{
"cells": [
{
"cell_type": "markdown",
"id": "a85db976-8206-49b8-a9e0-4dda9e8cfd01",
"metadata": {},
"source": [
"## Auto-correlation of volatility\n",
"\n",
"In this workbook, we look at the auto-correlation between returns and volatility and see whether it could be used to add some predictive edge.\n",
"\n",
"Auto-correlation is the correlation of a series with itself over a specified time lag. \n",
"\n",
"A simple definition could be found [here](https://www.investopedia.com/terms/a/autocorrelation.asp)\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "f4c1b8e2-00a2-4287-8639-34a85053410a",
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"sns.set()\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "75b39dac-c40e-4e43-ab31-30daab858ce6",
"metadata": {},
"outputs": [
{
"data": {
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"
\n",
"\n",
"
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" \n",
"
\n",
"
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"
open
\n",
"
high
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"
low
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"
close
\n",
"
volume
\n",
"
adj close
\n",
"
ret
\n",
"
\n",
"
\n",
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date
\n",
"
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" \n",
" \n",
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"
2021-11-24
\n",
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4675.779785
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4702.870117
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4659.890137
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4701.459961
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2464040000
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4701.459961
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0.002294
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\n",
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\n",
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2021-11-26
\n",
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4664.629883
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4664.629883
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4585.430176
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4594.620117
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2676740000
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4594.620117
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-0.022725
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2021-11-29
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4628.750000
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4672.950195
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4625.259766
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4655.270020
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3471380000
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4655.270020
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0.013200
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2021-11-30
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4640.250000
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4646.020020
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4560.000000
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4567.000000
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4950190000
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4567.000000
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-0.018961
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2021-12-01
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4602.819824
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4652.939941
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4510.270020
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4513.040039
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4078260000
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4513.040039
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-0.011815
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"text/plain": [
" open high low close volume \\\n",
"date \n",
"2021-11-24 4675.779785 4702.870117 4659.890137 4701.459961 2464040000 \n",
"2021-11-26 4664.629883 4664.629883 4585.430176 4594.620117 2676740000 \n",
"2021-11-29 4628.750000 4672.950195 4625.259766 4655.270020 3471380000 \n",
"2021-11-30 4640.250000 4646.020020 4560.000000 4567.000000 4950190000 \n",
"2021-12-01 4602.819824 4652.939941 4510.270020 4513.040039 4078260000 \n",
"\n",
" adj close ret \n",
"date \n",
"2021-11-24 4701.459961 0.002294 \n",
"2021-11-26 4594.620117 -0.022725 \n",
"2021-11-29 4655.270020 0.013200 \n",
"2021-11-30 4567.000000 -0.018961 \n",
"2021-12-01 4513.040039 -0.011815 "
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_csv('/home/pi/data/sp500.csv', parse_dates=['Date']).rename(\n",
"columns = lambda x:x.lower()).sort_values(by='date').set_index('date')\n",
"df['ret'] = df.close.pct_change()\n",
"df.tail()"
]
},
{
"cell_type": "markdown",
"id": "b314ab35-63b0-406a-b4f6-aea37bc93457",
"metadata": {},
"source": [
"Let us calculate the monthly returns and the volatility.\n",
"\n",
" * For volatility, I would be calculating a simple standard deviation of the daily returns \n",
" * I would be using the close price instead of the adjusted close price. (Use adjusted close for stocks since they are prone to splits and other corporate actions that has a big impact on price)\n",
""
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "aea99bff-e40c-4edf-bc8f-d16569fff4b8",
"metadata": {},
"outputs": [],
"source": [
"monthly_returns = df.resample('M').close.ohlc().close.pct_change()\n",
"monthly_volatility = df.resample('M').ret.std()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "a8a72a32-9360-4770-a6b7-ff18aa7763bb",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(10,4))\n",
"\n",
"monthly_returns.plot(title='Monthly Returns (in %)', ax=axes[0])\n",
"monthly_volatility.plot(title='Monthly volatility (in %)', ax=axes[1])"
]
},
{
"cell_type": "markdown",
"id": "ad318476-8ef3-44d6-be40-0711c1db145b",
"metadata": {},
"source": [
"So, we could see a big spike in volatility in the expected periods , the 2008 financial crisis and the 2020 covid crisis. We can also observe the big dip in returns.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "921600f9-a45e-4984-8fd2-fcb009ff92e4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Autocorrelation for returns = 0.0581\n",
"Autocorrelation for volatility = 0.6581\n"
]
}
],
"source": [
"print(f\"Autocorrelation for returns = {monthly_returns.autocorr() :.4f}\")\n",
"print(f\"Autocorrelation for volatility = {monthly_volatility.autocorr() :.4f}\")"
]
},
{
"cell_type": "markdown",
"id": "ed04345c-ffd9-42fd-b6e1-b711841b2f3b",
"metadata": {},
"source": [
"Hurrah! There is a big correlation between this month and next month's volatility.\n",
"\n",
"\n",
"Let us do the auto-correlation plot for different months.\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "32f01f47-aa26-4c02-9356-fd94a9b8877d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(10,4))\n",
"pd.plotting.autocorrelation_plot(monthly_returns.dropna(), ax=axes[0])\n",
"pd.plotting.autocorrelation_plot(monthly_volatility.dropna(),ax=axes[1])"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "c7555753-6324-4010-b286-fda905a2732e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Auto-correlation for month 1 = 0.6581\n",
"Auto-correlation for month 2 = 0.4646\n",
"Auto-correlation for month 3 = 0.3669\n",
"Auto-correlation for month 4 = 0.2495\n",
"Auto-correlation for month 5 = 0.2351\n",
"Auto-correlation for month 6 = 0.2306\n"
]
}
],
"source": [
"for i in range(1,7):\n",
" print(f\"Auto-correlation for month {i} = {monthly_volatility.autocorr(lag=i) :.4f}\")\n",
" "
]
},
{
"cell_type": "markdown",
"id": "2fe686f4-76dd-4e71-930b-84a72994c44a",
"metadata": {},
"source": [
"From the above plots, it is clear that returns are random and previous 1 month or 2 months returns doesn't have a big impact in the forthcoming months. So, if you see some positive returns for some months, the next month may not necessarily have positive return and vice-versa; same with the second or third month. The unconditional probability of returns being positive or negative is 50% - equivalent to coin toss.\n",
"\n",
"But the volatility has a good auto-correlation that extends to even 6 months, which suggests that volatility even though it shoots up suddenly has a lasting effect. The volatility of this month is going to be likely that of the previous month and there is going to be no sudden decline or increase so as to make it entirely random."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ff7c9bf7-17a6-4775-96c2-255a800f5b64",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let us plot the rolling monthly volatility\n",
"\n",
"monthly_volatility.rolling(12).mean().plot()\n",
"\n",
"# So, the rolling volatility in 2021 is less than that of 2008"
]
},
{
"cell_type": "markdown",
"id": "b589b545-3ef2-4253-976f-47a481f96ee5",
"metadata": {},
"source": [
"## Is there a predictive edge?\n",
"\n",
"Let us try a simple filter based on volatility."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "33e419e1-aac4-4043-a784-84eb04d60dff",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
"
\n",
"
\n",
"
count
\n",
"
mean
\n",
"
std
\n",
"
min
\n",
"
25%
\n",
"
50%
\n",
"
75%
\n",
"
max
\n",
"
\n",
"
\n",
"
is_volatile
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
\n",
"
\n",
" \n",
" \n",
"
\n",
"
0.0
\n",
"
152.0
\n",
"
0.016845
\n",
"
0.034129
\n",
"
-0.092291
\n",
"
0.000111
\n",
"
0.018150
\n",
"
0.035785
\n",
"
0.107546
\n",
"
\n",
"
\n",
"
1.0
\n",
"
112.0
\n",
"
-0.010584
\n",
"
0.049312
\n",
"
-0.169425
\n",
"
-0.034967
\n",
"
-0.005509
\n",
"
0.014216
\n",
"
0.126844
\n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" count mean std min 25% 50% \\\n",
"is_volatile \n",
"0.0 152.0 0.016845 0.034129 -0.092291 0.000111 0.018150 \n",
"1.0 112.0 -0.010584 0.049312 -0.169425 -0.034967 -0.005509 \n",
"\n",
" 75% max \n",
"is_volatile \n",
"0.0 0.035785 0.107546 \n",
"1.0 0.014216 0.126844 "
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"vol_df = pd.DataFrame({\n",
" 'returns': monthly_returns,\n",
" 'volatility': monthly_volatility\n",
"})\n",
"# I am shifting this by one row so that the previous monthly volatility is looked into\n",
"vol_df['rolling_vol'] = vol_df.volatility.rolling(12).median().shift(1)\n",
"vol_df['is_volatile'] = vol_df.eval('(volatility > rolling_vol)+0')\n",
"vol_df.groupby('is_volatile').returns.describe()"
]
},
{
"cell_type": "markdown",
"id": "089d69b4-b8e8-4c43-827e-ca18b18280d0",
"metadata": {},
"source": [
"Looks like there is an edge to exploit that need to be investigated further.\n",
"\n",
"We may try to develop a strategy based on this"
]
},
{
"cell_type": "markdown",
"id": "97ea3d47-2b78-4f96-9735-609b56a2c3f7",
"metadata": {},
"source": [
"Footnotes\n",
"---------\n",
" \n",
" * For a detailed description of autocorrelation, you could look at the [wikipedia page](https://en.wikipedia.org/wiki/Autocorrelation)\n",
" \n",
" * This [kaggle notebook](https://www.kaggle.com/jeegarmaru/timeseriesanalysis-autocorrelation) has a rich set of python code on this topic\n",
" \n",
" * Though returns don't have autocorrelation and so the probability of positive or negative returns is 50%, there is a slight edge if the probability is conditioned on some variable."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.2"
},
"nikola": {
"category": "volatility",
"date": "2021-12-01 18:50:05 UTC",
"slug": "autocorrelation-volatility",
"tags": "filters,volatility,correlation,index",
"title": "Autocorrelation in volatility"
}
},
"nbformat": 4,
"nbformat_minor": 5
}