{ "cells": [ { "cell_type": "markdown", "metadata": { "nbpages": { "level": 0, "link": "[](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html)", "section": "" }, "pycharm": {} }, "source": [ "\n", "*This notebook contains material from [CBE40455-2020](https://jckantor.github.io/CBE40455-2020);\n", "content is available [on Github](https://github.com/jckantor/CBE40455-2020.git).*\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 0, "link": "[](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html)", "section": "" }, "pycharm": {} }, "source": [ "\n", "< [7.6 Portfolio Optimization using Mean Absolute Deviation](https://jckantor.github.io/CBE40455-2020/07.06-Portfolio-Optimization-using-Mean-Absolute-Deviation.html) | [Contents](toc.html) | [7.8 Log-Optimal Growth and the Kelly Criterion](https://jckantor.github.io/CBE40455-2020/07.08-Log-Optimal-Growth-and-the-Kelly-Criterion.html) >

\"Open

\"Download\"" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 1, "link": "[7.7 Portfolio Optimization](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7-Portfolio-Optimization)", "section": "7.7 Portfolio Optimization" }, "pycharm": {} }, "source": [ "# 7.7 Portfolio Optimization" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 1, "link": "[7.7 Portfolio Optimization](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7-Portfolio-Optimization)", "section": "7.7 Portfolio Optimization" }, "pycharm": {} }, "source": [ "This [IPython notebook](http://ipython.org/notebook.html) demonstrates portfolio optimization using the Mean Absolute Deviation (MAD) criterion. A portion of these notes is adapted from [GLPK Wikibook tutorial on the subject](http://en.wikibooks.org/wiki/GLPK/Portfolio_Optimization) written by me.\n", "\n", "J.C. Kantor (Kantor.1@nd.edu)\n", "\n", "The latest version of this IPython notebook is available at [http://github.com/jckantor/CBE20255](http://github.com/jckantor/CBE20255) for noncommercial use under terms of the [Creative Commons Attribution Noncommericial ShareAlike License](http://creativecommons.org/licenses/by-nc-sa/4.0/)." ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.1 Investment Objectives](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.1-Investment-Objectives)", "section": "7.7.1 Investment Objectives" }, "pycharm": {} }, "source": [ "## 7.7.1 Investment Objectives" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.1 Investment Objectives](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.1-Investment-Objectives)", "section": "7.7.1 Investment Objectives" }, "pycharm": {} }, "source": [ "* Maximize returns\n", "* Reduce Risk through diversification" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.2 Why Diversify?](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2-Why-Diversify?)", "section": "7.7.2 Why Diversify?" }, "pycharm": {} }, "source": [ "## 7.7.2 Why Diversify?" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.2 Why Diversify?](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2-Why-Diversify?)", "section": "7.7.2 Why Diversify?" }, "pycharm": {} }, "source": [ "Investment portfolios are collections of investments that are managed for overall investment return. Compared to investing all of your capital into a single asset, maintaining a portfolio of investments allows you to manage risk through diversification." ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[7.7.2.1 Reduce Risk through Law of Large Numbers](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2.1-Reduce-Risk-through-Law-of-Large-Numbers)", "section": "7.7.2.1 Reduce Risk through Law of Large Numbers" }, "pycharm": {} }, "source": [ "### 7.7.2.1 Reduce Risk through Law of Large Numbers" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[7.7.2.1 Reduce Risk through Law of Large Numbers](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2.1-Reduce-Risk-through-Law-of-Large-Numbers)", "section": "7.7.2.1 Reduce Risk through Law of Large Numbers" }, "pycharm": {} }, "source": [ "Suppose there are a set of independent investment opportunities that will pay back between 0 and 300% of your original investment, and that all outcomes in that range are equally likely. You have $100,000 to invest. Should you put it all in one opportunity? Or should you spread it around?\n", "\n", "Here we simulate the outcomes of 1000 trials where we place all the money into a sigle investment of $100,000." ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false, "nbpages": { "level": 3, "link": "[7.7.2.1 Reduce Risk through Law of Large Numbers](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2.1-Reduce-Risk-through-Law-of-Large-Numbers)", "section": "7.7.2.1 Reduce Risk through Law of Large Numbers" }, "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average Profit = $49126\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "W0 = 100000.00\n", "\n", "Ntrials = 10000\n", "Profit = list()\n", "for n in range(0,Ntrials):\n", " W1 = W0*random.uniform(0,3.00)\n", " Profit.append(W1 - W0)\n", "\n", "figure(figsize=(10,4))\n", "hist(Profit,bins=100);\n", "xlabel('Profit')\n", "ylabel('Frequency')\n", "\n", "print \"Average Profit = ${:.0f}\".format(mean(Profit))" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[7.7.2.1 Reduce Risk through Law of Large Numbers](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2.1-Reduce-Risk-through-Law-of-Large-Numbers)", "section": "7.7.2.1 Reduce Risk through Law of Large Numbers" }, "pycharm": {} }, "source": [ "As you would expect, about 1/3 of the time there is a loss, and about 2/3 of the time there is a profit. Is this an acceptable investment outcome?\n", "\n", "Let's see what happens if the $100,000 investment over a small number of equal sized investments." ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false, "nbpages": { "level": 3, "link": "[7.7.2.1 Reduce Risk through Law of Large Numbers](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2.1-Reduce-Risk-through-Law-of-Large-Numbers)", "section": "7.7.2.1 Reduce Risk through Law of Large Numbers" }, "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average Profit = $50177\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "W0 = 100000.00\n", "\n", "Ntrials = 10000\n", "Ninvestments = 5\n", "\n", "Profit = list()\n", "for n in range(0,Ntrials):\n", " W1 = sum([(W0/Ninvestments)*random.uniform(0,3.00) for _ in range(0,Ninvestments)])\n", " Profit.append(W1-W0)\n", "\n", "figure(figsize=(10,4))\n", "hist(Profit,bins=100);\n", "xlim(-W0,2*W0)\n", "xlabel('Profit')\n", "ylabel('Frequency')\n", "\n", "print \"Average Profit = ${:.0f}\".format(mean(Profit))" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[7.7.2.1 Reduce Risk through Law of Large Numbers](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2.1-Reduce-Risk-through-Law-of-Large-Numbers)", "section": "7.7.2.1 Reduce Risk through Law of Large Numbers" }, "pycharm": {} }, "source": [ "Even a modest degree of diversification reduces downside risk." ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false, "nbpages": { "level": 3, "link": "[7.7.2.1 Reduce Risk through Law of Large Numbers](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.2.1-Reduce-Risk-through-Law-of-Large-Numbers)", "section": "7.7.2.1 Reduce Risk through Law of Large Numbers" }, "pycharm": {} }, "outputs": [ { "data": { "image/png": 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tj8B17ep2NCIiFefqCFyhkxfYPXLkCN988w1t2rQxWsCJiH/Zvx+uv96+21TF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\n+y7Osh7Vq0ONGv49alaZsrK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from statsmodels.distributions import ECDF\n", "\n", "ecdf = ECDF(Profit)\n", "\n", "x = linspace(min(Profit),max(Profit))\n", "\n", "figure(figsize=(10,4))\n", "plot(x,ecdf(x))\n", "xlabel('Profit')\n", "ylabel('Cumulative Probability')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.3 Select a Portfolio from a Set of Candidate Portfolios](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3-Select-a-Portfolio-from-a-Set-of-Candidate-Portfolios)", "section": "7.7.3 Select a Portfolio from a Set of Candidate Portfolios" }, "pycharm": {} }, "source": [ "## 7.7.3 Select a Portfolio from a Set of Candidate Portfolios" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.3 Select a Portfolio from a Set of Candidate Portfolios](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3-Select-a-Portfolio-from-a-Set-of-Candidate-Portfolios)", "section": "7.7.3 Select a Portfolio from a Set of Candidate Portfolios" }, "pycharm": {} }, "outputs": [], "source": [ "djia = ['AXP','BA','CAT','CSCO','CVX','DD','DIS','GE', \\\n", " 'GS','HD','IBM','INTC','JNJ','JPM','KO','MCD', \\\n", " 'MMM','MRK','MSFT','NKE','PFE','PG','T','TRV', \\\n", " 'UNH','UTX','V','VZ','WMT','XOM']\n", "\n", "small_portfolio = ['F','AAPL','XOM','PG','KO']\n", "\n", "portfolio = small_portfolio\n", "portfolio = djia" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[7.7.3.1 Download Historical Data](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.1-Download-Historical-Data)", "section": "7.7.3.1 Download Historical Data" }, "pycharm": {} }, "source": [ "### 7.7.3.1 Download Historical Data" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false, "nbpages": { "level": 3, "link": "[7.7.3.1 Download Historical Data](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.1-Download-Historical-Data)", "section": "7.7.3.1 Download Historical Data" }, "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "AXP 754\n", "BA 754\n", "CAT 754\n", "CSCO 754\n", "CVX 754\n", "DD 754\n", "DIS 754\n", "GE 754\n", "GS 754\n", "HD 754\n", "IBM 754\n", "INTC 754\n", "JNJ 754\n", "JPM 754\n", "KO 754\n", "MCD 754\n", "MMM 754\n", "MRK 754\n", "MSFT 754\n", "NKE 754\n", "PFE 754\n", "PG 754\n", "T 754\n", "TRV 754\n", "UNH 754\n", "UTX 754\n", "V 754\n", "VZ 754\n", "WMT 754\n", "XOM 754\n" ] } ], "source": [ "import pandas as pd\n", "import datetime\n", "import pandas.io.data\n", "\n", "end = datetime.datetime.today().date()\n", "start = end - datetime.timedelta(3*365)\n", "\n", "adjclose = pd.DataFrame()\n", "\n", "for s in portfolio:\n", " data = pd.io.data.DataReader(s,\"yahoo\",start,end)\n", " print \"{:5s} {:d}\".format(s,len(data))\n", " adjclose[s] = data['Adj Close']\n", " \n", "adjclose.plot(logy=True, legend=False, figsize=(10,6))\n", "ylabel('Adjusted Close')\n", "title('Adjusted Close for All Portfolio Assets')" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[7.7.3.2 Equally Weighted Portfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.2-Equally-Weighted-Portfolio)", "section": "7.7.3.2 Equally Weighted Portfolio" }, "pycharm": {} }, "source": [ "### 7.7.3.2 Equally Weighted Portfolio" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "collapsed": false, "nbpages": { "level": 3, "link": "[7.7.3.2 Equally Weighted Portfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.2-Equally-Weighted-Portfolio)", "section": "7.7.3.2 Equally Weighted Portfolio" }, "pycharm": {} }, "outputs": [ { "data": { "image/png": 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giYiIiEiPFy+YPBuLCXQRxxow5Rgr5RgrZRgn5RgrZRgn5RgrZQzFKTYWWLtW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\nJp5Y2bGj2K9ffknHPW8e38/EBLh27RoeP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wYPJrDbvp0O2dmZy7MCizppEp+/ZQsBoQBY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\nI7B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PlkF1/Chs9EVvPOefiUUiRXL74Qj8Y9vbP1i/PqO5skQqhTE5AydvucPdTUAzt6eQ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\nGfuIEf9eti47y0petplKVdTMmiWO49ixj7che1ju3BHwGRIiJE1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x6RILS4vKMBQK1g0U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6O/0sbj/HlqGjw9yXC2by/0+T/9xIC0kut0786ao44dSYzMzFh83aRJ2SSuYUPW2jg6skZE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\nqO2lvr2g09jYKLTrHjt2L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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P_equal = pd.Series(0,index = adjclose.index)\n", "\n", "for s in portfolio:\n", " P_equal += 100.0*adjclose[s]/adjclose[s][0]/len(portfolio)\n", "\n", "figure(figsize=(12,6))\n", "\n", "for s in portfolio:\n", " (100.0*adjclose[s]/adjclose[s][0]).plot(lw=0.4)\n", "\n", "P_equal.plot(color='r',lw=4)\n", "ylabel('Value');\n", "title('Value of an equally weighted portfolio');\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[7.7.3.3 Compute Component Returns](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.3-Compute-Component-Returns)", "section": "7.7.3.3 Compute Component Returns" }, "pycharm": {} }, "source": [ "### 7.7.3.3 Compute Component Returns" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[7.7.3.3 Compute Component Returns](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.3-Compute-Component-Returns)", "section": "7.7.3.3 Compute Component Returns" }, "pycharm": {} }, "source": [ "Arithmetic returns are required because subsequent calculations will be combining returns across components of a portfolio." ] }, { "cell_type": "code", "execution_count": 159, "metadata": { "collapsed": false, "nbpages": { "level": 3, "link": "[7.7.3.3 Compute Component Returns](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.3-Compute-Component-Returns)", "section": "7.7.3.3 Compute Component Returns" }, "pycharm": {} }, "outputs": [ { "data": { "image/png": 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/evXiiy+iS5cuiEQiyMzMxO7du+0Tlp1uvvlm3HvvvcjIyHAtrBwlHcBBSQdw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#returns = adjclose.diff()[1:]/adjclose[1:]\n", "returns = log(adjclose/adjclose.shift(+1))\n", "rmean = returns.mean()\n", "mad = abs(returns-returns.mean()).mean()\n", "\n", "# plug NaN holes due to missing data\n", "for s in returns.columns:\n", " for t in returns.index:\n", " if isnan(returns[s][t]):\n", " returns[s][t] = rmean[s]\n", "\n", "figure(figsize = (15,0.35*len(returns.columns)))\n", "subplot(1,3,1)\n", "returns.mean().plot(kind='barh')\n", "title('Mean Returns');\n", "\n", "subplot(1,3,2)\n", "returns.std().plot(kind='barh')\n", "title('Standard Deviation');\n", "\n", "subplot(1,3,3)\n", "abs(returns-returns.mean()).mean().plot(kind='barh')\n", "title('Mean Absolute Difference');" ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "collapsed": false, "nbpages": { "level": 3, "link": "[7.7.3.3 Compute Component Returns](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.3-Compute-Component-Returns)", "section": "7.7.3.3 Compute Component Returns" }, "pycharm": {} }, "outputs": [ { "data": { "image/png": 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G41jaMbz/+/t4zeY1JPsmo22LtlWmV+cxWOUWQyyAI8jN3YdTp8q36KIvRBf9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\nTVuZpS3BYdkKUpGzq5dahW4LYl1EMmoNEwya2WX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(returns.std(),abs(returns-returns.mean()).mean(),'o')\n", "xlabel('Standard Deviation')\n", "ylabel('Mean Absolute Deviation')\n", "\n", "plot([0,returns.std().max()],[0,sqrt(2.0/pi)*returns.std().max()])\n", "legend(['Portfolio Components','sqrt(2/pi)'],loc='best');" ] }, { "cell_type": "code", "execution_count": 161, "metadata": { "collapsed": false, "nbpages": { "level": 3, "link": "[7.7.3.3 Compute Component Returns](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.3.3-Compute-Component-Returns)", "section": "7.7.3.3 Compute Component Returns" }, "pycharm": {} }, "outputs": [ { "data": { "image/png": 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Vw759+3Dw4EFYWloiNDQU3333Hdq3b1/htkuTy+VYu3YtAgMD0bRpU0RFRZW7r1tVe1tK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\nhASkpaXB3t4efn5+CA8Px9KlS3H+/HkEBATAw8MD3t7e6NatG4KDgxu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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,6))\n", "for s in portfolio:\n", " plot(mad[s],rmean[s],'s')\n", " text(mad[s]*1.03,rmean[s],s)\n", " \n", "axis([0, 1.1*max(mad), min([0,min(rmean)-.1*(max(rmean)-min(rmean))]), 1.1*max(rmean)])\n", "ax = axis()\n", "plot([ax[0],ax[1]],[0,0],'r--');\n", "\n", "#R_equal = P_equal.diff()[1:]/P_equal[1:]\n", "R_equal = log(P_equal/P_equal.shift(+1))\n", "M_equal = abs(R_equal-R_equal.mean()).mean()\n", "\n", "plot(M_equal,R_equal.mean(),'ro',ms=15)\n", "\n", "title('Risk/Return for an Equally Weighted Portfolio')\n", "xlabel('Mean Absolute Deviation')\n", "ylabel('Mean Return')\n", "\n", "grid();" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "source": [ "## 7.7.4 MAD Porfolio" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "source": [ "The linear program is formulated and solved using the pulp package. " ] }, { "cell_type": "code", "execution_count": 117, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied (use --upgrade to upgrade): pulp in /Users/jeff/anaconda/lib/python2.7/site-packages\r\n", "Requirement already satisfied (use --upgrade to upgrade): pyparsing<=1.9.9 in /Users/jeff/anaconda/lib/python2.7/site-packages (from pulp)\r\n", "Cleaning up...\r\n" ] } ], "source": [ "!pip install pulp" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "source": [ "The decision variables will be indexed by date/time. The pandas dataframes containing the returns data are indexed by timestamps that include characters that cannot be used by the GLPK solver. Therefore we create a dictionary to translate the pandas timestamps to strings that can be read as members of a GLPK set. The strings denote seconds in the current epoch as defined by python." ] }, { "cell_type": "code", "execution_count": 163, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "outputs": [], "source": [ "t = {tstamp:\"{:%s}\".format(tstamp) for tstamp in returns.index}" ] }, { "cell_type": "code", "execution_count": 193, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal\n" ] } ], "source": [ "import pulp\n", "\n", "# mean absolute deviation for the portfolio\n", "m = pulp.LpVariable('m', lowBound = 0)\n", "\n", "# dictionary of portfolio weights\n", "w = pulp.LpVariable.dicts('w', portfolio, lowBound = 0)\n", "\n", "# dictionary of absolute deviations of portfolio returns\n", "y = pulp.LpVariable.dicts('y', t.values(), lowBound = 0)\n", "z = pulp.LpVariable.dicts('z', t.values(), lowBound = 0)\n", "\n", "# create problem instance\n", "lp = pulp.LpProblem('MAD Portfolio',pulp.LpMinimize)\n", "\n", "# add objective\n", "lp += m\n", "\n", "# calculate mean absolute deviation of portfolio returns\n", "lp += m == pulp.lpSum([(y[k] + z[k]) for k in t.values()])/float(len(t))\n", "\n", "# relate the absolute deviations to deviations in the portfolio returns\n", "for ts in returns.index:\n", " lp += y[t[ts]] - z[t[ts]] == pulp.lpSum([w[s]*(returns[s][ts]-returns[s].mean()) for s in portfolio]) \n", " \n", "# portfolio weights\n", "lp += pulp.lpSum([w[s] for s in portfolio]) == 1.0\n", "\n", "# bound on average portfolio return\n", "lp += pulp.lpSum([w[s]*(returns[s].mean()) for s in portfolio]) >= 0*R_equal.mean()\n", "\n", "lp.solve()\n", "print pulp.LpStatus[lp.status]" ] }, { "cell_type": "code", "execution_count": 194, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "outputs": [ { "data": { "image/png": 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UCZKyuC0hO3+jR4/Gm2++GXXdwoULkZaWhuzsbHvp378/0tLS8PHHHyciBhFR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/75LW7bo0cPjBgxAuvWrUMikcg1SuAcx7EdoV3MaAYzhk/+1CbHdgAPx3YAD8d2AA/HdgCXpDoh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\nHxqciIHM96kAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize = (15,0.35*len(returns.columns)))\n", "\n", "ws = pd.Series({s: w[s].varValue for s in portfolio},index=portfolio)\n", "\n", "subplot(1,3,1)\n", "ws.plot(kind='barh')\n", "title('Porfolio Weight');\n", "\n", "subplot(1,3,2)\n", "returns.mean().plot(kind='barh')\n", "title('Mean Returns');\n", "\n", "subplot(1,3,3)\n", "abs(returns-returns.mean()).mean().plot(kind='barh')\n", "title('Mean Absolute Difference');" ] }, { "cell_type": "code", "execution_count": 195, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 195, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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h2+mytAs1q9Tkj/A/+PvS37R2aM35hPMALDi6gGZ1mzGwyUAqm5kmzfQ/68/h6MP8ePJH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\nY7o6dMXLy4szx8+gWCg8SHjApt2bsK5qne38wJhAHEwdys2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ZsOHqBrZc30LLmi2Z1mYa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\nrb36xB5oI1uwYAFGj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "P_mad = pd.Series(0,index=adjclose.index)\n", "for s in portfolio:\n", " P_mad += 100.0*ws[s]*adjclose[s]/adjclose[s][0]\n", " \n", "figure(figsize=(12,6))\n", "P_mad.plot()\n", "P_equal.plot()\n", "legend(['MAD','Equal'],loc='best')\n", "ylabel('Unit Value')" ] }, { "cell_type": "code", "execution_count": 196, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.4 MAD Porfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.4-MAD-Porfolio)", "section": "7.7.4 MAD Porfolio" }, "pycharm": {} }, "outputs": [ { "data": { "image/png": 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WFvD398ePP/6Idu3albvtkkxNTbFu3Tr4+PigUaNGCA4OLnNft8r2thRfrVv86tKlCwBg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,6))\n", "for s in portfolio:\n", " plot(mad[s],rmean[s],'s')\n", " text(mad[s]*1.03,rmean[s],s)\n", " \n", "axis([0, 1.1*max(mad), min([0,min(rmean)-.1*(max(rmean)-min(rmean))]), 1.1*max(rmean)])\n", "ax = axis()\n", "plot([ax[0],ax[1]],[0,0],'r--');\n", "\n", "#R_equal = P_equal.diff()[1:]/P_equal[1:]\n", "R_equal = log(P_equal/P_equal.shift(+1))\n", "M_equal = abs(R_equal-R_equal.mean()).mean()\n", "\n", "plot(M_equal,R_equal.mean(),'ro',ms=15)\n", "\n", "#R_mad = P_mad.diff()[1:]/P_mad[1:]\n", "R_mad = log(P_mad/P_mad.shift(+1))\n", "M_mad = abs(R_mad-R_mad.mean()).mean()\n", "\n", "for s in portfolio:\n", " if ws[s] >= 0.0001:\n", " plot([M_mad,mad[s]],[R_mad.mean(),rmean[s]],'g--')\n", "\n", "plot(M_mad,R_mad.mean(),'go',ms=15)\n", "\n", "title('Risk/Return for an Equally Weighted Portfolio')\n", "xlabel('Mean Absolute Deviation')\n", "ylabel('Mean Return')\n", "\n", "grid();" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.5 Problem 1: Solve for Dominating MAD Portfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.5-Problem-1:-Solve-for-Dominating-MAD-Portfolio)", "section": "7.7.5 Problem 1: Solve for Dominating MAD Portfolio" }, "pycharm": {} }, "source": [ "## 7.7.5 Problem 1: Solve for Dominating MAD Portfolio" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.5 Problem 1: Solve for Dominating MAD Portfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.5-Problem-1:-Solve-for-Dominating-MAD-Portfolio)", "section": "7.7.5 Problem 1: Solve for Dominating MAD Portfolio" }, "pycharm": {} }, "outputs": [ { "ename": "NameError", "evalue": "name 'tmap' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\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 1\u001b[0m \u001b[0mlp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLpProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'MAD Portfolio'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLpMinimize\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mlp\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mlp\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mm\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlpSum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mz\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[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreturns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtmap\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0mlp\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlpSum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msymbols\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'tmap' is not defined" ] } ], "source": [ "lp = pulp.LpProblem('MAD Portfolio',pulp.LpMinimize)\n", "lp += m \n", "lp += m == pulp.lpSum([(y[t] + z[t])/float(len(returns.index)) for t in tmap.values()])\n", "lp += pulp.lpSum([w[s] for s in symbols]) == 1.0\n", "\n", "for t in returns.index:\n", " lp += y[tsec[t]] - z[tsec[t]] == pulp.lpSum([w[s]*(returns[s][t]-rmean[s]) for s in symbols]) \n", " \n", "lp.solve()\n", "m_min = m.varValue\n", "m_min" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false, "nbpages": { "level": 2, "link": "[7.7.5 Problem 1: Solve for Dominating MAD Portfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.5-Problem-1:-Solve-for-Dominating-MAD-Portfolio)", "section": "7.7.5 Problem 1: Solve for Dominating MAD Portfolio" }, "pycharm": {} }, "outputs": [ { "ename": "NameError", "evalue": "name 'symbols' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\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 5\u001b[0m \u001b[0mlp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLpProblem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'MAD Portfolio'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLpMaximize\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0mlp\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mlp\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mr\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlpSum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mrmean\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msymbols\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0mlp\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mm_min\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlpSum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mz\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[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreturns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtmap\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mlp\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mpulp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlpSum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mw\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msymbols\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'symbols' is not defined" ] } ], "source": [ "# Solve for maximum return at minimum MAD\n", "\n", "r = pulp.LpVariable('r',lowBound = 0)\n", "\n", "lp = pulp.LpProblem('MAD Portfolio',pulp.LpMaximize)\n", "lp += r\n", "lp += r == pulp.lpSum([w[s]*rmean[s] for s in symbols])\n", "lp += m_min == pulp.lpSum([(y[t] + z[t])/float(len(returns.index)) for t in tmap.values()])\n", "lp += pulp.lpSum([w[s] for s in symbols]) == 1.0\n", "for t in returns.index:\n", " lp += y[tsec[t]] - z[tsec[t]] == pulp.lpSum([w[s]*(returns[s][t]-rmean[s]) for s in symbols]) \n", " \n", "lp.solve()\n", "r_min = r.varValue\n", "w_min = pd.Series([pulp.value(w[s]) for s in symbols], index= symbols)" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[7.7.5 Problem 1: Solve for Dominating MAD Portfolio](https://jckantor.github.io/CBE40455-2020/07.07-MAD-Portfolio-Optimization.html#7.7.5-Problem-1:-Solve-for-Dominating-MAD-Portfolio)", "section": "7.7.5 Problem 1: Solve for Dominating MAD Portfolio" }, "pycharm": {} }, "source": [ "\n", "< [7.6 Portfolio Optimization using Mean Absolute Deviation](https://jckantor.github.io/CBE40455-2020/07.06-Portfolio-Optimization-using-Mean-Absolute-Deviation.html) | [Contents](toc.html) | [7.8 Log-Optimal Growth and the Kelly Criterion](https://jckantor.github.io/CBE40455-2020/07.08-Log-Optimal-Growth-and-the-Kelly-Criterion.html) >

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