ml-finance-python

notebook.ipynb

(487120B)

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     "# Discrete and Continuous Random Variables\n",
     "by Maxwell Margenot\n",
     "\n",
     "Revisions by Delaney Granizo Mackenzie\n",
     "\n",
     "Part of the Quantopian Lecture Series:\n",
     "www.quantopian.com/lectures\n",
     "github.com/quantopian/research_public\n",
     "\n",
     "A random variable is variable that takes on values according to chance. When discussing random variables, we typically describe them in terms of probability distributions. That is, the probability that each value can come out of the random variable. The classic example of this is a die, which can produce the values 1-6 with uniform probability.\n",
     "\n",
     "We typically separate random variables into two different classes:\n",
     "\n",
     "* Discrete random variables\n",
     "* Continuous random variables\n",
     "\n",
     "How each of these is handled varies, but the principles underlying them remain the same. We can easily see how modeling random variables can come in handy when dealing with finance; financial assets are often expressed as moving according to deterministic and random patterns, with the random patterns being expressed with random variables. To do this we would 'sample' from the random variable at each timestep, then move the financial instrument by that amount. This analysis is used because much of the motion in assets is unexplained using determinstic models.\n",
     "\n",
     "Each random variable follows a **probability distribution**, a function which describes it. The probability distribution assigns probabilities to all possible values of a random variable. For a given random variable $X$, we express the probability that $X$ is equal to a value $x$ as $P(X = x)$. For discrete random variables, we can express $p(x) = P(X = x)$ in shorthand. This is also known as the **probability mass function** (PMF). For continuous random variables we cannot use a PMF, as we will cover later, so we must use a **probability density function** (PDF). Probability distributions form the basis for the Black-Scholes and binomial pricing models as well as the CAPM. An understanding of them is also necessary in order to perform Monte Carlo simulations.\n",
     "\n",
     "For each probability distribution function, we also have a **cumulative distribution function** (CDF). This is defined as $P(X \\leq x)$, the probability that the random variable is less than or equal to a particular value. The shorthand for the CDF is $F(x) = P(X \\leq x)$. In order to find $F(x)$ in the discrete case, we sum up the values of the PMF for all outcomes less than or equal to $x$. In the continuous case, we use calculus to integrate the PDF over all values up to $x$."
    ]
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   {
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    "source": [
     "import pandas as pd\n",
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
     "import statsmodels.stats as stats\n",
     "from statsmodels.stats import stattools\n",
     "from __future__ import division"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Discrete Random Variables\n",
     "A discrete random variable is one with a countable number of outcomes. Each of these outcomes has a separate probability associated with it. Consider a coin flip or a die roll, some of the most basic uniformly distributed random variables. For the coin flip, there are two possible outcomes, either heads or tails, each with a $1/2$ probability of occurring. Discrete random variables do not always have equal weights for all outcomes. The basic unit of a discrete random variable is its **probability mass function** (PMF), another name for the probability function $p(x)$. The PMF, or probability function, gives a probability, a mass, to each point in the domain of the probability distribution. A probability function has two main properties:\n",
     "\n",
     "1. $0 \\leq p(x) \\leq 1$ because all probabilities are in the interval $[0, 1]$\n",
     "2. The sum of all probabilities $p(x)$ over all values of X is equal to $1$. The total weights for all values of the random variable must add to $1$.\n",
     "\n",
     "Here we will consider some examples of the most prevalent discrete probability distributions."
    ]
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    "source": [
     "class DiscreteRandomVariable:\n",
     "    def __init__(self, a=0, b=1):\n",
     "        self.variableType = \"\"\n",
     "        self.low = a\n",
     "        self.high = b\n",
     "        return\n",
     "    def draw(self, numberOfSamples):\n",
     "        samples = np.random.random_integers(self.low, self.high, numberOfSamples)\n",
     "        return samples"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Uniform Distribution\n",
     "The most basic type of probability distribution is the uniform distribution. With a discrete uniform distribution, equal weight is assigned to all outcomes. Take the example of rolling a die. It has six faces, numbered $1$ through $6$, each equally likely to occur with a $1/6$ chance each. With this, we know the the PMF must be $p(x) = 1/6$ for all values of our uniform random variable $X$."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 3,
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    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
       "/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:8: DeprecationWarning: This function is deprecated. Please call randint(1, 6 + 1) instead\n",
       "  \n"
      ]
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CAABAcYQQAABQHCEEAAAURwgBAADFEUIAAEBxhBAAAFAcIQQAABRHCAEAAMURQgAAQHGE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\nRU5ErkJggg==\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefcbb6ce10>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "DieRolls = DiscreteRandomVariable(1, 6)\n",
     "plt.hist(DieRolls.draw(10), bins = [1,2,3,4,5,6,7], align = 'mid')\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Occurences')\n",
     "plt.legend(['Die Rolls']);"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Each time we roll the die, we have an equal chance of getting each face. In the short run this looks uneven, but if we take many samples it is apparent that each face is occurring the same percentage of rolls."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
    "metadata": {
     "collapsed": false,
     "scrolled": false
    },
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
       "/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:8: DeprecationWarning: This function is deprecated. Please call randint(1, 6 + 1) instead\n",
       "  \n"
      ]
     },
     {
      "data": {
       "image/png": 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bq6OhoSHf/e53Ox6ffvrpWbBgQXbs2JHPfe5z2bp1ayoqKrJq1apceeWVeemll7JkyZKM\nGDEiDz74YE4++eTuHJceqrqyqtwjAADQw3VpKK1ZsyazZs3Khg0bUl1dnaVLl+YrX/lK+vbtm+S3\n1x0lv73pw/Tp0zN16tRUVlZm2rRp6dOnT8aMGZNHH300EydOTE1NTWbNmtWV4wIAACTp4lAaOHBg\nFixY8LrP/+AHP+j4ubGxMY2NjXs8X1lZmZkzZ3bZfAAAAL9Pt9/MAQAAYF8nlAAAAAqEEgAAQIFQ\nAgAAKBBKAAAABUIJAACgQCgBAAAUCCUAAIACoQQAAFAglAAAAAqEEgAAQIFQAgAAKBBKAAAABUIJ\nAACgQCgBAAAUCCUAAIACoQQAAFAglAAAAAqEEgAAQIFQAgAAKBBKAAAABUIJAACgQCgBAAAUCCUA\nAIACoQQAAFAglAAAAAqEEgAAQIFQAgAAKBBKAAAABUIJAACgQCgBAAAUCCUAAIACoQQAAFAglAAA\nAAqEEgAAQIFQAgAAKBBKAAAABUIJAACgQCgBAAAUCCUAAIACoQQAAFDQ5aG0du3ajB49OgsXLkyS\n/Od//mc+9rGPpampKVOnTs2mTZuSJIsXL87YsWMzfvz43HPPPUmS9vb2XHTRRZk4cWKampqyfv36\nrh4XAACga0Opra0tM2bMyPDhwzvWZs+enQkTJmTBggX5i7/4i/yf//N/0tbWljlz5mTevHmZP39+\n5s2blxdffDH3339/+vXrlzvvvDPnn39+brzxxq4cFwAAIEkXh1JNTU3mzp2b+vr6jrUvfOELaWxs\nTJLU1dVl8+bNWb16dQYNGpTa2trU1NRkyJAhWbFiRZYvX54zzjgjSXLKKadk5cqVXTkuAABAki4O\npcrKyvTu3XuPtYMOOigVFRXZvXt37rzzzvzVX/1VWltbU1dX17FNXV1dWlpa9livqKhIZWVl2tvb\nu3JkAACA8tzMYffu3bn44oszfPjw/Omf/ulrni+VSq/7Ongz7bt3lXsEAAB6uLKE0uWXX55jjz02\nF1xwQZKkvr4+LS0tHc83NzenoaEh9fX1aW1tTZKOI0nV1dXdPzA9SnVlVblHAACgh+v2UFq8eHF6\n9+6dT37ykx1rH/jAB/LUU09l69at2bZtW1atWpWhQ4dmxIgRWbJkSZLkwQcfzMknn9zd4wIAAAeg\nLj08s2bNmsyaNSsbNmxIdXV1li5dmhdeeCG9e/dOU1NTKioqctxxx+Wqq67K9OnTM3Xq1FRWVmba\ntGnp06dPxowZk0cffTQTJ05MTU1NZs2a1ZXjAgAAJOniUBo4cGAWLFjQqW0bGxs77ob3qsrKysyc\nObMrRgMAAHhdZblGCQAAYF8mlAAAAAqEEgAAQIFQAgAAKBBKAAAABUIJAACgQCgBAAAUCCUAAIAC\noQQAAFAglAAAAAqEEgAAQIFQAgAAKBBKAAAABUIJAACgQCgBAAAUCCUAAIACoQQAAFAglAAAAAqE\nEgAAQIFQAgAAKBBKAAAABUIJAACgQCgBAAAUCCUAAIACoQQAAFAglAAAAAqEEgAAQIFQAgAAKBBK\nAAAABUIJAACgQCgBAAAUCCUAAIACoQQAAFAglAAAAAqEEgAAQIFQAgAAKBBKAAAABUIJAACgQCgB\nAAAUCCUAAIACoQQAAFDQ5aG0du3ajB49OgsXLkySPP/882lqasrkyZPz2c9+Nq+88kqSZPHixRk7\ndmzGjx+fe+65J0nS3t6eiy66KBMnTkxTU1PWr1/f1eMCAAB0bSi1tbVlxowZGT58eMfa7Nmz09TU\nlDvuuCPvete7cu+996atrS1z5szJvHnzMn/+/MybNy8vvvhi7r///vTr1y933nlnzj///Nx4441d\nOS4AAECStxBKW7duTZK0trbmRz/6UXbv3v2mr6mpqcncuXNTX1/fsfb4449n1KhRSZJRo0Zl2bJl\nWb16dQYNGpTa2trU1NRkyJAhWbFiRZYvX54zzjgjSXLKKadk5cqVb+mXAwAA2BudCqUvfvGLeeCB\nB7J58+ZMmDAhCxYsyBe+8IU3f/PKyvTu3XuPtba2tvTq1StJ0r9//2zcuDGbNm1KXV1dxzZ1dXVp\naWlJa2trx3pFRUUqKyvT3t7e2d8NAABgr3QqlH76059m3LhxeeCBB3LOOedk9uzZefbZZ//gnZdK\npbe03pmjWNC+e1e5RwAAoIfrVCi9Gi4//OEPc/rppydJdu7cuVc7rK2t7Xhtc3NzGhoaUl9fn5aW\nlo5tfne9tbU1STqOJFVXV+/VfjlwVFdWlXsEAAB6uE6F0rHHHpsxY8Zk27Zted/73pf77rsv/fr1\n26sdDh8+PEuXLk2SLF26NCNHjsygQYPy1FNPZevWrdm2bVtWrVqVoUOHZsSIEVmyZEmS5MEHH8zJ\nJ5+8V/sEAAB4Kzp1eGbGjBlZu3ZtBgwYkCQ57rjjcv3117/p69asWZNZs2Zlw4YNqa6uztKlS/Ol\nL30pl112Wb7xjW/kyCOPzDnnnJOqqqpMnz49U6dOTWVlZaZNm5Y+ffpkzJgxefTRRzNx4sTU1NRk\n1qxZf9hvCwAA0AmdCqWtW7dm8eLFaW1tzQ033JCNGzfmyCOPfNPXDRw4MAsWLHjN+m233faatcbG\nxjQ2Nu6xVllZmZkzZ3ZmRAAAgD+aTp1697nPfS5HHHFEfv3rXyf57fVJl156aZcOBgAAUC6dCqUX\nXnghU6ZM6bit91/+5V/m5Zdf7tLBAAAAyqXTXzj7yiuvpKKiIslvv3R2+/btXTYUAABAOXXqGqXJ\nkydn7NixaWlpyfnnn58nn3wyV155ZVfPBgAAUBadCqWzzjorgwcPzqpVq9K7d+9ce+21qa+v7+rZ\nAAAAyqJTp9794he/yMKFC3PWWWflL/7iL3LTTTdl7dq1XT0bAABAWXQqlK655pqcdtppHY/PPffc\nfPGLX+yyoQAAAMqpU6G0a9eufPCDH+x4/MEPfjClUqnLhgIAACinTl2jdMghh+TOO+/MySefnN27\nd+eRRx5JbW1tV88GAABQFp0KpZkzZ+bGG2/M17/+9STJ4MGDM3PmzC4dDAAAoFw6FUp1dXX5h3/4\nh66eBQAAYJ/QqVC6//77M3fu3GzZsmWPa5N++MMfdtVcAAAAZdOpUPrnf/7nzJgxI0ceeWRXzwMA\nAFB2nQqld7/73fnQhz7U1bMAAADsEzoVSoMHD87/+l//K8OGDUtVVVXH+vDhw7tsMAAAgHLpVCgt\nW7YsSbJq1aqOtYqKCqEEAADslzoVSgsWLEiSlEqlVFRUdOlAAAAA5VbZmY1+9rOf5SMf+UjOOuus\nJMnNN9+c1atXd+lgAAAA5dKpULr22mvzj//4jzn88MOTJGPGjPGFswAAwH6rU6FUXV2d448/vuPx\nsccem+rqTp21BwAA0ON0OpR+/etfd1yf9PDDD+/xxbMAAAD7k04dFrr00ktzwQUX5JlnnsnQoUNz\n1FFH5frrr+/q2QAAAMqiU6F06KGH5tvf/nZeeOGF9O7dO3369OnquQAAAMqmU6feXXTRRUmSuro6\nkQQAAOz3OnVE6Zhjjskll1ySwYMHp1evXh3rY8eO7bLBAAAAyqVTofTKK6+kqqoqP/nJT/ZYF0oA\nAMD+qFOh5DuTAACAA0mnQum0007ruDX47/rhD3/4x54HAACg7DoVSnfeeWfHz6+88kqWL1+el19+\nucuGAgAAKKdOhdJRRx21x+NjjjkmH//4x/Oxj32sS4YCAAAop06F0vLly/d4/Pzzz+dXv/pVlwwE\nAABQbp0KpTlz5nT8XFFRkT59+uSaa67psqEAAADKqVOhtGDBgrz00ks55JBDkiStra057LDDunQw\nAACAcqnszEYLFy7MpZde2vH47//+73PHHXd02VAAAADl1KlQWrx4cb785S93PL7tttty//33d9lQ\nAAAA5dSpUNq1a1eqq//rLL2KioqUSqUuGwoAAKCcOnWN0umnn54JEyZk6NCh2b17d/793/89jY2N\nXT0bAABAWXQqlC644IIMGzYsP/nJT1JRUZGrr746J510UlfPBgAAUBadCqWNGzfmpz/9aaZOnZok\nuemmm3LEEUekoaGhS4cDAAAoh05do3T55ZfvcTvw9773vbniiiu6bCgAAIBy6tQRpZ07d2bMmDEd\nj8eMGZNFixbt1Q63b9+eSy+9NFu2bMkrr7ySCy+8MIcddli+8IUvpLKyMu9973tz9dVXJ0nmzp2b\npUuXprKyMhdccEFOO+20vdonAADAW9GpUEqSf/3Xf82wYcOye/fuPPLII3u9w29+85t5z3vek89+\n9rNpaWnJlClTUl9fn89//vMZOHBgpk+fnkceeSTHHntsHnjggdx1113ZsmVLJk2alFNPPTUVFRV7\nvW8AAIDO6NSpdzNmzMhtt92WU045JSNHjszdd9+dL37xi3u1w0MPPTS/+c1vkiSbN2/O29/+9qxf\nvz4DBw5M8ts77C1btiyPPfZYTj311FRVVaWuri5HHXVUfvGLX+zVPgEAAN6KNw2l5cuX5/LLL8+P\nf/zjlEqlnHDCCbnwwgvz7ne/e692OGbMmGzYsCGNjY1pamrKJZdckn79+nU8X1dXl40bN2bTpk2p\nq6vbY72lpWWv9gkAAPBWvOGpd9/5zncyZ86c/P3f/33H7cCffPLJXHPNNfnUpz6V008//S3vcPHi\nxTnyyCMzd+7c/PznP8+FF16Yvn37vunrfMEtndW+e1d6lXsIAAB6tDcMpdtvvz3/+3//7xxxxBEd\na6eddlre97735dOf/vRehdLKlSszcuTIJL+9e97LL7+cXbt2dTzf3NychoaG1NfX5+mnn95jvb6+\n/i3vjwNPdWVVuUc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       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefce35db90>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "plt.hist(DieRolls.draw(10000), bins = [1,2,3,4,5,6,7], align = 'mid')\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Occurences')\n",
     "plt.legend(['Die Rolls']);"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "So with a die roll, we can easily see illustrated that the $p(x) = 1/6$ for all values of the random variable $X$. Let's look at the possibilities for all values of both the probability function and the cumulative distribution function:\n",
     "\n",
     "Value: $X = x$ | PMF: $p(x) = P(X = x)$ | CDF: $F(x) = P(X \\leq x)$ |\n",
     "--- | --- | --- | \n",
     "1 | $1/6$ | $1/6$\n",
     "2 | $1/6$ | $1/3$\n",
     "3 | $1/6$ | $1/2$\n",
     "4 | $1/6$ | $2/3$\n",
     "5 | $1/6$ | $5/6$\n",
     "6 | $1/6$ | $1$\n",
     "\n",
     "Using this table we can easily see that the probability function satisfies the necessary conditions. Each value of the probability function is in the interval $[0,1]$, satisfying the first condition. The second condition is satisfied because all values of $p(x)$ sum to $1$, as evidenced in the cumulative distribution function. The demonstrates two properties of the cumulative distribution function:\n",
     "\n",
     "1. The CDF is between $0$ and $1$ for all $x$. This parallels the value of the probability distribution function.\n",
     "2. The CDF is nondecreasing in $x$. This means that as $x$ increases, the CDF either increases or remains constant.\n",
     "\n",
     "When attempting to sample other probability distributions, we can use compositions of the uniform distribution with certain functions in order to get the appropriate samples. However, this method can be tremendously inefficient. As such, we will instead use the built-in NumPy functions for each distribution to simplify matters."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Binomial Distribution\n",
     "A binomial distribution is used to describe successes and failures. This can be very useful in an investment context as many of our choices tend to be binary like this. When we take a single success/failure trial, we call it a Bernoulli trial. With the Bernoulli random variable, we have two possible outcomes:\n",
     "\n",
     "$$p(1) = P(Y = 1) = p \\ \\ \\ \\ \\ \\ \\\n",
     "p(0) = P(Y = 0) = 1-p$$\n",
     "\n",
     "We consider $Y$ taking on a value of $1$ to be a success, so the probability of a success occurring in a single trial is $p$.\n",
     "\n",
     "A binomial distribution takes a set of $n$ Bernoulli trials. As such, we can have somewhere between $0$ and $n$ successes. Each trial has the same probability of success, $p$, and all of the trials are independent of each other. We can describe the entire binomial random variable using only $n$ and $p$, signified by the notation $X$ **~** $B(n, p)$. This states that $X$ is a binomial random variable with parameters $n$ and $p$.\n",
     "\n",
     "In order to define the probability function of a binomial random variable, we must be able to choose some number of successes out of the total number of trials. This idea lends itself easily to the combination idea in combinatorics. A combination describes all possible ways of selecting items out of a collection such that order does not matter. For example, if we have $6$ pairs of socks and we want to choose $2$ of them, we would write the total number of combinations possible as $\\binom{6}{2}$. This is expanded as:\n",
     "\n",
     "$$\n",
     "\\binom{6}{2} = \\frac{6!}{4! \\ 2!} = 15\n",
     "$$\n",
     "\n",
     "Where $!$ denotes factorial and $n! = (n)(n-1)(n-2)\\ldots (1)$. In order to write the formula for a combination more generally, we write:\n",
     "\n",
     "$$\n",
     "\\binom{n}{x} = \\frac{n!}{(n-x)! \\ x!}\n",
     "$$\n",
     "\n",
     "We use this notation in order to choose successes with our binomial random variable. The combination serves the purpose of computing how many different ways we can reach the same result. The resulting probability function is:\n",
     "\n",
     "$$\n",
     "p(x) = P(X = x) = \\binom{n}{x}p^x(1-p)^{n-x} = \\frac{n!}{(n-x)! \\ x!} p^x(1-p)^{n-x}\n",
     "$$\n",
     "\n",
     "If $X$ is a binomial random variable distributed with $B(n, p)$."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 5,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
    "source": [
     "class BinomialRandomVariable(DiscreteRandomVariable):\n",
     "    def __init__(self, numberOfTrials = 10, probabilityOfSuccess = 0.5):\n",
     "        self.variableType = \"Binomial\"\n",
     "        self.numberOfTrials = numberOfTrials\n",
     "        self.probabilityOfSuccess = probabilityOfSuccess\n",
     "        return\n",
     "    def draw(self, numberOfSamples):\n",
     "        samples = np.random.binomial(self.numberOfTrials, self.probabilityOfSuccess, numberOfSamples)\n",
     "        return samples"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Take the example of a stock price moving up or down, each with probability $p = 0.5$. We can consider a move up, or $U$, to be a success and a move down, or $D$ to be a failure. With this, we can analyze the probability of each event using a binomial random variable. We will also consider an $n$-value of $5$ for $5$ observations of the stock price over time. The following table shows the probability of each event:\n",
     "\n",
     "Number of Up moves, $x$ | Ways of reaching $x$ Up moves $\\binom{n}{x}$ | Independent Trials with $p = 0.50$ | $p(x)$ Value | CDF: $F(x) = P(X \\leq x)$ |\n",
     "--- | --- | --- | --- | --- | \n",
     "$0$ | $1$ | $0.50^0 (1 - 0.50)^5 = 0.03125$ | $0.03125$ | $0.03125$\n",
     "$1$ | $5$ | $0.50^1 (1 - 0.50)^4 = 0.03125$ | $0.15635$ | $0.18750$\n",
     "$2$ | $10$ | $0.50^2 (1 - 0.50)^3 = 0.03125$ | $0.31250$ | $0.50000$\n",
     "$3$ | $10$ | $0.50^3 (1 - 0.50)^2 = 0.03125$ | $0.31250$ | $0.81250$\n",
     "$4$ | $5$ | $0.50^4 (1 - 0.50)^1 = 0.03125$ | $0.15635$ | $0.96875$\n",
     "$5$ | $1$ | $0.50^5 (1 - 0.50)^0 = 0.03125$ | $0.03125$ | $1.00000$\n",
     "\n",
     "Here we see that in the particular case where $p = 0.50$, the binomial distribution is symmetric. Because we have an equal probability for both an upward and a downward move, the only differentiating factor between probabilities ends up being the combination aspect of the probability function, which is itself symmetric. If we were to slightly modify the value of $p$ we would end up with an asymmetric distribution.\n",
     "\n",
     "Now we will draw some samples for the parameters above, where $X$ **~** $B(5, 0.50)$:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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DAAAUQfwAAABFED8AAEARxA8AAFAE8QMAABRB/AAAAEUQPwAAQBHEDwAAUATx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\ngz/O00JvAAAAAElFTkSuQmCC\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc98011d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "StockProbabilities = BinomialRandomVariable(5, 0.50)\n",
     "plt.hist(StockProbabilities.draw(50), bins = [0, 1, 2, 3, 4, 5, 6], align = 'left')\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Occurences')\n",
     "plt.legend(['Die Rolls']);"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Again, as in all cases of sampling, the more samples that you take, the more consistent your resulting distribution looks:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 7,
    "metadata": {
     "collapsed": false,
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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lzjjjjCTJqaeemueff76UcwEAAJKUOJQqKyvTt2/f3Y5t27Ytffr0SZIMGjQo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\nYII=\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc9745810>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "plt.hist(StockProbabilities.draw(10000), bins = [0, 1, 2, 3, 4, 5, 6], align = 'left')\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Occurences');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Say that we changed our parameters so that $p = 0.25$. This makes it so that $P(X = 0) = 0.23730$, skewing our distribution much more towards lower values. We can see this easily in the following graph:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 8,
    "metadata": {
     "collapsed": false,
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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UyD3sLw/+2c9+Ns8//3yS5IknnsjIkSPT3Nycjo6O7Nq1K7t378769eszduzY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\nQmCC\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc97c6410>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "StockProbabilities = BinomialRandomVariable(5, 0.25)\n",
     "plt.hist(StockProbabilities.draw(10000), bins = [0, 1, 2, 3, 4, 5, 6], align = 'left')\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Occurences');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Changing the value of $p$ from $0.50$ to $0.25$ clearly makes our distribution asymmetric. We can extend this idea of stock price moving with a binomial random variable into a framework that we call the Binomial Model of Stock Price Movement. This is used as one of the foundations for option pricing. In the Binomial Model, it is assumed that for any given time period a stock price can move up or down by a value determined by the up or down probabilities. This turns the stock price into the function of a binomial random variable, the magnitude of upward or downward movement, and the initial stock price. We can vary these parameters in order to approximate different stock price distributions."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Continuous Random Variables\n",
     "Continuous random variables differ from discrete random variables in that continuous ones can take infinitely many outcomes. They cannot be counted or described as a list. As such, it means very little when we assign individual probabilities to outcomes. Because there are infinitely many outcomes, the probability of hitting any individual outcome has a probability of 0.\n",
     "\n",
     "We can resolve this issue by instead taking probabilities across ranges of outcomes. This is managed by using calculus, though in order to use our sampling techniques here we do not actually have to use any. With a continuous random variable $P(X = 0)$ is meaningless. Instead we would look for something more like $P(-1 < X < 1)$. For continous random variables, rather than using a PMF, we define a **probability density function** (PDF), $f_X(x)$, such that we can say:\n",
     "$$P(a < X < b) = \\int_a^b f_X(x)dx$$\n",
     "\n",
     "Similar to our requirement for discrete distributions that all probabilities add to $1$, here we require that:\n",
     "\n",
     "1. $f_X(x) \\geq 0$ for all values of $X$\n",
     "2. $P(-\\infty < X < \\infty) = \\int_{-\\infty}^{\\infty} f_X(x) dx = 1$\n",
     "\n",
     "It is worth noting that because the probability at an individual point with a continuous distribution is $0$, the probabilities at the endpoints of a range are $0$. Hence, $P(a \\leq X \\leq b) = P(a < X \\leq b) = P(a \\leq X < B) = P(a < X < b)$. If we integrate the PDF across all possibilities, over the total possible range, the value should be $1$."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 9,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "class ContinuousRandomVariable:\n",
     "    def __init__(self, a = 0, b = 1):\n",
     "        self.variableType = \"\"\n",
     "        self.low = a\n",
     "        self.high = b\n",
     "        return\n",
     "    def draw(self, numberOfSamples):\n",
     "        samples = np.random.uniform(self.low, self.high, numberOfSamples)\n",
     "        return samples\n"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Uniform Distribution\n",
     "The uniform distribution can also be defined within the framework of a continous random variable. We take $a$ and $b$ to be constant, where $b$ is the highest possible value and $a$ is the lowest possible value that the outcome can obtain. Then the PDF of a uniform random variable is:\n",
     "\n",
     "$$f(x) = \\begin{cases}\\frac{1}{b - a} & \\text{for $a < x < b$} \\ 0 & \\text{otherwise}\\end{cases}$$\n",
     "\n",
     "Since this function is defined on a continuous interval, the PDF covers all values between $a$ and $b$. Here we have a plot of the PDF (feel free to vary the values of $a$ and $b$):"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 10,
    "metadata": {
     "collapsed": false,
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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AAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAABaIJAACgQDQBAAAUiCYA\nAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAABaIJAACgQDQBAAAUiCYAAIAC0QQAAFAgmgAA\nAApEEwAAQIFoAgAAKBBNAAAABaIJAACgQDQBAAAUiCYAAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAA\nKBBNAAAABaIJAACgQDQBAAAUiCYAAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAABaIJAACg\nQDQBAAAUiCYAAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAABf3r/Q3mzZuXBx54IJVKJXPm\nzMm4ceNqx3p6etLW1pZHHnkkS5cure1vb2/PqlWrsn379pxxxhmZPHly1q9fn/PPPz/VajXDhw9P\ne3t7dt9993qPDwAA9HF1vdK0cuXKrF27Nh0dHZk7d24uvfTSXsfb29szZsyYVCqV2r777rsva9as\nSUdHR6655ppcdtllSZIFCxZkxowZuf766/Pa1762V2QBAADUS12jacWKFWltbU2SjBo1Kps3b053\nd3ft+OzZs2vHn3X44YdnwYIFSZK99torW7duzY4dO3L//ffn2GOPTZIce+yxuffee+s5OgAAQJI6\nR1NXV1eGDh1a2x4yZEi6urpq2y0tLc85p1KpZODAgUmSJUuW5Jhjjsluu+2WrVu31m7HGzZsWJ54\n4ol6jg4AAJBkFzzT9Ieq1epOv/bOO+/MzTffnGuvvTZJet3Ct7Pv09nZ+ecNSF1Yh+ZgHRrPGjQH\n69AcrEPjWYPmYB1eHuoaTSNGjOh1ZWnDhg0ZPnz4C553zz335Oqrr87ixYszaNCgJL+/KtXT05MB\nAwbk8ccfz4gRI17wfSZMmPCXD89LorOz0zo0AevQeNagOViH5mAdGs8aNAfr0Bx2JlzrenvexIkT\ns3z58iTJ6tWrM3LkyOfckletVntdOdqyZUvmz5+fRYsWZfDgwbX9Rx55ZO29li9fnre97W31HB0A\nACBJna80jR8/PmPHjs20adPSr1+/tLW1ZdmyZRk8eHBaW1sza9asrF+/Po8++mhmzpyZqVOnpru7\nO5s2bcq5556barWaSqWS9vb2nHPOObnwwgvzjW98I/vvv39OPPHEeo4OAACQZBc80zR79uxe26NH\nj659/eyn5P2xk08++Xn3P/t8EwAAwK5S19vzAAAAXu5EEwAAQIFoAgAAKBBNAAAABaIJAACgQDQB\nAAAUiCbWdJl6AAALwElEQVQAAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAABaIJAACgQDQB\nAAAUiCYAAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAABaIJAACgQDQBAAAUiCYAAIAC0QQA\nAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAABaIJAACgQDQBAAAUiCYAAIAC0QQAAFAgmgAAAApEEwAA\nQIFoAgAAKBBNAAAABaIJAACgQDQBAAAUiCYAAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAA\nBaIJAACgQDQBAAAUiCYAAIAC0QQAAFAgmgAAAApEEwAAQIFoAgAAKBBNAAAABaIJAACgQDQBAAAU\niCYAAICCukfTvHnzMm3atLz3ve/Ngw8+2OtYT09PLrroopx00km99v/sZz/L5MmTc8MNN9T2/ehH\nP8opp5ySmTNn5oMf/GD+3//7f/UeHQAAoL7RtHLlyqxduzYdHR2ZO3duLr300l7H29vbM2bMmFQq\nldq+rVu3Zu7cuTnyyCN7vXbevHmZN29evva1r2X8+PHp6Oio5+gAAABJ6hxNK1asSGtra5Jk1KhR\n2bx5c7q7u2vHZ8+eXTv+rD322CNf+cpXMmLEiF77hw4dmqeeeipJ8vTTT2fIkCH1HB0AACBJ0r+e\nb97V1ZVDDz20tj1kyJB0dXVl0KBBSZKWlpZs3Lix1zm77bZbBgwY8Jz3uuiiizJjxozsvffe2Xvv\nvXPeeefVc3QAAIAkdY6mP1atVv/ic+fOnZuFCxfmsMMOS3t7e2644YbMmDGjeE5nZ+df/P146ViH\n5mAdGs8aNAfr0BysQ+NZg+ZgHV4e6hpNI0aMSFdXV217w4YNGT58+F/0Xg8//HAOO+ywJMlRRx2V\n2267rfj6CRMm/EXfBwAA4A/V9ZmmiRMnZvny5UmS1atXZ+TIkWlpaen1mmq1ulNXoIYPH541a9Yk\nSR588MEcdNBBL/3AAAAAf6RSfTH3zO2Ez33uc7n//vvTr1+/tLW15X/+538yePDgtLa2ZtasWVm/\nfn1+/vOfZ+zYsZk6dWpe97rX5fLLL8+6devSv3//jBw5MldddVXWrFmT9vb27L777tlnn31y2WWX\nZc8996zn6AAAAPWPJgAAgJezuv9xWwAAgJcz0QQAAFAgmgAAAAp26d9p2lXmzZuXBx54IJVKJXPm\nzMm4ceMaPVKf9LOf/SxnnXVW3ve+92X69OmNHqfPam9vz6pVq7J9+/acccYZmTx5cqNH6lN++9vf\n5qKLLsqTTz6Znp6enHnmmTnmmGMaPVaftG3btpxwwgk566yz8o//+I+NHqfPuf/++zNr1qz81V/9\nVarVakaPHp1LLrmk0WP1SbfccksWL16c/v3758Mf/nAmTZrU6JH6nJtuuinf/va3U6lUUq1Ws3r1\n6qxatarRY/Upv/nNb3LhhRfm6aefzu9+97ucddZZeetb3/onX/+Ki6aVK1dm7dq16ejoyJo1a/Kx\nj30sHR0djR6rz9m6dWvmzp2bI488stGj9Gn33Xdf1qxZk46OjmzatCknnniiaNrF7r777owbNy6n\nn3561q1bl3/6p38STQ2ycOHC7LPPPo0eo087/PDDs2DBgkaP0adt2rQpX/rSl/Ktb30r3d3d+cIX\nviCaGmDKlCmZMmVKkt//7nrHHXc0eKK+Z9myZXn961+fj3zkI9mwYUNOO+20fOc73/mTr3/FRdOK\nFSvS2tqaJBk1alQ2b96c7u7uDBo0qMGT9S177LFHvvKVr+Tqq69u9Ch92uGHH543v/nNSZK99tor\nW7duTbVaTaVSafBkfcfxxx9f+3rdunXZb7/9GjhN3/WLX/wiv/jFL/xy2GA+sLfx7r333kycODGv\netWr8qpXvSqf/vSnGz1Sn/elL30pn/3sZxs9Rp8zZMiQPPzww0mSp59+OkOHDi2+/hX3TFNXV1ev\nH3rIkCHp6upq4ER902677ZYBAwY0eow+r1KpZODAgUmSJUuWZNKkSYKpQaZNm5YLLrggc+bMafQo\nfdIVV1yRiy66qNFj9Hlr1qzJhz70oUyfPj333ntvo8fpkx577LFs3bo1Z555Zk499dSsWLGi0SP1\naQ8++GD222+/DBs2rNGj9DnHH3981q1bl7/7u7/LjBkzcuGFFxZf/4q70vTH/FctSO68887cfPPN\nWbx4caNH6bM6Ojry0EMP5bzzzsstt9zS6HH6lG9961sZP358DjjggCT+f6FRDjrooJx99tk57rjj\n8qtf/SozZ87M9773vfTv/4r/VaSpVKvVbNq0KQsXLsyvf/3rzJw5M9///vcbPVaftWTJkrz73e9u\n9Bh90i233JL9998/X/nKV/LQQw/lYx/7WJYuXfonX/+K+5dqxIgRva4sbdiwIcOHD2/gRNBY99xz\nT66++uosXrw4e+65Z6PH6XNWr16dYcOGZd99980hhxyS7du356mnnnrB2wB46fzwhz/Mr3/963z/\n+9/P+vXrs8cee2Tffff1zOUuNnLkyBx33HFJkgMPPDCvfvWr8/jjj9dill3j1a9+dcaPH59KpZID\nDzwwgwYN8m9SA91///1pa2tr9Bh90qpVq/K2t70tSXLIIYdkw4YNxUcYXnG3502cODHLly9P8vtf\nVkaOHJmWlpYGTwWNsWXLlsyfPz+LFi3K4MGDGz1On7Ry5cpce+21SX5/+/DWrVv9crKLXXnllVmy\nZEm+8Y1v5D3veU8+9KEPCaYGuPXWW2v/W3jiiSfy5JNPZuTIkQ2equ+ZOHFi7rvvvlSr1WzcuDG/\n+c1v/JvUIBs2bMigQYNcbW2Qgw46KD/5yU+S/P621UGDBhUfYXjFrdL48eMzduzYTJs2Lf369VPv\nDbJ69epcfvnlWbduXfr375/ly5fnqquuyl577dXo0fqU22+/PZs2bcq5555b+68n7e3t2XfffRs9\nWp/x3ve+N3PmzMn06dOzbdu2fOITn2j0SNAQb3/72/PRj340d911V5555pl86lOf8stiA4wcOTLv\nfOc7c/LJJ6dSqfg9qYGeeOIJzzI10NSpUzNnzpzMmDEj27dvf8EPRalU3dwNAADwJ73ibs8DAAB4\nKYkmAACAAtEEAABQIJoAAAAKRBMAAECBaAIAACgQTQC87Jx66qm5++67e+3btm1bDj/88Dz++OPP\ne86MGTOyYsWKXTEeAK8wogmAl50pU6Zk2bJlvfZ973vfy2GHHZaRI0c2aCoAXqlEEwAvO3//93+f\nzs7OPP3007V93/rWtzJlypTceeedmTZtWk477bSceuqpWbduXa9z77///pxyyim17Ysvvjg33XRT\nkuT222/P9OnTM3369Jxzzjm93h+Avks0AfCyM3DgwEyePDm33XZbkmTDhg156KGH8va3vz2bN2/O\n5z//+fz7v/97jj766Fx//fXPOb9SqTxn3/r16/Ov//qv+epXv5obbrghb3nLW7Jo0aK6/ywANL/+\njR4AAP4SJ510Uj796U9n+vTpufXWW/Oud70r/fv3z7Bhw3LBBRekWq2mq6srhx122E69349//OM8\n8cQTOf3001OtVvO73/0ur3nNa+r8UwDwciCaAHhZetOb3pSenp6sWbMm3/72t3PllVfmmWeeyUc+\n8pF8+9vfzoEHHpgbbrgh//3f/93rvD++ytTT05MkGTBgQN70pje5ugTAc7g9D4CXrSlTpmThwoVp\naWnJqFGj0t3dnX79+mX//ffPtm3bctddd9Wi6Fl77rln7RP2tm7dmv/6r/9KkowbNy4PPvhgurq6\nkiR33HHHcz6hD4C+yZUmAF623vWud+Uzn/lM2trakiR77713TjjhhJx00kk54IAD8v73vz8XXHBB\nli9fXrvCdMghh2T06NF597vfnde+9rX5m7/5myTJiBEj8rGPfSz//M//nJaWlgwcODBXXHFFw342\nAJpHpVqtVhs9BAAAQLNyex4AAECBaAIAACgQTQAAAAWiCQAAoEA0AQAAFIgmAACAAtEEAABQ8P8B\ntyqajxkQ+qoAAAAASUVORK5CYII=\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc9df7e90>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "a = 0.0\n",
     "b = 8.0\n",
     "x = np.linspace(a, b, 100)\n",
     "y = [1/(b-a) for i in x]\n",
     "plt.plot(x, y)\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Probability');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "As before in the discrete uniform case, the continuous uniform distribution PDF is constant for all values the variable can take on. The only difference here is that we cannot take the probability for any individual point. The CDF, which we get from integrating the PDF is:\n",
     "\n",
     "$$ F(x) = \\begin{cases} 0 & \\text{for $x \\leq a$} \\ \\frac{x - a}{b - a} & \\text{for $a < x < b$} \\ 1 & \\text{for $x \\geq b$}\\end{cases}$$\n",
     "\n",
     "And is plotted on the same interval as the PDF as:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 11,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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P4Jl9QF++/dc9IPuAjonvhfJzBpXBOVQG51B+Aw2iJQ1CM2fOzDXXXJPzzjsv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\nSUVORK5CYII=\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc96f9fd0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "y = [(i - a)/(b - a) for i in x]\n",
     "plt.plot(x, y)\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Probability');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### Normal Distribution\n",
     "The normal distribution is a very common and important distribution in statistics. Many important tests and methods in statistics, and by extension, finance, are based on the assumption of normality. A large part of this is due to the results of the Central Limit Theorem (CLT), which states that large enough samples of independent trials are normally distributed. The convenience of the normal distribution finds its way into certain algorithmic trading strategies as well. For example, as covered in the [pairs trading](https://www.quantopian.com/lectures/introduction-to-pairs-trading) notebook, we can search for stock pairs that are cointegrated, and bet on the direction the spread between them will change based on a normal distribution."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 12,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "class NormalRandomVariable(ContinuousRandomVariable):\n",
     "    def __init__(self, mean = 0, variance = 1):\n",
     "        ContinuousRandomVariable.__init__(self)\n",
     "        self.variableType = \"Normal\"\n",
     "        self.mean = mean\n",
     "        self.standardDeviation = np.sqrt(variance)\n",
     "        return\n",
     "    def draw(self, numberOfSamples):\n",
     "        samples = np.random.normal(self.mean, self.standardDeviation, numberOfSamples)\n",
     "        return samples"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {
     "collapsed": true
    },
    "source": [
     "When describing a normal random variable we only need to know its mean ($\\mu$) and variance ($\\sigma^2$, where $\\sigma$ is the standard deviation). We denote a random variable $X$ as a normal random variable by saying $X$ **~** $N(\\mu, \\sigma^2)$. In modern portfolio theory, stock returns are generally assumed to follow a normal distribution. One major characteristic of a normal random variable is that a linear combination of two or more normal random variables is another normal random variable. This is useful for considering mean returns and variance of a portfolio of multiple stocks. Up until this point, we have only considered single variable, or univariate, probability distributions. When we want to describe random variables at once, as in the case of observing multiple stocks, we can instead look at a multivariate distribution. A multivariate normal distribution is described entirely by the means of each variable, their variances, and the distinct correlations between each and every pair of variables. This is important when determining characteristics of portfolios because the variance of the overall portfolio depends on both the variances of its securities and the correlations between them.\n",
     "\n",
     "The PDF of a normal random variable is:\n",
     "\n",
     "$$\n",
     "f(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}}e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}}\n",
     "$$\n",
     "\n",
     "And is defined for $-\\infty < x < \\infty$. When we have $\\mu = 0$ and $\\sigma = 1$, we call this the standard normal distribution."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 13,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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JdpthdTl+lZoUpZTEKO2tOCqPx2N1OQCAc0Q4AgCYam9F/6zKcDnf6JMm5ifL2dajmoZ2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\nd0+5EYPeoHWk49a1l31KkjSpE33flFFdTev61tEjAE9XD+6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pyrxpMVrHEaLPuvyMeAx6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OAAAG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\nJEmSJMByJEmSJEmA5UiSJEmSAPgDoY0OVOL0wjYAAAAASUVORK5CYII=\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc9276550>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "mu_1 = 0\n",
     "mu_2 = 0\n",
     "sigma_1 = 1\n",
     "sigma_2 = 2\n",
     "x = np.linspace(-8, 8, 200)\n",
     "y = (1/(sigma_1 * np.sqrt(2 * 3.14159))) * np.exp(-(x - mu_1)*(x - mu_1) / (2 * sigma_1 * sigma_1))\n",
     "z = (1/(sigma_2 * np.sqrt(2 * 3.14159))) * np.exp(-(x - mu_2)*(x - mu_2) / (2 * sigma_2 * sigma_2))\n",
     "plt.plot(x, y, x, z)\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Probability');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "By changing the mean and standard deviation of the normal distribution, we can change the depth and width of the bell curve. With a larger standard deviation, the values of the distribution are less concentrated around the mean.\n",
     "\n",
     "Rather than using normal distribution to model stock prices, we use it to model returns. Stock prices cannot go below $0$ while the normal distribution can take on all values on the real line, making it better suited to returns. Given the mean and variance of a normal distribution, we can make the following statements:\n",
     "\n",
     "* Around $68\\%$ of all observations fall within one standard deviations around the mean ($\\mu \\pm \\sigma$)\n",
     "* Around $95\\%$ of all observations fall within two standard deviations around the mean ($\\mu \\pm 2\\sigma$)\n",
     "* Around $99\\%$ of all observations fall within three standard deviations aroud the mean ($\\mu \\pm 3\\sigma$)\n",
     "\n",
     "These values are important for understanding confidence intervals as they relate to the normal distribution. When considering the mean and variance of a sample distribution, we like to look at different confidence intervals around the mean.\n",
     "\n",
     "Using the central limit theorem, we can standardize different random variables so that they become normal random variables. A very common tool in statistics is a standard normal probability table, used for looking up the values of the standard normal CDF for given values of $x$. By changing random variables into a standard normal we can simply check these tables for probability values. We standardize a random variable $X$ by subtracting the mean and dividing by the variance, resulting in the standard normal random variable $Z$.\n",
     "\n",
     "$$\n",
     "Z = \\frac{X - \\mu}{\\sigma}\n",
     "$$\n",
     "\n",
     "Let's look at the case where $X$ **~** $B(n, p)$ is a binomial random variable. In the case of a binomial random variable, the mean is $\\mu = np$ and the variance is $\\sigma^2 = np(1 - p)$."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 14,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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0Rq666qrMmzcvDz/8cI477rhccMEFaWxszNy5c3PZZZeloaEhc+bMyahRo2o9\nKgAAcJipaTRdeeWVAz/fd999+z3f3t6e9vb2ao4EAACwj5p9TxMAAEA9EE0AAAAFRBMAAEAB0QQA\nAFBANAEAABQQTQAAAAVEEwAAQAHRBAAAUEA0AQAAFBBNAAAABUQTAABAAdEEAABQQDQBAAAUEE0A\nAAAFRBMAAEAB0QQAAFBANAEAABQQTQAAAAVEEwAAQAHRBAAAUEA0AQAAFBBNAAAABUQTAABAAdEE\nAABQQDQBAAAUEE0AAAAFRBMAAEAB0QQAAFBANAEAABQQTQAAAAVEEwAAQAHRBAAAUEA0AQAAFBBN\nAAAABUQTAABAAdEEAABQQDQBAAAUEE0AAAAFmmo9ADA4e/bsSVdX16D27e7urvA0VFJ5796DWsPx\n48ensbGxghMBwOFNNEGd6OrqSsd1S9Lc0nbAfTev/1HGHP+eKkxFJfRv7c38u/vS3HLgSN6xZVMW\nL5iVCRMmVGEyADg8iSaoI80tbRl19LgD7rdjS08VpqGSBrvWAEDluaYJAACggGgCAAAoIJoAAAAK\niCYAAIACogkAAKCAaAIAACggmgAAAAqIJgAAgAKiCQAAoIBoAgAAKCCaAAAACogmAACAAqIJAACg\ngGgCAAAo0FSLN73tttuyZs2a7NmzJ5/+9Kdz6qmn5pprrkm5XM6xxx6b2267LcOGDcvy5ctz//33\np7GxMR//+Mczc+bMWowLAAAcxqoeTU8++WS6urry0EMP5ZVXXskFF1yQD3zgA7nkkkvyoQ99KHfc\ncUeWLVuWj370o1m4cGGWLVuWpqamzJw5M+3t7TnyyCOrPTIAAHAYq/rpee973/ty5513JkmOPPLI\n7NixI08//XTOPvvsJMmMGTOyatWqPPvss5k8eXJGjhyZESNG5LTTTsuaNWuqPS4AAHCYq3o0lUql\nHHHEEUmSpUuX5qyzzkp/f3+GDRuWJBkzZkw2bdqUzZs3p7W1deB1ra2t6e3trfa4AADAYa4m1zQl\nyfe+970sW7Ys9957b9rb2we2l8vlN9z/zba/kc7Ozrc8H7Vh7d7cunXraj0CQ9TatWuzdevWt/x7\nfP7ql7Wrb9avflm7w0dNoumJJ57I3XffnXvvvTejRo3KyJEjs2vXrgwfPjw9PT0ZO3Zs2tra9jmy\n1NPTkylTpgzq90+dOrVSo1NBnZ2d1q7A6NGjkxUbaz0GQ9CkSZMyYcKEt/Q7fP7ql7Wrb9avflm7\n+nawwVuSWmpHAAAOHUlEQVT10/O2bduWL3/5y/n617/+838JTDJt2rSsXLkySbJy5cqcfvrpmTx5\nctauXZtt27Zl+/bteeaZZ/wfEwAAqLqqH2n6zne+k1deeSWf+9znUi6XUyqVcuutt+b666/PN7/5\nzRx33HG54IIL0tjYmLlz5+ayyy5LQ0ND5syZk1GjRlV7XAAA4DBX9Wi68MILc+GFF+63/b777ttv\nW3t7+z7XOwEAAFRb1U/PAwAAqCeiCQAAoIBoAgAAKCCaAAAACogmAACAAqIJAACgQNVvOQ7A26e8\nd2+6u7sHvf/48ePT2NhYwYkA4NAjmgDqWP/W3sy/uy/NLV0H3HfHlk1ZvGBWJkyYUIXJAODQIZoA\n6lxzS1tGHT2u1mMAwCHLNU0AAAAFRBMAAEAB0QQAAFBANAEAABQQTQAAAAVEEwAAQAHRBAAAUEA0\nAQAAFBBNAAAABUQTAABAAdEEAABQQDQBAAAUEE0AAAAFmmo9ABzO9uzZk66urkHt293dXeFpAAB4\nI6IJaqirqysd1y1Jc0vbAffdvP5HGXP8e6owFQAA/5toghprbmnLqKPHHXC/HVt6qjANAAD/l2ua\nAAAACogmAACAAqIJAACggGuaAA4T5b173/QujOvWrcvo0aP32TZ+/Pg0NjZWYzQAGNJEE8Bhon9r\nb+bf3Zfmlje5zf2KjQM/7tiyKYsXzMqECROqNB0ADF2iCeAwMti7NQIA/8M1TQAAAAVEEwAAQAHR\nBAAAUEA0AQAAFBBNAAAABUQTAABAAdEEAABQwPc0wdtsz5496ep6ky8P/T+6u7srPA0AAG+VaIK3\nWVdXVzquW5LmlrYD7rt5/Y8y5vj3VGEqAAB+WaIJKqC5pS2jjh53wP12bOmpwjQAALwVrmkCAAAo\nIJoAAAAKiCYAAIACrmkCYD/lvXsP6u6O48ePT2NjYwUnAoDaEU0A7Kd/a2/m392X5pYD3z5/x5ZN\nWbxgViZMmFCFyQCg+kQTAG9osHeBBIBDnWuaAAAACogmAACAAqIJAACggGgCAAAoIJoAAAAKuHse\nAG+J73QC4FAnmgB4S3ynEwCHOtEEwFvmO50AOJQN+WhasGBBnn322ZRKpXzxi1/MqaeeWuuROMzs\n2bMnXV0H/i/ov3AwpykBADD0Deloevrpp7Nu3bo89NBD6erqyvXXX5+HHnqo1mNxmOnq6krHdUvS\n3NI2qP03r/9Rxhz/ngpPBfXpYK9/SlwDBUDtDeloWr16dc4555wkP/+H5quvvprt27dn5MiRNZ6M\noehgjgjt2bMnSQb1L2Ld3d0HderRji09g9oPDkcHc/1Tkmx/ZWP+/E+m593vfvcB9z2Yz3UixgAY\nvCEdTX19fZk0adLA46OPPjp9fX2iqc5t2rQpTz755H7bf/rTn2bDhg37bHvHO96RE088cVC/t7u7\nO9fc/u0cMar1gPtu6XkhI0YeNeh9j3rn4C9a79/6syQl+x7EvkNljqGw71CZo5L7vmP0mEHtmySv\nbXu5Ip/r17b9LF+++qODirGhbt26dRk9enStx+CXZP3q15utnRvdHJpK5XK5XOsh3sz8+fNz1lln\n5eyzz06SzJo1KwsWLMi73vWuN31NZ2dntcYDAADq1NSpUwe975A+0tTW1pa+vr6Bx5s2bcqxxx5b\n+JqD+cMDAAAcSEOtBygyffr0rFy5Mkny3HPPZezYsWlubq7xVAAAwOFkSB9pmjJlSk455ZRcfPHF\naWxszPz582s9EgAAcJgZ0tc0AQAA1NqQPj0PAACg1kQTAABAAdEEAABQYEjfCOJgPPXUU/nc5z6X\nBQsW5Mwzz0yS/PjHP86XvvSlNDQ0ZOLEifmzP/uzGk/Jm1mwYEGeffbZlEqlfPGLX8ypp55a65E4\ngOeffz5XXHFF/vAP/zCzZ8/Oxo0bc80116RcLufYY4/NbbfdlmHDhtV6TN7AbbfdljVr1mTPnj35\n9Kc/nVNPPdXa1YnXXnst1157bTZv3pxdu3bls5/9bE4++WTrV0d27tyZ888/P1dccUU+8IEPWLs6\n8dRTT+VP//RP8+u//uspl8uZOHFiPvWpT1m/OrJ8+fLce++9aWpqylVXXZWJEyce1PodEkeaXnzx\nxXzjG9/Y7zua/vIv/zI33nhjlixZkldffTVPPPFEjSakyNNPP51169bloYceys0335y/+Iu/qPVI\nHEB/f39uvvnmTJs2bWDbnXfemY6OjjzwwAM58cQTs2zZshpOyJt58skn09XVlYceeih///d/n7/8\ny7/MnXfemUsuucTa1YHHHnssp556ahYvXpw77rgjCxYssH51ZuHChTnqqKOS+Huz3rzvfe/L/fff\nn8WLF+eGG26wfnXklVdeyde+9rU89NBD+bu/+7t8//vfP+j1OySiqa2tLV/72tcyatSogW2vv/56\nXnrppZxyyilJkrPPPjurVq2q1YgUWL16dc4555wkyfjx4/Pqq69m+/btNZ6KIiNGjMg999yTtra2\ngW1PPfVUZsyYkSSZMWOGz9sQ9b73vS933nlnkuTII4/Mjh078vTTT+fss89OYu2GuvPOOy+f/OQn\nkyQbNmzIO9/5TutXR1544YW88MILOfPMM1Mul/P000/7e7OO/N8bTvvnXv1YtWpVpk+fnne84x05\n5phjctNNNx30+h0S0TRixIiUSqV9tr388stpaWkZeNza2pre3t5qj8Yg9PX1pbW1deDx0Ucfnb6+\nvhpOxIE0NDRk+PDh+2zr7+8fOKw9ZswYn7chqlQq5YgjjkiSLF26NGeddZa1q0MXX3xx5s2bl+uu\nu8761ZFbb70111577cBja1dfurq6cvnll2f27NlZtWpVXnvtNetXJ1566aX09/fns5/9bC655JKs\nXr36oNev7q5p+ta3vpWlS5emVCqlXC6nVCplzpw5mT59eq1H423iq8PqnzUc+r73ve9l2bJluffe\ne9Pe3j6w3drVh4ceeig//vGPc/XVV++zZtZv6HrkkUcyZcqUjBs37g2ft3ZD27ve9a5ceeWV+fCH\nP5wXX3wxl156aXbv3j3wvPUb2srl8sApei+99FIuvfTSg/67s+6i6eMf/3g+/vGPH3C/1tbWvPzy\nywOPe3p69jmViKGjra1tnyNLmzZtyrHHHlvDifhljBw5Mrt27crw4cN93oa4J554InfffXfuvffe\njBo1ytrVkeeeey5jxozJr/zKr+Tkk0/O3r17rV+dePzxx7N+/fr84Ac/SE9PT4YNG5bm5mZrVyfG\njh2bD3/4w0mSE044Icccc0zWrl1r/erEMccckylTpqShoSEnnHBCRo4cmaampoNav0Pi9Lz/7Rel\n2NTUlJNOOilr1qxJknz3u9/N6aefXsvReBPTp0/PypUrk/z8XwjGjh2b5ubmGk/FwZo2bdrAOq5c\nudLnbYjatm1bvvzlL+frX/96Ro8encTa1ZOnn3469913X5Kfn9q8Y8eOTJs2LY8++mgS6zeU3XHH\nHfnWt76Vb37zm5k5c2auuOIKa1dH/vmf/3ngs9fb25vNmzfnD/7gD6xfnZg+fXqefPLJlMvlvPzy\ny7/U352l8iFwPPHxxx/PPffck+7u7rS2tubYY4/Nvffem66ursyfPz/lcjnvfe9784UvfKHWo/Im\n/uqv/ipPPfVUGhsbM3/+/EycOLHWI1Hgueeeyy233JINGzakqakpY8eOze23355rr702u3btynHH\nHZcFCxaksbGx1qPyfzz88MO566678qu/+qsDpzjfeuutuf76661dHdi5c2e++MUvZuPGjdm5c2fm\nzJmTU045JfPmzbN+deSuu+7K8ccfn9/5nd+xdnVi+/btmTt3brZu3Zrdu3fnyiuvzMknn5wvfOEL\n1q9OPPzww/nWt76VUqmUyy+/PJMmTTqoz98hEU0AAACVcsidngcAAPB2Ek0AAAAFRBMAAEAB0QQA\nAFBANAEAABQQTQAAAAVEEwB14ZJLLsljjz22z7adO3fmfe97X3p6et7wNR0dHVm9enU1xgPgECaa\nAKgLM2fOzD/90z/ts+1f//Vf85u/+ZsZO3ZsjaYC4HAgmgCoC7/3e7+Xzs7ObNmyZWDbI488kpkz\nZ+Z73/teLr744nziE5/IJZdckg0bNuzz2qeeeiqzZs0aeHzddddl6dKlSZLvfOc7mT17dmbPnp05\nc+bs8/sBIBFNANSJI444Iueee25WrFiRJNm0aVN+/OMf5+yzz86rr76ar371q1m0aFHOOOOMPPDA\nA/u9vlQq7bdt48aN+bu/+7t84xvfyIMPPpjf/u3fzte//vWK/1kAqC9NtR4AAAbrYx/7WG666abM\nnj07//zP/5yPfOQjaWpqypgxYzJv3ryUy+X09fXlN3/zNwf1+5555pn09vbmk5/8ZMrlcl5//fUc\nf/zxFf5TAFBvRBMAdWPy5MnZtWtXurq68u1vfzt33HFHdu/enc9//vP59re/nRNOOCEPPvhg1q5d\nu8/r/u9Rpl27diVJhg8fnsmTJzu6BEAhp+cBUFdmzpyZhQsXprm5OePHj8/27dvT2NiY4447Ljt3\n7sz3v//9gSj6hVGjRg3cYa+/vz//8R//kSQ59dRT85//+Z/p6+tLkjz66KP73aEPABxpAqCufOQj\nH8ntt9+e+fPnJ0laWlpy/vnn52Mf+1jGjRuXT33qU5k3b15Wrlw5cITp5JNPzsSJE/MHf/AHOfHE\nE3PaaaclSdra2nL99dfnT/7kT9Lc3Jwjjjgit956a83+bAAMTaVyuVyu9RAAAABDldPzAAAACogm\nAACAAqIJAACggGgCAAAoIJoAAAAKiCYAAIACogkAAKDA/we/d9jUlHPADwAAAABJRU5ErkJggg==\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc94b55d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "n = 50\n",
     "p = 0.25\n",
     "X = BinomialRandomVariable(n, p)\n",
     "X_samples = X.draw(10000)\n",
     "Z_samples = (X_samples - n * p) / np.sqrt(n * p * (1 - p))\n",
     "\n",
     "plt.hist(X_samples, bins = range(0, n + 2), align = 'left')\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Probability');"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 15,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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x7rnnntTW1uaqq67KSSedlOuuuy4dHR057rjjcuutt6ZPnz5ZvHhx7r///tTU\n1OSCCy7IpEmTyogLAKVq39qamXe3pd/g5tIybFr3mww54f2l7Q/Q3bq9KL366qv5xje+kYcffjjb\nt2/P3/7t3+bRRx9NY2NjJk6cmDvuuCMPPfRQPvnJT2bOnDl56KGHUltbm0mTJmXixIkZNGhQd0cG\ngNL1G9yQAccMK23/HZtbStsboAzdfo7SsmXLMm7cuPyrf/Wvcuyxx+arX/1qnn766YwfPz5JMn78\n+CxbtizPPvtsRo0alf79+6euri6nnHJKVqxY0d1xAQCAI1C3H1F6+eWX097env/0n/5Ttm7dmi98\n4Qv5wx/+kD59+iRJhgwZko0bN2bTpk2pr6/vfF59fX1aW1u7Oy4AAHAE6vai1NHR0fn2u5dffjmX\nXHJJOjo69rr/QM/rqqampreck/0z28ow1/1bu3Zt2RGAHmbVqlXZunXrm36+19vKMNfKMdvydHtR\nOvbYYzN69OhUV1fnxBNPTP/+/VNbW5udO3emb9++aWlpydChQ9PQ0LDXEaSWlpaMHj26S3uMGTOm\nUvGPaE1NTWZbAeZ6YAMHDkyWbCg7BtCDjBw5MiNGjHhTz/V6WxnmWjlmWzldKaDdfo7SuHHj8tRT\nT6WjoyO///3vs2PHjowdOzaPPvpokmTp0qU544wzMmrUqKxatSrbtm3L9u3bs3LlSr8oAABAt+j2\nI0pDhw7Nxz72sVx44YWpqqrKzJkzM3LkyFx//fX5/ve/n+OPPz7nn39+ampqMn369Fx66aWprq7O\ntGnTMmDAgO6OCwAAHIFK+RylCy+8MBdeeOFea/fee+8+j5s4cWImTpzYXbEAAACSlPDWOwAAgJ5O\nUQIAAChQlAAAAAoUJQAAgAJFCQAAoEBRAgAAKFCUAAAAChQlAACAAkUJAACgQFECAAAoUJQAAAAK\nFCUAAIACRQkAAKBAUQIAAChQlAAAAAoUJQAAgAJFCQAAoEBRAgAAKFCUAAAAChQlAACAAkUJAACg\nQFECAAAoUJQAAAAKFCUAAIACRQkAAKBAUQIAAChQlAAAAAoUJQAAgILasgMAPdPu3bvT3NxcaoY1\na9aUuj8AcORSlID9am5uTuMNC9NvcENpGTat+02GnPD+0vYHAI5cihJwQP0GN2TAMcNK23/H5pbS\n9gYAjmzOUQIAAChQlAAAAAoUJQAAgAJFCQAAoEBRAgAAKFCUAAAAChQlAACAAkUJAACgQFECAAAo\nKK0ovfbR5kFdAAASv0lEQVTaa5kwYUIefvjhbNiwIY2Njbn44otzzTXX5PXXX0+SLF68OJMmTcrk\nyZOzaNGisqICAABHmNKK0pw5c3L00UcnSe688840NjbmgQceyDve8Y489NBDaW9vz5w5czJv3rzc\nf//9mTdvXrZs2VJWXAAA4AhSSlF68cUX8+KLL+ass85KR0dHnnnmmYwfPz5JMn78+CxbtizPPvts\nRo0alf79+6euri6nnHJKVqxYUUZcAADgCFNKUbrlllsyY8aMztvt7e3p06dPkmTIkCHZuHFjNm3a\nlPr6+s7H1NfXp7W1tduzAgAAR55uL0oPP/xwRo8enWHDhu33/o6Ojj9pHQAA4FCr7e4Nn3zyyaxb\nty5PPPFEWlpa0qdPn/Tr1y87d+5M375909LSkqFDh6ahoWGvI0gtLS0ZPXp0l/ZoamqqVPwjntlW\nRk+c69q1a8uOALCPVatWZevWrW/6+T3x9bY3MNfKMdvydHtRuuOOOzq/vuuuu3LCCSdkxYoVefTR\nR/Mf/sN/yNKlS3PGGWdk1KhR+eIXv5ht27alqqoqK1euzE033dSlPcaMGVOp+Ee0pqYms62AnjrX\ngQMHJks2lB0DYC8jR47MiBEj3tRze+rr7eHOXCvHbCunKwW024vS/lx11VW5/vrr8/3vfz/HH398\nzj///NTU1GT69Om59NJLU11dnWnTpmXAgAFlRwUAAI4ApRalK6+8svPre++9d5/7J06cmIkTJ3Zn\nJAAAgPI+RwkAAKCnUpQAAAAKFCUAAIACRQkAAKBAUQIAAChQlAAAAAoUJQAAgAJFCQAAoEBRAgAA\nKFCUAAAAChQlAACAAkUJAACgQFECAAAoUJQAAAAKFCUAAIACRQkAAKBAUQIAAChQlAAAAAoUJQAA\ngAJFCQAAoEBRAgAAKFCUAAAAChQlAACAAkUJAACgQFECAAAoUJQAAAAKFCUAAIACRQkAAKBAUQIA\nACioLTsAsH+7d+9Oc3NzafuvWbOmtL0BAMqmKEEP1dzcnMYbFqbf4IZS9t+07jcZcsL7S9kbAKBs\nihL0YP0GN2TAMcNK2XvH5pZS9gUA6AmcowQAAFCgKAEAABQoSgAAAAWKEgAAQIGiBAAAUKAoAQAA\nFChKAAAABYoSAABAgaIEAABQUFvGprfeemtWrFiR3bt35/Of/3w+8IEP5LrrrktHR0eOO+643Hrr\nrenTp08WL16c+++/PzU1NbngggsyadKkMuICAABHmG4vSk899VSam5vz4IMP5tVXX83555+fP//z\nP8/FF1+cj33sY7njjjvy0EMP5ZOf/GTmzJmThx56KLW1tZk0aVImTpyYQYMGdXdkAADgCNPtb707\n9dRTc+eddyZJBg0alB07duSZZ57J2WefnSQZP358li1blmeffTajRo1K//79U1dXl1NOOSUrVqzo\n7rgAAMARqNuLUlVVVY466qgkyaJFi/LRj3407e3t6dOnT5JkyJAh2bhxYzZt2pT6+vrO59XX16e1\ntbW74wIAAEegUs5RSpKf/vSneeihh3LPPfdk4sSJnesdHR37ffyB1venqanpLedj/8y2MvY317Vr\n15aQBKBnW7VqVbZu3fqmn+//Y5VhrpVjtuUppSj94he/yN1335177rknAwYMSP/+/bNz58707ds3\nLS0tGTp0aBoaGvY6gtTS0pLRo0d36fuPGTOmUtGPaE1NTWZbAQea68CBA5MlG0pIBNBzjRw5MiNG\njHhTz/X/scow18ox28rpSgHt9rfebdu2LV/72tfyrW9961/+IZhk7NixWbp0aZJk6dKlOeOMMzJq\n1KisWrUq27Zty/bt27Ny5Uq/KAAAQLfo9iNKjzzySF599dVcffXV6ejoSFVVVW655ZbcdNNN+d73\nvpfjjz8+559/fmpqajJ9+vRceumlqa6uzrRp0zJgwIDujgsAAByBur0oXXjhhbnwwgv3Wb/33nv3\nWZs4ceJe5y8BAAB0h25/6x0AAEBPpygBAAAUKEoAAAAFihIAAEBBaR84CwDwp+jYsydr1qx5089f\nu3Zt50eTvFnDhw9PTU3NW/oewOFBUQIADgvtW1sz8+629Bvc/Oa/yVv4IO8dmzdm/qwpb/oDb4HD\ni6IEABw2+g1uyIBjhpUdAzgCOEcJAACgQFECAAAoUJQAAAAKFCUAAIACRQkAAKBAUQIAAChQlAAA\nAAoUJQAAgAJFCQAAoKC27ADQE+3evTvNzc3dstfatWszcODAfdbXrFnTLfsDALAvRQn2o7m5OY03\nLEy/wQ3ds+GSDfssbVr3mww54f3dsz8AAHtRlOAA+g1uyIBjhpW2/47NLaXtDQBwpHOOEgAAQIGi\nBAAAUOCtdwAAXdCxZ0+PuNDO8OHDU1NTU3YM6PUUJQCALmjf2pqZd7el3+DuuSrq/uzYvDHzZ03J\niBEjSssARwpFCQCgi8q+0A/QfZyjBAAAUKAoAQAAFChKAAAABYoSAABAgaIEAABQ4Kp39Di7d+9O\nc3N5l15N0iM+JwMAgPIoSvQ4zc3NabxhYfoNbigtw6Z1v8mQE95f2v4AAJRLUaJHKvtzKnZsbilt\nbwAAyuccJQAAgAJHlAAADhMde/aUfh7t8OHDU1NTU2oG6A6KEgDAYaJ9a2tm3t2WfoPLuejRjs0b\nM3/WlIwYMaKU/aE7KUoAAIeRss/jhSOFc5QAAAAKFCUAAIACRQkAAKBAUQIAAChwMQcAALpkf5cn\nX7t2bQYOHNitOVyinO7Q44vSrFmz8uyzz6aqqio33nhjPvCBD5QdqdfbvXt3mpv3vexod70Qlv35\nEADA/h3w8uRLNnRbBpcop7v06KL0zDPPZO3atXnwwQfT3Nycm266KQ8++GDZsXq95ubmNN6wMP0G\nN+x7Zze8EG5a95sMOeH9Fd8HAPjTuTz5gf+ofKgd7I/UjqpVXo8uSsuXL88555yT5F9+GbZs2ZLt\n27enf//+JSerrIXfezjbdrSXtn9ba0upL4I7NreUsi8A0PPt7+1/3W3NmjWZeffy/f9R+VDbzx+p\nHVXrHj26KLW1tWXkyJGdt4855pi0tbX1+qL0vR/9PB1HdcN/eAfQ9s+/yu6B7ytt//atrySpKm1/\nGXrG/j0hQ9n7y9Az9u8JGcreX4aesX9PyFD2/knyyvrnc91tv85RA+pLy7C55cUc/XYlpbfr0UWp\nqKOjo0uPa2pqqnCSypp5TWPJCT5W8v6nlbx/IkNP2D8pP0PZ+ycy9IT9k/IzlL1/IkNP2D8pP0PZ\n+yc9I0P5tm7detj/m7en69FFqaGhIW1tbZ23N27cmOOOO+6gzxkzZkylYwEAAL1cj/4cpXHjxmXp\n0qVJktWrV2fo0KHp169fyakAAIDerkcfURo9enROPvnkXHTRRampqcnMmTPLjgQAABwBqjq6euIP\nAADAEaJHv/UOAACgDIoSAABAgaIEAABQ0CuLUltbW0499dQ888wzZUfpNV555ZVcdtllueSSSzJl\nypT86le/KjtSr7F79+7MmDEjU6ZMyUUXXZQVK1aUHalXefrpp3P66afnySefLDtKrzBr1qxcdNFF\n+fSnP53nnnuu7Di9zgsvvJAJEyZkwYIFZUfpVW699dZcdNFFueCCC/KTn/yk7Di9xh/+8IdcffXV\naWxszOTJk/Pzn/+87Ei9zmuvvZYJEybk4YcfLjtKr/H0009n7NixueSSS9LY2Jibb775gI/t0Ve9\ne7O+9rWv5cQTTyw7Rq+yePHi/Mf/+B/z7//9v88zzzyTO++8M/fcc0/ZsXqFH/7wh+nXr18WLlyY\n3/3ud7nhhhvygx/8oOxYvcJLL72U++67z+erHSLPPPNM1q5dmwcffDDNzc256aab8uCDD5Ydq9do\nb2/PzTffnLFjx5YdpVd56qmn0tzcnAcffDCvvvpqzj///EyYMKHsWL3C448/ng984AP53Oc+l/Xr\n1+ezn/1sPvrRj5Ydq1eZM2dOjj766LJj9Dqnnnpq7rzzzjd8XK8rSv/4j/+YAQMGZMSIEWVH6VX+\n8i//svPr9evX521ve1t5YXqZT37ykznvvPOSJPX19dm8eXPJiXqPhoaGfOMb38iNN95YdpReYfny\n5TnnnHOSJMOHD8+WLVuyffv29O/fv+RkvUNdXV3mzp2bu+++u+wovcqpp56aD37wg0mSQYMGpb29\nPR0dHamqqio52eHv3HPP7fx6/fr1efvb315imt7nxRdfzIsvvpizzjqr7Ci9Tlcv+t2r3nr3+uuv\n5xvf+EauueaasqP0Sm1tbZk0aVK+/e1v5+qrry47Tq9RU1OTvn37JknmzZvXWZp46+rq6vxj6BBq\na2tLfX195+1jjjkmbW1tJSbqXaqrqztfCzh0qqqqctRRRyVJfvCDH+Sss87yunCIXXTRRbn++uv9\nUeoQu+WWWzJjxoyyY/RKzc3NueKKKzJ16tQsW7bsgI87bI8o/eAHP8iiRYtSVVXV+Zehj3zkI7nw\nwgszYMCAJF1vi+xtf7OdNm1axo0bl0WLFuUf/uEfMmPGDG+9exMONtsFCxbk17/+db71rW+VHfOw\ndLDZUhleYzmc/PSnP83//J//0/+7KuDBBx/Mb3/721x77bVZvHhx2XF6hYcffjijR4/OsGHDkni9\nPZTe+c535sorr8zHP/7xvPTSS7nkkkvyk5/8JLW1+9aiw7YoXXDBBbngggv2Wvv0pz+d//W//lce\neOCB/PM//3Oee+653HnnnRk+fHhJKQ9P+5vtM888ky1btmTQoEE588wzc/3115eU7vC2v9km//KP\n/J///OeZM2dOampqSkh2+DvQbDl0Ghoa9jqCtHHjxhx33HElJoKu+cUvfpG7774799xzT+cfU3nr\nVq9enSFDhuRtb3tb3ve+92X37t155ZVX9jryzJvz5JNPZt26dXniiSeyYcOG1NXV5W1ve5tzGA+B\noUOH5uMf/3iS5MQTT8yxxx6blpaWzlL6/zpsi9L+fPe73+38+oYbbsinPvUpJekQeeyxx/LrX/86\nn/nMZ/L888/n+OOPLztSr/HSSy/le9/7XhYsWJA+ffqUHafX8te4t27cuHG56667cuGFF2b16tUZ\nOnRo+vXrV3YsOKht27bla1/7Wu67774MHDiw7Di9yjPPPJP169fnxhtvTFtbW9rb25WkQ+SOO+7o\n/Pquu+7KCSecoCQdIj/60Y/S2tqaSy+9NK2trdm0aVOGDh2638f2qqJE5VxxxRWZMWNGfvKTn+T1\n11/Pl7/85bIj9RqLFi3K5s2bc9lll3W+Zezee+/d7yFg/jRPPvlk5s6dmzVr1mT16tWZP3++t928\nBaNHj87JJ5+ciy66KDU1NZk5c2bZkXqV1atXZ/bs2Vm/fn1qa2uzdOnS3HXXXRk0aFDZ0Q5rjzzy\nSF599dVcffXVna+xt956q4sSHQKf/vSnc+ONN2bq1Kl57bXX8jd/8zdlR4I3dPbZZ2f69On52c9+\nll27duUrX/nKAf/NVdXhz6wAAAB76VVXvQMAADgUFCUAAIACRQkAAKBAUQIAAChQlAAAAAoUJQAA\ngAJFCYDDwsUXX5zHH398r7XXXnstp556alpaWvb7nMbGxixfvrw74gHQyyhKABwWJk2alL//+7/f\na+0nP/lJPvShDx3wU9UB4M1SlAA4LPy7f/fv0tTUlM2bN3euPfzww5k0aVJ++tOf5qKLLspnPvOZ\nXHzxxVm/fv1ez3366aczZcqUzts33HBDFi1alCR55JFHMnXq1EydOjXTpk3b6/sDcORSlAA4LBx1\n1FGZMGFClixZkiTZuHFjfvvb3+bss8/Oli1b8vWvfz3z5s3LmWeemQceeGCf51dVVe2ztmHDhnz7\n29/OfffdlwULFuTDH/5wvvWtb1X8ZwGg56stOwAAdNVf/MVf5Ktf/WqmTp2aH/3oR/nEJz6R2tra\nDBkyJNdff306OjrS1taWD33oQ136fitXrkxra2s+97nPpaOjI6+//npOOOGECv8UABwOFCUADhuj\nRo3Kzp0709zcnB/+8Ie54447smvXrlxzzTX54Q9/mBNPPDELFizIqlWr9npe8WjSzp07kyR9+/bN\nqFGjHEUCYB/eegfAYWXSpEmZM2dO+vXrl+HDh2f79u2pqanJ8ccfn9deey0/+9nPOovQHw0YMKDz\nynjt7e351a9+lST5wAc+kOeeey5tbW1JkkcffXSfK+sBcGRyRAmAw8onPvGJ3HbbbZk5c2aSZPDg\nwTnvvPPyF3/xFxk2bFj+6q/+Ktdff32WLl3aeSTpfe97X0466aR86lOfyjve8Y6ccsopSZKGhobc\ndNNN+eu//uv069cvRx11VG655ZbSfjYAeo6qjo6OjrJDAAAA9CTeegcAAFCgKAEAABQoSgAAAAWK\nEgAAQIGiBAAAUKAoAQAAFChKAAAABf8fxnrKYgdXSPEAAAAASUVORK5CYII=\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc9307e90>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "plt.hist(Z_samples, bins=20)\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Probability');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The idea that we can standardize random variables is very important. By changing a random variable to a distribution that we are more familiar with, the standard normal distribution, we can easily answer any probability questions that we have about the original variable. This is dependent, however, on having a large enough sample size.\n",
     "\n",
     "Let's assume that stock returns are normally distributed. Say that $Y$ is the price of a stock. We will simulate its returns and plot it."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 16,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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fp2+eUCGXxxEREdHEwyA0Qovj/WFvo8CWn7KwL7VU7HJGRKvT49kPjuCxfx3EJ/89BZ2O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\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefafe66190>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "Y_initial = 100\n",
     "X = NormalRandomVariable(0, 1)\n",
     "Y_returns = X.draw(100) # generate 100 daily returns\n",
     "Y = pd.Series(np.cumsum(Y_returns), name = 'Y') + Y_initial\n",
     "Y.plot()\n",
     "plt.xlabel('Time')\n",
     "plt.ylabel('Value');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Say that we have some other stock, $Z$, and that we have a portfolio of $Y$ and $Z$, called $W$."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 17,
    "metadata": {
     "collapsed": false,
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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291HhV9/KRnpCMI6cbcIvXz4Bg9FywQjqH3xlyYzOgqHpU8iluHZtPPRGC3Yf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\nilXvC3H7AAAAAElFTkSuQmCC\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefafe1f2d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "Z_initial = 50\n",
     "Z_returns = X.draw(100)\n",
     "Z = pd.Series(np.cumsum(Z_returns), name = 'Z') + Z_initial\n",
     "Z.plot()\n",
     "plt.xlabel('Time')\n",
     "plt.ylabel('Value');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "We construct $W$ by taking a weighted average of $Y$ and $Z$ based on their quantity."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 18,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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S4RjyYNg1/cDQg2d68HZTFxqqcvGxOxrmtKaJVHG7EhFRirlivTahTVJWaMDF9kHYnB6U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\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7ff0794f73d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "Y_quantity = 20\n",
     "Z_quantity = 50\n",
     "Y_weight = Y_quantity/(Y_quantity + Z_quantity)\n",
     "Z_weight = 1 - Y_weight\n",
     "\n",
     "W_initial = Y_weight * Y_initial + Z_weight * Z_initial\n",
     "W_returns = Y_weight * Y_returns + Z_weight * Z_returns\n",
     "W = pd.Series(np.cumsum(W_returns), name = 'Portfolio') + W_initial\n",
     "W.plot()\n",
     "plt.xlabel('Time')\n",
     "plt.ylabel('Value');"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 19,
    "metadata": {
     "collapsed": false,
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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H5uQ8tqcWsD21ADvLHmIjfQnycWH97lwqq+sxmWB4jD+zxoYTH+3fJe809HS9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\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefafdb23d0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "pd.concat([Y, Z, W], axis = 1).plot()\n",
     "plt.xlabel('Time')\n",
     "plt.ylabel('Value');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Note how the returns of our portfolio, $W$, are also normally distributed"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 20,
    "metadata": {
     "collapsed": false,
     "scrolled": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc4127cd0>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "plt.hist(W_returns);\n",
     "plt.xlabel('Return')\n",
     "plt.ylabel('Occurrences');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The normal distribution is very widely utilized in finance especially in risk and portfolio theory. Extensive literature can be found utilizing the normal distribution for purposes ranging from risk analysis to stock price modeling."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Fitting a Distribution\n",
     "Now we will attempt to fit a probability distribution to the returns of a stock. We will take the returns of Tesla and try to fit a normal distribution to them. The first thing to check is whether the returns actually exhibit properties of a normal distribution. For this purpose, we will use the Jarque-Bera test, which indicates non-normality if the p-value is below a cutoff."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 21,
    "metadata": {
     "collapsed": true
    },
    "outputs": [],
    "source": [
     "start = '2015-01-01'\n",
     "end = '2016-01-01'\n",
     "prices = get_pricing('TSLA', fields=['price'], start_date=start, end_date=end)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 22,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "The JB test p-value is:  [  4.42333138e-12]\n",
       "We reject the hypothesis that the data are normally distributed  [ True]\n",
       "The skewness of the returns is:  [ 0.21123495]\n",
       "The kurtosis of the returns is:  [ 5.19572153]\n"
      ]
     },
     {
      "data": {
       "image/png": 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r09ra2u9xDz74YEaOHJnf//3fz5FHHpne3t4MGTIkPT09GTRoUDo7O2v6Oe3t7bWMCa8Y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\nAAAASUVORK5CYII=\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefc934cf50>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# Take the daily returns\n",
     "returns = prices.pct_change()[1:]\n",
     "\n",
     "#Set a cutoff\n",
     "cutoff = 0.01\n",
     "\n",
     "# Get the p-value of the JB test\n",
     "_, p_value, skewness, kurtosis = stattools.jarque_bera(returns)\n",
     "print \"The JB test p-value is: \", p_value\n",
     "print \"We reject the hypothesis that the data are normally distributed \", p_value < cutoff\n",
     "print \"The skewness of the returns is: \", skewness\n",
     "print \"The kurtosis of the returns is: \", kurtosis\n",
     "plt.hist(returns.price, bins = 20)\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Occurrences');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The low p-value of the JB test leads us to *reject* the null hypothesis that the returns are normally distributed. This is due to the high kurtosis (normal distributions have a kurtosis of $3$).\n",
     "\n",
     "We will proceed from here assuming that the returns are normally distributed so that we can go through the steps of fitting a distribution. Next we calculate the sample mean and standard deviation of the series."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 23,
    "metadata": {
     "collapsed": false
    },
    "outputs": [],
    "source": [
     "# Take the sample mean and standard deviation of the returns\n",
     "sample_mean = np.mean(returns.price)\n",
     "sample_std_dev = np.std(returns.price)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Now let's see how a theoretical normal curve fits against the actual values."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 24,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
     {
      "data": {
       "image/png": 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ta4PWH9piOgcA4HIRDaNwOCyf7y/vurMsS47jRC0KgLssPnlDVy7R7TbXjzxx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\n",
       "text/plain": [
        "<matplotlib.figure.Figure at 0x7fefadbe6c90>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "x = np.linspace(-(sample_mean + 4 * sample_std_dev), (sample_mean + 4 * sample_std_dev), len(returns))\n",
     "sample_distribution = ((1/np.sqrt(sample_std_dev * sample_std_dev * 2 * np.pi)) * \n",
     "                       np.exp(-(x - sample_mean)*(x - sample_mean) / (2 * sample_std_dev * sample_std_dev)))\n",
     "plt.hist(returns.price, bins = 20, normed = True);\n",
     "plt.plot(x, sample_distribution)\n",
     "plt.xlabel('Value')\n",
     "plt.ylabel('Occurrences');"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Our theoretical curve for the returns has a substantially lower peak than the actual values, which makes sense because the returns are not actually normally distributed. This is again due to the kurtosis of the normal distribution. The returns have a kurtosis value of around $5.20$, while the kurtosis of the normal distribution is $3$. A higher kurtosis leads to a higher peak. A major reason why it is so difficult to model prices and returns is due to the underlying probability distributions. A lot of theories and frameworks in finance require that data be somehow related to the normal distribution. This is a major reason for why the normal distribution seems to be so prevalent. For example, the basis of the Black-Scholes pricing model for options assumes that stock prices are log-normally distributed. However, it is exceedingly difficult to find real-world data that fits nicely into the assumptions of normality. When actually implementing a strategy, you should not assume that data follows a distribution that it demonstrably does not unless there is a very good reason for it.\n",
     "\n",
     "Generally, when trying to fit a probability distribution to real-world values, we should have a particular distribution (or distributions) in mind. There are a variety of tests for different distributions that we can apply to see what might be the best fit. In additon, as more information becomes available, it will become necessary to update the sample mean and standard deviation or maybe even to find a different distribution to more accurately reflect the new information. The shape of the distribution will change accordingly."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company.  In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*"
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
    "display_name": "Python 2",
    "language": "python",
    "name": "python2"
   },
   "language_info": {
    "codemirror_mode": {
     "name": "ipython",
     "version": 2
    },
    "file_extension": ".py",
    "mimetype": "text/x-python",
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython2",
    "version": "2.7.12"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 0
 }