September Effect

!pip install yfinance --upgrade --no-cache-dir

import numpy as np import matplotlib.pyplot as plt import pandas as pd import datetime as dt import yfinance as yf

# Question: find the symbol (i.e., google the instrument + 'yahoo finance') to any data series you are interested at # e.g., market/sector index ETF for your chosen country and various asset classes (e.g., Comex Gold's symbol is 'GC=F') # e.g., SPY (https://finance.yahoo.com/quote/SPY/) #SPY is S&P 500 index #IWM is the Russel 2000 for small cap company #DJIA is the Dow Jones industrial index symbols_list_SPY = ['SPY'] symbols_list_DJ = ['DJIA'] symbols_list_IWM = ['IWM'] start = dt.datetime(2015,9,1) end = dt.datetime(2020,10,31) data_SPY = yf.download(symbols_list_SPY, start=start, end=end) data_DJ = yf.download(symbols_list_DJ, start=start, end=end) data_IWM = yf.download(symbols_list_IWM, start=start, end=end) data_SPY.info() data_DJ.info() data_IWM.info()

data_SPY.head()

data_DJ.head()

data_IWM.head()

df_SPY = data_SPY.reset_index() df_DJ = data_DJ.reset_index() df_IWM = data_IWM.reset_index() df_SPY.info() df_DJ.info() df_IWM.info()

# filter column adjusted close df_SPY = df_SPY[['Date','Adj Close', 'Volume']] df_DJ = df_DJ[['Date','Adj Close', 'Volume']] df_IWM = df_IWM[['Date','Adj Close', 'Volume']] df_SPY.info() df_DJ.info() df_IWM.info()

# create variables df_SPY['month_SPY'] = df_SPY['Date'].dt.month df_DJ['month_DJ'] = df_DJ['Date'].dt.month df_IWM['month_IWM'] = df_IWM['Date'].dt.month df_SPY['return'] = df_SPY['Adj Close'].pct_change() df_DJ['return'] = df_DJ['Adj Close'].pct_change() df_IWM['return'] = df_IWM['Adj Close'].pct_change() df_SPY['annualized_volatility'] = (df_SPY['return'].rolling(252).std())*(252)**(1/2) df_DJ['annualized_volatility'] = (df_DJ['return'].rolling(252).std())*(252)**(1/2) df_IWM['annualized_volatility'] = (df_IWM['return'].rolling(252).std())*(252)**(1/2) #use 252 trading days in a year, and we are looking at Sep. and Oct.'s Difference, so we divide 252 by 12= 21

df_SPY.tail()

df_DJ.tail()

df_IWM.tail()

# create dataframes containing Sep. and Oct. returns respectively to the three indexes September_returns_SPY = df_SPY.query('''month_SPY == 9''')[1:] September_returns_DJ = df_DJ.query('''month_DJ == 9''')[1:] September_returns_IWM = df_IWM.query('''month_IWM == 9''')[1:] October_returns_SPY = df_SPY.query('''month_SPY == 10''')[1:] October_returns_DJ = df_DJ.query('''month_DJ == 10''')[1:] October_returns_IWM = df_IWM.query('''month_IWM == 10''')[1:]

September_returns_SPY.dropna() September_returns_DJ.dropna() September_returns_IWM.dropna() October_returns_SPY.dropna() October_returns_DJ.dropna() October_returns_IWM.dropna() #first 252 will be nan for volatiliy, need to be drop

September_returns_SPY['return'].hist(bins=80, color='r', alpha=0.5) October_returns_SPY['return'].hist(bins=80, color='g', alpha=0.5) plt.title('SPY Return')

September_returns_DJ['return'].hist(bins=80, color='r', alpha=0.5) October_returns_DJ['return'].hist(bins=80, color='g', alpha=0.5) plt.title('DJ Return')

September_returns_IWM['return'].hist(bins=80, color='r', alpha=0.5) October_returns_IWM['return'].hist(bins=80, color='g', alpha=0.5) plt.title('IWM Return')

September_returns_SPY['return'].describe()

September_returns_DJ['return'].describe()

September_returns_DJ['return'].describe()

October_returns_SPY['return'].describe()

October_returns_DJ['return'].describe()

October_returns_IWM['return'].describe()

import scipy.stats as stats print("Difference in mean return of SPY: ") print((September_returns_SPY['return'].mean() - October_returns_SPY['return'].mean())*100) stat, p = stats.ttest_ind(September_returns_SPY['return'], October_returns_SPY['return'], equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean return of SPY is significantly different (reject H0)') else: print('The difference in mean return of SPY is not significantly different (fail to reject H0)') print("Difference in mean return of DJ: ") print((September_returns_DJ['return'].mean() - October_returns_DJ['return'].mean())*100) stat, p = stats.ttest_ind(September_returns_DJ['return'], October_returns_DJ['return'], equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean return of DJ is significantly different (reject H0)') else: print('The difference in mean return of DJ is not significantly different (fail to reject H0)') print("Difference in mean return of IWM: ") print((September_returns_IWM['return'].mean() - October_returns_IWM['return'].mean())*100) stat, p = stats.ttest_ind(September_returns_IWM['return'], October_returns_IWM['return'], equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean return of IWM is significantly different (reject H0)') else: print('The difference in mean return of IWM is not significantly different (fail to reject H0)')

September_returns_SPY['annualized_volatility'].hist(bins=80, color='r', alpha=0.5) October_returns_SPY['annualized_volatility'].hist(bins=80, color='g', alpha=0.5) plt.title('SPY Volatility')

September_returns_DJ['annualized_volatility'].hist(bins=80, color='r', alpha=0.5) October_returns_DJ['annualized_volatility'].hist(bins=80, color='g', alpha=0.5) plt.title('DJ Volatility')

September_returns_IWM['annualized_volatility'].hist(bins=80, color='r', alpha=0.5) October_returns_IWM['annualized_volatility'].hist(bins=80, color='g', alpha=0.5) plt.title('IWM Volatility')

September_returns_SPY['annualized_volatility'].describe()

September_returns_DJ['annualized_volatility'].describe()

September_returns_IWM['annualized_volatility'].describe()

October_returns_SPY['annualized_volatility'].describe()

October_returns_DJ['annualized_volatility'].describe()

October_returns_IWM['annualized_volatility'].describe()

import scipy.stats as stats print("Difference in mean return of SPY volatility: ") print((September_returns_SPY['annualized_volatility'].notna().mean() - October_returns_SPY['annualized_volatility'].notna().mean())*100) stat, p = stats.ttest_ind(September_returns_SPY['annualized_volatility'].notna(), October_returns_SPY['annualized_volatility'].notna(), equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean return SPY　volatility is significantly different (reject H0)') else: print('The difference in mean return SPY volatility is not significantly different (fail to reject H0)') print("Difference in mean return of DJ volatility: ") print((September_returns_DJ['annualized_volatility'].notna().mean() - October_returns_DJ['annualized_volatility'].notna().mean())*100) stat, p = stats.ttest_ind(September_returns_DJ['annualized_volatility'].notna(), October_returns_DJ['annualized_volatility'].notna(), equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean return DJ volatility is significantly different (reject H0)') else: print('The difference in mean return DJ volatility is not significantly different (fail to reject H0)') print("Difference in mean return of IWM volatility: ") print((September_returns_IWM['annualized_volatility'].notna().mean() - October_returns_IWM['annualized_volatility'].notna().mean())*100) stat, p = stats.ttest_ind(September_returns_IWM['annualized_volatility'].notna(), October_returns_IWM['annualized_volatility'].notna(), equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean return IWM volatility is significantly different (reject H0)') else: print('The difference in mean return IWM volatility is not significantly different (fail to reject H0)')

stat, p = stats.ttest_ind(df_SPY['annualized_volatility'], df_SPY['annualized_volatility'].notna(), equal_var=False) print("p value is " + str(p))

September_returns_SPY['Volume'].hist(bins=100, color='r', alpha=0.5) October_returns_SPY['Volume'].hist(bins=100, color='g', alpha=0.5) plt.title('SPY Volume')

September_returns_DJ['Volume'].hist(bins=100, color='r', alpha=0.5) October_returns_DJ['Volume'].hist(bins=100, color='g', alpha=0.5) plt.title('DJ Volume')

September_returns_IWM['Volume'].hist(bins=100, color='r', alpha=0.5) October_returns_IWM['Volume'].hist(bins=100, color='g', alpha=0.5) plt.title('IWM Volume')

September_returns_SPY['Volume'].describe()

September_returns_DJ['Volume'].describe()

September_returns_IWM['Volume'].describe()

October_returns_SPY['Volume'].describe()

October_returns_DJ['Volume'].describe()

October_returns_IWM['Volume'].describe()

import scipy.stats as stats print("Difference in mean trading volume of SPY: ") print(September_returns_SPY['Volume'].mean() - October_returns_SPY['Volume'].mean()) stat, p = stats.ttest_ind(September_returns_SPY['Volume'], October_returns_SPY['Volume'], equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean trading volume of SPY is significantly different (reject H0)') else: print('The difference in mean trading volume of SPY is not significantly different (fail to reject H0)') #DJ print("Difference in mean trading volume of SPY: ") print(September_returns_DJ['Volume'].mean() - October_returns_DJ['Volume'].mean()) stat, p = stats.ttest_ind(September_returns_DJ['Volume'], October_returns_DJ['Volume'], equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean trading volume of DJ is significantly different (reject H0)') else: print('The difference in mean trading volume of DJ is not significantly different (fail to reject H0)') #IWM print("Difference in mean trading volume of SPY: ") print(September_returns_IWM['Volume'].mean() - October_returns_IWM['Volume'].mean()) stat, p = stats.ttest_ind(September_returns_IWM['Volume'], October_returns_IWM['Volume'], equal_var=False) # interpret p-value alpha = 0.05 print("p value is " + str(p)) if p <= alpha: print('The difference in mean trading volume of IWM is significantly different (reject H0)') else: print('The difference in mean trading volume of IWM is not significantly different (fail to reject H0)')