Verify the calendar effect of monthly returns

Experiment to see the calendar effect that is said in the streets such as Halloween effect and Sell in May using decompose of stats models


import numpy as np
import pandas as pd

import statsmodels.api as sm
import pandas_datareader.data as web

import warnings
warnings.filterwarnings('ignore')

import matplotlib.pyplot as plt
plt.style.use('seaborn-darkgrid')
plt.rcParams['axes.xmargin'] = 0.01
plt.rcParams['axes.ymargin'] = 0.01

window = 250*3

'''S&P500 data acquisition'''
data1 = web.DataReader("^GSPC", "yahoo", "1980/1/1").dropna()

#Treasury Yield 10 Years Data Acquisition
data2 = web.DataReader("^TNX", "yahoo", "1980/1/1").dropna()

#Daily annual volatility= 10%Leverage adjusted settings
ret = pd.DataFrame(data1['Adj Close'] / data1['Adj Close'].shift(1) - 1)
ret = 0.1 * ret / (ret.rolling(252).std()*np.sqrt(252)).shift(1)
data1 = 100*((1 + ret).cumprod()).dropna(axis=0)

data1_freq = data1.resample('M').last().fillna(method='ffill')
data1_freq['ret1'] = data1_freq['Adj Close']/data1_freq['Adj Close'].shift(1) - 1

#Recreate monthly turns
data1_freq_equity_curve = 100*((1 + data1_freq['ret1']).cumprod()).dropna(axis=0)
data1_freq_equity_curve.index = pd.to_datetime(data1_freq_equity_curve.index)

#10 years for the full year(120 months), 5 years(60 months)
res_all = sm.tsa.seasonal_decompose(data1_freq_equity_curve, freq=12)
res_10Y = sm.tsa.seasonal_decompose(data1_freq_equity_curve[-120:], freq=12)
res_5Y = sm.tsa.seasonal_decompose(data1_freq_equity_curve[-60:], freq=12)

seasonality = pd.concat([res_all.seasonal, 
                         res_10Y.seasonal, 
                         res_5Y.seasonal], axis=1)

seasonality.columns = ['1981-', '10Y', '5Y']
m_seasonality = seasonality.groupby(seasonality.index.month).mean()

# Creat Figure
month = m_seasonality.index
height = m_seasonality * 100

bar_width = 0.3

plt.figure(figsize=(10, 4), dpi=80)
plt.bar(month, height['1981-'], tick_label=month, 
        width=0.3, label='1981-')
plt.bar(month + bar_width, height['10Y'], tick_label=month, 
        width=0.3, label='10Y')
plt.bar(month + 2*bar_width, height['5Y'], tick_label=month, 
        width=0.3, label='5Y')
plt.xticks(month + bar_width, month)
plt.legend()
plt.title("Average Return by Month")
plt.xlabel("Month")
plt.ylabel("Ave.Ret(%)")
plt.show()

Looking at the returns in seasonal

Sell in May seems to be true in recent years
Year-end sale / year-end buy?

Decomposition(Trend, Seasonality, Residual)

res_10Y.plot()
plt.show()

Used for short-term mean reversion and market trends
Adjustment of past market environment (difference in volatility level etc.) seems to be devised

Time Series Decomposition

Verify the calendar effect of monthly returns