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@sharavsambuunev
Forked from humdings/pair-trade.ipynb
Created August 7, 2023 07:09
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Pair Trade in Zipline
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Pairs Trading\n",
"\n",
"####- Reduce systemic risk by taking opposite positions in two assets that share a \"common trend.\""
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"\n",
"import zipline\n",
"from zipline.api import (\n",
" add_history,\n",
" history,\n",
" symbol,\n",
" record,\n",
" order_target_percent\n",
")\n",
"from zipline.utils.factory import load_bars_from_yahoo\n",
"from zipline import TradingAlgorithm\n",
"\n",
"import pytz\n",
"import numpy as np\n",
"import pandas as pd\n",
"import statsmodels.api as sm"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"###A Simple Model\n",
" - Assume two similar assets $A \\& B$ have risk factor exposures that differ by a scalar and satisfy the necessary conditions for cointegration.\n",
" \n",
"\n",
"###$Spread_t = \\log(price^{A}_t) - \\gamma\\log(price^{B}_t) = \\epsilon{_t}$\n",
"\n",
"Where $\\epsilon{_t}$ is a normally distributed series with a mean of 0. After a single time step,\n",
"\n",
"###$\\log(price^{A}_t) - \\log(price^{A}_{t-1}) - \\gamma[\\log(price^{B}_t) - \\log(price^{B}_{t-1})] = \\epsilon{_t} - \\epsilon_{t-1}$\n",
"\n",
"\n",
"###$r^{Spread}_t = r^{A}_t - \\gamma r^{B}_t = \\Delta\\epsilon _t$\n",
"\n",
"So predicting the spread return at time $t$ is the same as predicting the direction of change in a stationary series of mean 0.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Selecting Pairs\n",
"\n",
" - #### Most importantly (opinion), both companies should have similar market risk exposures\n",
" - Better than 90% confidence on cointegration tests\n",
" - Consistent historical evidence of a \"common trend\"\n",
" - Must make economic sense \n",
" \n",
"###Case Study: EOG ~ PXD\n",
"\n",
"EOG Resources (EOG) and Pioneer Natural Resources Company (PXD) are two Texas based independent producers of oil and natural gas.\n",
" \n",
"Due to their similar market risk profiles (oil price sensitivity), PXD and EOG trend with similar trajectories.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"EOG\n",
"PXD\n",
"SPY\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.axes.AxesSubplot at 0x110eeecd0>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x110eee6d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Historical Data from Yahoo\n",
"data = load_bars_from_yahoo(\n",
" stocks=('EOG', 'PXD', 'SPY'),\n",
" start=pd.Timestamp('2011-01-01', tz='utc'),\n",
" end=pd.Timestamp.utcnow(),\n",
" indexes={}\n",
")\n",
"prices = data.minor_xs('price')\n",
"log_returns = np.log(prices).diff()\n",
"compound_returns = (1 + log_returns).cumprod()\n",
"compound_returns.plot(figsize=(14, 6))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test for cointegration\n",
"Intuition is not enough, so it's good to test for cointegration. The most commonly used test is the Dicky-Fuller cointegration test."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Test statistic: -11.3864409753\n",
"Critical Values: {'5%': -2.8644316780522177, '1%': -3.4368995989062348, '10%': -2.5683096665272789}\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.axes.AxesSubplot at 0x113072a10>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"YII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x113072f90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def adf_test(y, X, intercept=True, window=None):\n",
" ''' \n",
" Dicky-Fuller cointegration test \n",
" returns the ols obj and the adf test. e.g. (ols, adf)\n",
" '''\n",
" model = pd.ols(y=y, x=X, intercept=intercept, window=window)\n",
" return model, sm.tsa.adfuller(model.resid) \n",
"\n",
"model, adf = adf_test(prices.EOG, prices.PXD, window=20)\n",
"\n",
"spread = prices.EOG - model.beta['x'] * prices.PXD\n",
"\n",
"t_stat = adf[0]\n",
"critical_values = adf[4]\n",
"\n",
"print 'Test statistic: ', t_stat\n",
"print 'Critical Values:', critical_values\n",
"\n",
"spread.plot(figsize=(14,4))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Trading Algorithm\n",
"import numpy as np\n",
"import statsmodels.api as sm\n",
"\n",
"\n",
"def initialize(context):\n",
" context.x = symbol('EOG')\n",
" context.y = symbol('PXD')\n",
" context.nobs = 20\n",
" add_history(context.nobs, '1d', 'price')\n",
" context.tick = 0\n",
"\n",
"\n",
"def handle_data(context, data):\n",
" # Allow the history frame to accumulate data\n",
" context.tick += 1\n",
" if context.tick < context.nobs:\n",
" return\n",
" \n",
" prices = np.log(history(context.nobs, '1d', 'price'))\n",
" y = prices[context.y]\n",
" X = prices[context.x]\n",
" \n",
" model = sm.OLS(y, sm.add_constant(X)).fit()\n",
" hedge_ratio = model.params[context.x]\n",
" \n",
" spread = y - hedge_ratio * X\n",
" zscore = (spread.iloc[-1] - spread.mean()) / spread.std()\n",
" \n",
" record(\n",
" hedge_ratio=hedge_ratio,\n",
" spread=spread.iloc[-1],\n",
" zscore=zscore\n",
" )\n",
" # Get direction of the trades, and place orders\n",
" # Re-hedge to a dollar-neutral position daily in the direction of anticipated reversion. \n",
" # More traditionally an entry is made when the magnitude of the z-score is large.\n",
" side = np.copysign(0.5, zscore)\n",
" order_target_percent(context.y, -side)\n",
" order_target_percent(context.x, side * model.params[context.x])\n",
" \n",
" "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[2015-01-27 04:37:14.000959] INFO: Performance: Simulated 1022 trading days out of 1022.\n",
"[2015-01-27 04:37:14.001827] INFO: Performance: first open: 2011-01-03 14:31:00+00:00\n",
"[2015-01-27 04:37:14.002566] INFO: Performance: last close: 2015-01-26 21:00:00+00:00\n"
]
}
],
"source": [
"algo = TradingAlgorithm(\n",
" initialize=initialize,\n",
" handle_data=handle_data\n",
")\n",
"\n",
"perf = algo.run(data)\n",
"perf.index = perf.index.tz_localize(pytz.utc)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes.AxesSubplot at 0x115064390>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
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"RK5CYII=\n"
],
"text/plain": [
"<matplotlib.figure.Figure at 0x119becc50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"perf.spread.plot(figsize=(14,7))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes.AxesSubplot at 0x102990310>"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x1199e05d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x114ddf250>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"compound_pair_returns = (1 + perf.returns).cumprod()\n",
"results = compound_returns.to_dict()\n",
"results['EOG ~ PXD'] = compound_pair_returns\n",
"results = pd.DataFrame(results).ffill()\n",
"results[['PXD', 'EOG', 'EOG ~ PXD']].plot(figsize=(14,7))\n",
"results[['SPY', 'EOG ~ PXD']].plot(figsize=(14,7))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.axes.AxesSubplot at 0x119ba6990>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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],
"text/plain": [
"<matplotlib.figure.Figure at 0x1199dc3d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"perf[['long_exposure', 'short_exposure', 'net_leverage']].plot(figsize=(14,7))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Risk Metrics"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Index([u'algo_volatility', u'algorithm_period_return', u'alpha', u'benchmark_period_return', u'benchmark_volatility', u'beta', u'excess_return', u'information', u'max_drawdown', u'period_label', u'sharpe', u'sortino', u'trading_days', u'treasury_period_return'], dtype='object')\n"
]
},
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>one_month</th>\n",
" <th>six_month</th>\n",
" <th>three_month</th>\n",
" <th>twelve_month</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0 </th>\n",
" <td> 0</td>\n",
" <td> 0.399064</td>\n",
" <td> 0.1751205</td>\n",
" <td> 1.891121</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1 </th>\n",
" <td> -0.2303534</td>\n",
" <td> 0.06056268</td>\n",
" <td> 0.4051947</td>\n",
" <td> 2.081803</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2 </th>\n",
" <td> 0.6720155</td>\n",
" <td> 1.415842</td>\n",
" <td> 1.463952</td>\n",
" <td> 2.175454</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3 </th>\n",
" <td> 0.4959671</td>\n",
" <td> 1.185801</td>\n",
" <td> 0.3694682</td>\n",
" <td> 1.768673</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4 </th>\n",
" <td> 1.17063</td>\n",
" <td> 1.540741</td>\n",
" <td> -0.2464215</td>\n",
" <td> 1.233226</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5 </th>\n",
" <td> -1.118294</td>\n",
" <td> 1.678988</td>\n",
" <td> 0.6653211</td>\n",
" <td> 1.02713</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6 </th>\n",
" <td> -0.5931036</td>\n",
" <td> 1.99515</td>\n",
" <td> 1.174621</td>\n",
" <td> 1.862708</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7 </th>\n",
" <td> 2.033294</td>\n",
" <td> 2.716927</td>\n",
" <td> 2.285227</td>\n",
" <td> 2.53893</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8 </th>\n",
" <td>-0.08176557</td>\n",
" <td> 1.479004</td>\n",
" <td> 1.767422</td>\n",
" <td> 2.25566</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9 </th>\n",
" <td> 1.268055</td>\n",
" <td> 1.181162</td>\n",
" <td> 1.543545</td>\n",
" <td> 2.183615</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td> 1.42794</td>\n",
" <td> 0.08121069</td>\n",
" <td> 1.242962</td>\n",
" <td> 1.824025</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td> -0.444197</td>\n",
" <td> -0.4190961</td>\n",
" <td> 0.1417493</td>\n",
" <td> 1.130034</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td> 0.9053201</td>\n",
" <td> 0.4090032</td>\n",
" <td> 0.04302299</td>\n",
" <td> 1.734644</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>-0.08242315</td>\n",
" <td> 0.5739339</td>\n",
" <td> -0.9432394</td>\n",
" <td> 1.176115</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td> -0.4266107</td>\n",
" <td> 1.508455</td>\n",
" <td> -0.6499409</td>\n",
" <td> 1.495482</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td> -1.108201</td>\n",
" <td> 1.763178</td>\n",
" <td> 0.5388966</td>\n",
" <td> 1.851867</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td> 0.6875907</td>\n",
" <td> 2.659631</td>\n",
" <td> 2.269167</td>\n",
" <td> 2.180863</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td> 1.635488</td>\n",
" <td> 2.132488</td>\n",
" <td> 3.292805</td>\n",
" <td> 1.773212</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td> 1.369677</td>\n",
" <td> 2.053531</td>\n",
" <td> 1.999118</td>\n",
" <td> 1.333311</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td> 2.325417</td>\n",
" <td> 1.059135</td>\n",
" <td> 1.363741</td>\n",
" <td> 1.103552</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td> -0.2270935</td>\n",
" <td> 0.5245296</td>\n",
" <td>-0.08113302</td>\n",
" <td> 1.096163</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td> 0.395192</td>\n",
" <td> 0.7399767</td>\n",
" <td> 0.8561812</td>\n",
" <td> 1.047849</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td> -0.4168844</td>\n",
" <td> 0.2779619</td>\n",
" <td> 0.04189832</td>\n",
" <td> 1.139825</td>\n",
" </tr>\n",
" <tr>\n",
" <th>23</th>\n",
" <td> 1.6534</td>\n",
" <td> 0.3620893</td>\n",
" <td> 0.8247335</td>\n",
" <td> 1.425947</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24</th>\n",
" <td> -1.046189</td>\n",
" <td> 0.008985382</td>\n",
" <td> 0.1675946</td>\n",
" <td> 0.9222007</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25</th>\n",
" <td> 0.7705466</td>\n",
" <td> 0.4913982</td>\n",
" <td> 0.349238</td>\n",
" <td> 1.10515</td>\n",
" </tr>\n",
" <tr>\n",
" <th>26</th>\n",
" <td> 0.3631654</td>\n",
" <td> 0.9482038</td>\n",
" <td> -0.2755495</td>\n",
" <td> 1.136325</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27</th>\n",
" <td> -0.9101462</td>\n",
" <td> 0.7065436</td>\n",
" <td> -0.1099011</td>\n",
" <td> 0.9122471</td>\n",
" </tr>\n",
" <tr>\n",
" <th>28</th>\n",
" <td>-0.05254148</td>\n",
" <td> 1.155817</td>\n",
" <td> 0.3470793</td>\n",
" <td> 1.331254</td>\n",
" </tr>\n",
" <tr>\n",
" <th>29</th>\n",
" <td> 0.3586327</td>\n",
" <td> 1.499308</td>\n",
" <td> 1.460123</td>\n",
" <td> 1.507445</td>\n",
" </tr>\n",
" <tr>\n",
" <th>30</th>\n",
" <td> 0.6268109</td>\n",
" <td> 1.255211</td>\n",
" <td> 1.179911</td>\n",
" <td> 1.642905</td>\n",
" </tr>\n",
" <tr>\n",
" <th>31</th>\n",
" <td> 1.367809</td>\n",
" <td> 0.9888387</td>\n",
" <td> 1.187544</td>\n",
" <td> 1.493357</td>\n",
" </tr>\n",
" <tr>\n",
" <th>32</th>\n",
" <td> -0.7228139</td>\n",
" <td> 0.5936103</td>\n",
" <td> 0.5557084</td>\n",
" <td> 0.5932982</td>\n",
" </tr>\n",
" <tr>\n",
" <th>33</th>\n",
" <td> 0.5704613</td>\n",
" <td> 0.5453151</td>\n",
" <td> 0.5665684</td>\n",
" <td> 0.8791801</td>\n",
" </tr>\n",
" <tr>\n",
" <th>34</th>\n",
" <td> 0.5775891</td>\n",
" <td> 0.6057297</td>\n",
" <td> 0.02198625</td>\n",
" <td> 0.8407119</td>\n",
" </tr>\n",
" <tr>\n",
" <th>35</th>\n",
" <td> -0.5182931</td>\n",
" <td> 0.481271</td>\n",
" <td> 0.2531073</td>\n",
" <td> 0.4785539</td>\n",
" </tr>\n",
" <tr>\n",
" <th>36</th>\n",
" <td> -0.1662931</td>\n",
" <td> 0.938908</td>\n",
" <td> 0.164244</td>\n",
" <td> 0.7670049</td>\n",
" </tr>\n",
" <tr>\n",
" <th>37</th>\n",
" <td> 0.9211245</td>\n",
" <td> 1.052431</td>\n",
" <td> 0.7901755</td>\n",
" <td> 0.5383184</td>\n",
" </tr>\n",
" <tr>\n",
" <th>38</th>\n",
" <td> -0.7683404</td>\n",
" <td> 0.203883</td>\n",
" <td> 0.4149857</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39</th>\n",
" <td> 0.7212907</td>\n",
" <td> 0.6930835</td>\n",
" <td> 1.123166</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>40</th>\n",
" <td> 0.2959122</td>\n",
" <td> 0.57153</td>\n",
" <td> 0.6666565</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>41</th>\n",
" <td> 1.000188</td>\n",
" <td> 0.2394808</td>\n",
" <td> -0.2446549</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42</th>\n",
" <td> -0.2450061</td>\n",
" <td> 0.2787647</td>\n",
" <td> -0.4324159</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43</th>\n",
" <td> -1.004149</td>\n",
" <td>-6.329155e-05</td>\n",
" <td> 0.1321612</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>44</th>\n",
" <td> 0.807929</td>\n",
" <td> NaN</td>\n",
" <td> 0.3495203</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45</th>\n",
" <td> 0.7595933</td>\n",
" <td> NaN</td>\n",
" <td> 0.4474621</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46</th>\n",
" <td> 0.0335916</td>\n",
" <td> NaN</td>\n",
" <td> -0.0445592</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>47</th>\n",
" <td> 0.6829041</td>\n",
" <td> NaN</td>\n",
" <td> NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>48</th>\n",
" <td> -1.275649</td>\n",
" <td> NaN</td>\n",
" <td> NaN</td>\n",
" <td> NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" one_month six_month three_month twelve_month\n",
"0 0 0.399064 0.1751205 1.891121\n",
"1 -0.2303534 0.06056268 0.4051947 2.081803\n",
"2 0.6720155 1.415842 1.463952 2.175454\n",
"3 0.4959671 1.185801 0.3694682 1.768673\n",
"4 1.17063 1.540741 -0.2464215 1.233226\n",
"5 -1.118294 1.678988 0.6653211 1.02713\n",
"6 -0.5931036 1.99515 1.174621 1.862708\n",
"7 2.033294 2.716927 2.285227 2.53893\n",
"8 -0.08176557 1.479004 1.767422 2.25566\n",
"9 1.268055 1.181162 1.543545 2.183615\n",
"10 1.42794 0.08121069 1.242962 1.824025\n",
"11 -0.444197 -0.4190961 0.1417493 1.130034\n",
"12 0.9053201 0.4090032 0.04302299 1.734644\n",
"13 -0.08242315 0.5739339 -0.9432394 1.176115\n",
"14 -0.4266107 1.508455 -0.6499409 1.495482\n",
"15 -1.108201 1.763178 0.5388966 1.851867\n",
"16 0.6875907 2.659631 2.269167 2.180863\n",
"17 1.635488 2.132488 3.292805 1.773212\n",
"18 1.369677 2.053531 1.999118 1.333311\n",
"19 2.325417 1.059135 1.363741 1.103552\n",
"20 -0.2270935 0.5245296 -0.08113302 1.096163\n",
"21 0.395192 0.7399767 0.8561812 1.047849\n",
"22 -0.4168844 0.2779619 0.04189832 1.139825\n",
"23 1.6534 0.3620893 0.8247335 1.425947\n",
"24 -1.046189 0.008985382 0.1675946 0.9222007\n",
"25 0.7705466 0.4913982 0.349238 1.10515\n",
"26 0.3631654 0.9482038 -0.2755495 1.136325\n",
"27 -0.9101462 0.7065436 -0.1099011 0.9122471\n",
"28 -0.05254148 1.155817 0.3470793 1.331254\n",
"29 0.3586327 1.499308 1.460123 1.507445\n",
"30 0.6268109 1.255211 1.179911 1.642905\n",
"31 1.367809 0.9888387 1.187544 1.493357\n",
"32 -0.7228139 0.5936103 0.5557084 0.5932982\n",
"33 0.5704613 0.5453151 0.5665684 0.8791801\n",
"34 0.5775891 0.6057297 0.02198625 0.8407119\n",
"35 -0.5182931 0.481271 0.2531073 0.4785539\n",
"36 -0.1662931 0.938908 0.164244 0.7670049\n",
"37 0.9211245 1.052431 0.7901755 0.5383184\n",
"38 -0.7683404 0.203883 0.4149857 NaN\n",
"39 0.7212907 0.6930835 1.123166 NaN\n",
"40 0.2959122 0.57153 0.6666565 NaN\n",
"41 1.000188 0.2394808 -0.2446549 NaN\n",
"42 -0.2450061 0.2787647 -0.4324159 NaN\n",
"43 -1.004149 -6.329155e-05 0.1321612 NaN\n",
"44 0.807929 NaN 0.3495203 NaN\n",
"45 0.7595933 NaN 0.4474621 NaN\n",
"46 0.0335916 NaN -0.0445592 NaN\n",
"47 0.6829041 NaN NaN NaN\n",
"48 -1.275649 NaN NaN NaN"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"risk_report = pd.Panel({\n",
" period: pd.DataFrame(algo.risk_report[period])\n",
" for period in algo.risk_report\n",
"})\n",
"print risk_report.minor_axis \n",
"risk_report.minor_xs('sharpe')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## R-style formulas with statsmodels"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>EOG</td> <th> R-squared: </th> <td> 0.941</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.941</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td>1.631e+04</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Mon, 26 Jan 2015</td> <th> Prob (F-statistic):</th> <td> 0.00</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>20:37:21</td> <th> Log-Likelihood: </th> <td> 1238.5</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 1022</td> <th> AIC: </th> <td> -2473.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 1020</td> <th> BIC: </th> <td> -2463.</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>Intercept</th> <td> 0.0261</td> <td> 0.033</td> <td> 0.799</td> <td> 0.424</td> <td> -0.038 0.090</td>\n",
"</tr>\n",
"<tr>\n",
" <th>PXD</th> <td> 0.8583</td> <td> 0.007</td> <td> 127.723</td> <td> 0.000</td> <td> 0.845 0.872</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td>71.465</td> <th> Durbin-Watson: </th> <td> 0.034</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.000</td> <th> Jarque-Bera (JB): </th> <td> 94.314</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 0.599</td> <th> Prob(JB): </th> <td>3.31e-21</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 3.883</td> <th> Cond. No. </th> <td> 73.2</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: EOG R-squared: 0.941\n",
"Model: OLS Adj. R-squared: 0.941\n",
"Method: Least Squares F-statistic: 1.631e+04\n",
"Date: Mon, 26 Jan 2015 Prob (F-statistic): 0.00\n",
"Time: 20:37:21 Log-Likelihood: 1238.5\n",
"No. Observations: 1022 AIC: -2473.\n",
"Df Residuals: 1020 BIC: -2463.\n",
"Df Model: 1 \n",
"==============================================================================\n",
" coef std err t P>|t| [95.0% Conf. Int.]\n",
"------------------------------------------------------------------------------\n",
"Intercept 0.0261 0.033 0.799 0.424 -0.038 0.090\n",
"PXD 0.8583 0.007 127.723 0.000 0.845 0.872\n",
"==============================================================================\n",
"Omnibus: 71.465 Durbin-Watson: 0.034\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 94.314\n",
"Skew: 0.599 Prob(JB): 3.31e-21\n",
"Kurtosis: 3.883 Cond. No. 73.2\n",
"==============================================================================\n",
"\"\"\""
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import statsmodels.formula.api as smf\n",
"\n",
"model = smf.ols(formula=\"EOG ~ PXD\", data=np.log(prices)).fit()\n",
"\n",
"model.summary()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "IPython (Python 2)",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"mimetype": "text/x-python",
"name": "python",
"pygments_lexer": "ipython2"
},
"signature": "sha256:783f940c637ff5d6dbde92fdf4b9e55fe29285493a8f8abdf2e41a6fa00a6d54"
},
"nbformat": 4,
"nbformat_minor": 0
}
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