ml-finance-python

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

(183559B)
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     10     "#Exercises: Hypothesis Testing - Answer Key\n",
     11     "By Christopher van Hoecke and Maxwell Margenot\n",
     12     "\n",
     13     "## Lecture Link\n",
     14     "\n",
     15     "https://www.quantopian.com/lectures/hypothesis-testing\n",
     16     "\n",
     17     "###IMPORTANT NOTE: \n",
     18     "This lecture corresponds to the Hypothesis Testing 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",
     19     "\n",
     20     "When you feel comfortable with the topics presented here, see if you can create an algorithm that qualifies for the Quantopian Contest. Participants are evaluated on their ability to produce risk-constrained alpha and the top 10 contest participants are awarded cash prizes on a daily basis.\n",
     21     "\n",
     22     "https://www.quantopian.com/contest\n",
     23     "\n",
     24     "Part of the Quantopian Lecture Series:\n",
     25     "\n",
     26     "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n",
     27     "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n",
     28     "\n",
     29     "----"
     30    ]
     31   },
     32   {
     33    "cell_type": "code",
     34    "execution_count": 1,
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     41    "source": [
     42     "# Useful Libraries\n",
     43     "import pandas as pd\n",
     44     "import numpy as np\n",
     45     "import matplotlib.pyplot as plt\n",
     46     "from scipy.stats import t\n",
     47     "import scipy.stats"
     48    ]
     49   },
     50   {
     51    "cell_type": "markdown",
     52    "metadata": {
     53     "deletable": true,
     54     "editable": true
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     56    "source": [
     57     "# Exercise 1: Hypothesis Testing.\n",
     58     "## a. One tail test. \n",
     59     "\n",
     60     "Using the techniques laid out in lecture, verify if we can state that the returns of TSLA **are greater** than 0.\n",
     61     "- Start by stating the null and alternative hypothesis\n",
     62     "    - Are we dealing with a one or two tailed test? Why? \n",
     63     "- Calculate the mean differences, and the Z-test using the formula provided in class. \n",
     64     "    - *Recall: This is a one parameter test, use the appropriate Z-test*\n",
     65     "- Use the stat library to calculate the associated p value with your t statistic. \n",
     66     "    - Compare your found p-value to the set $\\alpha$ value, and conclude. \n",
     67     "    \n",
     68     "\n",
     69     "###### Useful Formulas: \n",
     70     "$$ \\text{Test statistic} =  \\frac{\\bar{X}*\\mu - \\theta_0}{s*{\\bar{X}}} = \\frac{\\bar{X}_\\mu - 0}{s\\sqrt{n}} $$  "
     71    ]
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     75    "execution_count": 2,
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     81    "outputs": [
     82     {
     83      "name": "stdout",
     84      "output_type": "stream",
     85      "text": [
     86       "Tesla return sample mean 0.0006611637458\n",
     87       "Tesla return sample standard deviation 0.024566905352\n",
     88       "Tesla return sample size 251\n"
     89      ]
     90     }
     91    ],
     92    "source": [
     93     "prices1 = get_pricing('TSLA', start_date = '2015-01-01', end_date = '2016-01-01', fields = 'price')\n",
     94     "returns_sample_tsla = prices1.pct_change()[1:]\n",
     95     "\n",
     96     "print 'Tesla return sample mean', returns_sample_tsla.mean()\n",
     97     "print 'Tesla return sample standard deviation', returns_sample_tsla.std()\n",
     98     "print 'Tesla return sample size', len(returns_sample_tsla)"
     99    ]
    100   },
    101   {
    102    "cell_type": "markdown",
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    107    "source": [
    108     "###### One tail hypotheses.\n",
    109     "- *Null hypothesis: No difference in average returns in both population, the mean **is less** than 0*\n",
    110     "- *Althernative hypothesis: There is a difference in average returns of both populations, the mean is **not less** than 0*"
    111    ]
    112   },
    113   {
    114    "cell_type": "code",
    115    "execution_count": 3,
    116    "metadata": {
    117     "collapsed": false,
    118     "deletable": true,
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    120    },
    121    "outputs": [
    122     {
    123      "name": "stdout",
    124      "output_type": "stream",
    125      "text": [
    126       "t-statistic is: 0.426378639576\n",
    127       "p-value is:  0.335099432105\n"
    128      ]
    129     }
    130    ],
    131    "source": [
    132     "# Testing\n",
    133     "\n",
    134     "## Z- Statistic: \n",
    135     "test_stat = (returns_sample_tsla.mean() - 0) / \\\n",
    136     "    ( returns_sample_tsla.std() / np.sqrt( len(returns_sample_tsla) ) )\n",
    137     "print 't-statistic is:', test_stat\n",
    138     "\n",
    139     "## Finding the p-value for one tail test\n",
    140     "p_val = (1 - t.cdf(test_stat, len(returns_sample_tsla) - 1))\n",
    141     "print 'p-value is: ', p_val"
    142    ]
    143   },
    144   {
    145    "cell_type": "markdown",
    146    "metadata": {
    147     "deletable": true,
    148     "editable": true
    149    },
    150    "source": [
    151     "###### Comparing p-value with different $\\alpha$ values\n",
    152     "With $\\alpha = 0.01$, our p-value is greater than our $\\alpha$ value, we thus **fail to reject** the null hypothesis.   \n",
    153     "With $\\alpha = 0.5$, our p-value is greater than our $\\alpha$ value, we thus **fail to reject** the null hypothesis.   \n",
    154     "With $\\alpha = 0.1$, our p-value is greater than our $\\alpha$ value, we thus **fail to reject** the null hypothesis. "
    155    ]
    156   },
    157   {
    158    "cell_type": "code",
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    165    "outputs": [
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p0qVERERQt25d7t27B8C9e/fw8/MjPT0dtVpNQEAADg4OdO3aFS8vL/bv309O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\nuDbDdBwAV0FBAnDdDp4s1oHMEt2RFKvBfTuZjgMAXmH8iJ7qGhOh1Tt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RALdya0FKS0tT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\nTkSuQmCC\n",
    169       "text/plain": [
    170        "<matplotlib.figure.Figure at 0x7f3bbfad2090>"
    171       ]
    172      },
    173      "metadata": {},
    174      "output_type": "display_data"
    175     }
    176    ],
    177    "source": [
    178     "## Graph for visualization.\n",
    179     "\n",
    180     "x = np.linspace(-3, 3, 100)\n",
    181     "norm_pdf = lambda x: (1/np.sqrt(2 * np.pi)) * np.exp(-x * x / 2)\n",
    182     "y = norm_pdf(x)\n",
    183     "\n",
    184     "fig, ax = plt.subplots(1, 1, sharex=True)\n",
    185     "ax.plot(x, y)\n",
    186     "\n",
    187     "ax.fill_between(x, 0, y, where = x > 1.282, label = 'Confidence region alpha = 0.1')\n",
    188     "ax.fill_between(x, 0, y, where = x > 1.645, label = 'Confidence region alpha = 0.05', color = 'green')\n",
    189     "ax.fill_between(x, 0, y, where = x > 2.326, label = 'Confidence region alpha = 0.01', color = 'red')\n",
    190     "plt.axvline(p_val, linestyle = 'dashed', label = 'Location of P Value')\n",
    191     "\n",
    192     "plt.title('Graph of rejection region and P-value')\n",
    193     "plt.xlabel('x')\n",
    194     "plt.ylabel('p(x)')\n",
    195     "plt.legend();"
    196    ]
    197   },
    198   {
    199    "cell_type": "markdown",
    200    "metadata": {
    201     "deletable": true,
    202     "editable": true
    203    },
    204    "source": [
    205     "In the graph above, we can clearly see the rejection region for all three values of $\\alpha$ are bellow the found p-value."
    206    ]
    207   },
    208   {
    209    "cell_type": "markdown",
    210    "metadata": {
    211     "deletable": true,
    212     "editable": true
    213    },
    214    "source": [
    215     "## b. Two tailed test. \n",
    216     "Using the techniques laid out in lecture, verify if we can state that the returns of TSLA are equal to 0."
    217    ]
    218   },
    219   {
    220    "cell_type": "markdown",
    221    "metadata": {
    222     "deletable": true,
    223     "editable": true
    224    },
    225    "source": [
    226     "###### Two tail hypotheses.\n",
    227     "- *Null hypothesis: No difference in average returns in both population, the mean **is** 0*\n",
    228     "- *Althernative hypothesis: There is a difference in average returns of both populations, the mean **is not** 0*"
    229    ]
    230   },
    231   {
    232    "cell_type": "code",
    233    "execution_count": 5,
    234    "metadata": {
    235     "collapsed": false,
    236     "deletable": true,
    237     "editable": true
    238    },
    239    "outputs": [
    240     {
    241      "name": "stdout",
    242      "output_type": "stream",
    243      "text": [
    244       "p-value is:  0.670198864209\n"
    245      ]
    246     }
    247    ],
    248    "source": [
    249     "## Finding the p-value for two tailed test. \n",
    250     "p_val = 2*(1 - t.cdf(test_stat, len(returns_sample_tsla) - 1))\n",
    251     "print 'p-value is: ', p_val"
    252    ]
    253   },
    254   {
    255    "cell_type": "markdown",
    256    "metadata": {
    257     "deletable": true,
    258     "editable": true
    259    },
    260    "source": [
    261     "With $\\alpha = 0.01$, our p-value is greater than our $\\alpha$ value, we thus **fail to reject** the null hypothesis.   \n",
    262     "With $\\alpha = 0.5$, our p-value is greater than our $\\alpha$ value, we thus **fail to reject** the null hypothesis.   \n",
    263     "With $\\alpha = 0.1$, our p-value is greater than our $\\alpha$ value, we thus **fail to reject** the null hypothesis. "
    264    ]
    265   },
    266   {
    267    "cell_type": "code",
    268    "execution_count": 6,
    269    "metadata": {
    270     "collapsed": false,
    271     "deletable": true,
    272     "editable": true
    273    },
    274    "outputs": [
    275     {
    276      "data": {
    277       "image/png": 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XiRMn4uvri5mZGQkJCdy4cYMvvviC6OhoUlNTeffdd3nzzTeJiIggJCSElStX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\niIiIiEif/w+FUvmRbV7HwQAAAABJRU5ErkJggg==\n",
    278       "text/plain": [
    279        "<matplotlib.figure.Figure at 0x7f3bbfdda650>"
    280       ]
    281      },
    282      "metadata": {},
    283      "output_type": "display_data"
    284     }
    285    ],
    286    "source": [
    287     "x = np.linspace(-3, 3, 100)\n",
    288     "norm_pdf = lambda x: (1/np.sqrt(2 * np.pi)) * np.exp(-x * x / 2)\n",
    289     "y = norm_pdf(x)\n",
    290     "\n",
    291     "fig, ax = plt.subplots(1, 1, sharex=True)\n",
    292     "ax.plot(x, y)\n",
    293     "\n",
    294     "ax.fill_between(x, 0, y, where = x > 1.645, label = 'Confidence region at alpha = 0.1')\n",
    295     "ax.fill_between(x, 0, y, where = x < -1.645)\n",
    296     "\n",
    297     "ax.fill_between(x, 0, y, where = x > 1.96, label = 'Confidence region at alpha = 0.05', color = 'green')\n",
    298     "ax.fill_between(x, 0, y, where = x < -1.96, color = 'green')\n",
    299     "\n",
    300     "ax.fill_between(x, 0, y, where = x > 2.576, label = 'Confidence region at alpha = 0.05', color='red')\n",
    301     "ax.fill_between(x, 0, y, where = x < -2.576, color = 'red')\n",
    302     "plt.axvline(p_val, linestyle = 'dashed', label = 'Location of P Value')\n",
    303     "\n",
    304     "plt.title('Graph of rejection region and P-value')\n",
    305     "plt.xlabel('x')\n",
    306     "plt.ylabel('p(x)')\n",
    307     "plt.legend();"
    308    ]
    309   },
    310   {
    311    "cell_type": "markdown",
    312    "metadata": {
    313     "deletable": true,
    314     "editable": true
    315    },
    316    "source": [
    317     "----"
    318    ]
    319   },
    320   {
    321    "cell_type": "markdown",
    322    "metadata": {
    323     "deletable": true,
    324     "editable": true
    325    },
    326    "source": [
    327     "# Exercise 2: \n",
    328     "## a. Critical Values. \n",
    329     "Find the critical values associated with $\\alpha = 1\\%, 5\\%, 10\\%$ and graph the rejection regions on a plot for a two tailed test. \n",
    330     "\n",
    331     "Useful formula: \n",
    332     "$$ f = 1 - \\frac{\\alpha}{2} $$ \n",
    333     "\n",
    334     "In order to find the z-value associated with each f value use the [z-table](http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf) here.   \n",
    335     "*You can read more about how to read z-tables [here](http://www.dummies.com/education/math/statistics/how-to-find-probabilities-for-z-with-the-z-table/)*"
    336    ]
    337   },
    338   {
    339    "cell_type": "code",
    340    "execution_count": 7,
    341    "metadata": {
    342     "collapsed": false,
    343     "deletable": true,
    344     "editable": true
    345    },
    346    "outputs": [
    347     {
    348      "name": "stdout",
    349      "output_type": "stream",
    350      "text": [
    351       "alpha = 10%: f =  0.95\n",
    352       "alpha = 5%: f =  0.975\n",
    353       "alpha = 1%: f =  0.995\n"
    354      ]
    355     }
    356    ],
    357    "source": [
    358     "# For alpha = 10%\n",
    359     "alpha = 0.1\n",
    360     "f = 1 - (alpha/2)\n",
    361     "print 'alpha = 10%: f = ', f\n",
    362     "\n",
    363     "# For alpha = 5%\n",
    364     "alpha = 0.05\n",
    365     "f = 1 - (alpha/2)\n",
    366     "print 'alpha = 5%: f = ', f\n",
    367     "\n",
    368     "# For alpha = 1%\n",
    369     "alpha = 0.01\n",
    370     "f = 1 - (alpha/2)\n",
    371     "print 'alpha = 1%: f = ', f"
    372    ]
    373   },
    374   {
    375    "cell_type": "markdown",
    376    "metadata": {
    377     "deletable": true,
    378     "editable": true
    379    },
    380    "source": [
    381     "Using the z-table above, we find that for   \n",
    382     "$\\alpha = 10\\%$, x = $\\pm 1.645$  \n",
    383     "$\\alpha = 5\\%$, x = $\\pm 1.96$  \n",
    384     "$\\alpha = 1\\%$, x = $\\pm 2.575$  "
    385    ]
    386   },
    387   {
    388    "cell_type": "code",
    389    "execution_count": 8,
    390    "metadata": {
    391     "collapsed": false,
    392     "deletable": true,
    393     "editable": true
    394    },
    395    "outputs": [
    396     {
    397      "data": {
    398       "image/png": 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KSv8t+Pd+zM3NiYuL4/Dhw7Rr107927BgwQJGjx7NH3/8QadOnbCzswMKfjN+//33Sut/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\niIiIiIjIABUkERERERGRAf8Pn2pOFcZgGZUAAAAASUVORK5CYII=\n",
    399       "text/plain": [
    400        "<matplotlib.figure.Figure at 0x7f3bbfad23d0>"
    401       ]
    402      },
    403      "metadata": {},
    404      "output_type": "display_data"
    405     }
    406    ],
    407    "source": [
    408     "# Plot a standard normal distribution and mark the critical regions with shading\n",
    409     "x = np.linspace(-3, 3, 100)\n",
    410     "norm_pdf = lambda x: (1/np.sqrt(2 * np.pi)) * np.exp(-x * x / 2)\n",
    411     "y = norm_pdf(x)\n",
    412     "\n",
    413     "fig, ax = plt.subplots(1, 1, sharex=True)\n",
    414     "ax.plot(x, y)\n",
    415     "\n",
    416     "# Value for alpha = 1%\n",
    417     "ax.fill_between(x, 0, y, where =  x > 1.645, label = 'alpha = 10%')\n",
    418     "ax.fill_between(x, 0, y, where = x < -1.645)\n",
    419     "\n",
    420     "# Value for alpha = 5%\n",
    421     "ax.fill_between(x, 0, y, where = x > 1.96, color = 'red', label = 'alpha = 5%')\n",
    422     "ax.fill_between(x, 0, y, where = x < -1.96, color = 'red')\n",
    423     "\n",
    424     "#Value for alpha = 10%\n",
    425     "ax.fill_between(x, 0, y, where = x > 2.575, facecolor='green', label = 'alpha = 1%')\n",
    426     "ax.fill_between(x, 0, y, where = x < -2.575, facecolor='green')\n",
    427     "\n",
    428     "plt.title('Rejection regions for a two-tailed hypothesis test at 90%, 95%, 99% confidence')\n",
    429     "plt.xlabel('x')\n",
    430     "plt.ylabel('p(x)')\n",
    431     "plt.legend();"
    432    ]
    433   },
    434   {
    435    "cell_type": "markdown",
    436    "metadata": {
    437     "deletable": true,
    438     "editable": true
    439    },
    440    "source": [
    441     "## b. Mean T-Test\n",
    442     "Run a T-test on the SPY returns, to determine if the mean returns is 0.01.   \n",
    443     "- Find the two critical values for a 90% two tailed $z$-test\n",
    444     "- Use the formula above to run a t-test on the sample data.\n",
    445     "- Conclude about the test results."
    446    ]
    447   },
    448   {
    449    "cell_type": "code",
    450    "execution_count": 9,
    451    "metadata": {
    452     "collapsed": false,
    453     "deletable": true,
    454     "editable": true
    455    },
    456    "outputs": [
    457     {
    458      "name": "stdout",
    459      "output_type": "stream",
    460      "text": [
    461       "0.95\n"
    462      ]
    463     }
    464    ],
    465    "source": [
    466     "# Calculating Critical Values probability\n",
    467     "\n",
    468     "alpha = 0.1\n",
    469     "v = 1 - (alpha/2)\n",
    470     "print v"
    471    ]
    472   },
    473   {
    474    "cell_type": "markdown",
    475    "metadata": {
    476     "deletable": true,
    477     "editable": true
    478    },
    479    "source": [
    480     "From the previous question, we find a critical value of 1.645. "
    481    ]
    482   },
    483   {
    484    "cell_type": "code",
    485    "execution_count": 10,
    486    "metadata": {
    487     "collapsed": false,
    488     "deletable": true,
    489     "editable": true
    490    },
    491    "outputs": [
    492     {
    493      "name": "stdout",
    494      "output_type": "stream",
    495      "text": [
    496       "t test statistic:  1.05168962394\n"
    497      ]
    498     }
    499    ],
    500    "source": [
    501     "data = get_pricing('SPY', start_date = '2016-01-01', end_date = '2017-01-01', fields = 'price')\n",
    502     "returns_sample = data.pct_change()[1:]\n",
    503     "\n",
    504     "# Running the T-test.\n",
    505     "n = len(returns_sample)\n",
    506     "test_statistic = ((returns_sample.mean() - 0) /\n",
    507     "                (returns_sample.std()/np.sqrt(n)))\n",
    508     "print 't test statistic: ', test_statistic"
    509    ]
    510   },
    511   {
    512    "cell_type": "markdown",
    513    "metadata": {
    514     "deletable": true,
    515     "editable": true
    516    },
    517    "source": [
    518     "We find that\n",
    519     "$-1.645 < 1.05 < 1.645$.\n",
    520     "We thus conclude that we **fail to reject** our $H_0$"
    521    ]
    522   },
    523   {
    524    "cell_type": "markdown",
    525    "metadata": {
    526     "collapsed": true,
    527     "deletable": true,
    528     "editable": true
    529    },
    530    "source": [
    531     "# c. Mean p-value test\n",
    532     "Given the returns data above, use the p-value to determine the results of the previous hypothesis test. "
    533    ]
    534   },
    535   {
    536    "cell_type": "code",
    537    "execution_count": 11,
    538    "metadata": {
    539     "collapsed": false,
    540     "deletable": true,
    541     "editable": true
    542    },
    543    "outputs": [
    544     {
    545      "name": "stdout",
    546      "output_type": "stream",
    547      "text": [
    548       "p-value is:  0.293957454918\n",
    549       "p-value is greater than our significant level, we thus fail to reject the null hypothesis.\n"
    550      ]
    551     }
    552    ],
    553    "source": [
    554     "# Running p-value test. \n",
    555     "\n",
    556     "alpha = 0.1\n",
    557     "p_val = 2 * (1 - t.cdf(test_statistic, n - 1))\n",
    558     "print 'p-value is: ', p_val\n",
    559     "\n",
    560     "if p_val > alpha: \n",
    561     "    print 'p-value is greater than our significant level, we thus fail to reject the null hypothesis.'\n",
    562     "else: \n",
    563     "    print 'p-value is less than or equal to our significal level, we thus reject the null hypothesis.'"
    564    ]
    565   },
    566   {
    567    "cell_type": "markdown",
    568    "metadata": {
    569     "deletable": true,
    570     "editable": true
    571    },
    572    "source": [
    573     "As we can see above, our p-value is greater than our significant level, $\\alpha = 0.1$, we thus **fail to reject** the null hypothesis."
    574    ]
    575   },
    576   {
    577    "cell_type": "markdown",
    578    "metadata": {
    579     "deletable": true,
    580     "editable": true
    581    },
    582    "source": [
    583     "----"
    584    ]
    585   },
    586   {
    587    "cell_type": "markdown",
    588    "metadata": {
    589     "collapsed": true,
    590     "deletable": true,
    591     "editable": true
    592    },
    593    "source": [
    594     "# Exercise 3: Multiple Variables Tests.\n",
    595     "## a. Hypothesis testing on Means.\n",
    596     "- State the hypothesis tests for comparing two means\n",
    597     "- Find the test statistic along with the degrees of freedom for the following two assets. Assume variance is different (We assume XLF to be a safer buy than GS. \n",
    598     "- Use the [t-table](https://en.wikipedia.org/wiki/Student%27s_t-distribution#Table_of_selected_values) to conclude about your hypothesis test. *Pick $\\alpha = 10\\%$*\n",
    599     "\n",
    600     "######Useful Formulas: \n",
    601     "$$ t = \\frac{\\bar{X}_1 - \\bar{X}_2}{(\\frac{s_p^2}{n_1} + \\frac{s_p^2}{n_2})^{1/2}}$$\n",
    602     "$$ t = \\frac{\\bar{X}_1 - \\bar{X}_2}{(\\frac{s_1^2}{n_1} + \\frac{s_2^2}{n_2})^{1/2}}$$\n",
    603     "$$df = \\frac{(\\frac{s_1^2}{n_1} + \\frac{s_2^2}{n_2})^2}{(s_1^2/n_1)^2/(n_1-1) + (s_2^2/n_2)^2/(n_2-1)}$$\n",
    604     "\n",
    605     "*note: one formula for t involves equal variance, the other does not. Use the right one given the information above*\n",
    606     "\n",
    607     "\n",
    608     "-----------------"
    609    ]
    610   },
    611   {
    612    "cell_type": "markdown",
    613    "metadata": {
    614     "deletable": true,
    615     "editable": true
    616    },
    617    "source": [
    618     "Answer: \n",
    619     "<center>\n",
    620     "Hypothesis Tests when comparing two means: \n",
    621     "$$1. H_0: \\mu_1 - \\mu_2 = \\theta_0, \\ H_A: \\mu_1 - \\mu_2 \\neq \\theta_0$$\n",
    622     "$$2. H_0: \\mu_1 - \\mu_2 \\leq \\theta_0, \\ H_A: \\mu_1 - \\mu_2 > \\theta_0$$\n",
    623     "$$3. H_0: \\mu_1 - \\mu_2 \\geq \\theta_0, \\ H_A: \\mu_1 - \\mu_2 < \\theta_0$$\n",
    624     "</center>"
    625    ]
    626   },
    627   {
    628    "cell_type": "code",
    629    "execution_count": 12,
    630    "metadata": {
    631     "collapsed": false,
    632     "deletable": true,
    633     "editable": true
    634    },
    635    "outputs": [
    636     {
    637      "name": "stdout",
    638      "output_type": "stream",
    639      "text": [
    640       "t test statistic:  -1.12060529448\n",
    641       "Degrees of freedom (modified):  496.271031856\n",
    642       "p-value:  1.73700210188\n"
    643      ]
    644     }
    645    ],
    646    "source": [
    647     "# Data Collection\n",
    648     "alpha = 0.1\n",
    649     "symbol_list = ['XLF', 'MCD']\n",
    650     "start = '2015-01-01'\n",
    651     "end = '2016-01-01'\n",
    652     "pricing_sample = get_pricing(symbol_list, start_date = start, end_date = end, fields='price')\n",
    653     "pricing_sample.columns = map(lambda x: x.symbol, pricing_sample.columns)\n",
    654     "returns_sample = pricing_sample.pct_change()[1:]\n",
    655     "\n",
    656     "\n",
    657     "# Sample mean values\n",
    658     "mu_xlf, mu_gs = returns_sample.mean()\n",
    659     "s_xlf, s_gs = returns_sample.std()\n",
    660     "n_xlf = len(returns_sample['XLF'])\n",
    661     "n_gs = len(returns_sample['MCD'])\n",
    662     "\n",
    663     "test_statistic = ((mu_xlf - mu_gs) - 0)/((s_xlf**2/n_xlf) + (s_gs**2/n_gs))**0.5\n",
    664     "df = ((s_xlf**2/n_xlf) + (s_gs**2/n_gs))**2/ \\\n",
    665     "     (((s_xlf**2 / n_xlf)**2 /(n_xlf-1))+((s_gs**2 / n_gs)**2/(n_gs-1)))\n",
    666     "\n",
    667     "print 't test statistic: ', test_statistic\n",
    668     "print 'Degrees of freedom (modified): ', df\n",
    669     "print 'p-value: ', 2 * (1 - t.cdf(test_statistic, df))"
    670    ]
    671   },
    672   {
    673    "cell_type": "markdown",
    674    "metadata": {
    675     "deletable": true,
    676     "editable": true
    677    },
    678    "source": [
    679     "With a confidence level of 90%, our test statistic belongs to the range -1.645, 1.645. Since our test statistic is above these values we **accept** the null hypothesis and determine that the difference between XLF and MCD returns **is** significantly different from $0$."
    680    ]
    681   },
    682   {
    683    "cell_type": "markdown",
    684    "metadata": {
    685     "deletable": true,
    686     "editable": true
    687    },
    688    "source": [
    689     "## b. Hypothesis Testing on Variances. \n",
    690     "- State the hypothesis tests for comparing two means. \n",
    691     "- Calculate the returns and compare their variances.\n",
    692     "- Calculate the F-test using the variances\n",
    693     "- Check that both values have the same degrees of freedom. "
    694    ]
    695   },
    696   {
    697    "cell_type": "markdown",
    698    "metadata": {
    699     "collapsed": true,
    700     "deletable": true,
    701     "editable": true
    702    },
    703    "source": [
    704     "Answer: \n",
    705     "\n",
    706     "$$1. H_0: \\sigma_1^2 = \\sigma_2^2, \\ H_A: \\sigma_1^2 \\neq \\sigma_2^2$$\n",
    707     "$$2. H_0: \\sigma_1^2 \\leq \\sigma_2^2, \\ H_A: \\sigma_1^2 > \\sigma_2^2$$\n",
    708     "$$3. H_0: \\sigma_1^2 \\geq \\sigma_2^2, \\ H_A: \\sigma_1^2 < \\sigma_2^2$$\n"
    709    ]
    710   },
    711   {
    712    "cell_type": "code",
    713    "execution_count": 13,
    714    "metadata": {
    715     "collapsed": false,
    716     "deletable": true,
    717     "editable": true
    718    },
    719    "outputs": [
    720     {
    721      "name": "stdout",
    722      "output_type": "stream",
    723      "text": [
    724       "XLF standard deviation is:  0.0110764148949\n",
    725       "MCD standard deviation is:  0.0120820314786\n",
    726       "F Test statistic:  1.18982063302\n",
    727       "250\n",
    728       "250\n",
    729       "Upper critical value at a = 0.05 with df1 = 250 and df2 = 250:  1.28208064948\n",
    730       "Lower critical value at a = 0.05 with df1 = 250 and df2 = 250:  0.779982133263\n"
    731      ]
    732     }
    733    ],
    734    "source": [
    735     "# Data\n",
    736     "symbol_list = ['XLF', 'MCD']\n",
    737     "start = \"2015-01-01\"\n",
    738     "end = \"2016-01-01\"\n",
    739     "pricing_sample = get_pricing(symbol_list, start_date = start, end_date = end, fields = 'price')\n",
    740     "pricing_sample.columns = map(lambda x: x.symbol, pricing_sample.columns)\n",
    741     "returns_sample = pricing_sample.pct_change()[1:]\n",
    742     "\n",
    743     "# Take returns from above, MCD and XLF, and compare their variances\n",
    744     "xlf_std_dev, mcd_std_dev = returns_sample.std()\n",
    745     "print 'XLF standard deviation is: ', xlf_std_dev\n",
    746     "print 'MCD standard deviation is: ', mcd_std_dev\n",
    747     "\n",
    748     "# Calculate F-test with MCD.std > XLF.std\n",
    749     "test_statistic = (mcd_std_dev / xlf_std_dev)**2\n",
    750     "print \"F Test statistic: \", test_statistic\n",
    751     "\n",
    752     "#degree of freedom \n",
    753     "df1 = len(returns_sample['XLF']) - 1\n",
    754     "df2 = len(returns_sample['MCD']) - 1\n",
    755     "print df1\n",
    756     "print df2\n",
    757     "\n",
    758     "# Calculate critical values. \n",
    759     "from scipy.stats import f\n",
    760     "upper_crit_value = f.ppf(0.975, df1, df2)\n",
    761     "lower_crit_value = f.ppf(0.025, df1, df2)\n",
    762     "print 'Upper critical value at a = 0.05 with df1 = {0} and df2 = {1}: '.format(df1, df2), upper_crit_value\n",
    763     "print 'Lower critical value at a = 0.05 with df1 = {0} and df2 = {1}: '.format(df1, df2), lower_crit_value"
    764    ]
    765   },
    766   {
    767    "cell_type": "markdown",
    768    "metadata": {
    769     "deletable": true,
    770     "editable": true
    771    },
    772    "source": [
    773     "We can see that our F-test statistic is bellow the Upper Critical Value, thus we **accept** the null hypothesis and **reject** the alternative and conclude that the variances of XLF and MCD indeed do **not** differ."
    774    ]
    775   },
    776   {
    777    "cell_type": "markdown",
    778    "metadata": {
    779     "deletable": true,
    780     "editable": true
    781    },
    782    "source": [
    783     "---\n",
    784     "\n",
    785     "Congratulations on completing the Hypothesis Testing answer key!\n",
    786     "\n",
    787     "As you learn more about writing trading models and the Quantopian platform, enter the daily [Quantopian Contest](https://www.quantopian.com/contest). Your strategy will be evaluated for a cash prize every day.\n",
    788     "\n",
    789     "Start by going through the [Writing a Contest Algorithm](https://www.quantopian.com/tutorials/contest) tutorial."
    790    ]
    791   },
    792   {
    793    "cell_type": "markdown",
    794    "metadata": {
    795     "collapsed": true,
    796     "deletable": true,
    797     "editable": true
    798    },
    799    "source": [
    800     "*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.*"
    801    ]
    802   }
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