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Book6_Ch07_Python_Codes/Bk6_Ch07_01.py

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+
+
+###############
+# Authored by Weisheng Jiang
+# Book 6  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+import pandas_datareader 
+import scipy.stats as stats
+import pylab
+
+df_price = pandas_datareader.data.DataReader(['sp500'], 
+                                       data_source='fred', 
+                                       start='08-01-2018', end='08-01-2021')
+df_price = df_price.dropna()
+
+#%% Rolling max, min
+
+df_max_100 = df_price.rolling(100).max()
+df_min_100 = df_price.rolling(100).min()
+
+fig, ax = plt.subplots()
+# sp500 price
+ax.plot(df_price['sp500'], label = 'Price')
+ax.plot(df_max_100, label = 'Max, 100')
+ax.plot(df_min_100, label = 'Min, 100')
+
+plt.ylabel('Price level')
+plt.legend(loc='upper left')
+plt.xticks(rotation = 45) 
+# Rotates X-Axis Ticks by 45-degrees
+fig.tight_layout()
+
+#%% Rolling mean
+
+df_mean_50 = df_price.rolling(50).mean()
+df_mean_100 = df_price.rolling(100).mean()
+df_mean_250 = df_price.rolling(250).mean()
+
+fig, ax = plt.subplots()
+# sp500 price
+ax.plot(df_price['sp500'], label = 'Price')
+ax.plot(df_mean_50, label = 'Mean, 50')
+ax.plot(df_mean_100,label = 'Mean, 100')
+ax.plot(df_mean_250,label = 'Mean, 150')
+
+plt.ylabel('Price level')
+plt.legend(loc='upper left')
+plt.xticks(rotation = 45) 
+# Rotates X-Axis Ticks by 45-degrees
+fig.tight_layout()
+
+
+
+#%% daily log return
+
+daily_log_r = df_price.apply(lambda x: np.log(x) - np.log(x.shift(1)))
+
+daily_log_r = daily_log_r.dropna()
+
+#%% Rolling mean, skew, kurtosis on returns 
+
+daily_log_r_mean = daily_log_r.rolling(50).mean()
+daily_log_r_std = daily_log_r.rolling(50).std()
+daily_log_r_skew = daily_log_r.rolling(50).skew()
+daily_log_r_kurt = daily_log_r.rolling(50).kurt()
+
+fig, axes = plt.subplots(5,1)
+
+# plot daily log returns
+axes[0].plot(daily_log_r[daily_log_r_mean.first_valid_index():daily_log_r_mean.index[-1]],
+             marker='.', markersize = 3, 
+             color = 'b',linestyle='None',
+             label = 'Daily log r')
+axes[0].axhline(y = 0, color='r', linestyle='-')
+axes[0].set_ylabel ('Log return')
+axes[0].set_xticks([])
+
+# plot first moment, mean
+axes[1].plot(daily_log_r_mean,label = 'Mean', color = 'b')
+axes[1].axhline(y = 0, color='r', linestyle='-')
+axes[1].set_ylabel ('Mean')
+axes[1].set_xticks([])
+
+# plot second moment, std
+axes[2].plot(daily_log_r_std,label = 'Std', color = 'b')
+axes[2].axhline(y = 0, color='r', linestyle='-')
+axes[2].set_ylabel ('Volatility')
+axes[2].set_xticks([])
+
+# plot third moment, skew
+axes[3].plot(daily_log_r_skew,label = 'Skew', color = 'b')
+axes[3].axhline(y = 0, color='r', linestyle='-')
+axes[3].set_ylabel ('Skew')
+axes[3].set_xticks([])
+
+# plot fourth moment, kurtosis
+axes[4].plot(daily_log_r_kurt,label = 'Kurtosis', color = 'b')
+axes[4].set_ylabel ('Kurt')
+axes[4].axhline(y = 3, color='r', linestyle='-')
+
+plt.xticks(rotation = 45) 
+# Rotates X-Axis Ticks by 45-degrees
+fig.tight_layout()
+
+
+#%% Moving quantile
+
+alpha_95 = 0.95
+
+df_95_percent = daily_log_r.rolling(100).quantile(alpha_95)
+df_05_percent = daily_log_r.rolling(100).quantile(1 - alpha_95)
+
+fig, ax = plt.subplots()
+ax.plot(daily_log_r,marker='.', color = 'b',linestyle='None')
+ax.plot(df_95_percent,label = '95% percentile')
+ax.plot(df_05_percent,label = '5% percentile')
+
+plt.axhline(y=0, color='r', linestyle='-')
+
+plt.xlabel('Date')
+plt.ylabel('Daily log return')
+plt.xticks(rotation = 45) # Rotates X-Axis Ticks by 45-degrees
+fig.tight_layout() 
+plt.legend(loc='upper left')
+
+#%% Moving average volatility
+
+MA_vol_50  = daily_log_r.rolling(50).std()
+MA_vol_100 = daily_log_r.rolling(100).std()
+MA_vol_250 = daily_log_r.rolling(250).std()
+
+# plot daily log returns
+fig, axes = plt.subplots(2,1)
+# sp500 daily log returns
+axes[0].plot((daily_log_r**2)[MA_vol_250.first_valid_index():MA_vol_250.index[-1]],
+             color = 'b')
+
+axes[0].set_xticks([])
+axes[0].axhline(y=0, color='r', linestyle='-')
+axes[0].set_ylabel('Daily log return squared')
+
+# Moving average volatility
+axes[1].plot(MA_vol_50[MA_vol_250.first_valid_index():MA_vol_250.index[-1]], label = 'Window = 50')
+axes[1].plot(MA_vol_100[MA_vol_250.first_valid_index():MA_vol_250.index[-1]],label = 'Window = 100')
+axes[1].plot(MA_vol_250[MA_vol_250.first_valid_index():MA_vol_250.index[-1]],label = 'Window = 250')
+axes[1].set_xlabel("Date")
+plt.xticks(rotation = 45) # Rotates X-Axis Ticks by 45-degrees
+axes[1].set_ylabel("MA vol")
+fig.tight_layout() 
+plt.legend(loc='upper left')
+
+list_df = [MA_vol_50, MA_vol_100, MA_vol_250]
+
+for data in zip(list_df):
+    
+    data = data[0]
+    
+    fig, ax = plt.subplots()
+    
+    # daily return of selected date range
+    plt.plot(daily_log_r[data.first_valid_index():data.index[-1]],
+                 marker='.', markersize = 3, 
+                 color = 'b',linestyle='None')
+    
+    upper_bound = 2*data[data.first_valid_index():data.index[-1]];
+    lower_bound = -upper_bound;
+    
+    ax.plot(upper_bound, color = 'r')
+    ax.plot(lower_bound, color = 'r')
+    ax.fill_between(upper_bound.index, upper_bound['sp500'], 
+                    lower_bound['sp500'], color = '#DBEEF3')
+    ax.axhline(y=0, color='k', linestyle='-')
+    
+    ax.set_ylabel('Daily log return')
+    plt.xticks(rotation = 45) # Rotates X-Axis Ticks by 45-degrees
+    plt.tight_layout()
+
+#%% squared root of time
+
+# plot daily log returns
+fig, ax = plt.subplots()
+
+# Moving average volatility
+ax.plot(MA_vol_50*np.sqrt(250)*100,  label = 'Window = 50')
+ax.plot(MA_vol_100*np.sqrt(250)*100, label = 'Window = 100')
+ax.plot(MA_vol_250*np.sqrt(250)*100, label = 'Window = 250')
+ax.set_xlabel("Date")
+plt.xticks(rotation = 45) # Rotates X-Axis Ticks by 45-degrees
+ax.set_ylabel("MA annualized volatility, %")
+fig.tight_layout() 
+plt.legend(loc='upper left')
+
+#%% EWMA mean
+
+df_mean_99  = df_price.ewm(alpha=0.01,  adjust=False).mean()
+df_mean_975 = df_price.ewm(alpha=0.025, adjust=False).mean()
+df_mean_94  = df_price.ewm(alpha=0.06,  adjust=False).mean()
+
+fig, ax = plt.subplots()
+# sp500 price
+ax.plot(df_price['sp500'])
+ax.plot(df_mean_99, label = 'Lambda = 0.99')
+ax.plot(df_mean_975,label = 'Lambda = 0.975')
+ax.plot(df_mean_94, label = 'Lambda = 0.94')
+
+plt.ylabel('Price level')
+plt.legend(loc='upper left')
+plt.xticks(rotation = 45) 
+# Rotates X-Axis Ticks by 45-degrees
+fig.tight_layout()
+plt.legend(loc='upper left')
+
+
+#%% EWMA rolling volatility
+
+EWMA_vol_99  = daily_log_r.ewm(alpha=0.01,  adjust=False).std()
+EWMA_vol_975 = daily_log_r.ewm(alpha=0.025, adjust=False).std()
+EWMA_vol_94  = daily_log_r.ewm(alpha=0.06,  adjust=False).std()
+
+# plot daily log returns
+fig, axes = plt.subplots(2,1)
+# sp500 daily log returns
+axes[0].plot((daily_log_r**2)[MA_vol_250.first_valid_index():MA_vol_250.index[-1]],
+             color = 'b')
+
+axes[0].set_xticks([])
+axes[0].axhline(y=0, color='r', linestyle='-')
+axes[0].set_ylabel('Daily log return')
+
+# Moving average volatility
+
+axes[1].plot(EWMA_vol_99[MA_vol_250.first_valid_index():MA_vol_250.index[-1]], label = 'Lambda = 0.99')
+axes[1].plot(EWMA_vol_975[MA_vol_250.first_valid_index():MA_vol_250.index[-1]],label = 'Lambda = 0.975')
+axes[1].plot(EWMA_vol_94[MA_vol_250.first_valid_index():MA_vol_250.index[-1]], label = 'Lambda = 0.94')
+axes[1].set_xlabel("Date")
+plt.xticks(rotation = 45) # Rotates X-Axis Ticks by 45-degrees
+axes[1].set_ylabel("EWMA volatility")
+fig.tight_layout() 
+plt.legend(loc='upper left')
+
+list_df = [EWMA_vol_99, EWMA_vol_975, EWMA_vol_94]
+
+for data in zip(list_df):
+    
+    data = data[0]
+    
+    fig, ax = plt.subplots()
+    
+    # daily return of selected date range
+    plt.plot(daily_log_r[data.first_valid_index():data.index[-1]],
+                 marker='.', markersize = 3, 
+                 color = 'b',linestyle='None')
+    
+    upper_bound = 2*data[data.first_valid_index():data.index[-1]];
+    lower_bound = -upper_bound;
+    
+    ax.plot(upper_bound, color = 'r')
+    ax.plot(lower_bound, color = 'r')
+    ax.fill_between(upper_bound.index, upper_bound['sp500'], 
+                    lower_bound['sp500'], color = '#DBEEF3')
+    ax.axhline(y=0, color='k', linestyle='-')
+    
+    ax.set_ylabel('Daily log return')
+    plt.xticks(rotation = 45) # Rotates X-Axis Ticks by 45-degrees
+    plt.tight_layout()
+
+#%% Compare volatilities
+
+fig, ax = plt.subplots()
+plt.plot(MA_vol_50*np.sqrt(250)*100,   label = 'MA, 50',  linestyle = '--')
+plt.plot(MA_vol_100*np.sqrt(250)*100,  label = 'MA, 100', linestyle = '--')
+plt.plot(MA_vol_250*np.sqrt(250)*100,  label = 'MA, 250', linestyle = '--')
+plt.plot(EWMA_vol_99*np.sqrt(250)*100, label = 'EWMA, $\lambda$ = 0.99')
+plt.plot(EWMA_vol_975*np.sqrt(250)*100,label = 'EWMA, $\lambda$ = 0.975')
+plt.plot(EWMA_vol_94*np.sqrt(250)*100, label = 'EWMA, $\lambda$ = 0.94')
+
+ax.set_xlabel("Date")
+plt.xticks(rotation = 45) 
+# Rotates X-Axis Ticks by 45-degrees
+ax.set_ylabel("Annualized volatility, %")
+fig.tight_layout() 
+plt.legend(loc='upper left')

Book6_Ch07_Python_Codes/Bk6_Ch07_02.py

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+
+
+###############
+# Authored by Weisheng Jiang
+# Book 6  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+lambdas = np.linspace(0.9,0.99,10)
+i_day   = np.linspace(1,20,20)
+
+lambda_l, ii = np.meshgrid(lambdas,i_day)
+
+ww = (1 - lambda_l)*lambda_l**(ii - 1)
+
+fig, ax = plt.subplots()
+
+colors = plt.cm.jet(np.linspace(0,1,10))
+
+for i in np.linspace(1,10,10):
+    plt.plot(i_day,ww[:,int(i)-1],marker = 'x',
+             color = colors[int(i)-1],
+             label = '$\lambda = {lll:.2f}$'.format(lll = lambdas[int(i)-1]))
+
+plt.xlabel('Day, i')
+plt.ylabel('EWMA weight')
+plt.xticks(i_day)
+plt.legend()
+ax.invert_xaxis()
+
+HL = np.log(0.5)/np.log(lambdas)
+
+fig, ax = plt.subplots()
+
+plt.plot(lambdas,HL,marker = 'x')
+plt.xlabel('$\lambda$')
+plt.ylabel('Half life')

Book6_Ch07_Python_Codes/Bk6_Ch07_03.py

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+
+
+###############
+# Authored by Weisheng Jiang
+# Book 6  |  From Basic Arithmetic to Machine Learning
+# Published and copyrighted by Tsinghua University Press
+# Beijing, China, 2022
+###############
+
+
+# initializations and download results 
+import pandas as pd
+import pandas_datareader as web
+import seaborn as sns
+import matplotlib.pyplot as plt
+import numpy as np
+import scipy.stats as stats
+import pandas_datareader as web
+tickers = ['^GSPC','TSLA'];
+df = web.get_data_yahoo(tickers, start = '2015-08-01', end = '2021-08-01')
+
+df = df.dropna()
+
+#%% daily log return
+
+daily_log_r = df['Adj Close'].apply(lambda x: np.log(x) - np.log(x.shift(1)))
+daily_log_r = daily_log_r.dropna()
+
+df_corr = daily_log_r['^GSPC'].rolling(100).corr(daily_log_r['TSLA'])
+
+fig, ax = plt.subplots()
+
+# daily return of selected date range
+ax.plot(df_corr[df_corr.first_valid_index():df_corr.index[-1]])
+ax.axhline(y=0.5, color='r', linestyle='-')
+ax.set_ylabel('Rolling correlation')