Lab 6
Team C'est La Vie - Ziqin, Ruiyang, Hanut and Tim
Introduction
!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
# 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/)
symbols_list = ['SPY']
start = dt.datetime(2000,12,1)
end = dt.datetime(2020,1,31)
data = yf.download(symbols_list, start=start, end=end)
data.info()
data.head()
df = data.reset_index()
df.info()
# filter column adjusted close
# need to include month instead of date!!!!!!!!!!
df = df[['Date','Adj Close', 'Volume']]
df.info()
df.head()
# create variables for our usage
df['month'] = df['Date'].dt.month
df['year']=df['Date'].dt.year
df['return'] = df['Adj Close'].pct_change()
df['annualized_volatility'] = (df['return'].rolling(252).std())*(252)**(1/2)
df.head()
# create two dataframes containing December and January returns respectively
dec_returns= df.query('''month == 12''')[1:]
jan_returns= df.query('''month == 1''')[1:]
dec_returns.head()
jan_returns.head(32)
SPY Returns Test
dec_returns['return'].hist(bins=100, color='r', alpha=0.5)
jan_returns['return'].hist(bins=100, color='b', alpha=0.5)
av_dec_ret = np.mean(dec_returns['return'])
av_jan_ret = np.mean(jan_returns['return'])
print("Average December return: ", av_dec_ret)
print("Average January return: ", av_jan_ret)
av_dec_ret = np.median(dec_returns['return'])
av_jan_ret = np.median(jan_returns['return'])
print("Median December return: ", av_dec_ret)
print("Median January return: ", av_jan_ret)
dec_returns['return'].describe()
jan_returns['return'].describe()
import scipy.stats as stats
print("Difference in mean return: ")
print((jan_returns['return'].mean() - dec_returns['return'].mean())*100)
stat, p = stats.ttest_ind(dec_returns['return'], jan_returns['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 is significantly different (reject H0)')
else:
print('The difference in mean return is not significantly different (fail to reject H0)')
SPY Volatility Test
dec_returns['annualized_volatility'].hist(bins=100, color='r', alpha=0.5)
jan_returns['annualized_volatility'].hist(bins=100, color='g', alpha=0.5)
dec_returns['annualized_volatility'].describe()
jan_returns['annualized_volatility'].describe()
import scipy.stats as stats
print("Difference in mean return volatility: ")
print((jan_returns['annualized_volatility'].notna().mean() - dec_returns['annualized_volatility'].notna().mean())*100)
stat, p = stats.ttest_ind(dec_returns['annualized_volatility'].notna(), jan_returns['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 volatility is significantly different (reject H0)')
else:
print('The difference in mean return volatility is not significantly different (fail to reject H0)')
SPY Volume Test
dec_returns['Volume'].hist(bins=100, color='r', alpha=0.5)
jan_returns['Volume'].hist(bins=100, color='b', alpha=0.5)
dec_returns['Volume'].describe()
jan_returns['Volume'].describe()
import scipy.stats as stats
print("Difference in volume: ")
print((jan_returns['Volume'].mean() - dec_returns['Volume'].mean())*100)
stat, p = stats.ttest_ind(dec_returns['Volume'], jan_returns['Volume'], equal_var=False)
# interpret p-value
alpha = 0.05
print("p value is " + str(p))
if p <= alpha:
print('The difference in mean Volume is significantly different (reject H0)')
else:
print('The difference in mean Volume is not significantly different (fail to reject H0)')
Summary: Since the p value for the return, volume and annualized volatility of return are all greater than our chosen alpha, we fail to reject our null hypothesis that the difference in return, volume and annualized volatility of return in December and January is not statistically different.
Comparison with China's SSE Composite Index
Since we could not reject the null hypothesis for SPY in the U.S., we decided to analyze the China's SSE Composite Index similarly to see if the January Effect exists in China, where Christmas is not an official holiday.
symbols_list = ['000001.SS']
start = dt.datetime(2000,12,1)
end = dt.datetime(2020,1,31)
data = yf.download(symbols_list, start=start, end=end)
data.info()
data.head()
df = data.reset_index()
df.info()
# create variables for our usage
df['month'] = df['Date'].dt.month
df['year']=df['Date'].dt.year
df['return'] = df['Adj Close'].pct_change()
df['annualized_volatility'] = (df['return'].rolling(252).std())*(252)**(1/2)
df.head()
# create two dataframes containing December and January returns respectively
dec_returnsch= df.query('''month == 12''')[1:]
jan_returnsch= df.query('''month == 1''')[1:]
dec_returnsch.head()
jan_returnsch.head(32)
SSE Return Test
dec_returnsch['return'].hist(bins=100, color='r', alpha=0.5)
jan_returnsch['return'].hist(bins=100, color='b', alpha=0.5)
av_dec_retch = np.mean(dec_returnsch['return'])
av_jan_retch = np.mean(jan_returnsch['return'])
print("China Average December return: ", av_dec_retch)
print("China Average January return: ", av_jan_retch)
median_dec_retch = np.median(dec_returnsch['return'])
median_jan_retch = np.median(jan_returnsch['return'])
print("China Median December return: ", median_dec_retch)
print("China Average January return: ", median_jan_retch)
dec_returnsch['return'].describe()
jan_returnsch['return'].describe()
import scipy.stats as stats
print("China Difference in mean return: ")
print((jan_returnsch['return'].mean() - dec_returnsch['return'].mean())*100)
stat, p = stats.ttest_ind(dec_returnsch['return'], jan_returnsch['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 is significantly different (reject H0)')
else:
print('The difference in mean return is not significantly different (fail to reject H0)')
SSE Volatility Test
dec_returnsch['annualized_volatility'].hist(bins=100, color='r', alpha=0.5)
jan_returnsch['annualized_volatility'].hist(bins=100, color='g', alpha=0.5)
dec_returnsch['annualized_volatility'].describe()
jan_returnsch['annualized_volatility'].describe()
import scipy.stats as stats
print("China Difference in mean return volatility: ")
print((jan_returnsch['annualized_volatility'].notna().mean() - dec_returnsch['annualized_volatility'].notna().mean())*100)
stat, p = stats.ttest_ind(dec_returnsch['annualized_volatility'].notna(), jan_returnsch['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 volatility is significantly different (reject H0)')
else:
print('The difference in mean return volatility is not significantly different (fail to reject H0)')
SSE Volume Test
dec_returnsch['Volume'].hist(bins=100, color='r', alpha=0.5)
jan_returnsch['Volume'].hist(bins=100, color='b', alpha=0.5)
dec_returnsch['Volume'].describe()
jan_returnsch['Volume'].describe()
import scipy.stats as stats
print("China difference in volume: ")
print((jan_returnsch['Volume'].mean() - dec_returnsch['Volume'].mean())*100)
stat, p = stats.ttest_ind(dec_returnsch['Volume'], jan_returnsch['Volume'], equal_var=False)
# interpret p-value
alpha = 0.05
print("p value is " + str(p))
if p <= alpha:
print('China the difference in mean Volume is significantly different (reject H0)')
else:
print('China the difference in mean Volume is not significantly different (fail to reject H0)')
Summary: Since the p value for the return and volume are greater than our chosen alpha, we fail to reject our null hypothesis. However, for annualized volatility of return, we see that the p value is smaller than alpha, which means we can reject our null hypothesis that the annualized volatility of return in January is greater than that of December.
Conclusion
USA versus China
diff_ret_jan = jan_returns['return'] - jan_returnsch['return']
diff_ret_dec = dec_returns['return'] - dec_returnsch['return']
diff_ret_jan.describe()
diff_ret_dec.describe()
print("US-China difference in returns: ")
print(diff_ret_jan.mean() - diff_ret_dec.mean())
stats, p = stats.ttest_ind(diff_ret_jan, diff_ret_dec, equal_var=False)
# interpret p-value
alpha = 0.05
print("p value is " + str(p))
if p <= alpha:
print('The US-China difference in mean returns is significantly different (reject H0)')
else:
print('The US-China difference in mean returns is not significantly different (fail to reject H0)')