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@gjlr2000
Created April 25, 2018 09:40
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Finding Mean Reversion: 2nd part
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "MeanReversionTutorial_3.ipynb",
"version": "0.3.2",
"views": {},
"default_view": {},
"provenance": []
},
"kernelspec": {
"name": "python2",
"display_name": "Python 2"
}
},
"cells": [
{
"metadata": {
"id": "OlbdQwIzFwFY",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"# Finding Mean Reversion\n",
"## Comparison between PCA and the Johansen Test\n",
"\n",
"In the initial example ([\"Mean Reversion: How to find it ?](https://drive.google.com/file/d/1a1zFFd4MwZ8ljXtEE16JXyO8W4SWcS4P/view?usp=sharing)) USD 2-5-10 we found that PCA and Johansen gave pretty similar results.\n",
"\n",
"Here I will only make a small change: I'll add the 20yr maturity to the set. \n",
"\n",
"**Spoiler alert**: the PCA and the Johansen results will be different.\n",
"\n",
"(this notebook has all the code - the next section defines functions required later - keep scrolling)"
]
},
{
"metadata": {
"id": "cH2jPzYc9WTI",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"height": 258
},
"outputId": "fbf39f83-bd7a-4f3f-fb74-940057bfbf6d",
"executionInfo": {
"status": "ok",
"timestamp": 1524646138403,
"user_tz": 0,
"elapsed": 2173,
"user": {
"displayName": "GE Lr",
"photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
"userId": "102764421838822582009"
}
}
},
"cell_type": "code",
"source": [
"!pip install johansen\n",
"# Request: allow HTTP-post API calls\n",
"import requests\n",
"# Json: to format as json calls to API\n",
"import json \n",
"# Pandas: to plot the timeseries\n",
"import pandas as pd\n",
"# Datetime: to convert different date formats\n",
"import datetime as dt\n",
"# Import the Time Series library\n",
"import statsmodels.tsa.stattools as ts\n",
"\n",
"from numpy import cumsum, log, polyfit, sqrt, std, subtract\n",
"\n",
"# Useful links\n",
"# https://www.quantstart.com/articles/Basics-of-Statistical-Mean-Reversion-Testing\n",
"# https://www.quantstart.com/articles/Basics-of-Statistical-Mean-Reversion-Testing-Part-II\n",
"# https://www.quantopian.com/posts/pair-trade-with-cointegration-and-mean-reversion-tests\n",
"def hurst(ts):\n",
"\t\"\"\"Returns the Hurst Exponent of the time series vector ts\"\"\"\n",
"\t# Create the range of lag values\n",
"\tlags = range(2, 100)\n",
"\n",
"\t# Calculate the array of the variances of the lagged differences\n",
"\ttau = [sqrt(std(subtract(ts[lag:], ts[:-lag]))) for lag in lags]\n",
"\n",
"\t# Use a linear fit to estimate the Hurst Exponent\n",
"\tpoly = polyfit(log(lags), log(tau), 1)\n",
"\n",
"\t# Return the Hurst exponent from the polyfit output\n",
"\treturn poly[0]*2.0\n",
"\n",
"def MarkovCalibration(df_ts, column_name = None, calType = \"MeanReverting\"):\n",
" # if no column name is given takes only the first one.\n",
" # to send data to the Azure API we need to:\n",
" # - sort the dates increasing\n",
" # - remove NaNs\n",
" # - put dates in string format readable by Azure\n",
" panda_ts = df_ts.copy() \n",
" panda_ts.sort_index(inplace = True)\n",
" panda_ts['dates_'] = panda_ts.index\n",
" panda_ts = panda_ts.dropna()\n",
"\n",
" json_ts['dates'] = panda_ts['dates_'].apply(lambda x: x.strftime('%Y-%m-%d')).tolist()\n",
" if not column_name:\n",
" json_ts['vals'] = panda_ts[panda_ts.columns[0]].tolist()\n",
" else:\n",
" json_ts['vals'] = panda_ts[column_name].tolist()\n",
" json_ts['calType'] = calType\n",
" r = requests.post(url = API_ENDPOINT, json = json_ts)\n",
" r_json = r.json()\n",
" theta = r_json['calibrationResult']['Lambda']\n",
" half_life = -np.log(0.5) * 365.25 / theta\n",
" r_json['calibrationResult']['HalfLife'] = half_life\n",
" sigma = r_json['calibrationResult']['Sigma']\n",
" r_json['calibrationResult']['Std_band'] = np.sqrt(sigma * sigma / (2 * theta))\n",
" return r_json\n",
"\n",
"def adf_critical_value_test(input_ts):\n",
" # returns 1: if the t-stat of the ADF-test is less than the 1% critical value\n",
" # returns 5: if the t-stat of the ADF-test is less than the 5% critical value (but greater than the 1% level)\n",
" # returns 10: if the t-stat of the ADF-test is less than the 10% critical value (but greater than the 1% and 5% levels)\n",
" # return 99: if the t-stat of the ADF-test is greater than the 10% critical value\n",
" adf_test = ts.adfuller(input_ts, 1)\n",
" t_stat = adf_test[0]\n",
" critical_values = adf_test[4]\n",
" if t_stat < critical_values['1%']:\n",
" return int(1)\n",
" if t_stat < critical_values['5%']:\n",
" return int(5)\n",
" if t_stat < critical_values['10%']:\n",
" return int(10)\n",
" return int(99)\n",
"\n",
"\n",
"\n",
"# defining the api-endpoint \n",
"API_ENDPOINT = \"https://markovsimulator.azurewebsites.net/api/MarkovCalibrator_01?code=UFYL9CcFRERnVbZJ3ELdRRY7u59vD3BgONzaGLNEOekTfKf0Ug9Bfw==\"\n"
],
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"text": [
"Requirement already satisfied: johansen in /usr/local/lib/python2.7/dist-packages\r\n",
"Requirement already satisfied: numpy>=1.11.1 in /usr/local/lib/python2.7/dist-packages (from johansen)\r\n",
"Requirement already satisfied: pandas>=0.18.1 in /usr/local/lib/python2.7/dist-packages (from johansen)\r\n",
"Requirement already satisfied: statsmodels>=0.6.1 in /usr/local/lib/python2.7/dist-packages (from johansen)\r\n",
"Requirement already satisfied: scipy>=0.18.0 in /usr/local/lib/python2.7/dist-packages (from johansen)\n",
"Requirement already satisfied: pytz>=2011k in /usr/local/lib/python2.7/dist-packages (from pandas>=0.18.1->johansen)\n",
"Requirement already satisfied: python-dateutil in /usr/local/lib/python2.7/dist-packages (from pandas>=0.18.1->johansen)\n",
"Requirement already satisfied: patsy in /usr/local/lib/python2.7/dist-packages (from statsmodels>=0.6.1->johansen)\n",
"Requirement already satisfied: six>=1.5 in /usr/local/lib/python2.7/dist-packages (from python-dateutil->pandas>=0.18.1->johansen)\n",
"\u001b[33mYou are using pip version 9.0.3, however version 10.0.1 is available.\n",
"You should consider upgrading via the 'pip install --upgrade pip' command.\u001b[0m\n"
],
"name": "stdout"
},
{
"output_type": "stream",
"text": [
"/usr/local/lib/python2.7/dist-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
" from pandas.core import datetools\n"
],
"name": "stderr"
}
]
},
{
"metadata": {
"id": "-d7PmBmuHvug",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"The Johansen test library has to be installed every time - please be patient\n",
"\n",
"(notice that using the interactive notebook you can add more maturities by changing the 'cols' vector just below)"
]
},
{
"metadata": {
"id": "fI3_cXT5Hp8Z",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
}
}
},
"cell_type": "code",
"source": [
"\n",
"# Treasury rates\n",
"QUAND_TS = \"https://www.quandl.com/api/v3/datasets/USTREASURY/YIELD.json?api_key=o6YKGjyDcseE3LFKrSK3\"\n",
"# [u'Date', u'1 MO', u'3 MO', u'6 MO', u'1 YR', u'2 YR', u'3 YR', u'5 YR', u'7 YR', u'10 YR', u'20 YR', u'30 YR']\n",
"# [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]\n",
"cols = [5, 7, 9, 10]\n",
"# correspond to [ 2yr, 5yr, 10yr and 20yr]\n",
"# Try adding more maturities (uncomment below):\n",
"# cols = [ 2, 3, 5, 8, 9, 10]\n",
"# correspond to [3mo, 6mo, 2yr, 7yr, 10yr, 20yr]\n",
"# Name of the TimeSeries to be sent to Markov API\n"
],
"execution_count": 0,
"outputs": []
},
{
"metadata": {
"id": "J3stVWVHSH4g",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"The following section of code load data from Quandl."
]
},
{
"metadata": {
"id": "Iq6ACdEcSF-f",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"height": 375
},
"outputId": "eb594888-ae42-441c-ced6-8816fb1f8de0",
"executionInfo": {
"status": "ok",
"timestamp": 1524646141114,
"user_tz": 0,
"elapsed": 2027,
"user": {
"displayName": "GE Lr",
"photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
"userId": "102764421838822582009"
}
}
},
"cell_type": "code",
"source": [
"seriesName = 'Condor'\n",
"previousTradingDays = 252*10\n",
"\n",
"# Time Series seed\n",
"json_ts = {\n",
" \"calType\" : \"\",\n",
" \"seriesName\" : seriesName,\n",
" \"colName\" : \"Value\",\n",
" \"dates\": [], \n",
" \"vals\" : []\n",
"}\n",
"\n",
"# Call Quandl to get all the data\n",
"q = requests.get(url = QUAND_TS)\n",
"q_json = q.json() \n",
"q_data = q_json['dataset']['data']\n",
"\n",
"# Compute derived series from Quandl Data\n",
"dates = []\n",
"values = []\n",
"q_len = len(q_data)\n",
"column_len = len(q_data[0])\n",
"column = column_len-1\n",
"columns = q_json['dataset']['column_names']\n",
"print (columns)\n",
"\n",
"\n",
"# The following could be easily done using Quandl's\n",
"# python API - but I keep it the 'hard way' to allow\n",
"# compatibility with Google Colaboratory\n",
"df_rates = pd.DataFrame.from_records(q_data, columns = columns)\n",
"df_rates['Date'] = pd.to_datetime(df_rates['Date'])\n",
"df_rates.set_index('Date', inplace=True)\n",
"\n",
"columns_fly = [columns[i] for i in cols]\n",
"df_rates[columns_fly].plot()\n"
],
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": [
"[u'Date', u'1 MO', u'3 MO', u'6 MO', u'1 YR', u'2 YR', u'3 YR', u'5 YR', u'7 YR', u'10 YR', u'20 YR', u'30 YR']\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f7002e30310>"
]
},
"metadata": {
"tags": []
},
"execution_count": 3
},
{
"output_type": "display_data",
"data": {
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qu3y9XYXH7UNLswMet7A3zXFipLPJK9xkaHgvRtWswS8DbgQAfPX+Hlx32zgiwAQCoVcz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\npPgKIYQQvUyKrxBCCNHL/j8zGtC1mShI9QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7027df8290>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "o4wR8r6IG0ZI",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"Lets compute PCA and then check factor by factors whether that could be mean reverting: "
]
},
{
"metadata": {
"id": "8qMADm3cCTnb",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"height": 579
},
"outputId": "2dc9a4f6-6acb-4e4e-fc85-8d6fb3f2195c",
"executionInfo": {
"status": "ok",
"timestamp": 1524646151306,
"user_tz": 0,
"elapsed": 10095,
"user": {
"displayName": "GE Lr",
"photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
"userId": "102764421838822582009"
}
}
},
"cell_type": "code",
"source": [
"\n",
"\n",
"TimeSeries = df_rates[columns_fly]\n",
"TS = TimeSeries - TimeSeries.mean()\n",
"TScov = TS.cov()\n",
"\n",
"import numpy as np\n",
"eig_val_sc, eig_vec_sc = np.linalg.eig(TScov)\n",
"# Make a list of (eigenvalue, eigenvector) tuples\n",
"eig_pairs = [(np.abs(eig_val_sc[i]), eig_vec_sc[:,i]) for i in range(len(eig_val_sc))]\n",
"\n",
"# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
"eig_pairs.sort(key=lambda x: x[0], reverse=True)\n",
"\n",
"column_names = []\n",
"df_ts = TS.copy()\n",
"\n",
"for factor in range(0, len(eig_val_sc)):\n",
" # Eigenvector to analyse\n",
" last_eig = eig_pairs[factor][1]\n",
"\n",
" # Keep the eigenvalues linked to the column names\n",
" TSeig = pd.DataFrame(last_eig, index = TS.columns)\n",
"\n",
" Weights = TSeig / (abs(TSeig)).max()\n",
"\n",
" # Using pandas I can simply multiply the original Timeseries\n",
" # by the Weights,\n",
" column_names.append('factor'+str(factor+1)) \n",
" df_ts[column_names[factor]] = (TS.dot(Weights)) \n",
" df_ts = df_ts.dropna()\n",
" column_name = column_names[factor]\n",
" print (\"----- \"+column_name+\" -----\")\n",
"\n",
"\n",
" print (\"Hurst: %s\" % hurst(df_ts[column_name]))\n",
" ad_test = adf_critical_value_test(df_ts[column_name])\n",
" if (ad_test == 99):\n",
" print (\"Not Mean Reverting\")\n",
" else:\n",
" print (\"Mean Reverting at\", ad_test,\"%\")\n",
" r_json = MarkovCalibration(df_ts, column_name = column_name)\n",
" half_life = r_json['calibrationResult']['HalfLife']\n",
"\n",
" print(column_name, \"half life\", half_life)\n",
" \n",
"\n",
"df_ts[column_names].plot()\n",
"\n"
],
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"text": [
"----- factor1 -----\n",
"Hurst: 0.5397014661881975\n",
"Not Mean Reverting\n",
"----- factor2 -----\n",
"Hurst: 0.4813513654404485\n",
"Not Mean Reverting\n",
"----- factor3 -----\n",
"Hurst: 0.5028224185375778\n",
"Not Mean Reverting\n",
"----- factor4 -----\n",
"Hurst: 0.37995305992645884\n",
"('Mean Reverting at', 1, '%')\n",
"('factor4', 'half life', 90.37706106938407)\n"
],
"name": "stdout"
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7f7002ca5a90>"
]
},
"metadata": {
"tags": []
},
"execution_count": 4
},
{
"output_type": "display_data",
"data": {
"image/png": 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Kwnd/JAIAJg0JbTOx8wRCZ6DDfdvKjfIrG9PaHroCHsepmcKag05DtmSybq3E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\nP8PaglAIs05CAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7002ca5f10>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "dGRhxPOEG9_P",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"(I expect only the last factor to show mean reversion - if you have changed the number of columns you might get more mean reverting factors).\n",
"\n",
"Let's compare with the Johansen result:"
]
},
{
"metadata": {
"id": "rPlqwKYODUGG",
"colab_type": "code",
"colab": {
"autoexec": {
"startup": false,
"wait_interval": 0
},
"base_uri": "https://localhost:8080/",
"height": 838
},
"outputId": "2f7a9b38-3237-4ca5-decc-e8333801c48e",
"executionInfo": {
"status": "ok",
"timestamp": 1524646162093,
"user_tz": 0,
"elapsed": 10723,
"user": {
"displayName": "GE Lr",
"photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
"userId": "102764421838822582009"
}
}
},
"cell_type": "code",
"source": [
"\n",
"from johansen import Johansen\n",
"#\n",
"x = TimeSeries.dropna().as_matrix()\n",
"x_centered = x - np.mean(x, axis=0)\n",
"\n",
"johansen = Johansen(x_centered, model=2, significance_level=2)\n",
"eigenvectors, r = johansen.johansen()\n",
"\n",
"print \"r values are: {}\".format(r)\n",
"\n",
"eig = [x[1] for x in eig_pairs]\n",
"\n",
"for k in r:\n",
" \n",
" print (\"----------------------------------\")\n",
" print (\"The\",k,\"th cointegrating relation:\")\n",
" \n",
" j_ev = eigenvectors[:, k]/max(abs(eigenvectors[:,k])) \n",
" pca_ev = eig_pairs[len(eig_pairs)-k-1][1] / max(abs(eig_pairs[len(eig_pairs)-k-1][1])) \n",
" \n",
"\n",
" bb = pd.DataFrame(TimeSeries.dot(j_ev))\n",
" r_json = MarkovCalibration(bb)\n",
" half_life = r_json['calibrationResult']['HalfLife']\n",
" mu = r_json['calibrationResult']['Mu']\n",
" cc = bb - mu\n",
" print \"Johansen Vector\"\n",
" print (j_ev)\n",
" print(\"Johansen vector half life\", half_life)\n",
"\n",
" \n",
" bb['pca'] = TimeSeries.dot(pca_ev)\n",
" r_json = MarkovCalibration(bb, column_name= 'pca')\n",
" half_life = r_json['calibrationResult']['HalfLife']\n",
" mu = r_json['calibrationResult']['Mu']\n",
" cc['pca'] = bb['pca'] - mu\n",
"\n",
" print \"PCA Vector\"\n",
" print (pca_ev)\n",
" print(\"PCA vector half life\", half_life)\n",
"\n",
" \n",
" cc.plot() \n",
"\n",
" cc.plot(x = 0, y = 'pca', kind = 'scatter')\n",
"\n"
],
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"text": [
"r values are: [0]\n",
"----------------------------------\n",
"('The', 0, 'th cointegrating relation:')\n",
"Johansen Vector\n",
"[ 0.02767801 -0.41851962 1. -0.57369868]\n",
"('Johansen vector half life', 53.74265149596533)\n",
"PCA Vector\n",
"[-0.41755453 1. -0.63043134 0.00244951]\n",
"('PCA vector half life', 90.37751378927585)\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
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O/ol9Jds6QoipEaAD2HRqu+nfvZT3puT76tINOF5XwH8PdtCylyWcActTpIPp6IRxrUH1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jXmzp0b6tsYMJ72w4EDBxxC+d1338Vbb72FmpoaLFy4MCzeC0/7oaamBj09PcjIyMC7776Ll156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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7002ca51d0>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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cprjv5DjV6uL32E0D72Yra4TRODBRZ8wbjIS3Fr7sevvDZWo5CD/+iTX42o/e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\nCIKQIFEnC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"text/plain": [
"<matplotlib.figure.Figure at 0x7f7000a10dd0>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "-ZMYfNfsIK3V",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"They are different !\n",
"\n",
"(and when showing the scatter plot, they look to be quite uncorrelated - we might even be able to trade them as independent signals)\n",
"\n",
"Ignoring weights less than 10%: \n",
"\n",
"* Johansen returns a 5-10-20 fly (roughly with weights 0.42-1-0.57) with a half life of 53 days, while \n",
"\n",
"* PCA shows a 2-5-10 fly with (0.42-1-0.53 weights) and a 90 day half life.\n",
"\n",
"\n",
"\n",
"Which one to trade ? it will depend on the current level of the strategy - see [Trade Simulator](https://docs.wixstatic.com/ugd/99b304_ac0bd3fd79d44de9bdea773d666baa1f.pdf) for an example of a tool that can analyse both trades, by showing ex-ante Sharpe Ratios derived from known trading horizons and the mean reversion parameters. \n",
"\n",
"But remember: in Fixed Income whenever you buy a bond the maturity will reduce every day -- holding a 2-5-10 fly for 180 days (twice the half life) would end up giving you a differen trade: a 1.5-4.5-9.5. Practitioners would weight the extra liquidity of a 2-5-10 versus the lower half life of a 5-10-20 (where the 20yr leg might be less liquid).\n"
]
}
]
}
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