ml-finance-python

python scripts for finance machine learning
git clone https://9o.is/git/ml-finance-python.git
notebook.ipynb

(108931B)
      1 {
      2  "cells": [
      3   {
      4    "cell_type": "markdown",
      5    "metadata": {},
      6    "source": [
      7     "# Exercises: Linear Correlation Analysis - Answer Key\n",
      8     "\n",
      9     "## Lecture Link : \n",
     10     "https://www.quantopian.com/lectures/linear-correlation-analysis\n",
     11     "\n",
     12     "###IMPORTANT NOTE: \n",
     13     "This lecture corresponds to the Linear Correlation Analysis lecture, which is part of the Quantopian lecture series. This homework expects you to rely heavily on the code presented in the corresponding lecture. Please copy and paste regularly from that lecture when starting to work on the problems, as trying to do them from scratch will likely be too difficult.\n",
     14     "\n",
     15     "Part of the Quantopian Lecture Series:\n",
     16     "\n",
     17     "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n",
     18     "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n",
     19     "\n",
     20     "----"
     21    ]
     22   },
     23   {
     24    "cell_type": "markdown",
     25    "metadata": {
     26     "deletable": true,
     27     "editable": true
     28    },
     29    "source": [
     30     "## Key Concepts"
     31    ]
     32   },
     33   {
     34    "cell_type": "code",
     35    "execution_count": 1,
     36    "metadata": {
     37     "collapsed": true,
     38     "deletable": true,
     39     "editable": true
     40    },
     41    "outputs": [],
     42    "source": [
     43     "# Useful Functions\n",
     44     "def find_most_correlated(data):\n",
     45     "    n = data.shape[1]\n",
     46     "    keys = data.keys()\n",
     47     "    pair = []\n",
     48     "    max_value = 0\n",
     49     "    for i in range(n):\n",
     50     "        for j in range(i+1, n):\n",
     51     "            S1 = data[keys[i]]\n",
     52     "            S2 = data[keys[j]]\n",
     53     "            result = np.corrcoef(S1, S2)[0,1]\n",
     54     "            if result > max_value:\n",
     55     "                pair = (keys[i], keys[j])\n",
     56     "                max_value = result\n",
     57     "    return pair, max_value"
     58    ]
     59   },
     60   {
     61    "cell_type": "code",
     62    "execution_count": 2,
     63    "metadata": {
     64     "collapsed": false,
     65     "deletable": true,
     66     "editable": true
     67    },
     68    "outputs": [],
     69    "source": [
     70     "# Useful Libraries\n",
     71     "import numpy as np\n",
     72     "import pandas as pd\n",
     73     "import matplotlib.pyplot as plt"
     74    ]
     75   },
     76   {
     77    "cell_type": "markdown",
     78    "metadata": {
     79     "deletable": true,
     80     "editable": true
     81    },
     82    "source": [
     83     "----"
     84    ]
     85   },
     86   {
     87    "cell_type": "markdown",
     88    "metadata": {
     89     "deletable": true,
     90     "editable": true
     91    },
     92    "source": [
     93     "# Exercise 1: Dependence of Artificial Variables\n",
     94     "\n",
     95     "## a. Finding Variance, Covariance, and Correlation I\n",
     96     "\n",
     97     "By reading the matrix output from the `np.cov()` and `np.corrcoef()` functions, find the variance of the variables $A$ and $B$ and the covariance and correlation of their relationship. "
     98    ]
     99   },
    100   {
    101    "cell_type": "code",
    102    "execution_count": 3,
    103    "metadata": {
    104     "collapsed": false,
    105     "deletable": true,
    106     "editable": true
    107    },
    108    "outputs": [
    109     {
    110      "name": "stdout",
    111      "output_type": "stream",
    112      "text": [
    113       "Covariance matrix: \n",
    114       "[[ 0.08237163 -0.24773898]\n",
    115       " [-0.24773898  0.74865838]]\n",
    116       "\n",
    117       "Correlation matrix: \n",
    118       "[[ 1.         -0.99761661]\n",
    119       " [-0.99761661  1.        ]]\n",
    120       "\n",
    121       "Variance of A: 0.0823716314393\n",
    122       "Variance of B: 0.748658383296\n",
    123       "\n",
    124       "Covariance of A and B: -0.247738983929\n",
    125       "Correlation of A and B: -0.997616611853\n"
    126      ]
    127     }
    128    ],
    129    "source": [
    130     "A = np.random.rand(100)\n",
    131     "B = -3 * A + np.random.exponential(0.05, 100)\n",
    132     "\n",
    133     "#Your code goes here\n",
    134     "\n",
    135     "covm = np.cov(A, B)\n",
    136     "corrm = np.corrcoef(A, B)\n",
    137     "\n",
    138     "print 'Covariance matrix: \\n' + str(covm) + '\\n'\n",
    139     "print 'Correlation matrix: \\n' + str(corrm) + '\\n'\n",
    140     "\n",
    141     "print 'Variance of A: ' + str(covm[0,0])\n",
    142     "print 'Variance of B: ' + str(covm[1,1]) + '\\n'\n",
    143     "\n",
    144     "print 'Covariance of A and B: ' + str(covm[1,0])\n",
    145     "print 'Correlation of A and B: ' + str(corrm[1,0])"
    146    ]
    147   },
    148   {
    149    "cell_type": "markdown",
    150    "metadata": {
    151     "deletable": true,
    152     "editable": true
    153    },
    154    "source": [
    155     "## b. Finding Variance, Covariance, and Correlation II\n",
    156     "\n",
    157     "By reading the matrix output from the `np.cov()` and `np.corrcoef()` functions, find the variance of the variables $C$ and $D$ and the covariance and correlation of their relationship. "
    158    ]
    159   },
    160   {
    161    "cell_type": "code",
    162    "execution_count": 4,
    163    "metadata": {
    164     "collapsed": false,
    165     "deletable": true,
    166     "editable": true,
    167     "scrolled": true
    168    },
    169    "outputs": [
    170     {
    171      "name": "stdout",
    172      "output_type": "stream",
    173      "text": [
    174       "Covariance matrix: \n",
    175       "[[ 0.09119246  0.00740988]\n",
    176       " [ 0.00740988  0.24265135]]\n",
    177       "\n",
    178       "Correlation matrix: \n",
    179       "[[ 1.          0.04981272]\n",
    180       " [ 0.04981272  1.        ]]\n",
    181       "\n",
    182       "Variance of C: 0.0911924610123\n",
    183       "Variance of D: 0.242651347657\n",
    184       "\n",
    185       "Covariance of C and D: 0.00740987878297\n",
    186       "Correlation of C and D: 0.0498127228365\n"
    187      ]
    188     }
    189    ],
    190    "source": [
    191     "C = np.random.rand(100)\n",
    192     "D = np.random.normal(0, 0.5, 100)\n",
    193     "\n",
    194     "#Your code goes here\n",
    195     "\n",
    196     "covm = np.cov(C, D)\n",
    197     "corrm = np.corrcoef(C, D)\n",
    198     "\n",
    199     "print 'Covariance matrix: \\n' + str(covm) + '\\n'\n",
    200     "print 'Correlation matrix: \\n' + str(corrm) + '\\n'\n",
    201     "\n",
    202     "print 'Variance of C: ' + str(covm[0,0])\n",
    203     "print 'Variance of D: ' + str(covm[1,1]) + '\\n'\n",
    204     "\n",
    205     "print 'Covariance of C and D: ' + str(covm[1,0])\n",
    206     "print 'Correlation of C and D: ' + str(corrm[1,0])"
    207    ]
    208   },
    209   {
    210    "cell_type": "markdown",
    211    "metadata": {
    212     "deletable": true,
    213     "editable": true
    214    },
    215    "source": [
    216     "----"
    217    ]
    218   },
    219   {
    220    "cell_type": "markdown",
    221    "metadata": {
    222     "deletable": true,
    223     "editable": true
    224    },
    225    "source": [
    226     "# Exercise 2: Constructing Example Relationships\n",
    227     "\n",
    228     "## a. Positive Correlation Example\n",
    229     "\n",
    230     "Construct a variable $Y$ which has a strong, but not perfect, positive correlation with $X$ $(0.9 < Corr(X,Y) < 1)$, and plot their relationship."
    231    ]
    232   },
    233   {
    234    "cell_type": "code",
    235    "execution_count": 5,
    236    "metadata": {
    237     "collapsed": false,
    238     "deletable": true,
    239     "editable": true
    240    },
    241    "outputs": [
    242     {
    243      "name": "stdout",
    244      "output_type": "stream",
    245      "text": [
    246       "Correlation of X and Y: 0.984086064122\n"
    247      ]
    248     },
    249     {
    250      "data": {
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HP9qUTZv+MDsCVNJZt6PDgbHLljwAoC60tm5OUknSm+SmPP10OcmKvselvkAFUF06TABA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\nCEwAAAAF/n8Nr5HyQ85yEgAAAABJRU5ErkJggg==\n",
    252       "text/plain": [
    253        "<matplotlib.figure.Figure at 0x7f16cfc4fb50>"
    254       ]
    255      },
    256      "metadata": {},
    257      "output_type": "display_data"
    258     }
    259    ],
    260    "source": [
    261     "X = np.random.rand(100)\n",
    262     "\n",
    263     "#Your code goes here\n",
    264     "\n",
    265     "Y = 2*X + np.random.normal(0, 0.1, 100)\n",
    266     "\n",
    267     "plt.scatter(X,Y)\n",
    268     "plt.xlabel('X Value')\n",
    269     "plt.ylabel('Y Value')\n",
    270     "\n",
    271     "print 'Correlation of X and Y: ' + str(np.corrcoef(X, Y)[0,1])"
    272    ]
    273   },
    274   {
    275    "cell_type": "markdown",
    276    "metadata": {
    277     "deletable": true,
    278     "editable": true
    279    },
    280    "source": [
    281     "## b. Negative Correlation Example\n",
    282     "\n",
    283     "Construct a variable $W$ which has a weak, negative correlation with $Z$ $(-0.3 < Corr(Z,W) < 0)$, and plot their relationship."
    284    ]
    285   },
    286   {
    287    "cell_type": "code",
    288    "execution_count": 6,
    289    "metadata": {
    290     "collapsed": false,
    291     "deletable": true,
    292     "editable": true
    293    },
    294    "outputs": [
    295     {
    296      "name": "stdout",
    297      "output_type": "stream",
    298      "text": [
    299       "Correlation of Z and W: -0.0498600763248\n"
    300      ]
    301     },
    302     {
    303      "data": {
    304       "image/png": 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CEgBURE/PunR0XNG70rgunZ3T0to6vuyyAIYdIQkAKuJzn1uZH/5wdpx+CDC0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\nl305v2DI9WkAAAAASUVORK5CYII=\n",
    305       "text/plain": [
    306        "<matplotlib.figure.Figure at 0x7f16d4f1cc90>"
    307       ]
    308      },
    309      "metadata": {},
    310      "output_type": "display_data"
    311     }
    312    ],
    313    "source": [
    314     "Z = np.random.rand(100)\n",
    315     "\n",
    316     "#Your code goes here\n",
    317     "\n",
    318     "W = -4*Z + np.random.normal(0, 10, 100)\n",
    319     "\n",
    320     "plt.scatter(Z,W)\n",
    321     "plt.xlabel('Z Value')\n",
    322     "plt.ylabel('W Value')\n",
    323     "\n",
    324     "print 'Correlation of Z and W: ' + str(np.corrcoef(Z, W)[0,1])"
    325    ]
    326   },
    327   {
    328    "cell_type": "markdown",
    329    "metadata": {
    330     "deletable": true,
    331     "editable": true
    332    },
    333    "source": [
    334     "----"
    335    ]
    336   },
    337   {
    338    "cell_type": "markdown",
    339    "metadata": {
    340     "deletable": true,
    341     "editable": true
    342    },
    343    "source": [
    344     "# Exercise 3: Correlation of Real Assets\n",
    345     "\n",
    346     "## a. Finding Correlation of Real Assets\n",
    347     "\n",
    348     "Find the correlation between the stocks OKE and LAKE. Also check how they correlate with the provided benchmark."
    349    ]
    350   },
    351   {
    352    "cell_type": "code",
    353    "execution_count": 7,
    354    "metadata": {
    355     "collapsed": false,
    356     "deletable": true,
    357     "editable": true
    358    },
    359    "outputs": [
    360     {
    361      "name": "stdout",
    362      "output_type": "stream",
    363      "text": [
    364       "Correlation coefficient of OKE and LAKE:  0.446484870844\n",
    365       "Correlation coefficient of OKE and benchmark:  0.853638499475\n",
    366       "Correlation coefficient of LAKE and benchmark:  0.625923407419\n"
    367      ]
    368     }
    369    ],
    370    "source": [
    371     "OKE = get_pricing('OKE', fields='price', start_date='2013-01-01', end_date='2015-01-01')\n",
    372     "LAKE = get_pricing('LAKE', fields='price', start_date='2013-01-01', end_date='2015-01-01')\n",
    373     "benchmark = get_pricing('SPY', fields='price', start_date='2013-01-01', end_date='2015-01-01')\n",
    374     "\n",
    375     "#Your code goes here\n",
    376     "\n",
    377     "print \"Correlation coefficient of OKE and LAKE: \", np.corrcoef(OKE, LAKE)[0,1]\n",
    378     "print \"Correlation coefficient of OKE and benchmark: \", np.corrcoef(OKE, benchmark)[0,1]\n",
    379     "print \"Correlation coefficient of LAKE and benchmark: \", np.corrcoef(LAKE, benchmark)[0,1]"
    380    ]
    381   },
    382   {
    383    "cell_type": "markdown",
    384    "metadata": {
    385     "deletable": true,
    386     "editable": true
    387    },
    388    "source": [
    389     "## b. Finding Correlated Pairs\n",
    390     "\n",
    391     "Find the most correlated pair of stocks in the following portfolio using 2015 pricing data and the `find_most_correlated` function defined in the Helper Functions section above."
    392    ]
    393   },
    394   {
    395    "cell_type": "code",
    396    "execution_count": 8,
    397    "metadata": {
    398     "collapsed": false,
    399     "deletable": true,
    400     "editable": true
    401    },
    402    "outputs": [
    403     {
    404      "data": {
    405       "text/plain": [
    406        "(('FB', 'AMZN'), 0.95751089566007552)"
    407       ]
    408      },
    409      "execution_count": 8,
    410      "metadata": {},
    411      "output_type": "execute_result"
    412     }
    413    ],
    414    "source": [
    415     "symbol_list = ['GSK', 'SNOW', 'FB', 'AZO', 'XEC', 'AMZN']\n",
    416     "data = get_pricing(symbol_list, fields=['price']\n",
    417     "                               , start_date='2015-01-01', end_date='2016-01-01')['price']\n",
    418     "data.columns = symbol_list\n",
    419     "\n",
    420     "#Your code goes here\n",
    421     "\n",
    422     "find_most_correlated(data)"
    423    ]
    424   },
    425   {
    426    "cell_type": "markdown",
    427    "metadata": {
    428     "deletable": true,
    429     "editable": true
    430    },
    431    "source": [
    432     "----"
    433    ]
    434   },
    435   {
    436    "cell_type": "markdown",
    437    "metadata": {
    438     "deletable": true,
    439     "editable": true
    440    },
    441    "source": [
    442     "# Exercise 4: Limitations of Correlation\n",
    443     "\n",
    444     "## a. Out of Sample Tests\n",
    445     "\n",
    446     "Using pricing data from the first half of 2016, find the correlation coefficient between FB and AMZN and compare it to the strong positive relationship predicted from the 2015 correlation coefficient to see if that result holds."
    447    ]
    448   },
    449   {
    450    "cell_type": "code",
    451    "execution_count": 9,
    452    "metadata": {
    453     "collapsed": false,
    454     "deletable": true,
    455     "editable": true
    456    },
    457    "outputs": [
    458     {
    459      "name": "stdout",
    460      "output_type": "stream",
    461      "text": [
    462       "2015 correlation coefficient:  0.95751089566\n",
    463       "2016 correlation coefficient:  0.651288727673\n",
    464       "The strong correlation from 2015 did not hold outside of the 2015 pricing sample.\n"
    465      ]
    466     }
    467    ],
    468    "source": [
    469     "FB_15 = get_pricing('FB', fields='price', start_date='2015-01-01', end_date='2016-01-01')\n",
    470     "AMZN_15 = get_pricing('AMZN', fields='price', start_date='2015-01-01', end_date='2016-01-01')\n",
    471     "FB_16 = get_pricing('FB', fields='price', start_date='2016-01-01', end_date='2016-07-01')\n",
    472     "AMZN_16 = get_pricing('AMZN', fields='price', start_date='2016-01-01', end_date='2016-07-01')\n",
    473     "\n",
    474     "#Your code goes here\n",
    475     "\n",
    476     "print \"2015 correlation coefficient: \", np.corrcoef(FB_15, AMZN_15)[0,1]\n",
    477     "print \"2016 correlation coefficient: \", np.corrcoef(FB_16, AMZN_16)[0,1]\n",
    478     "print \"The strong correlation from 2015 did not hold outside of the 2015 pricing sample.\""
    479    ]
    480   },
    481   {
    482    "cell_type": "markdown",
    483    "metadata": {
    484     "deletable": true,
    485     "editable": true
    486    },
    487    "source": [
    488     "## b. Rolling Correlation\n",
    489     "\n",
    490     "Plot the 60-day rolling correlation coefficient between FB and AMZN to make a conclusion about the stability of their relationship."
    491    ]
    492   },
    493   {
    494    "cell_type": "code",
    495    "execution_count": 10,
    496    "metadata": {
    497     "collapsed": false,
    498     "deletable": true,
    499     "editable": true
    500    },
    501    "outputs": [
    502     {
    503      "name": "stdout",
    504      "output_type": "stream",
    505      "text": [
    506       "Upon further investigation, FB and AMZN do not consistently have the strong correlation suggested by our result from question 3b.\n"
    507      ]
    508     },
    509     {
    510      "data": {
    511       "image/png": 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11dJJLJyWwUtbT7F5Ty0P/30/377rEpaF8RqZ8XKizreeqCQ/SeVIJpZWqyEv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\nQmCC\n",
    512       "text/plain": [
    513        "<matplotlib.figure.Figure at 0x7f16a3bfef10>"
    514       ]
    515      },
    516      "metadata": {},
    517      "output_type": "display_data"
    518     }
    519    ],
    520    "source": [
    521     "FB = get_pricing('FB', fields='price', start_date='2015-01-01', end_date='2017-01-01')\n",
    522     "AMZN = get_pricing('AMZN', fields='price', start_date='2015-01-01', end_date='2017-01-01')\n",
    523     "\n",
    524     "#Your code goes here\n",
    525     "\n",
    526     "rolling_correlation = FB.rolling(window=60).corr(AMZN)\n",
    527     "plt.plot(rolling_correlation)\n",
    528     "plt.xlabel('Day')\n",
    529     "plt.ylabel('60-day Rolling Correlation')\n",
    530     "print \"Upon further investigation, FB and AMZN do not consistently have the strong correlation suggested by our result from question 3b.\""
    531    ]
    532   },
    533   {
    534    "cell_type": "markdown",
    535    "metadata": {
    536     "deletable": true,
    537     "editable": true
    538    },
    539    "source": [
    540     "Congratulations on completing the Linear Correlation Analysis exercises!\n",
    541     "\n",
    542     "As you learn more about writing trading models and the Quantopian platform, enter a daily [Quantopian Contest](https://www.quantopian.com/contest). Your strategy will be evaluated for a cash prize every day.\n",
    543     "\n",
    544     "Start by going through the [Writing a Contest Algorithm](https://www.quantopian.com/tutorials/contest) tutorial."
    545    ]
    546   },
    547   {
    548    "cell_type": "markdown",
    549    "metadata": {
    550     "deletable": true,
    551     "editable": true
    552    },
    553    "source": [
    554     "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company.  In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*"
    555    ]
    556   }
    557  ],
    558  "metadata": {
    559   "kernelspec": {
    560    "display_name": "Python 2",
    561    "language": "python",
    562    "name": "python2"
    563   },
    564   "language_info": {
    565    "codemirror_mode": {
    566     "name": "ipython",
    567     "version": 2
    568    },
    569    "file_extension": ".py",
    570    "mimetype": "text/x-python",
    571    "name": "python",
    572    "nbconvert_exporter": "python",
    573    "pygments_lexer": "ipython2",
    574    "version": "2.7.12"
    575   }
    576  },
    577  "nbformat": 4,
    578  "nbformat_minor": 0
    579 }