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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"This work derives from the works of Michael Halls-Moore on [Quantstart](https://www.quantstart.com/) and [Quantopian Lecture Series](https://www.quantopian.com/lectures/). \n", | |
"# Random Variables" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"A **random variable**, X, is a variable quantity (i.e., not necessarily fixed) whose possible values depend on a set of random events. Like a traditional mathematical variable, its value is unknown a priori (before the outcome of the events is known)\n", | |
"A random variable's possible values might represent the possible outcomes of a yet to occur event. This event can take on a range of values, each with an associated probability, giving the random variable a probability distribution\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For example, the value of a roll of a die is a random variable. This variable,X, can take values 1 - 6, each with a probability of ⅙, but it’s exact value is unknown till the die roll is actually performed." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"A **probability distribution** is a mathematical function that assigns a probability to every possible value of a random variable.\n", | |
"For example, the random variable X that represents the value of a die rolls and can take values 1 to 6, each with a probability of ⅙ has a distribution: $P(X=i) = 1/6$, where i = 1,2,3,4,5,6" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Random variables can be separated into two different classes:\n", | |
" - Discrete random variables\n", | |
" - Continuous random variables" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### Discrete Random Variables" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Discrete Random Variable have finitely countable outcomes. For example, the value of a coin toss can only be H or T, each with a probability of $1/2$. Similarly the value of a die roll can only be between 1 and 6" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For discrete random variables where X can take a finite set of values, the probability distribution function, gives the probability $p(x)$ that X is exactly equal to some value.\n", | |
"$p(x) = P(X=x)$, where x belongs to the finite set of values that are possible" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"A probability distribution function has two main properties:\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 $1$." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Uniform Distrobution\n", | |
"\n", | |
"Let's look at the distribution of a die roll below. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 39, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [], | |
"source": [ | |
"import pandas as pd\n", | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"import scipy\n", | |
"from auquanToolbox import dataloader as dl\n", | |
"from __future__ import division" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"collapsed": true | |
}, | |
"outputs": [], | |
"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.randint(self.low, self.high, numberOfSamples)\n", | |
" return samples" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"A die roll can have 6 values, each value can occur with a probability of $1/6$. Each time we roll the die, we have an equal chance of getting each face. This is an example of uniform distribution. The chart below shows distribution for 10 die rolls." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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IeHNE/CwifhER59TZliRpZLUFfkT0AJcDbwEOAd4ZEYfU1Z4kaWR1XuEvAn6RmY9k5nPA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\nGPiSVAgDX5IKYeBLUiEMfEkqxP8B8RYdhviuez8AAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x436b358>" | |
] | |
}, | |
"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'])\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In the short run this looks uneven, but if we take a large number of samples it is apparent that each face is occurring the same percentage of times. The chart below shows distribution for 10,000 die rolls" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x94385c0>" | |
] | |
}, | |
"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']);\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"A random variable is **independent and identically distributed** *(i.i.d)* if each random variable has the same probability distribution as the others and all are mutually independent, i.e. outcome of one doesn’t affect the other. For example, random variables representing die rolls are i.i.d. The value of one die roll does not affect the value of next die roll." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Binomial Distribution\n", | |
"\n", | |
"A binomial distribution is used to describe successes and failures in a binary experiment. This can be very useful in an investment context as many of our choices tend to be binary like this. A single experiment which can result in success with probability p and failure with probability (1-p) is called a Bernoulli trial.\n", | |
"\n", | |
"$$p(1) = P(X = 1) = p \\ \\ \\ \\ \\ \\ \\\\\n", | |
"p(0) = P(X = 0) = 1-p$$\n", | |
"\n", | |
"A binomial distribution is a set of $n$ Bernoulli trials. There can be between $0$ and $n$ successes in $n$ trials, with each trial having the same probability of success, $p$, and all of the trials being independent of each other. A binomial random variable is denoted as $X$ **~** $B(n, p)$. \n", | |
"\n", | |
"The probability function of a binomial random variable $p(x)$ is the probability that there are exactly $x$ sucesses in $n$ trials. This is defined by choosing $x$ trials which should result in success and multiplying by the probability that these $x$ trails result in success and the remaining $n - x$ trials result in failure. 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": false | |
}, | |
"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": [ | |
"Let's draw the distribution of 10000 samples of a binomial random variable $B(5, 0.5)$, i.e 5 trials with 50% probability of success." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x94ed588>" | |
] | |
}, | |
"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');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We see that the dsitribution is symmetric, since probability of success = probability of failure. If we skew the probabilities such that probability of success is 0.25, we get an asymmetric distribution." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa25ae10>" | |
] | |
}, | |
"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');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We can extend this idea of an experiment following 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" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For continuous random variables (where X can take an infinite number of values over a continuous range), the probability of a single point, the probability that X is exactly equal to some value is zero. In this case, the probability distribution function, gives the probability over intervals which can include infinitely many outcomes. Here we define a **probability density function** (PDF), $f(x)$, such that we can say:\n", | |
"$$P(a < X < b) = \\int_a^b f(x)dx$$\n", | |
"\n", | |
"For example, if you buy a piece of rope and the scale reads 1 meter, this value is possible but the probability that the length is exactly 1 meter is zero; You can keep increasing the accuracy of your instrument so that the probability of measuring exactly 1m tends to zero. However, we might be able to say that there is 99% probability that the length is between 99cm and 1.01 m. \n", | |
"Just like a probability distribution function $f(x)$ gives the probability that a random variable lies in a range, a cumulative distribution function $F(x)$ describes the probability that a random variable is less than or equal to a given value.\n", | |
"$$F(x) = P(X \\leq x) = \\int_{-\\infty}^{x} f(t) dt $$\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": { | |
"collapsed": true | |
}, | |
"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" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The most widely used distribution with widespread applications in finance is the normal distribution.\n", | |
"\n", | |
"# Normal Distribution\n", | |
"\n", | |
"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 the sum of many independent random variables tends toward a normal distribution, even if the original variables themselves are not normally distributed. The convenience of the normal distribution finds its way into certain algorithmic trading strategies as well. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"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": {}, | |
"source": [ | |
"Normal distributions are described by their mean ($\\mu$) and variance ($\\sigma^2$, where $\\sigma$ is the standard deviation). The probability density of the normal distribution 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.\n", | |
"\n", | |
"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." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 15, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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CMz2eJQzTO713n7Mi3af/F/oNOrp558Ej1DQEemWHd9iU4f0pq66noqbh2MaM\nITDnLihdAR884F1wpkezhGF6n4Nb4bWfwoRLYPJxs9GwNtS2P6WX1zDgWOf+USdcBYUXwiv/Dyp3\nehCZ6eksYZjeRdUZFeVPhkvu/sS05ev2VJHsF8b3ojmkWpoy3Kk9rS9tkTBE4NJfOq+f+3fn38qY\nTrCEYXqX1Y/Atjfhwh9C/+Gf2L2+tJoJeVmkJPXeX/2stGTGZGd8sh8DYGCBM9S25CVY91T8gzM9\nWu/9qzF9T80+ePE7MOpMmP7FT+xWVdbtqerVHd5hU4b3/2STVNisL0H+DPjnf8LhA/ENzPRoljBM\n7/HP/4SmeueeC98nf7VLK+uoPNLElF54w15LU/MHsPtQHZVHWll9z+eHy38D9VVOgjUmSpYwTO+w\n8XnY8Ayc+5+QXdTqIeEmmqnDe+8IqbBwLWr9njamfBs6Bc76Onz4OJS8EsfITE9mCcP0fPVV8Pw3\nYOhUOPOrbR62fk8Vfp8waVjvTxjhju+1LTu+I539TRhSBM99DRpq4xSZ6cksYZie76X/htp9TjOL\nP7nNw9bsqqQoN5O0ZH8cg/PGoIwURg7ux0e7K9s+KDkNLv+tM8T2tZ/ELzjTY1nCMD3b9ndg5R/h\ntNsgv+01rINB5cNdlUwrGNTmMb3NySMHsWZnOwkDYNTpMPMWeO/3sGt5fAIzPZYlDNNzNdXB4jtg\n4CiY/e12D926/zDV9QGmFQyMU3DemzZyIHuq6imrqm//wPP/2xmCvPgOCLTSSW5MiCUM03O9/nNn\nJtrLf+PMytqO1TsPAc6HaF8RTo5rdh1q/8C0/nDpPVDxMbz9yzhEZnoqSximZ9qzGpb9FqZdf9xM\ntG1ZvauSrFRnJte+YvLw/qT4fazuqFkKYPzFcMLV8ObdUP6x+8GZHsnVhCEic0SkWERKROTOVvZP\nFJF3RaRBRL7ZmbKmD2tugmfvgIyc42aibc+anZWcXDAQn6/3rOHdkdQkP5OH92f1rigSBsCcn0Nq\nFjx7u81oa1rlWsIQET9wLzAXmAxcKyKTWxx2EPgKcHcXypq+6p1fw761cMkvoF/HTUxHGgNsLKvu\nU81RYdMKBvLR7koCzcGOD87Ihrn/E5rRdqH7wZkex80axiygRFW3qmoj8ARw3NShqlquqsuBps6W\nNX1UxSZnFb3JV8CkS6MqsmZnJUGFaaP6zgipsOkFg6hvCrJhbxs38LV0wlVQdJEzo+2h7a7GZnoe\nNxNGPrBBEcalAAAZkklEQVQr4v3u0LaYlhWRBSKyQkRWVFRUdClQ00MEg86iSMnpzjoXUfpg+0FE\n4JQ+mDBmjh4MwAfbDkZXQAQu+SWID/7xNZvR1hynx3d6q+pCVZ2hqjNycnK8Dse4afmDsOt9p609\nMzfqYiu2H2JiXn/6p7V9U19vlTcgjZGD+7FiewcjpSINHAkX/AC2vgZrHnMrNNMDuZkwSoGREe9H\nhLa5Xdb0RpU74eUfwLjz4aT5URcLNAdZtfMQs0b3vdpF2MzRg1m+/SDamdrCjJuh4HRY+m1nFmBj\ncDdhLAeKRGSMiKQA84HFcShreptgEJ79stNcctmvPrEoUnvW76nmSGMzM0JNM33RzNGDOXC4ka37\nD0dfyOeDy37j3Bz5nDVNGYdrCUNVA8DtwFLgY+BJVV0vIreKyK0AIpInIruBfwe+KyK7RaR/W2Xd\nitUkuOUPOIsiXfwTZwGgzhTd7rTdz+zjCQNgxfYo+zHCcsbD+d+D4iXWNGUASHLz5Kq6BFjSYtv9\nEa/LcJqboipr+qD9m+Gl7zsjd6Z/odPFP9h2kJGD+5E3IM2F4HqGcTkZDM5I4f2tB/nczM4lXE67\nDYr/CS/cCWPOcfo3TJ/V4zu9TS/WHIBF/wrJ/ZxZVTvRFAXQHFTe23qAM8ZmuxRgzyAinD52CMu2\nHOhcPwY4iy1dcR9oEJ69zWkeNH2WJQyTuN65B0pXOjfoZeV1uvj6PVVU1wc4o3CIC8H1LKePG0JZ\ndT3bOtOPETZotNMcuO1Nu6Gvj7OEYRLT3g+dyQWnXAlTP9ulUyzb4qxXffo4SxhnFjq1rHe2dHEN\n7+lfgMIL4eX/dpoJTZ9kCcMknqY6WHQrpGc7tYsueqdkP+OHZpKb1Xf7L8JGD0ln+IA03t2yv2sn\nEIF5v3OaBxf9qzOfl+lzLGGYxLP0O1C+AebdC+ldG93UGAiyfPtBzhjXt/svwkSE08dl8+6WAwSD\nXRwim5XnTINeuhJejW7SR9O7WMIwiWXDs7DiD3DGHVB0QZdPs3LHIeqbgpxhzVFHnVk4hENHmli/\nJ8p5pVoz5TNwyhfhnV9BySsxi830DJYwTOI4tMOZtnz4dPjU97t1qtc3lZPsF84otBpG2Dnjnalz\nXi8u796JLv4Z5ExymqbsLvA+xRKGSQzNTfDULYDCVQ9BUkq3Tvf6xgpmjh5MZqqrtxr1KNmZqZw4\nYgCvdTdhpKTD1X+EhlpYtMCG2vYhljBMYnjtJ7D7A2fqj8FjunWqPZV1FO+rYfaE6Cco7CvOm5DL\nml2VHDrczbW7cyfB3Ltg6+vO8GfTJ1jCMN4reQXevscZutnFIbSRXi92prmfPdFmL25p9oQcggpv\nbo7BUgDTb3CGPb/6E9j5XvfPZxKeJQzjrUM7nKaonEnOtOUx8FpxOfkD+/Wp9bujdeKIgQzOSOG1\njd1sloJjk0EOLIC/fdH6M/oASxjGO0118NfrnPWj5z/qtI1305HGAG9uquDCyUORTk4l0hf4fcKn\nJuby6sZyGgMx6HtIGwCfewTqq+BvX4BAN5u6TEKzhGG8oQr/+CqUrYXPPgBDxsXktK8XV9AQCHLx\nlM5PJdJXzJmSR3V9gPe2dvGu75bypjpzfe1811k/w/RaljCMN96/Hz76K8z+Noy/OGanfWFdGYMz\nUpjZhxdM6shZRdmkp/h5YX1Z7E56wlXOvTPLH4BVf4ndeU1CsYRh4m/TUueb6MRL4exvxuy0DYFm\nXt1YzoWThpLkt1/ttqQl+5k9MZcX1++juat3fbfm/B/A2PPgua/Dtrdid16TMFz9qxKROSJSLCIl\nInJnK/tFRH4T2v+RiEyP2LddRNaKyBoRWeFmnCaOytbC32+CvBPgyoXOym4x8tam/dQ2BJgz1Zqj\nOjJnSh77axv4YFsnF1Vqjz8Jrn4YBo91+qZsksJex7WEISJ+4F5gLjAZuFZEJrc4bC5QFHosAH7f\nYv9sVT1ZVWe4FaeJo+q98NjnnI7Sa/8KKRkxPf2iNaUMzkjhrCK7u7sjF0waSkaKn2fXlMb2xP0G\nwuefBF8SPHo1HI5RP4lJCG7WMGYBJaq6VVUbgSeAeS2OmQf8WR3vAQNFZJiLMRmv1FXCY1c7o2n+\n5a/QP7b/zdX1Tby8YR+XnTiMZGuO6lC/FD8XT83j+bV7qW9qju3JB42Gax+H6j3w+OegsQtrcJiE\n5OZfVj6wK+L97tC2aI9R4GURWSkiC1yL0riv8Qg8Ph/KN8I1DzvNUTH2wtoyGgJBrpjW8lfMtOXK\naSOoqQ/waizuyWhp5Cy46g/OzLZ/vQ4CDbG/hom7RP4qdpaqnozTbPVlETmntYNEZIGIrBCRFRUV\nMbh71cRWc5MzPn/ne06fRWHXZ6Btz1OrdjMmO4OTRw505fy90enjhpCblcrTq3a7c4FJl8Flv4Et\nr8LTC5z7bUyP5mbCKAUiV4wfEdoW1TGqGn4uBxbhNHF9gqouVNUZqjojJ8emgkgo4TW5N7/orKMw\n9UpXLlNSXsv72w5y9YwRdrNeJ/h9wlWnjODVjeXsqaxz5yLTr4cLfwQbnnHuu7GJCns0NxPGcqBI\nRMaISAowH1jc4pjFwA2h0VKnAVWquldEMkQkC0BEMoCLgHUuxmpirbkJnr4F1j0FF/wQZtzo2qUe\nfX8HyX7hmhkjOz7YHOfaWQUo8MQHO927yJlfgXP+A1b/Bf5xhyWNHsy1uZ9VNSAitwNLAT/wkKqu\nF5FbQ/vvB5YAnwZKgCNA+FNlKLAo9G0xCXhMVV9wK1YTY81NztDZjxc73y7P/Iprl6prbOaplbuZ\nM3UY2Zmprl2ntxo5OJ3zxufwxPJd3HF+kXsDBmZ/B8QHb9zlJIx5vwOf351rGde4uliAqi7BSQqR\n2+6PeK3Al1sptxU4yc3YjEua6uDvN0Px885CO6ff5urlFq0upbo+wOdPLXD1Or3Z9aeP4qY/rWDJ\n2r3MO9mlQQMizl394ofXfwrNjXDF77u97omJr0Tu9DY9zZGD8OcroHgJfPpu15NFc1BZ+OYWThwx\ngFPHdG3tbwPnjc9lXE4G97+xFec7nJsX+y+44Aew7u+hYdbdWC7WxJ0lDBMblbvgoTmwZ5WzGtus\nL7l+yRfWlbH9wBH+7dxx1tndDT6f8K/njuPjvdW8sSkOIw3P+jrMu8+ZPuRPn7Zp0XsQSxim+3a+\nDw+eDzVlcP0imPIZ1y8ZDCr3vV7CmOwMLrKZabvtipPzyeufxr2vlbhfywCY9nnnBs4DW53fnT1r\n3L+m6TZLGKZ7VvwR/nQJJKfDzUth9Flxuexza/eyfk81d3yqEL/PahfdlZLk47bZ41i+/VD31/yO\nVtGFcOPzoEF46GL46Mn4XNd0mSUM0zVNdc64+ue+BmPOgQWvOes8x0FjIMjdS4uZmJflXidtHzR/\nZgGjhqTzPy8Ux3YW2/YMnwYL3oD8U+DpL8EL37JFmBKYJQzTeWXrYOF5sPJPTnv05/8G/eK3/sTD\ny7az8+AR/mvORKtdxFBKko9vXjSBjWU1PLliV8cFYiUzB254Fk69Fd67z2miqtgUv+ubqFnCMNEL\nNsO798IDs6HuEFz3tDPiJY7j6Usr6/jlS5s4f2Iu502wO/tj7dIThzFrzGB+/s+N7K+N4/xP/mSY\nexfMfwyqdsP/nQPL/2A3+SUYSxgmOmXr4A8XOQsfjTsf/m0ZFJ4f1xBUle8/49zw/8N5U2xklAtE\nhJ9+5gSONAb4f//YEP8AJl7i/G4VnAbP/zs8fKnVNhKIJQzTvoYaePkHsPBcOLQdrnzAmbo6I/5r\nTjzy/k5e2VjONy+ewIhB6XG/fl9RmJvJ7bOLWPzhHhatdmliwvb0H+bUXi//LexbB/efCa/9zJn1\n2HjKEoZpXXPAaRL4zTR4+x44cT7cvhxOvMa5azfONuyp5kfPbeDc8TnceMbouF+/r/ny7HHMGj2Y\n7y5ax9aK2vgH4PPB9Bvg9hUw6XJ44+fw21Ng9aM2662HLGGY4zUH4KO/we9Pd5oEhhTBLa/CFfdC\nujd3U++rrufmh5czKD2ZX1xzEj7r6HZdkt/Hr+afTGqyn5v+tJxDhz0auZSZ66yrceMLTs3j2duc\n/o31z1j/hgcsYRhHUx2sfBh+N8OZZVb88LlH4cYlMOIUz8KqPNLITX9aTlVdE3/4wkybYDCOhg/s\nxwM3nMKeqnpu+fMKahsC3gUz6nS45RX47B8gUO+ssXLfabDmcRuGG0cSl7s642TGjBm6YsUKr8Po\nWQ5ugxUPOVNP1x1yxsWf/U2Y8GmnWcDL0A43ct2D71NSXsvCG07hvAm5nsbTV72wbi9ffmw1J40Y\nwJ9umkX/tGRvAwo2O+trvPVLp48jI8dpvjrlRhhoU9x3loisVNUZUR1rCaMPOnIQNjwLa/8GO95x\nahOTLoWZt8Dosz3po2ipuKyGW/68nPLqBhbeMINzx9sQWi+9sK6M2x9bxagh6Tz4hZmMyc7wOiRQ\nhS2vOH1tm15w3o85x+lnm3QZpA3wOsIewRKG+aTKnVD8Amz6pzPpW7DJ6Z848RqYdh30H+51hIAz\nR9Sj7+/gp0s2kpWWxP9dfwrTCuJ3U6Bp27tbDnDboysJNCvfu2wyV5+SQCscVu6E1Y8404sc2gb+\nVBhzNhRd5DwGj/E6woRlCcM4f0Db33FqEDvegYNbne1DCmHCXJh6FQw7KSFqE2Grdh7iJ89/zMod\nhzi7KJu7rz6Jof3TvA7LRNh18Ajf+NuHfLDtIKeNHcx3L5nM1PwE+iavCqUrYd3TsHkpHChxtg8p\ngnGfgpGzYOSpMGBEQv3ueylhEoaIzAF+jbPi3oOq+vMW+yW0/9M4K+59UVVXRVO2NX0yYQSDULkD\nytZGPD6C6tDy6WkDoOAMZ1LA8RdDdpG38bbQGAjyWnE5f3pnO+9uPUBOVir/cfGExPr2ao4TDCqP\nfrCTe17axMHDjZw7PofPn1rAOeNzSEtOsFX0DmyBzS85yWPne9AUupcjaxiMmAl5JzpzoOVOgkGj\n++QqgAmRMETED2wCLgR246zxfa2qbog45tPAHTgJ41Tg16p6ajRlW9MrE0agwZk2vHaf81xT5txA\nd3Cr8zi0HZpDUziID7LHw9Cpzh/D6DMhd4rnndeRVJVdB+t4Z8t+3t68n7dL9lNV10Re/zRuPHM0\n1502ioxUVxeCNDFSVdfEI+/t4I/vbGd/bQOZqUlcMCmXcyfkcPLIQYwekp5YSb854HSS7/oAdn/g\nPFfuOLY/Kc2piQwaBQNHwcAC59F/GGTkOjerJvW+UXqJkjBOB36gqheH3n8LQFV/FnHM/wGvq+rj\noffFwHnA6I7KtsaThKHqTM8cbA49NznD/AL1oUeD84EeaDj2PvxorIH6KmfVsfoqaKiOeF/pJIf6\nyk9eMzkdBo1x2mUHj3WamfJOcL4lJfeL78+P842zIRCkvqmZuqZm6puaOXSkiYqaBipqG6ioaWBf\nVT2by2vYvK+WmtDwzKH9UzmrMIdLTxzG2UXZJLm1nrRxVVNzkHe3HOD5j/aydEMZlUeaABiYnsyE\noVkUDE6nYHA6QwekMSg9hYHpyQxKT6Z/v2T6JftJSfKR4vd5k1waaqGiGMo3QMVG2L/Jac6t3Hms\nNhIpbUAoeeQ49yWlZh3/SMmE1P7O66TU0CMN/CnO6/BzeJsvyanViN9pIvPg36AzCcPNr3L5QOSU\nl7txahEdHZMfZdmY2fGjE0gN1uMjiI8ggh57rXrcdn/Efj+xuXEogJ9a0qmVDOeZDGpkIAcZzX7/\nIA7IIPYziAoGc0AGcZABaCVQCWx1chYcBN4hMv0f/11AW91+/PHaxva2j2kMBGkItP/vIAJDMlIZ\nl5PBZ6bnM35oFqeOGUxhbmZifQM1XZLs93HO+BzOGZ/DT4MnsGlfDWt2VbJmZyVbKmp5Y1MF5TUd\nT2SY4vc5ySPJh08EX+jzUxBEwBf6XQm/dvaFtoded/33qSD0uMh5m6YMSK0mT/cxJHiQQVrJQK1i\nUHMlg6oqGVhZSZaW0k/ryKCODD0ck8+D5qOfNs4nztHXErndh+L8nIqgCLVJAyn8zvJuX78jPb7u\nLyILgAUABQUFXTrHnswTkGAAFSGIH5VjKaPlNhWfsy/0rMgntjX5UglIMoHws6Q4D5/z3ORLISDJ\nNPjSafBn0ihpEPoDOPpzHfczOv9Rw4DhEXuOO/64v5M2jmlxzmPbozm+9T/E1CQfacl+0pL99Es+\n9npAejI5mankZqUyOCPFag99hN8nTBrWn0nD+nPtrGN/j3WNzeyvbeDQkUYqjzRx6EgjVXVNNDQF\naWx2vnQ4Xz6aaQwEcZbjUIJBUNSpyAPB0Ivw65bbY6s/MIIDwIGODlUlWRtJCx4mLVhHWvAwSdpI\nsjaSpE2hx7HX4e0+DaUIbT72RVWbnVShEWkj/Dp0vIT+EQR1/p1SMimM9Y/fCjcTRikQeRfNiNC2\naI5JjqIsAKq6EFgITpNUVwI9/euPdaWYMSZK/VL8jByczsjBNmlkT+bm177lQJGIjBGRFGA+sLjF\nMYuBG8RxGlClqnujLGuMMSaOXKthqGpARG4HluIMjX1IVdeLyK2h/fcDS3BGSJXgDKu9sb2ybsVq\njDGmY3bjnjHG9GGdGSVlPZHGGGOiYgnDGGNMVCxhGGOMiYolDGOMMVGxhGGMMSYqvWqUlIhUADs6\nPLB12cD+GIYTKxZX51hcnWNxdU5vjGuUqka1QlmvShjdISIroh1aFk8WV+dYXJ1jcXVOX4/LmqSM\nMcZExRKGMcaYqFjCOGah1wG0weLqHIurcyyuzunTcVkfhjHGmKhYDcMYY0xULGFEEJGTReQ9EVkj\nIitEZJbXMYWJyB0islFE1ovI/3gdTyQR+YaIqIhkex0LgIj8b+jf6iMRWSQiAz2MZY6IFItIiYjc\n6VUcLYnISBF5TUQ2hH6nvup1TGEi4heR1SLynNexRBKRgSLy99Dv1sehZag9JyJfD/0frhORx0Uk\nza1rWcI43v8AP1TVk4Hvh957TkRmA/OAk1R1CnC3xyEdJSIjcda13Ol1LBFeAqaq6onAJuBbXgQh\nIn7gXmAuMBm4VkQmexFLKwLAN1R1MnAa8OUEiu2rwMdeB9GKXwMvqOpE4CQSIEYRyQe+AsxQ1ak4\ny0HMd+t6ljCOpzjrMgIMAPZ4GEukfwN+rqoNAKpa7nE8ke4B/hMXFsjsKlV9UVUDobfv4azY6IVZ\nQImqblXVRuAJnMTvOVXdq6qrQq9rcD788r2NCkRkBHAJ8KDXsUQSkQHAOcAfAFS1UVUrvY3qqCSg\nn4gkAem4+LllCeN4XwP+V0R24XyL9+SbaSvGA2eLyPsi8oaIzPQ6IAARmQeUquqHXsfSjpuAf3p0\n7XxgV8T73STAh3JLIjIamAa8720kAPwK5wtI0OtAWhgDVAB/DDWXPSgiGV4HpaqlOJ9VO4G9OKuW\nvujW9dxc0zshicjLQF4ru74DnA98XVWfEpFrcL5NXJAAcSUBg3GaDmYCT4rIWI3DELcO4vo2TnNU\n3LUXl6o+GzrmOzhNL4/GM7aeREQygaeAr6lqtcexXAqUq+pKETnPy1hakQRMB+5Q1fdF5NfAncD3\nvAxKRAbh1FrHAJXA30TkOlV9xI3r9bmEoaptJgAR+TNO+ynA34hjtbiDuP4NeDqUID4QkSDO3DEV\nXsUlIifg/JJ+KCLgNPusEpFZqlrmVVwR8X0RuBQ4Px6JtQ2lwMiI9yNC2xKCiCTjJItHVfVpr+MB\nzgQuF5FPA2lAfxF5RFWv8zgucGqHu1U1XAv7O07C8NoFwDZVrQAQkaeBMwBXEoY1SR1vD3Bu6PWn\ngM0exhLpGWA2gIiMB1LweAI0VV2rqrmqOlpVR+P8QU2PR7LoiIjMwWnWuFxVj3gYynKgSETGiEgK\nTmfkYg/jOUqcLP8H4GNV/aXX8QCo6rdUdUTo92k+8GqCJAtCv9e7RGRCaNP5wAYPQwrbCZwmIumh\n/9PzcbEzvs/VMDrwJeDXoc6jemCBx/GEPQQ8JCLrgEbgCx5+a+4JfgekAi+Faj/vqeqt8Q5CVQMi\ncjuwFGf0ykOquj7ecbThTOB6YK2IrAlt+7aqLvEwpkR3B/BoKPlvBW70OB5CzWN/B1bhNL+uxsW7\nvu1Ob2OMMVGxJiljjDFRsYRhjDEmKpYwjDHGRMUShjHGmKhYwjDGGBMVSxjGdEJohteLW2z7moj8\nvp0yte5HZoz7LGEY0zmP88nZQOeHthvTq1nCMKZz/g5cErp5Kzxx33BgtYi8IiKrRGRtaGLG44jI\neZFrPIjI70JTmCAip4QmllwpIktFZFg8fhhjOsMShjGdoKoHgQ9w1rgAp3bxJFAHfEZVp+NM4/KL\n0FQNHQrN6fRb4CpVPQXnzv6fxDp2Y7rLpgYxpvPCzVLPhp5vBgT4qYicgzM1dz4wFIhmbq0JwFSO\nTWXix5mq2piEYgnDmM57FrhHRKYD6aHpuL8I5ACnqGqTiGzHmXE1UoDja/Xh/QKsV9WEWPLTmLZY\nk5QxnaSqtcBrOE1H4c7uAThrOTSFltQd1UrRHcBkEUkNrTN+fmh7MZATXiNaRJJFZIqrP4QxXWA1\nDGO65nFgEcdGTD0K/ENE1gIrgI0tC6jqLhF5ElgHbMOZWRRVbRSRq4DfhJYCTcJZeS5RZrY1BrDZ\nao0xxkTJmqSMMcZExRKGMcaYqFjCMMYYExVLGMYYY6JiCcMYY0xULGEYY4yJiiUMY4wxUbGEYYwx\nJir/H60uMU1Dyp1CAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa835be0>" | |
] | |
}, | |
"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');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In modern portfolio theory, stock returns are generally assumed to follow a normal distribution. We use the distribution to model returns instead of stock prices because prices cannot go below $0$ while the normal distribution can take on all values on the real line, making it better suited to returns. \n", | |
"\n", | |
"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." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## 68-95-99.7 rule or 3 sigma rule\n", | |
"\n", | |
"This rule of thumb states that 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 ($\\mu \\pm 3\\sigma$)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Standardzing Random Variables to Normal Distribution\n", | |
"\n", | |
"**The power of normal dsitributions lies in the fact that using the central limit theorem, we can standardize different random variables so that they become normal random variables** \n", | |
"\n", | |
"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": 16, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa8800b8>" | |
] | |
}, | |
"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');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 17, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa11aa58>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(Z_samples, bins=20)\n", | |
"plt.xlabel('Value')\n", | |
"plt.ylabel('Probability');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"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." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Stock Returns as Normal Distribution\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": 27, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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oOu13Uc0rF93+Ol6wyMB3cll2IDF/aHprbZo9nQERYcHERqzYkVqQSOEoNQ75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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa20ca20>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"Y_initial = 100\n", | |
"X = NormalRandomVariable(0, 1)\n", | |
"Y_returns = X.draw(1000) # generate 1000 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')\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"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": 28, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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U2mH+HNL7u4lU1+4P9Jjuoz/NHRtKe32lIytoa0cAX0Dz7XOm8K1zIi/1OtGR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\n/xL7UlxmUXmGAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x974ffd0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"Z_initial = 50\n", | |
"Z_returns = X.draw(1000)\n", | |
"Z = pd.Series(np.cumsum(Z_returns), name = 'Z') + Z_initial\n", | |
"Z.plot()\n", | |
"plt.xlabel('Time')\n", | |
"plt.ylabel('Value');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 29, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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guOetjXwrZi/FRXPGJ/U62d4M7rhwZq/a0JlWXyBqlY1KP+EeRnfFpO6/fHbc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\n4LzevLbq8Nnb32ZnfRvnHD6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2pvtQSg1+wy5ggDWB3dRN7qet+6wKf9NGWlX9nMkL61r8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\nrkJggg==\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa25a9b0>" | |
] | |
}, | |
"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');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"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": 30, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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0j6GiysEPqrJO+csXH1796NKYMDNJkU2vd6QOpW1TrWoDTZGlipgwM2kJ4Zwp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\nGo1G4xfakGg0Go3GL/4/K7+Mt1y1ujAAAAAASUVORK5CYII=\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa2e0e48>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"pd.concat([Y, Z, W], axis = 1).plot()\n", | |
"plt.xlabel('Time')\n", | |
"plt.ylabel('Value');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Note how the returns of our portfolio, $W$, are also normally distributed" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 31, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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4YGz9wa5NkrTMpu0MYkFJNgObu9XHktzTLZ8OfGWYqno3y32D2e7fLPcNZrt/U923vPUp\nHf69STZX1fb5dpq2gNgPrBlbP6tr+1tdh/5ep5LsqqqN/ZY3jFnuG8x2/2a5bzDb/ZvlvsGofzR+\nl46btktMtwLrkpyd5LuAi4HrB65Jko5JU3UGUVWHkvwScCNwHHBVVd01cFmSdEyaqoAAqKqPAh99\nEofOe6q0ws1y32C2+zfLfYPZ7t8s9w0m6F+qajkKkSStMNN2D0KSNCVmKiCS/FaSO5PckeQvkjxn\n6JqWSpK3JflC178PJXn20DUtpSQ/k+SuJN9JMhMjR2Z52pgkVyV5JMnuoWtZaknWJPlEkj3df5Nv\nGLqmpZLkGUluSfI/u779x3n3n6VLTEmeVVWPdsuvB9ZX1esGLmtJJHkJ8PHuRv5bAarq1wYua8kk\n+SHgO8C7gV+pql0Dl/SUdNPG/DXwzxl94fNW4JKq6mVWgOWW5MeBx4D3VtU/GrqepZTkTODMqro9\nySnAbcArZuHfLkmAk6rqsSRPBz4NvKGqPtvaf6bOIObCoXMSMDPpV1V/UVWHutXPMvqOyMyoqrur\n6p6F91wx/nbamKr6f8DctDEzoao+BXxt6Dr6UFUPVdXt3fJB4G5mZEaHGnmsW3169zrq78mZCgiA\nJNuSPAD8K+A/DF1PT34e+NjQRWheThszA5KsBV4IfG7YSpZOkuOS3AE8AtxUVUft24oLiCQ3J9nd\neG0CqKpfr6o1wDXALw1b7eIs1Ldun18HDjHq34oySf+kaZHkZOA64LIjrk6saFV1uKo2MLoKcU6S\no14inLrvQSykql484a7XMPo+xVt6LGdJLdS3JP8GeBlwXq3Am0eL+LebBQtOG6Pp1V2fvw64pqo+\nOHQ9faiqbyT5BHAB0BxssOLOIOaTZN3Y6ibgC0PVstSSXAD8KvAvqupbQ9ejBTltzArV3ci9Eri7\nqt45dD1LKcmquRGQSU5kNIjiqL8nZ20U03XADzAaDXM/8Lqqmom/2pLsBU4Avto1fXZWRmgBJHkl\n8PvAKuAbwB1Vdf6wVT01SS4Efo8npo3ZNnBJSybJ+4BzGc14+jDwlqq6ctCilkiSHwP+B/B5Rr9L\nAN7czfKwoiV5AXA1o/8mnwbsqKrfPOr+sxQQkqSlM1OXmCRJS8eAkCQ1GRCSpCYDQpLUZEBIkpoM\nCOkokhzuZgbeneTPFppBN8mzk/zictUn9c2AkI7u21W1oZut9GvAlgX2fzaw6IDoZn6Vpo4BIU3m\nM4xNtpfkTUlu7Z7PMTen/hXA93VnHW9Lcm6Sj4wd865uuhSS7Evy1iS3Az+T5JPd+i1J/jrJP13G\nvklNBoS0gO4v/PPopsrons2xjtGU3huAH+6ej7AV+FJ31vGmCd76q1X1oqq6tls/vqrOAS5jBc0h\nptm14ibrk5bRid20yKsZPRPgpq79Jd3rr7r1kxkFxv9a5Pu//4j1uUnhbgPWLrZYaal5BiEd3be7\naZG/FwhP3IMI8J+7M4UNVfX9R5mH6BB/9/+xZxyx/ZtHrD/e/TyMf7xpChgQ0gK62XNfD7wxyfHA\njcDPd88LIMnqJN8DHAROGTv0fmB9khO6EVDnLXPp0lPiXynSBKrqr5Lcyei50n/cPUP7M6OZoXkM\neFVVfSnJXybZDXysqt6UZAejufbv44lLUtKK4GyukqQmLzFJkpoMCElSkwEhSWoyICRJTQaEJKnJ\ngJAkNRkQkqQmA0KS1PT/AQ0ZK8438CuJAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa5d8b70>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.hist(W_returns);\n", | |
"plt.xlabel('Return')\n", | |
"plt.ylabel('Occurrences');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"## Fitting a Distribution \n", | |
"\n", | |
"Let's attempt to fit a probability distribution to the returns of a stock. We will take the returns of AAPL 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": 67, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Reading AAPL\n" | |
] | |
} | |
], | |
"source": [ | |
"start = '2014-01-01'\n", | |
"end = '2016-12-31'\n", | |
"data = dl.load_data_nologs('nasdaq', ['AAPL'], start, end)\n", | |
"prices = data['ADJ CLOSE']['AAPL']\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 68, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"('The JB test p-value is: ', 8.6122250241313796e-22)\n", | |
"('We reject the hypothesis that the data are normally distributed ', True)\n", | |
"('The skewness of the returns is: ', 0.38138558143920764)\n", | |
"('The kurtosis of the returns is: ', 4.231909703399142)\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": 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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa0a55f8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"# Take the daily returns\n", | |
"returns = prices/prices.shift(-1) -1\n", | |
"\n", | |
"#Set a cutoff\n", | |
"cutoff = 0.01\n", | |
"\n", | |
"# Get the p-value of the normality test\n", | |
"k2, p_value = scipy.stats.mstats.normaltest(returns[:-1].values)\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: \", scipy.stats.skew(returns[:-1].values))\n", | |
"print(\"The kurtosis of the returns is: \", scipy.stats.kurtosis(returns[:-1].values))\n", | |
"plt.hist(returns[:-1], bins = 20)\n", | |
"plt.xlabel('Value')\n", | |
"plt.ylabel('Occurrences')\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The low p-value of the 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. We calculate the sample mean and standard deviation of the series and see how a theoretical normal curve fits against the actual values." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 69, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"('Mean: ', -0.0004662534806121209)\n" | |
] | |
} | |
], | |
"source": [ | |
"# Take the sample mean and standard deviation of the returns\n", | |
"sample_mean = np.mean(returns[:-1])\n", | |
"sample_std_dev = np.std(returns[:-1])\n", | |
"print(\"Mean: \", sample_mean)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 70, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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hYe1TxCgwOnUdP089yXW53bkg90s81ANf4+r8T/mE1RmVuo4bMxdzRMNpfEmXEPcpUl66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\nBxyoAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0xa3f9588>" | |
] | |
}, | |
"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/(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[:-1], bins = 20, normed=True)\n", | |
"plt.plot(x, sample_distribution)\n", | |
"plt.xlabel('Value')\n", | |
"plt.ylabel('Occurrences');\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": { | |
"collapsed": true | |
}, | |
"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 $5.29$, while the kurtosis of the normal distribution is $3$. A higher kurtosis leads to a higher peak. \n", | |
"\n", | |
"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. 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." | |
] | |
} | |
], | |
"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": "2.7.13" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 1 | |
} |
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