{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "###### The latest version of this IPython notebook is available at [http://github.com/jckantor/ESTM60203](http://github.com/jckantor/ESTM60203) for noncommercial use under terms of the [Creative Commons Attribution Noncommericial ShareAlike License (CC BY-NC-SA 4.0)](http://creativecommons.org/licenses/by-nc-sa/4.0/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "J.C. Kantor (Kantor.1@nd.edu)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Stochastic Price Models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This [IPython notebook](http://ipython.org/notebook.html) demonstrates the development and analysis of stochastic price models for commodity and financial goods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Initializations" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "import pandas as pd\n", "import datetime\n", "from pandas.io.data import DataReader\n", "\n", "from IPython.core.display import HTML\n", "HTML(open(\"styles/custom.css\", \"r\").read())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Where to get Price Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Price data is available from a number of sources. Here we demonstrate the process of obtaining price data on financial goods from [Yahoo Finance](http://finance.yahoo.com/) and [Google Finance](https://www.google.com/finance), and downloading price data sets from [Quandl](http://www.quandl.com/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Yahoo Finance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Yahoo Finance](http://finance.yahoo.com/) provides historical Open, High, Low, Close, and Volume date for quotes on traded securities. In addition, Yahoo Finance provides historical [Adjusted Close](http://marubozu.blogspot.com/2006/09/how-yahoo-calculates-adjusted-closing.html) price data that corrects for splits and dividend distributions. The Adjusted Close is a useful tool for computing the return on long-term investments.\n", "\n", "The following cell demonstrates how to download historical Adjusted Close price for a selected security into a pandas DataFrame." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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2j/xm4IImDyl7yKyW5mtN88+Uw3K8no6ZKY+ZFewdaXoxbh07wGxAfSOD5jMB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\ngnB/87mHMwPRed5eiRQ7vJC3dyENxb7aduMHwdLc0/P+saQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "symbol = 'XOM'\n", "description = 'ExxonMobil, Inc.'\n", "\n", "end = datetime.datetime.today().date()\n", "start = end - datetime.timedelta(3*365)\n", "\n", "S = DataReader(symbol,\"yahoo\",start,end)['Adj Close']\n", "\n", "plt.figure(figsize=(10,4))\n", "S.plot()\n", "plt.title(description)\n", "plt.ylabel('Price $/share')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Google Finance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Google Finance](https://www.google.com/finance) provides historical Open, High, Low, Close, and Volume date for quotes on traded securities. The following cell demonstrates how to download historical Close price for a selected security into a pandas DataFrame." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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M839GLhORa0VkvHudGhZaRMb56eaaJpTN1Qjj8dP+fKc1DWxYxvqD4be9Q9OfwYXbwy+2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\naT1J3wI+AKwBnCNp15aLNeXyP+IrgCOA0yW9oe0yNUHSh4C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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "symbol = 'XOM'\n", "description = 'ExxonMobil, Inc.'\n", "\n", "end = datetime.datetime.today().date()\n", "start = end - datetime.timedelta(3*365)\n", "\n", "S = DataReader(symbol,\"google\",start,end)['Close']\n", "\n", "plt.figure(figsize=(10,4))\n", "S.plot()\n", "plt.title(description)\n", "plt.ylabel('Price $/share')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Quandl" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Quandl](http://www.quandl.com/) is a searchable source of time-series data on a wide range of commodities, financials, and many other economic and social indicators. Data from Quandl can be downloaded as files in various formats, or accessed directly using the [Quandl API](http://www.quandl.com/help/api) or software-specific package. Here we use demonstrate use of the [Quandl Python package](http://www.quandl.com/help/packages#Python). \n", "\n", "The first step is execute a system command to check that the Quandl package has been installed." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied (use --upgrade to upgrade): Quandl in /Users/jeff/anaconda/lib/python2.7/site-packages\r\n" ] } ], "source": [ "!pip install Quandl" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are examples of energy datasets. These were found by searching Quandl, then identifying the Quandl code used for accessing the dataset, a description, the name of the field containing the desired price information." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "code = 'WSJ/NG_HH'\n", "description = 'Cash commodity price for Natural Gas, Henry Hub. Units: $ per MMBTU'\n", "field = 'Value'\n", "\n", "code = 'OFDP/FUTURE_CL1'\n", "description = 'NYMEX Crude Oil Futures, Continuous Contract #1 (CL1) (Front Month)'\n", "field = 'Settle'" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "No authentication tokens found: usage will be limited.\n", "See www.quandl.com/api for more information.\n", "Returning Dataframe for OFDP/FUTURE_CL1\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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E/a5bE2QdX3uJqML4Vgf+ocqvsyzvpcrFAKqpigyF8pL7vgeGNWHCBcBVTstT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\ntyrHV+XYwPGVneMrt07EF8FzwPV934ex7X6foXgMmJmZma1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import Quandl\n", "\n", "end = datetime.datetime.today().date()\n", "start = end - datetime.timedelta(5*365)\n", "\n", "S = Quandl.get(code, collapse='daily', \\\n", " trim_start=start.isoformat(), trim_end=end.isoformat())[field]\n", "\n", "plt.figure(figsize=(10,4))\n", "S.plot()\n", "plt.title(description)\n", "plt.ylabel('Price $/bbl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The statistical properties of financial series are usually studied in terms of the change in prices. There are several reasons for this, key among them is that the changes can often be closely approximated as stationary random variables whereas prices are generally non-stationary sequences. \n", "\n", "A common model is \n", "\n", "$$S_{t+1} = R_{t} S_{t}$$\n", "\n", "so, recursively,\n", "\n", "$$S_{t+1} = R_{t} R_{t-1} \\cdots R_{0} S_{0}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compounded (Log) Returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compounded, or log returns, are defined as\n", "\n", "$$r^{log}_{t} = \\log R_t = \\log \\frac{S_{t+1}}{S_{t}}$$\n", "\n", "The log returns have a very useful compounding property for aggregating price changes across time\n", "\n", "$$ \\log \\frac{S_{t+k}}{S_{t}} = r^{log}_{t} + r^{log}_{t+1} + \\cdots + r^{log}_{t+k-1}$$\n", "\n", "If the compounded returns are statistically independent and identically distributed, then this property provides a means to aggregate returns and develop statistical price projections." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear Returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear, or arithmetic returns, are defined as\n", "\n", "$$S_{t+1} = \\left(1 + r^{lin}_{t+1}\\right) S_{t}$$\n", "\n", "so that \n", "\n", "$$r^{lin}_{t} = \\left(\\frac{S_{t+1}}{S_{t}} - 1\\right) = R_{t} - 1$$\n", "\n", "Linear returns can be aggregated across a portfolio. Consider a portfolio composed of $N$ different assets that holds $x_{t,n}$ units of asset $n$ at time $t$. The value of portfolio at time $t$ is\n", "\n", "$$W_t = x_{t,n} S_{t,1} + x_{t,n} S_{t,2} + \\cdots x_{t,N} S_{t,N}$$\n", "\n", "The value of the portfolio at time $t+1$ (before any rebalancing) is given by\n", "\n", "$$\\begin{align*}\n", "W_{t+1} & = x_{t,1} S_{t+1,1} + x_{t,2} S_{t+1,2} + \\cdots x_{t,N} S_{t+1,N} \\\\\n", "& = x_{t,1}(1+r^{lin}_{t,1})S_{t,1} + x_{t,2}(1+r^{lin}_{t,2})S_{t,2} + \\cdots + x_{t,N}(1+r^{lin}_{t,N})S_{t,N} \\\\\n", "& = W_{t} + r^{lin}_{t,1}x_{t,1}S_{t,1} + r^{lin}_{t,2}x_{t,2}S_{t,2} + \\cdots + r^{lin}_{t,N}x_{t,N}S_{t,N}\n", "\\end{align*}$$\n", "\n", "Defining $w_{t,n}$ as the fraction of the portfolio's value invested in asset $n$ at time $t$\n", "\n", "$$w_{t,n} = \\frac{x_{t,n}S_{t,n}}{W_t}$$\n", "\n", "gives the final result\n", "\n", "$$\\begin{align*}\n", "r^{lin}_{t,W} & = \\frac{W_{t+1}}{W_t} - 1 \\\\\n", "& = w_{t,1}r^{lin}_{t,1} + w_{t,2}r^{lin}_{t,2} + \\cdots + w_{t,N}r^{lin}_{t,N}\n", "\\end{align*}$$\n", "\n", "showing that the linear return on the portfolio is a weighted linear sum of the linear returns on the individual assets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Volatility Drag and the Relationship between Linear and Log Returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For long-term financial decision making, it's important to understand the relationship between $r_t^{log}$ and $r_t^{lin}$. Algebraically, the relationships are simple.\n", "\n", "$$r^{log}_t = \\log \\left(1+r^{lin}_t\\right)$$\n", "\n", "$$r^{lin}_t = e^{r^{log}_t} - 1$$\n", "\n", "The linear return $r_t^{lin}$ is the fraction of value that is earned from an asset in a single period. It is a direct measure of earnings. The average value $\\bar{r}^{lin}$ over many periods this gives the average fractional earnings per period. If you care about consuming the earnings from an asset and not about growth in value, then $\\bar{r}^{lin}$ is the quantity of interest to you.\n", "\n", "Log return $r_t^{log}$ is the rate of growth in value of an asset over a single period. When averaged over many periods, $\\bar{r}^{log}$ measures the compounded rate of growth of valuu. If you care about the growth in value of an asset, then $\\bar{r}^{log}$ is the quantity of interest to you.\n", "\n", "The compounded rate of growth $r_t^{log}$ is generally smaller than average linear return $\\bar{r}^{lin}$ due to the effects of volatility. To see this, consider an asset that has a linear return of -50% in period 1, and +100% in period 2. The average linear return is would be +25%, but the compounded growth in value would be 0%.\n", "\n", "A general formula for the relationship between $\\bar{r}^{log}$ and $\\bar{r}^{lin}$ is derived as follows:\n", "\n", "$$\\begin{align*}\n", "\\bar{r}^{log} & = \\frac{1}{T}\\sum_{t=0}^{T-1} r_t^{log} \\\\\n", "& = \\frac{1}{T}\\sum_{t=0}^{T-1} \\log\\left(1+r_t^{lin}\\right) \\\\\n", "& = \\frac{1}{T}\\sum_{t=0}^{T-1} \\left(\\log(1) + r_t^{lin} - \\frac{1}{2} (r_t^{lin})^2 + \\cdots\n", "\\right) \\\\\n", "& = \\frac{1}{T}\\sum_{t=0}^{T-1} r_t^{lin} - \\frac{1}{2}\\frac{1}{T}\\sum_{t=0}^{T-1} (r_t^{lin})^2 + \\cdots \\\\\n", "& = \\bar{r}^{lin} - \\frac{1}{2}\\left(\\frac{1}{T}\\sum_{t=0}^{T-1} (r_t^{lin})^2\\right) + \\cdots \\\\\n", "& = \\bar{r}^{lin} - \\frac{1}{2}\\left((\\bar{r}^{lin})^2 + \\frac{1}{T}\\sum_{t=0}^{T-1} (r_t^{lin}-\\bar{r}^{lin})^2\\right) + \\cdots\n", "\\end{align*}$$\n", "\n", "For typical values $\\bar{r}^{lin}$ of and long horizons $T$, this results in a formula\n", "\n", "$$\\begin{align*}\n", "\\bar{r}^{log} & \\approx \\bar{r}^{lin} - \\frac{1}{2} \\left(\\sigma^{lin}\\right)^2\n", "\\end{align*}$$\n", "\n", "where $\\sigma^{lin}$ is the standard deviation of linear returns, more commonly called the volatility.\n", "\n", "The difference $- \\frac{1}{2} \\left(\\sigma^{lin}\\right)^2$ is the _volatility drag_ imposed on the compounded growth in value of an asset due to volatility in linear returns. This can be significant and a source of confusion for many investors. \n", "\n", "It's indeed possible to have a positive average linear return, but negative compounded growth. To see this, consider a \\$100 investment which earns 20% on even-numbered years, and loses 18% on odd-numbered years. The average linear return is 1%, and the average log return is -0.81%.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing Linear and Log Returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given the price data stored as a pandas `DataSeries` `S`, a corresponding data series for returns is computed using the pandas `shift()` function, followed by the `dropna()` function to remove missing values." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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esUoZJCHghkDxSRMSAyXeaKZhyq62A4nL62Bt2iKUVavcVsd9NWvhcuDE4JM8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\nHg38inL7OVlQ2SYAqOotqvpOVT1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rLog = (np.log(S/S.shift(+1))).dropna()\n", "rLin = (S/S.shift(+1)).dropna() - 1.0\n", "\n", "plt.figure(figsize=(10,9))\n", "plt.subplot(3,1,1)\n", "S.plot()\n", "plt.ylabel('Price')\n", "plt.title(description)\n", "\n", "plt.subplot(3,1,2)\n", "rLog.plot()\n", "plt.ylabel('Log Return')\n", "\n", "plt.subplot(3,1,3)\n", "rLin.plot()\n", "plt.ylabel('Linear Return')\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean Linear Return = -0.000185\n", "Linear Volatility = 0.018409\n", "Volatility Drag -0.5*vol**2 = -0.000169\n", "rLin - 0.5*vol = -0.000355\n", "\n", "Mean Log Return = -0.000355\n" ] } ], "source": [ "print \"Mean Linear Return = {0:.6f}\".format(rLin.mean())\n", "print \"Linear Volatility = {0:.6f}\".format(rLin.std())\n", "print \"Volatility Drag -0.5*vol**2 = {0:.6f}\".format(-0.5*rLin.std()**2)\n", "print \"rLin - 0.5*vol = {0:.6f}\\n\".format(rLin.mean() - 0.5*rLin.std()**2)\n", "\n", "print \"Mean Log Return = {0:.6f}\".format(rLog.mean())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Statistical Properties of Returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Distribution of Returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A basic assumption in developing developing stochastic price models is that the residuals are indepdendent and identically distributed (i.i.d.) random variates. Here we show the results of several common statistical tests that would screen out non-i.i.d. random variates." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ITxjzIMfRdsrFFWQMhNmGaWlspPPaRyalev+UBgAAlo5GD5DJzwkbfGzGRuI3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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bins = np.linspace(-0.12,0.10,50)\n", "plt.figure(figsize=(10,5))\n", "\n", "plt.subplot(2,2,1)\n", "rLog.hist(bins=bins, normed=True, color='b', alpha=0.5)\n", "plt.xlim(bins.min(),bins.max())\n", "plt.title('Log Returns')\n", "\n", "plt.subplot(2,2,3)\n", "rLog.hist(bins=bins, normed=True, cumulative=True, color='b',alpha=0.5)\n", "plt.xlim(bins.min(),bins.max())\n", "\n", "plt.subplot(2,2,2)\n", "rLin.hist(bins=bins, normed=True, color='y', alpha=0.5)\n", "plt.xlim(bins.min(),bins.max())\n", "plt.title('Linear Returns')\n", "\n", "plt.subplot(2,2,4)\n", "rLin.hist(bins=bins, normed=True, cumulative=True, color='y',alpha=0.5)\n", "plt.xlim(bins.min(),bins.max())\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Distribution of First Half versus Second Half of the Data Set" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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sg/GxA7x8wgmf2EfsjWlpUTdij7p+EWL6NewiMl5E3hCRTSLymYh8z0wfJSKv\niMg2EXlZRLL7a0ejiVrS0jwj9uO3b88FcIu43kpNbffXLf5y8cVbC2tr3fHdxuFLHUlJWVW5uYkD\nVNPEMAON2J3AzUqpY4D5wHdEZAbwY+AVpVQp8JoZ1/SB9h96iSZdSEWFkJLiGdRMOHQIgMPZ2bta\nHY4BpzkOxscOsC8/v7M+Pb2y2GwfYPHxx196XknJBeeVlFywLStrXj/VI4Jo6hfhQL+GXSlVrZRa\nb4ZbgM+BIuAi4BGz2CPAokAKqdGEKaOIj08CSOrqco1qagJgZ2Hh1n5rDYPdhYVb7e4Yx0UXUbR4\ncV3R4sV1rszM5H6qamKQQfvYRaQEmAN8AIxRSlnDh0NE6aku/kL7D71EmS5KrMC4w4dd1pl1H8yc\nuWUwlQfrYwdYW1q61T7lsSk1NeL3h7ETZf0i5AzKsItIOvAPYKlSqtmep5RSgM+fnSKyQkSWmdd/\n2P95IlKu4zoeyXEefvh8Kz56zZqECjO84pxztrpaW1Pthnv7pk1F3W1tCfZ4TXV1nj1uL+9qbU1l\n5coZVvxeUGrDBivKkc8/71E+HPQxkjhQFk7yBDNuhleY1zL8gBh2uZ8CIgnA88BqpdTvzLQtQLlS\nqlpECoA3lFLTe9VTSil98K4mapGKiu8D9wJ895//5A9/+AN1GRn7cp999kcpN9xw+5UXXviavfwT\nq1YtuWzRoqcGSgN47Lnnzmp/4IE77WnL77770aW33RYHMHn//gNnrF//T4Bnnnpq4uG9ey/w88fT\nhAh/2M5+92MXEQEeAjZbRt3kWeBa4Ffm31UjEUKjiVBKrID14nR3QcGg3DAD4nJlj3v88R7GuvnI\nkW4gDqAzMTHLZz2NhoEP2jgFuArYKCLrzLTbgHuAp0TkeqASWBIwCaMAESnXb/0NokwXJZ6A+WLz\n49LSQRv2/nzscRC3MCOjzp62t6HBibnhWH1GRooCouUncZT1i5DTr2FXSr1N3374L/pfHI0moijx\nBEzD/viZZ/pnxO6D9Z2dnant7eltKSm0pqQ42pKSktI6OzsDdT9N5KJXngYBPRLxEi26kIoKASZY\n8ZLqappTUg5XzJlTP9g2BjuP3WJLYqJrwqFDnpdiyV1dg55VE+5ES78IF7Rh12iGRzbmkXSp7e3k\nNjWxZ8wYv89ft+MWIa+xscOKp3V2jg/k/TSRizbsQaDXtK6YJop0UeIJHDqEABsmT/58KA0MZR67\nRUpnZ4MZBKptAAAgAElEQVQVdjkcUbN+JIr6RVigDbtGMzwmWwFr4dAzp54aMP+6jRor0JqcrPdo\n0vhEG/YgoP2HXqJIF1M9gf37aU9MbPzHaadV91fhqAaG6GMHaEtK8uzfe2jUqMTR9fUpQ20jHImi\nfhEWaMOu0QwPr2GvqmLf6NFb3XFxAb9penu75+Xs7rFjmb1rV0HAb6qJOLRhDwLaf+glinQxxROo\nqmJzScmQ3TDD8bHnNpk7jQGVY8cy+cCBqDDsUdQvwoKBFihpNBpfKDUVMZYHTd2/n/88/vjR9pWi\ndS5XQPzfKV1dzpSODmd7cnJCV2IicW53ETDis1U10YUesQcB7T/0Eg26kIqKdETGAiQ4nYypq+vK\nKi3dtTAjo866HObS//4Yjo8dIMnpbLTCTSkpeWlud8Q/x9HQL8KJiO8QGk0I8LhhJh08yJGsrGpX\nXNyAB2v4i0Sn0zPlce/YsY4FHR16doymB9qwBwHtP/QSJbro4V/fN3r0wf4K98VwfOwAaR0dHj/7\nroICTunsHNVf+UggSvpF2KANu0YzdHpMddw+btyQpjmOlPT2do9h311QwJyurog37Br/og17END+\nQy/RoItEp9NzAMaUqio2Tpo0LMM+XB97ZmtrD8M+0+nMQSSin+Vo6BfhRER3Bo0mFKS3tc32hA8d\namtKS3MG8/45zc1ewz52LGlKxQMzgymDJrzRhj0IaP+hl2jQRVdCwkRPuKZm0Ls59ma4PvbcpqYm\nzJPP9o8eTVd8PMBJw5UjHIiGfhFOaMOu0QwBqahIb0lNzQBjquP++vraYMuQ4HK5E53OFgDlcLA3\nPx/g5GDLoQlftGEPAtp/6CXSdRHf3d1jquN78fHDHrEP18cOkNLV1cPPToSP2CO9X4Qb2rBrNEPg\nxK1bT7XCJdXVzo2Jia2hkCPVNuXRNOzTEMkNhSya8EMb9iCg/YdeIl0X2c3NC6xwXmNjlVuGf+ro\ncH3s0HMu++6xY63g/GELE2IivV+EG3qvGI1mCHQlJBxrhTPa2j4jROdJZ7S1eRcpFRYC8C7cfJvI\nTIAqaNqh1AOhkE0TevSIPQho/6GXSNdFY1qa5zg6MQ57HzYj8bFn2eeymyP2k2HsGti/BvYXmcf2\nRQqR3i/CDW3YNZrBIpK+f/ToNCu6fdy4F0IlSo5t+17Txw7GVgf6mdboThAMtP/QSyTrYnNx8WnV\nucb7yfjubvXqCScM6YzT3ozEx57d0tIqbrcboDY7m5bkZIAkICIPuI7kfhGODGjYReRvInJIRD61\npS0Tkf0iss68FgZWTI0m9GwuKTnPCo9uaGhS5eXdoZIlTimVbJvyuH3cOCs41XcNTSwxmBH7w0Bv\nw62A+5RSc8zrRf+LFj1o/6GXSNZFTXa2Z654amdn5UjbG4mPHSCto6POCm8uKbGCpSNpM1REcr8I\nRwY07EqptwBfizBCMhtAowkJIlKTnT3dinYmJq4PpTgAma2tnudy84QJVlCP2DUj8rHfJCIbROQh\nEdEb/feD9h96iWBdTKkcO9bz4vTAqFEfjbTBkfjYAXJaWo5Y4U0lJdZBH2OIsBkxENH9IiwZrmG/\nH5gIlAEHgXt9FRKRFaY/fpmI/If9nyci5Tqu45ES/yV8dW2rd5Gp+8EHU+z52zdtKrIb6u62tgR7\nfPumTUXdbW0J9nhNdXXeSOo733zTsw7l/Y4OV4VHOqZUwaRw0t9AcaAsnOQJZtwMrzCvZfgBUWrg\nE71EpAR4Til17GDzREQppbS7RhMdiNxf8PTT37JmxQCTVHn57vzi4ucvXrJkd+/iT6xateSyRYue\nGk7aYMt2JiTEP3r22d9CBIfbTevChSQ7nQDPng5vr1HqN8P/wJpQ4Q/bOawRu4gU2KKXAJ/2VVaj\niQYaU1NPsYy6w+Vyn3LOOUtOF7lFuruLQyVTktPZndzV1QjgdjjYNt4z01H72WOcwUx3fBx4F5gm\nIvtE5GvAr0Rko4hsAE4Hbg6wnBFNr5+cMU1E6kIkY1dh4TFWNLOt7fDbXV1718D+hBFsyzFSHztA\nenu7Z2bMJu/MmMnJEbZGJSL7RRgzYKdUSl3uI/lvAZBFowlXTtxZWOgxlNktLcM6vDoQZLS11dVm\nZ08E2DB5ctvlr7+eCiSeBoUhFk0TQiLqWz1S0XN0vUSoLk6yLQAiv77eL4dXj3QeO0BOc7NnxP5x\naWm7FT4eJviuEZ5EaL8IW7Rh12gG5hS7YS+uqfGLYfcHuY2NHsP++YQJnl/gkyPMsGv8izbsQUD7\nD71EnC5E4oFTdxR6PRul+/b5xbD7w8c+pr7es0jpQG5uRmeCMSOyKMIMe8T1izBHG3aNpn9mAxn2\nEfv8zZvDZsSe7HR2O44ccQIoh8Oxbdw4J0A65NBz9pomhtCGPQho/6GXCNTFgpbkZDxTHd1u1xnr\n1h0ZoM6g8IePHSDh4MFOK7x22rTDtqyIOQc1AvtFWKMNu0bTPwt2FHk9JhltbYfSOzrcIZTnKOIP\nHPAY9g9mzGixZZ3qo7gmBtCGPQho/6GXiNKFiAM4zW7Yc5qbD/mreX/42AHiq6o8hv2TqT3WJp3u\nj/aDQUT1iwhAG3aNpm9mArmBmOroTxL27vUY9p1FRRkY22oDzEFv0BeTaMMeBLT/0EuE6WIBwFbv\nUn3G+3Gqo9987Hv3dlnh+vT0MV3x8bvMqACn+eMegSbC+kXYow27RtM3CwDWT5niSZizffu+kEnT\nB472dndae3stgHI44j6ZOtUuY3lopNKEkmHvc6EZPCJSrkckBhGjCxEBFnQkJNj3YOH1jRunv1NS\n4rH0zS7XsF0d/vKxA+Q1Nla1pqTkAbx+/PGN8z/3HMda7q97BJKI6RcRgjbsGo1vJgMFn02cSHe8\n8Zg46upaJ519tn06Ie5Vq+JCIVxvCo8c2b9n7NjZAG8de6xyg3IYrhjDz65UQ4hF1AQR7YoJAnok\n4iWCdLEA4JNS7xGicQcONPrzBv7ysQNMOnBgvxXeVVg4thaseET42SOoX0QE2rBrNL2QoqIbPkhJ\nuRHgY5thV7t2he3zcvz27Z4viZqsrKLdsNOWXR58iTShJGw7ajSh5+h6iQhd5OVlzoRi6Dkv3LFv\nX1efdYaBP33sF777rsewN6anF66Nj7ef6lTur/sEiojoFxGENuwaTS9Oam3NzmhvH+2Mi2PjpEme\ndMeuXe39VAspU6uq2lPNQzfcDkfcE7NnNwHWClk9nz3G0IY9CGj/oZdI0MX/a2ycCLC5pISuxEQr\nuUZaWvy6lYA/fewAeU1NHj/73mOPzQE+MaNh72ePhH4RSWjDrtH0Yn5b2yQ4ann+UQdWhxsFR454\nDHtbSckYoMKWXR5seTShQxv2IKD9h14iQRclnZ3HQE/DnrZ9e5KMYM66L/zlY2+G7PNKSi44sm1b\nrpXWlJ09kwgy7JHQLyIJbdg1GjsiY8a5XOnQc0ZMWUfHXgeExZz13rhTU+OKFi+uKx4/3rPitHvs\n2GzgbbSfPSbRhj0IaP+hlwjQxWkALoeDdVOnWptpUVhbe7jvKsPD3z72MXV1nmPy3Lm5afLGG61E\niJ89AvpFRKENu0bTkwUA28aNoyMpSQASnc7WrNbWsJ0RY5HW2dmV6HS2AhAf7wAmEkHuGI3/0IY9\nCGj/oZcI0MUC6OmGyWhtrQnEjfw5j90izZzyaBIxfvYI6BcRxYB7xYjI34DzgcNKqWPNtFHAkxgH\n5lYCS5Tei0IT6YjkA8dBT8Oe09LidzdMoMhoa6urz8y09hmeBfwRw8/uUDDnMpHbq6HDXqcKmnYo\n9UCwZdUEjsGM2B8GFvZK+zHwilKqFHjNjGv6QPsPvYS5Ls7F8EXz9rHHelaZ5jU0BGTE7m8fO8Co\n5uZaW/QklGrE9LMLyJOQuQb2268iyPS3HEMlzPtFxDGgYVdKvQXU90q+CHjEDD8CLPKzXBpNUJgi\ncsPpIrecLnLLdvg+gFuEzyZO9MyAKTxyJGJG7OMPHz5ghaWz88zT4uNv/RBabUVmhEAsTZAZro99\njFLKOvvxEDDGT/JEJdp/6CXcdFHkHcEenApTAXYVFNCRlBQHkNDd3Z7T3NzafyvDIxA+9vz6+sYE\np7MNQCUlpVx39tkyFz6wFTnG3/f0B+HWLyKdEe/HrpRSIqJ85YnICgwfPEADsN76yWX9I3U8tuIW\n4SLPAlOe/4Gzp0JKOfDq9Oku1q+PA8iYNKlGMIxwd1tbgiV/b6NsxS33SndbW8L2TZuKrLiv+jXV\n1XkjqW8vb4/ntLQcOLxnzxSA1fPmTbt+9eq33wC3gKMcSoDsO6EA4Hb4PBz+H0CZiIS8P4Qiboav\nM/VQiR8QpXza5J6FREqA52wvT7cA5UqpahEpAN5QSk3vVUcppcQfQmo0geJ0kVvWGHuXX4kxSYAL\nv/vdjucXL04GmFRV9fGZ69a9B/DEqlVLLlu06Cl7fV9pQyk70vq+0t875pjjNk2cuABg2t697225\n9to/AD/BO1r/K/C6Rwcwbo1SvzlaO5pQ4A/bOVxXzLPAtWb4WmDVSITQaMKAOVZg7bRpnsS8xsaI\n8a9bFNXUePzs+/Lzp7scDoCPbUVOCLpQmqAyoGEXkceBd4FpIrJPRL4K3AN8SUS2AWeacU0faP+h\nl3DTxbasrHk3FRRcBhQCdIHrUElJkpU/tq4uIDNiIDA+doCimpoj0tHhBmhLTs759/z5+fQ07McA\nST4rh4hw6xeRzmBmxVyulCpUSiUqpcYrpR5WStUppb6olCpVSp2t57BrIhVXZmbyxca+KgC8f+yx\nB1R6ugDEuVxdoxsamkIn3fCIU0ol7N7tWSn7jwULpgE1B6DZTErAnK+viU70ytMgoOfoeglHXUzf\nt2+iFf7Xqad6BikZbW2HA/mSKBDz2C0St21rs8Lrp0yZDrAWqm1FwsodE479IpLRhl0T02S53XEF\nR454XCJvzJnjOUwju6UlYG6YQJO0ebPHsFeOGTMdoMKYmmxRhn7+oxb9jw0C2n/oJdx0cUFbW16c\nUg6AuoyM2v35+R63TG6AX5wGyscOkLh1a7vD7e4GaEpPL3hv5sysT6AR72LDDKC0zwaCTLj1i0hH\nG3ZNTHN2R4dncd32wsLKptTU0Va8IIAvTgONo6tL5dfX77Ti/3vWWaXmTxH7S9QvBFksTZDQhj0I\naP+hl7DShYhjXmdnvhX912mnHXEmJKQCxLlczvz6+oBOCgikjx1gSlXVViv84fTp1jqTsJz2GFb9\nIgrQhl0Ty8wZ5XYnAXQkJHQ8d/LJ6VbGqKamfY5BLN4LZ07atGmLFd5VWGgZ9k14d3ccAwTMHaQJ\nHdqwBwHtP/QSZro43wrsGTNmz4G8vAlWvLC2tjLQNw+kjx3guhdf3Ia5tPxIVlaJMyMjDugGNtqK\nhYU7Jsz6RcSjDbsmlvEY9vdnzNjXmJ5eaMWnVlVVhkQiPzJz7962UU1NewGUiNSfeGKOmbXWViws\nDLvGv4x4EzDNwGj/oZdQ6mKKyA3W3uOTIP1hmAvgFlGPLFyIEnEAOPbt685uaWnrry1/MPWYY6o+\n3r49oPeYdPDglrqsrAkAjWVlo3j9dYB1mIdvAFMmGzNkQop+RvyLHrFrYgbbFr37HzZ3NwQ4lJNz\ncGtxscctEvfZZ52hkdD/fGHbNs8L1Obp03PNYCtgpctFeo/2qEMb9iCg/YdewkgX1o69bJowYVeN\nOaoFiN+woct3Ff8SaB87wJWvvup5gdpWUpJdm5lp/Ur3uGPKwmCP9jDqF1GBNuyaWKQAmAbGm8QH\nzz+/1prmGN/d3eHYtcsZSuH8QTNkn1dScsHdzc2nJjY0tACohATHw+eea22f4Jn2OA6mIpIWEkE1\nAUEb9iCg/YdewkQXp1uBtxMTm9eXlnrcMnmNjXvE7fZdy88Ech67OzU1rmjx4rqixYvrcru791np\nr8+ZY017PIyxDz3xxru2CwMly2AIk34RNWjDrok1HNjcME+mpjZUjxpVYsXH1dRUhkCmgDKmvt6z\nP/uW4mL7gTjv28LfDJ5EmkCjDXsQ0P5DL2Ggi9mAtR9Mw3Njx7Y3p6Ya2woopabs3783WIIEw8cO\nPQ+43j969Iyq3NxEM1oBWKuwzkBkWu+6wSIM+kVUoQ27JtYot4XfajnxxHTE2Jw3q7W1Or2jI2pm\nxFjk19c3pnR0NAB0x8cn33Httdbc9Tp6bjGgR+1RgjbsQUD7D72EUhcTIA043pa0prOszLONwNi6\nuspgyhPovWIsBBhXU+OZ9vjKCSecZst+zRa+DpHkYMjUG/2M+Bdt2DUxw5WGUY8zo9takpOrO2fM\n8Bj2iQcOVIZEsCAws7LSY9j3jBlz3HszZ2aZ0Y3N3q18RwGXBl04jd/Rhj0IaP+hl5DpQkTmmitN\nTSqWL15cqlJSHACJXV0tRbW1R4IpUrB87ACjGxubEnbubANQDofj15ddNt/MUmvhA1vRG4Ilkx39\njPgXbdg1scIJOcZuhgCdwPur582bY2XmNzRUBvIYvHAg9d13G63wO8ce63HHPAofYUzpBzgVkZAv\nWNKMDG3Yg4D2H3oJoS6+Zgu/D3RsLinxGPbxhw9XBlugYPnYLVLefrvJOlWpJjt70uNnnlkIsNM4\n5HqVrWjQR+36GfEv2rBroh+RVOAKW0rF6rlz8+ozMsYBiNvtmlxVtT80wgWPuOZm9+QDBz6x4n+5\n6KJTbdkP2MLXmDrTRCjasAcB7T/0EiJdXIK5qyNQDWz94yWXWD5mclpaqpKdzm6fNQNIMH3sFue9\n//5bVvjj0tJTu+LjLQ/U64B1lF4WsCSYculnxL+MaNteEakEmgAX4FRKze2/hkYTZEQE+LYtpaIp\nNTWuYvbshVbC+EOHdgRfsNDw80ceWX//RRe1dCUmprempOT9+rLLpvP3vzejlBuRB4BfAxyC25eI\njO5dvwqadij1wFENa8KKkY7YFVCulJqjjXrfaP+hlxDo4hzgFACXMQB56/s33jivLSVlFICjudk1\ne+fOrf01ECiC7WMHyGlpcc2qrHzPiv9febndHbMC6AIYA5PWgMPa5ti6iry/fPyKfkb8iz9cMdE+\nmUATqRij9f+yop/CBy6Ho/6ZU07xnJyUWlFRl9jd7QqJfCHi8tdee9sKf15cPN9pbeWrVA3wD1vR\nc4IsmsZP+GPE/qqIrBWRb/hDoGhE+w+9BFkX/w/vStOOP8Hrd1111cza7OyJAHEulzP9hRfq+64e\nWILtY7e28n3tww+nJTU0NAM4ExJSPjv//Itsxf5iC59OkA671s+Ifxnp0XinKKUOiuGLe0VEtiil\nPC9nRGQFUGlGG4D11k8u6x+p47EVtwj0/VJEzvwn3Huueb+/wao3IM+1cOE8ANavp3jbto1djY2p\n4DWylnvEV7y7rS3Bkr+3Ue5dvrutLWH7pk1F/dWvqa7OG0n9/uT1Vb8LkosWL64DGPXWW/sPjh8/\ng7Iy2k8/faJHf7AGeLUCvgg4yuFy4L/v9J6y1ByI/xdQJiIh75+hiJvh60w9VOIHxDzEfOQNifwc\naFFK3WvGlVJKu2k0oUHkGuARM9YMTJw1f/6PN9199w8BUEo9eccdP/j+tm3fOPeKK+z7pfDEqlVL\nLlu06KneTfpKH2nZUN3rcHZ25rOnnnoNAC6XIi5ujCovrwFApEzBJ+J1s94FbAY4HcatUeo3vWXQ\n+A9/2M5hu2JEJFVEMsxwGnA28OlIhNFo/IJIInCHLeVelDqy74orPKstJx08+MmSNWuqgy9ceJDf\n0NCU2dJyEIC4OAF+5MlUav3mnrs+Xol+lxZRjMTHPgZ4S0TWY+w18bxS6mX/iBVdaP+hlyDp4nqg\nxAwfAX4rFRX5TTNnWtvV8vV///v5IMjRL6GYx25n2r59G2zR70lFxWQr8nt4CXOGDDARc2ZRoNDP\niH8ZtmFXSu1WSpWZ1yyl1N3+FEyjGRbGisnbbSn3oFQTcCNxcfEAo+vrd976xBMhmeIYThy3c+cO\nz6gdEoBfWXlboBF4wVb8K2YZTQSgV54GAT1H10sQdHEjxmHVAAeBP0lFRQrwHavAJW+//e+4IJ1r\n2h+hmMduR4ATt2x525a0WCoq7Hu1P4th4AFygXMJEPoZ8S/asGuiB2N21o9tKXeiVDtwDZAHkN7W\nVnvvn//8YSjEC0cmVlcfSti40f4Fc59UVFh2oQN42pZ3sXlYiSbM0YY9CGj/oZeA6cJYjPQwxsgS\njGljD0lFRR6wzCp25iefrE7v6Aj9cJ3Q+9gt0h97bAuGEQc4gZ4bpr0BWGemptxsTIP0O/oZ8S/a\nsGuihaXA+bb4d+SNN5wYuxaOBXC0tzff9+c/vxEK4cKZ+IMHO4D7bEl3d2VlWf50N/CYlTEbTkbk\nzGDKpxk6I12gpBkE2n/oZSS6mCJyQ++9SqqgaQesxdy8yuQ+lHqBioprMVafApD+179uvCkp6YuU\nlHgKNrtc2cOVZ6RMPeaYqo+3bw/V7T2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import t\n", "\n", "k = int(len(rLog)/2)\n", "r = np.linspace(rLog.min(),rLog.max())\n", "\n", "plt.figure();\n", "plt.hold(True)\n", "\n", "param = t.fit(rLog[:k])\n", "rLog[:k].hist(bins=r,normed=1,alpha=0.35,color='r')\n", "plt.plot(r,t.pdf(r,df=param[0],loc=param[1],scale=param[2]),'r-',lw=3);\n", "\n", "rLog[k:].hist(bins=r,normed=1,alpha=0.35,color='c')\n", "param = t.fit(rLog[k:])\n", "plt.plot(r,t.pdf(r,df=param[0],loc=param[1],scale=param[2]),'c-',lw=3);\n", "plt.hold(False)\n", "\n", "plt.legend(['rLog[:k]','rLog[k:]'])\n", "plt.title('Change in Distribution of Log Returns')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lag Plot of $r^{log}_{t+1}$ versus $r^{log}_t$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bapVI5uHTNHlBMleB1nMRQghRW2QWi8gsJoQQxZBZTAghRKVIufTB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\nUTr/H1iyAGR2NzgDAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(rLog[0:-1],rLog[1:],'.')\n", "plt.axis('equal');\n", "plt.xlabel('$r^{log}_{t}$')\n", "plt.ylabel('$r^{log}_{t+1}$')\n", "plt.grid()\n", "plt.title('Lag Plot for Log Returns');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Autocorrelation" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n", "plot_acf(rLog,lags=min(30,len(rLog)));\n", "plt.xlabel('Lag');\n", "plot_pacf(rLog,lags=min(30,len(rLog)));\n", "plt.xlabel('Lag');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Price Forecasting using the Bootstrap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our basic model for prices is \n", "\n", "$$S_{t+1} = R_{t}S_{t}$$ \n", "\n", "where $R_{t}$ represent total return and are assumed to be independent and identically distributed random variates. Previously we have computed log and linear returns as\n", "\n", "$$r^{log}_{t} = \\log \\frac{S_{t+1}}{S_{t}} = \\log R_t$$\n", "\n", "$$r^{lin}_{t} = \\frac{S_{t+1} - S_{t}}{S_{t}} = R_t - 1$$\n", "\n", "and executed several tests of the hypothesis that they behave as independent, identically distributed (i.i.d.) random variables. If we're satisfied with this hypothesis, then we can randomly sample the historical return data $R_{t}$ to simulate future prices. This bootstrap technique is relatively simple to implement as shown below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trading Days" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Typical sources of price data report information for trading days. Most years will have between 251 and 253 trading days. For the purpose of price forecasting, therefore, we create python functions for generating trading days for future years using the New York Stock Exchange calendar. These functions are implemented using rule sets from `dateutil` library." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NYSE Holidays\n", "\n", "May 25 2015\n", "Jul 03 2015\n", "Sep 07 2015\n", "Nov 26 2015\n", "Dec 25 2015\n", "Jan 01 2016\n", "Jan 18 2016\n", "Feb 15 2016\n", "Mar 25 2016\n", "\n", "\n", "Trading Days\n", "\n", "2015 252\n", "2016 252\n", "2017 251\n", "2018 252\n", "2019 252\n" ] } ], "source": [ "from dateutil import rrule \n", "import datetime\n", "\n", "# Generate ruleset for holiday observances on the NYSE\n", "\n", "def NYSE_holidays(a=datetime.date.today(), b=datetime.date.today()+datetime.timedelta(days=365)):\n", " rs = rrule.rruleset()\n", "\n", " # Include all potential holiday observances\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth=12, bymonthday=31, byweekday=rrule.FR)) # New Years Day \n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 1, bymonthday= 1)) # New Years Day \n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 1, bymonthday= 2, byweekday=rrule.MO)) # New Years Day \n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 1, byweekday= rrule.MO(3))) # Martin Luther King Day \n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 2, byweekday= rrule.MO(3))) # Washington's Birthday\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, byeaster= -2)) # Good Friday\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 5, byweekday= rrule.MO(-1))) # Memorial Day\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 7, bymonthday= 3, byweekday=rrule.FR)) # Independence Day\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 7, bymonthday= 4)) # Independence Day\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 7, bymonthday= 5, byweekday=rrule.MO)) # Independence Day\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth= 9, byweekday= rrule.MO(1))) # Labor Day\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth=11, byweekday= rrule.TH(4))) # Thanksgiving Day\n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth=12, bymonthday=24, byweekday=rrule.FR)) # Christmas \n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth=12, bymonthday=25)) # Christmas \n", " rs.rrule(rrule.rrule(rrule.YEARLY, dtstart=a, until=b, bymonth=12, bymonthday=26, byweekday=rrule.MO)) # Christmas \n", " \n", " # Exclude potential holidays that fall on weekends\n", " rs.exrule(rrule.rrule(rrule.WEEKLY, dtstart=a, until=b, byweekday=(rrule.SA,rrule.SU)))\n", "\n", " return rs\n", " \n", "# Generate ruleset for NYSE trading days\n", "\n", "def NYSE_tradingdays(a=datetime.date.today(), b=datetime.date.today()+datetime.timedelta(days=365)):\n", " rs = rrule.rruleset()\n", " rs.rrule(rrule.rrule(rrule.DAILY, dtstart=a, until=b))\n", " \n", " # Exclude weekends and holidays\n", " rs.exrule(rrule.rrule(rrule.WEEKLY, dtstart=a, byweekday=(rrule.SA,rrule.SU)))\n", " rs.exrule(NYSE_holidays(a,b))\n", " \n", " return rs\n", "\n", "# Examples\n", "\n", "# List all NYSE holiday observances for the coming year\n", "print \"NYSE Holidays\\n\"\n", "for dy in NYSE_holidays():\n", " print dy.strftime('%b %d %Y')\n", "\n", "# Count NYSE trading days in next 5 years\n", "print \"\\n\\nTrading Days\\n\"\n", "for yr in range(2015,2020):\n", " tdays = len(list(NYSE_tradingdays(datetime.datetime(yr,1,1),datetime.datetime(yr,12,31))))\n", " print \"{0} {1}\".format(yr,tdays)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Mffbz/oPJgmaJyJwMyzNtH3IDph+ejTmu3Edyjc/Hbp4uwALIC7FBUgvctlnPB5aRfhi7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\nf5NON4w1gcOBL8WqfmcCN3lRkoGDpEllX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import lognorm\n", "\n", "N = 400\n", "#start_date = S.index[-252]\n", "start_date = S.index[-1]\n", "end_date = datetime.date.today() + datetime.timedelta(days=365)\n", "\n", "plt.figure(figsize=(10,6))\n", "plt.subplot(2,1,1)\n", "\n", "plt.plot(S.index,S,lw=0.5)\n", "plt.title(description)\n", "\n", "# Initialize P using the last available price\n", "P = np.array([S.ix[start_date]]*N)\n", "\n", "# The generator returns one array of N random samples from the history of total returns\n", "# for each t in the history of future horizon.\n", "R = (S/S.shift(+1)).dropna() #[0:start_date]\n", "Zgenerator = ((d,np.array([np.random.choice(R) for _ in xrange(N)])) \n", " for d in NYSE_tradingdays(start_date,end_date))\n", "\n", "plt.hold(True)\n", "for d,Z in Zgenerator:\n", " P *= Z\n", " plt.plot([d]*N,P,'r.',ms=0.1,alpha=0.6)\n", " plt.plot([d]*5,np.percentile(P,[95,75,50,25,5]),'g.',ms=0.8,alpha=0.6)\n", " \n", "plt.hold(False)\n", "plt.grid()\n", "plt.ylim(0,plt.ylim()[1])\n", "\n", "# Histogram\n", "plt.subplot(2,2,3)\n", "plt.hold(True)\n", "plt.hist(P,bins=min(100,int(1.5*np.sqrt(N))),normed=1,alpha=0.35,color='b');\n", "shape,loc,scale = lognorm.fit(P,floc=0)\n", "x=np.linspace(0,max(P),100)\n", "pdf_fitted = lognorm.pdf(x, shape, loc=loc, scale=scale) # fitted distribution\n", "plt.plot(x,pdf_fitted,'b-',lw=3)\n", "p = np.mean(P)\n", "ylim = plt.ylim()\n", "plt.plot([p,p],ylim,'r--',lw=2)\n", "plt.ylim(ylim)\n", "plt.text(p,0.97*ylim[1],\" Mean = {0:.2f}\".format(p),va = 'top')\n", "plt.hold(False)\n", "\n", "plt.xlim(min(P),max(P))\n", "plt.xlabel('Final Price')\n", "plt.ylabel('Probability');\n", "plt.title(\"Price Distribution for {1}\".format(description,d.strftime(\"%b %d %Y\")))\n", "\n", "# Cumulative Distribution\n", "plt.subplot(2,2,4)\n", "nbins = min(100,int(1.5*np.sqrt(N)))\n", "plt.hist(P,bins=nbins,normed=1,cumulative=True,alpha=0.35,color='b');\n", "plt.xlim(min(P),max(P))\n", "plt.xlabel('Final Price')\n", "plt.ylabel('Probability');\n", "plt.title(\"Cumulative Distribution for {1}\".format(description,d.strftime(\"%b %d %Y\")))\n", "\n", "def plotPercentile(p,va='baseline'):\n", " x = np.percentile(P,100.0*p)\n", " dp = -0.02 if va=='top' else 0.02\n", " plt.text(min(P) + 0.05*(max(P)-min(P)),p+dp,'{0:.2f}'.format(x),ha='left',va=va)\n", " plt.plot([0,x,x],[p,p,0],'r--',lw=2)\n", "\n", "plt.hold(True)\n", "plotPercentile(0.05)\n", "plotPercentile(0.50)\n", "plotPercentile(0.95,va='top')\n", "plt.hold(False)\n", "plt.grid()\n", "plt.tight_layout()\n", "\n", "plt.savefig('img/StochasticPriceModelBootstrap.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geometric Brownian Motion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$S_{t+1} = S_t + \\mu h S_t + \\sigma \\sqrt{h} S_t Z_t$$\n", "\n", "where $Z_t \\sim N(0,1)$ and $h$ corresponds to a sampling period of 1 'trading day'. There are typically 252 trading days in a calendar year, 63 trading days in a quarter, and 21 trading days in a month.\n", "\n", "Defining return as\n", "\n", "$$r^{lin}_{t} = \\frac{S_{t+1} - S_{t}}{S_{t}} = \\mu h + \\sigma \\sqrt{h} Z_t$$\n", "\n", "then the statistical model for $r^{lin}_{t}$ becomes\n", "\n", "$$r^{lin}_{t} = \\mu h + \\sigma \\sqrt{h} Z_t$$\n", "\n", "For the case of Geometric Brownian Motion the hypothesis is that $r^{lin}_t$ is a random variable drawn from a the normal distribution $r^{lin}_t \\sim N(\\mu h, \\sigma\\sqrt{h}$)." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "ename": "TypeError", "evalue": "_parse_args() got an unexpected keyword argument 'args'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 41\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mrv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 42\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 43\u001b[0;31m \u001b[0mplotFittedReturns\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrLin\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'Linear Returns '\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mdescription\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mplotFittedReturns\u001b[0;34m(r, description, rv)\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0;31m# fit returns to a given distribution\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0mparams\u001b[0m \u001b[0;34m=\u001b[0m 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"\u001b[0;32m/Users/jeff/anaconda/lib/python2.7/site-packages/scipy/stats/_distn_infrastructure.pyc\u001b[0m in \u001b[0;36mfreeze\u001b[0;34m(self, *args, **kwds)\u001b[0m\n\u001b[1;32m 739\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 740\u001b[0m \"\"\"\n\u001b[0;32m--> 741\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mrv_frozen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 742\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 743\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/Users/jeff/anaconda/lib/python2.7/site-packages/scipy/stats/_distn_infrastructure.pyc\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, dist, *args, **kwds)\u001b[0m\n\u001b[1;32m 434\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 435\u001b[0m \u001b[0;31m# a, b may be set in _argcheck, depending on *args, **kwds. Ouch.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 436\u001b[0;31m \u001b[0mshapes\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_parse_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 437\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_argcheck\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mshapes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 438\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mTypeError\u001b[0m: _parse_args() got an unexpected keyword argument 'args'" ] }, { "data": { "image/png": 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4JXBb9Czu/F2x/k7A1AZvbeMds1mxPL4d+BXuwM0yZmUszedcJfMTYGUG4QDA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\ntIHzJ2b3f5zitIlV8n/q+iLvn9nt+vF8ygND1T6Goe4fndy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import norm\n", "from statsmodels.graphics.gofplots import qqplot\n", "\n", "rLin = (S/S.shift(+1)).dropna() - 1.0\n", "(mu,sigma) = norm.fit(rLin)\n", "rv = norm(mu, sigma )\n", "\n", "def plotFittedReturns(r,description = '',rv=norm):\n", " \n", " # plot returns\n", " plt.figure(figsize=(9,6))\n", " plt.subplot(2,1,1)\n", " r.plot()\n", " plt.title(description)\n", " \n", " # fit returns to a given distribution\n", " params = rv.fit(r)\n", " rv = rv(args=params)\n", "\n", " ax = plt.subplot(2,2,3)\n", " plt.hold(True)\n", " rSpace = np.linspace(r.min(),r.max())\n", " print rv.pdf(rSpace)\n", " r.hist(bins=rSpace,normed=1,alpha=0.4);\n", " plt.plot(rSpace,rv.pdf(rSpace),'r-',lw=3,alpha=0.6)\n", " plt.text(0.06,0.85,\"mean = {0:.3}\".format(rv.mean()),transform=ax.transAxes)\n", " plt.text(0.06,0.75,\"std = {0:.3}\".format(rv.std()),transform=ax.transAxes)\n", " plt.grid(False)\n", " plt.hold(False)\n", " plt.xlabel('$r^{log}_t$')\n", " plt.title('Histogram of Returns')\n", "\n", " ax = plt.subplot(2,2,4)\n", " plt.axis('equal')\n", " plt.hold(True)\n", " #qqplot(r,dist=t,distargs=(df,), loc=mu, scale=scale,line='45',ax=ax)\n", " plt.hold(False)\n", " plt.title('qqplot')\n", " plt.tight_layout()\n", " \n", " return rv\n", "\n", "plotFittedReturns(rLin,'Linear Returns ' + description,t);\n" ] }, { "cell_type": "code", "execution_count": 276, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(-0.0001528906763003357, 0.016887191281517788)\n" ] }, { "data": { "text/plain": [ "array([ 19.71795263, 11.59042784, 4.79786241, 1.39864271])" ] }, "execution_count": 276, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.stats import norm,t\n", "\n", "a = norm.fit(rLin)\n", "b = t.fit(rLin)\n", "print a\n", "q = norm(loc=a[-2],scale=a[-1])\n", "q.pdf([0.01, 0.02, 0.03, 0.04])\n", "\n" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "252 3.92795122383 0.26807585084\n", "0.267894472265 0 50.4745809156\n" ] }, { "data": { "image/png": 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huG1b4C9/AR54gDafhATgqKOAcC3lxhlyYMuWYBuWUjOXXMJc8x9/zGP/978D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RunIH8bqbF09+dNFYJ9SBUf5HDSxQ82HfqRDn1oCqYkpwCLF7sX0+5G3rqNPOnO6Z2uidv5Pvpo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\nx4rIWKwrG/tcp3jMGPN1MPMAS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 2000 # number of realizations\n", "T = 252 # simulation time horizon in trading days\n", "h = 1\n", "\n", "plt.figure(figsize=(10,6))\n", "plt.subplot(2,1,1)\n", "plt.plot(S.index,S)\n", "plt.title(description)\n", "\n", "start_date = S.index[-1]\n", "end_date = start_date + datetime.timedelta(365)\n", "\n", "# Initialize P\n", "P = np.array([S[-1]]*N)\n", "\n", "# generator of random variates\n", "Zgenerator = ((d,np.array(norm.rvs(loc=mu*h,scale=np.sqrt(h)*sigma,size=N)))\n", " for d in NYSE_tradingdays(start_date,end_date))\n", "\n", "plt.hold(True)\n", "for (d,Z) in Zgenerator:\n", " P += P*Z\n", " plt.plot([d]*N,P,'r.',ms=0.1,alpha=0.5)\n", " plt.plot([d]*5,np.percentile(P,[95,75,50,25,5]),'g.',ms=0.8,alpha=0.6)\n", " \n", "plt.hold(False)\n", "plt.grid()\n", "plt.ylim(0,plt.ylim()[1])\n", "\n", "# Histogram\n", "plt.subplot(2,2,3)\n", "plt.hold(True)\n", "plt.hist(P,bins=min(100,int(1.5*np.sqrt(N))),normed=1,alpha=0.35,color='b');\n", "shape,loc,scale = lognorm.fit(P,floc=0)\n", "x=np.linspace(0,max(P),100)\n", "pdf_fitted = lognorm.pdf(x, shape, loc=loc, scale=scale) # fitted distribution\n", "plt.plot(x,pdf_fitted,'b-',lw=3)\n", "p = np.mean(P)\n", "ylim = plt.ylim()\n", "plt.plot([p,p],ylim,'r--',lw=2)\n", "plt.ylim(ylim)\n", "plt.text(p,0.97*ylim[1],\" Mean = {0:.2f}\".format(p),va = 'top')\n", "\n", "T = len(list(NYSE_tradingdays(start_date,end_date)))\n", "\n", "alpha = np.log(S[-1]) + (mu-sigma*sigma/2.0)*T\n", "beta = sigma*np.sqrt(T)\n", "pdf_pred = lognorm.pdf(x, beta, loc=0, scale=np.exp(alpha)) # fitted distribution\n", "plt.plot(x,pdf_pred,'g--',lw=3)\n", "\n", "print T,alpha,beta\n", "print shape,loc,scale\n", "\n", "plt.hold(False)\n", "\n", "plt.xlim(min(P),max(P))\n", "plt.xlabel('Final Price')\n", "plt.ylabel('Probability');\n", "plt.title(\"Price Distribution for {1}\".format(description,d.strftime(\"%b %d %Y\")))\n", "\n", "# Cumulative Distribution\n", "plt.subplot(2,2,4)\n", "nbins = min(100,int(1.5*np.sqrt(N)))\n", "plt.hist(P,bins=nbins,normed=1,cumulative=True,alpha=0.35,color='b');\n", "plt.xlim(min(P),max(P))\n", "plt.xlabel('Final Price')\n", "plt.ylabel('Probability');\n", "plt.title(\"Cumulative Distribution for {1}\".format(description,d.strftime(\"%b %d %Y\")))\n", "\n", "def plotPercentile(p,va='baseline'):\n", " x = np.percentile(P,100.0*p)\n", " dp = -0.02 if va=='top' else 0.02\n", " plt.text(min(P) + 0.05*(max(P)-min(P)),p+dp,'{0:.2f}'.format(x),ha='left',va=va)\n", " plt.plot([0,x,x],[p,p,0],'r--',lw=2)\n", "\n", "plt.hold(True)\n", "plotPercentile(0.05)\n", "plotPercentile(0.50)\n", "plotPercentile(0.95,va='top')\n", "plt.hold(False)\n", "plt.grid()\n", "plt.tight_layout()\n", "\n", "plt.savefig('img/StochasticPriceModelGBM.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Price Forecasting with a Student's t-Distribution for Log Returns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The definition of log returns can be rearranged to a recursive form\n", "\n", "$$\\log S_{t+1} = \\log S_{t} + r^{log}_{t}$$\n", "\n", "Assuming log returns are independent and identically distributed, we begin by fitting a Student's T-distribution\n", "\n", "$$f(r | \\nu,\\mu,s) = \\frac{\\Gamma(\\frac{\\nu+1}{2})}{s\\Gamma(\\frac{\\nu}{2})\\sqrt{\\pi\\nu}}\\left(1+\\frac{1}{\\nu}\\left(\\frac{r-\\mu}{s}\\right)^2\\right)^{-\\frac{\\nu+1}{2}}$$\n", "\n", "to historical data. This particular version of the distribution is presented in 'location-scale' form where $\\nu$ denotes the 'degrees of freedom', $\\mu$ is location, and $s$ is scale. The distribution is frequently used to model heavy tailed data where the degrees of freedom controls and scale parameters controls kurtosis. The Student's t-distribution is symmetric around $\\mu$ (which is the mean, median, and mode of the distribution). Smaller values of $\\nu$ correspond to heavier tails. Key statistics for the distribution are\n", "\n", "$$\\begin{align*}\n", "E[r] & = \\mu \\quad\\mbox{for}\\quad \\nu > 1 \\\\\n", "\\mbox{Var}[r] & = s^2\\frac{\\nu}{\\nu-2} \\quad\\mbox{for}\\quad \\nu > 2\n", "\\end{align*}$$\n" ] }, { "cell_type": "code", "execution_count": 214, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lAk5lb2r2/2xt+OCDyI86QutDmAZw2TIaT9OBjCKAtpBmYdzcBPCHH4AJE+h/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cLmzZspKioCYMWKFeTm5u73c8vJyQHcMPFZZ53FZ599VnyusLCQt956i/PPP3+/14k3mas2kJXV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\nK2H8eDeW39dftzj5A7jhhtMZO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eF95HolTPNE5Iu2i7p2Dd2LiIwQkc9EpFhEbm7KsUFm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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import t\n", "\n", "# compute log returns, fit to t-distribution and freeze \n", "rLog = np.log(S/S.shift(+1)).dropna() \n", "df,mu,scale = t.fit(rLog)\n", "rv = t(df=df,loc=mu,scale=scale)\n", "\n", "plotFittedReturns(rLog,rv,'Log Returns ' + description)" ] }, { "cell_type": "code", "execution_count": 215, "metadata": { "collapsed": false }, "outputs": [], "source": [ "qqplot?" ] }, { "cell_type": "code", "execution_count": 190, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GzzffzGtqv34UQJbtl8JCeotvvplN+wAfnL77Dli2jE3+sl5SkrtdXByw886B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GOMaZsSuSvqaqCz97wzsEFVq1uwjCmXqbm7mVovCGdua6KsbunFWgSMMaZtSuSuqH8BXheRVUAn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\nswtiLa9hjeQiuzlJm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 2000 # number of realizations\n", "H = 365 # simulation horizon in calendar days\n", "\n", "# initialize simulation\n", "start_date = S.index[-1]\n", "end_date = start_date + datetime.timedelta(H)\n", "P = np.array([np.log(S[-1])]*N)\n", "\n", "# create generator for N samples for each trading day\n", "Zgenerator = ((d,np.array(rv.rvs(size=N))) \n", " for d in NYSE_tradingdays(start_date,end_date))\n", "\n", "# do simulation and plot results\n", "plt.figure(figsize=(10,6))\n", "plt.subplot(2,1,1)\n", "plt.hold(True)\n", "plt.plot(S.index,S)\n", "\n", "for (d,Z) in Zgenerator:\n", " P += Z\n", " plt.plot([d]*N,np.exp(P),'r.',ms=0.1,alpha=0.6)\n", " plt.plot([d]*5,np.percentile(np.exp(P),[95,75,50,25,5]),'g.',ms=0.8,alpha=0.5)\n", " \n", "plt.hold(False)\n", "plt.ylim(0,plt.ylim()[1])\n", "plt.grid()\n", "plt.title(description)\n", "\n", "P = np.exp(P)\n", "\n", "# histogram\n", "plt.subplot(2,2,3)\n", "plt.hold(True)\n", "nbins = min(100,int(1.5*np.sqrt(N)))\n", "plt.hist(P,bins=nbins,normed=1,alpha=0.35,color='b');\n", "ylim = plt.ylim()\n", "plt.plot([P.mean(),P.mean()],ylim,'r--',lw=2)\n", "plt.ylim(ylim)\n", "plt.text(p,0.97*ylim[1],\" Mean = {0:.2f}\".format(P.mean()),va = 'top')\n", "\n", "#T = len(list(NYSE_tradingdays(start_date,end_date)))\n", "#alpha = np.log(S[-1]) + (mu-sigma*sigma/2.0)*T\n", "#beta = sigma*np.sqrt(T)\n", "#pdf_pred = lognorm.pdf(x, beta, loc=0, scale=np.exp(alpha)) # fitted distribution\n", "#plt.plot(x,pdf_pred,'g--',lw=3)\n", "plt.hold(False)\n", "plt.xlim(min(P),max(P))\n", "plt.xlabel('Final Price')\n", "plt.ylabel('Probability');\n", "plt.title(\"Price Distribution {0}\".format(d.strftime(\"%b %d %Y\")))\n", "\n", "# Cumulative Distribution\n", "plt.subplot(2,2,4)\n", "plt.hist(P,bins=nbins,normed=1,cumulative=True,alpha=0.35,color='b');\n", "plt.xlim(min(P),max(P))\n", "plt.ylim(0,1)\n", "plt.xlabel('Final Price')\n", "plt.ylabel('Probability');\n", "plt.title(\"Cumulative Distribution {0}\".format(d.strftime(\"%b %d %Y\")))\n", "\n", "def plotPercentile(p,va='baseline'):\n", " x = np.percentile(P,100.0*p)\n", " dp = -0.02 if va=='top' else 0.02\n", " plt.text(min(P) + 0.05*(max(P)-min(P)),p+dp,'{0:.2f}'.format(x),ha='left',va=va)\n", " plt.plot([0,x,x],[p,p,0],'r--',lw=2)\n", "\n", "plt.hold(True)\n", "plotPercentile(0.05)\n", "plotPercentile(0.50)\n", "plotPercentile(0.95,va='top')\n", "plt.hold(False)\n", "plt.grid()\n", "plt.tight_layout()\n", "\n", "plt.savefig('img/StochasticPriceModelLogT.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regressing Returns to Alternative Models" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "df = pd.DataFrame({'S':S,'R':R}, index = R.index)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "df = pd.DataFrame({'Price':S,'LnS':log(S),'Return':R})\n", "df = df[~isnan(df['Return'])]\n", "#plot(df['LnS'],df['Return'],'.')\n", "\n", "import statsmodels.api as sm\n", "df = sm.add_constant(df)\n", "mod = sm.OLS(df['Return'],df[['const','LnS']])\n", "res = mod.fit()\n", "print res.summary()\n", "print res.params\n", "res.resid.plot()" ] } ], "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": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }