5CedhmAVR1MTYntR0R\nqcTm4SaEoorOnkRVHxeRl4BTRGRQxMBOweYbZ7d/9E4sj8k3FBsCfSkYjTh/CtuT8uxLgmxcphhP\n5il7PWz7he1yoAY4QUT+CtwHzFXVNar6QGKSOk6BuBF0egsDwnZjrkBEyrEe2qeAw7E5qhLa5sN2\ntxc1E/gGZmTvEJFjsWHYn6tqfSfa2Rj7f1jYjhKRjpxHDuzEOTpLXKYom/KU5Xp1JQCqWi8i52Hz\nmieHP0RkGTaUfLeq5mvHcYqCG0Fnj0dE+gGHYMZtRSjrD/wNOAp7eC/EemlLsfm2V7pwylnA1wlG\nkLah0c4MhQLEDV1uzd9azKGkPbq6eL+jtYUdGd+CzquqfwzetpOAs4FTsDnNMcBVInKcqq4tUFbH\n6RJuBJ3ewOlYT+T5yPDkDZgBnA1cGHPhH7BzE4WjqqvDMoOTRWQI9rBfS9tw5e6yLmw3qOpFXWwr\nZ8zyGbyqLra9S0LQgnvDHyJyHOYZOg6YCny52DI4DrhjjLOHIyJltD1Qo676x4Xtd6MGMPDhsO2K\nU8lM7P66CXg3cG/w7txtVHUVZkwPiy71yCEix4rIChH5QaS4vXPmhmUHxdqowuZFixIKTkTOE5GV\nIjI9Wq6qTwK3hn+H7Xyk4xQHN4LOHouI7IcZo/cDzwJ3RXa/GrZnx44ZT9tatcounP5+zBHmCsyg\nVHehrSjfx+SqFpGBuUIROQAz8u9jx7WAOQO/b6yd5ZiRvzrSRjm2Vq+YodZWYAvtrxWRd0fOXYrN\nzQI8VcTzO84O+HCosydwkohEF6D3AQZjxq8SUGCiqjZF6twNXAJ8WUROxwzHiHDMfGx5xGEisreq\nbumsQKpaJyKzgYuBpdGlA13kdsyZ5HTgHyLyFLYW7yTMA3MuNg+Z46WwnRKGeX8avDDvxNYyXi0i\nJ2LrKMdjaxznAmflOXeXl1uo6rMicgdwHfCCiDyKZfw4Cvv+l9C2ttFxio73BJ13Mrkhu4OB8yN/\nZ2PemAuAz2Phv3ZwdFHVZZhDxl+w4bfTMU/GS4Ezgb+H9icWcP72WBi2ne0FZttrW1VbMP2uwWKZ\njgeOxxafXw2cEw07pqqLgFsw55+PAmND+RPAhzAnoJHAB7HoMuOAF/Kcv12ZdmPfDdi834og++lY\nRJ9vAB+Irh90nGKTyWZ7chYYx3nnIiJ/xHpow1T1jbTlcRxnZ7wn6DgJIiJ9wvY84FRgjhtAx+m5\n+Jyg4yTLvSJyBjYX2Qh8LV1xHMfpCO8JOk6yLMbmwBT4pKo+l7I8juN0gM8JOo7jOL0W7wk6juM4\nvRY3go7jOE6vxY2g4ziO02txI+g4juP0WtwIOo7jOL0WN4KO4zhOr+X/ATbX81iOvXWtAAAAAElF\nTkSuQmCC\n",
   1606       "text/plain": [
   1607        "<matplotlib.figure.Figure at 0x7fd8d5d4d910>"
   1608       ]
   1609      },
   1610      "metadata": {},
   1611      "output_type": "display_data"
   1612     }
   1613    ],
   1614    "source": [
   1615     "sns.distplot(data_1, label='data IB', kde=False, norm_hist=True, color='.5')\n",
   1616     "for p in ppc_dist_normal:\n",
   1617     "    plt.plot(x, p, c='r', alpha=.1)\n",
   1618     "plt.plot(x, p, c='r', alpha=.5, label='Normal model')\n",
   1619     "plt.xlabel('Daily returns')\n",
   1620     "plt.legend();"
   1621    ]
   1622   },
   1623   {
   1624    "cell_type": "markdown",
   1625    "metadata": {
   1626     "slideshow": {
   1627      "slide_type": "slide"
   1628     }
   1629    },
   1630    "source": [
   1631     "# Can it be improved? Yes!\n",
   1632     "\n",
   1633     "Identical model as before, but instead, use a heavy-tailed T distribution:\n",
   1634     "\n",
   1635     "$ \\text{returns} \\sim \\text{T}(\\nu, \\mu, \\sigma^2)$"
   1636    ]
   1637   },
   1638   {
   1639    "cell_type": "code",
   1640    "execution_count": 115,
   1641    "metadata": {
   1642     "collapsed": false,
   1643     "slideshow": {
   1644      "slide_type": "fragment"
   1645     }
   1646    },
   1647    "outputs": [
   1648     {
   1649      "data": {
   1650       "image/png": 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5sXYDB5u+8hBwdmuKLiIisjrLbR36PrIHtG8hux+dAt8iGz3gL4APWmsbQ/70kY2TV1Rl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\n",
   1651       "text/plain": [
   1652        "<matplotlib.figure.Figure at 0x7fd8d5a05310>"
   1653       ]
   1654      },
   1655      "metadata": {},
   1656      "output_type": "display_data"
   1657     }
   1658    ],
   1659    "source": [
   1660     "sns.distplot(data_1, label='data IB', kde=False, norm_hist=True, color='.5')\n",
   1661     "for p in ppc_dist_t:\n",
   1662     "    plt.plot(x, p, c='y', alpha=.1)\n",
   1663     "plt.plot(x, p, c='y', alpha=.5, label='T model')    \n",
   1664     "plt.xlabel('Daily returns')\n",
   1665     "plt.legend();"
   1666    ]
   1667   },
   1668   {
   1669    "cell_type": "markdown",
   1670    "metadata": {
   1671     "slideshow": {
   1672      "slide_type": "skip"
   1673     }
   1674    },
   1675    "source": [
   1676     "# Volatility"
   1677    ]
   1678   },
   1679   {
   1680    "cell_type": "code",
   1681    "execution_count": 116,
   1682    "metadata": {
   1683     "collapsed": false,
   1684     "slideshow": {
   1685      "slide_type": "skip"
   1686     }
   1687    },
   1688    "outputs": [
   1689     {
   1690      "data": {
   1691       "image/png": 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cyiqSloJWRFqu7l7H7v5vd/8KYfL1scBvCAP6/xyYamY9ZrZLNsUUqYuCVkRarqEhGM1s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\nIiIiOVLQioiI5Oj/AdBm4y09BrPzAAAAAElFTkSuQmCC\n",
   1692       "text/plain": [
   1693        "<matplotlib.figure.Figure at 0x7fd8d6cd52d0>"
   1694       ]
   1695      },
   1696      "metadata": {},
   1697      "output_type": "display_data"
   1698     }
   1699    ],
   1700    "source": [
   1701     "sns.distplot(results_normal[1]['annual volatility'], hist=False, label='normal')\n",
   1702     "sns.distplot(results_t[1]['annual volatility'], hist=False, label='T')\n",
   1703     "plt.xlim((0, 0.2))\n",
   1704     "plt.xlabel('Posterior of annual volatility')\n",
   1705     "plt.ylabel('Probability Density');"
   1706    ]
   1707   },
   1708   {
   1709    "cell_type": "markdown",
   1710    "metadata": {
   1711     "slideshow": {
   1712      "slide_type": "slide"
   1713     }
   1714    },
   1715    "source": [
   1716     "# Lets compare posteriors of the normal and T model"
   1717    ]
   1718   },
   1719   {
   1720    "cell_type": "markdown",
   1721    "metadata": {
   1722     "slideshow": {
   1723      "slide_type": "slide"
   1724     }
   1725    },
   1726    "source": [
   1727     "# Mean returns"
   1728    ]
   1729   },
   1730   {
   1731    "cell_type": "code",
   1732    "execution_count": 117,
   1733    "metadata": {
   1734     "collapsed": false,
   1735     "slideshow": {
   1736      "slide_type": "-"
   1737     }
   1738    },
   1739    "outputs": [
   1740     {
   1741      "data": {
   1742       "image/png": 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FBpI47lg56rvGp1aLWqQFdRuo3X0FYaUsAMzsC8Dd7n5dPSpiZlsQvhx8lNCS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\nKIUAAAAASUVORK5CYII=\n",
   1743       "text/plain": [
   1744        "<matplotlib.figure.Figure at 0x7fd8d643a290>"
   1745       ]
   1746      },
   1747      "metadata": {},
   1748      "output_type": "display_data"
   1749     }
   1750    ],
   1751    "source": [
   1752     "sns.distplot(results_normal[1]['mean returns'], hist=False, color='r', label='normal model')\n",
   1753     "sns.distplot(results_t[1]['mean returns'], hist=False, color='y', label='T model')\n",
   1754     "plt.xlabel('Posterior of the mean returns'); plt.ylabel('Probability Density');"
   1755    ]
   1756   },
   1757   {
   1758    "cell_type": "markdown",
   1759    "metadata": {
   1760     "slideshow": {
   1761      "slide_type": "slide"
   1762     }
   1763    },
   1764    "source": [
   1765     "# Bayesian T-Sharpe ratio"
   1766    ]
   1767   },
   1768   {
   1769    "cell_type": "code",
   1770    "execution_count": 118,
   1771    "metadata": {
   1772     "collapsed": false,
   1773     "slideshow": {
   1774      "slide_type": "-"
   1775     }
   1776    },
   1777    "outputs": [
   1778     {
   1779      "data": {
   1780       "image/png": 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6oAPM7CuECQ7+MNTCijwHfAwgGX17DHAq8CCwJ7CHu/8nw8+T9lbJ470A5gLz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\nOI5TBq4wHcdxHKcM/h9ZEUJ3RmRPJwAAAABJRU5ErkJggg==\n",
   1781       "text/plain": [
   1782        "<matplotlib.figure.Figure at 0x7fd8d68dc1d0>"
   1783       ]
   1784      },
   1785      "metadata": {},
   1786      "output_type": "display_data"
   1787     }
   1788    ],
   1789    "source": [
   1790     "sns.distplot(results_normal[1]['sharpe'], hist=False, color='r', label='normal model')\n",
   1791     "sns.distplot(results_t[1]['sharpe'], hist=False, color='y', label='T model')\n",
   1792     "plt.xlabel('Bayesian Sharpe ratio'); plt.ylabel('Probability Density');"
   1793    ]
   1794   },
   1795   {
   1796    "cell_type": "markdown",
   1797    "metadata": {
   1798     "slideshow": {
   1799      "slide_type": "slide"
   1800     }
   1801    },
   1802    "source": [
   1803     "# But why? T distribution is more robust!"
   1804    ]
   1805   },
   1806   {
   1807    "cell_type": "code",
   1808    "execution_count": 119,
   1809    "metadata": {
   1810     "collapsed": false
   1811    },
   1812    "outputs": [
   1813     {
   1814      "data": {
   1815       "image/png": 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A8vlk1dfkCoXR6k/X5OYBhZyIhM1oBZbPp6ZQySVVyc0jCjkRCZvRcMpmU1Oo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\nYRhFy/8H6O8TF+0CqsQAAAAASUVORK5CYII=\n",
   1816       "text/plain": [
   1817        "<matplotlib.figure.Figure at 0x7fd8d66b1550>"
   1818       ]
   1819      },
   1820      "metadata": {},
   1821      "output_type": "display_data"
   1822     }
   1823    ],
   1824    "source": [
   1825     "sim_data = list(np.random.randn(75)*.01)\n",
   1826     "sim_data.append(-.2)\n",
   1827     "sns.distplot(sim_data, label='data', kde=False, norm_hist=True, color='.5'); sns.distplot(sim_data, label='Normal', fit=stats.norm, kde=False, hist=False, fit_kws={'color': 'r', 'label': 'Normal'}); sns.distplot(sim_data, fit=stats.t, kde=False, hist=False, fit_kws={'color': 'y', 'label': 'T'})\n",
   1828     "plt.xlabel('Daily returns'); plt.legend();"
   1829    ]
   1830   },
   1831   {
   1832    "cell_type": "markdown",
   1833    "metadata": {
   1834     "slideshow": {
   1835      "slide_type": "slide"
   1836     }
   1837    },
   1838    "source": [
   1839     "# Estimating tail risk using VaR"
   1840    ]
   1841   },
   1842   {
   1843    "cell_type": "code",
   1844    "execution_count": 120,
   1845    "metadata": {
   1846     "collapsed": false
   1847    },
   1848    "outputs": [
   1849     {
   1850      "data": {
   1851       "image/png": 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x9RngceBg4KRaBSgiUif16y4JtCCXdL08LRlnEaax7uvuN7r7i9lCd38Q+CCw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\n",
   1852       "text/plain": [
   1853        "<matplotlib.figure.Figure at 0x7fd8d538dc90>"
   1854       ]
   1855      },
   1856      "metadata": {},
   1857      "output_type": "display_data"
   1858     }
   1859    ],
   1860    "source": [
   1861     "ppc_normal = post_pred(var_cov_var_normal, results_normal[1], 1e6, .05, samples=800)\n",
   1862     "ppc_t = post_pred(var_cov_var_t, results_t[1], 1e6, .05, samples=800)\n",
   1863     "sns.distplot(ppc_normal, label='Normal', norm_hist=True, hist=False, color='r')\n",
   1864     "sns.distplot(ppc_t, label='T', norm_hist=True, hist=False, color='y')\n",
   1865     "plt.legend(loc=0); plt.xlabel('5% daily Value at Risk (VaR) with \\$1MM capital (in \\$)'); plt.ylabel('Probability density'); plt.xticks(rotation=15);"
   1866    ]
   1867   },
   1868   {
   1869    "cell_type": "markdown",
   1870    "metadata": {
   1871     "slideshow": {
   1872      "slide_type": "slide"
   1873     }
   1874    },
   1875    "source": [
   1876     "# Comparing the Bayesian T-Sharpe ratios"
   1877    ]
   1878   },
   1879   {
   1880    "cell_type": "code",
   1881    "execution_count": 121,
   1882    "metadata": {
   1883     "collapsed": false
   1884    },
   1885    "outputs": [
   1886     {
   1887      "data": {
   1888       "image/png": 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KK/ptuVu7fUWvdXtXRGJHQSpRGrFF2tvV/UHRzzvrXZCISFAKUolSJbd2QR2ORCTGFKQS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\n",
   1889       "text/plain": [
   1890        "<matplotlib.figure.Figure at 0x7fd8d66dbad0>"
   1891       ]
   1892      },
   1893      "metadata": {},
   1894      "output_type": "display_data"
   1895     }
   1896    ],
   1897    "source": [
   1898     "sns.distplot(results_t[0]['sharpe'], hist=False, label='etrade')\n",
   1899     "sns.distplot(results_t[1]['sharpe'], hist=False, label='IB')\n",
   1900     "plt.xlabel('Bayesian Sharpe ratio'); plt.ylabel('Probability Density');"
   1901    ]
   1902   },
   1903   {
   1904    "cell_type": "code",
   1905    "execution_count": 122,
   1906    "metadata": {
   1907     "collapsed": false
   1908    },
   1909    "outputs": [
   1910     {
   1911      "name": "stdout",
   1912      "output_type": "stream",
   1913      "text": [
   1914       "P(Sharpe ratio IB > Sharpe ratio etrade) = 5.68%\n"
   1915      ]
   1916     }
   1917    ],
   1918    "source": [
   1919     "print 'P(Sharpe ratio IB > Sharpe ratio etrade) = %.2f%%' % \\\n",
   1920     "    (np.mean(results_t[1]['sharpe'] > results_t[0]['sharpe']) * 100)"
   1921    ]
   1922   },
   1923   {
   1924    "cell_type": "markdown",
   1925    "metadata": {
   1926     "internals": {
   1927      "frag_helper": "fragment_end",
   1928      "frag_number": 31,
   1929      "slide_helper": "subslide_end",
   1930      "slide_type": "subslide"
   1931     },
   1932     "slide_helper": "slide_end",
   1933     "slideshow": {
   1934      "slide_type": "slide"
   1935     }
   1936    },
   1937    "source": [
   1938     "Conclusions\n",
   1939     "===========\n",
   1940     "\n",
   1941     "* **Probabilistic Programming** allows us to construct **complex models** in code and **automatically** estimate them.\n",
   1942     "* **Bayesian statistics** provides us with **uncertainty quantification** -- measure orthogonal sources of **risk**.\n",
   1943     "* **PyMC3** puts **advanced samplers** at your fingertips."
   1944    ]
   1945   },
   1946   {
   1947    "cell_type": "markdown",
   1948    "metadata": {
   1949     "internals": {
   1950      "frag_helper": "fragment_end",
   1951      "frag_number": 31,
   1952      "slide_helper": "subslide_end",
   1953      "slide_type": "subslide"
   1954     },
   1955     "slide_helper": "slide_end",
   1956     "slideshow": {
   1957      "slide_type": "slide"
   1958     }
   1959    },
   1960    "source": [
   1961     "# Further reading\n",
   1962     "\n",
   1963     "* [Quantopian](https://www.quantopian.com) -- Develop trading algorithms like this in your browser.\n",
   1964     "* [My blog for Bayesian linear regression (financial alpha and beta)](https://twiecki.github.io)\n",
   1965     "* [Probilistic Programming for Hackers](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/) -- IPython Notebook book on Bayesian stats using PyMC2.\n",
   1966     "* [Doing Bayesian Data Analysis](http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/) -- Great book by Kruschke.\n",
   1967     "* [PyMC3 repository](https://github.com/pymc-devs/pymc3)\n",
   1968     "* Twitter: [@twiecki](https://twitter.com/twiecki)"
   1969    ]
   1970   }
   1971  ],
   1972  "metadata": {
   1973   "celltoolbar": "Slideshow",
   1974   "kernelspec": {
   1975    "display_name": "Python 2",
   1976    "language": "python",
   1977    "name": "python2"
   1978   },
   1979   "language_info": {
   1980    "codemirror_mode": {
   1981     "name": "ipython",
   1982     "version": 2
   1983    },
   1984    "file_extension": ".py",
   1985    "mimetype": "text/x-python",
   1986    "name": "python",
   1987    "nbconvert_exporter": "python",
   1988    "pygments_lexer": "ipython2",
   1989    "version": "2.7.8"
   1990   }
   1991  },
   1992  "nbformat": 4,
   1993  "nbformat_minor": 0
   1994 }