Source of data: FactSets (All ETFs with some cleaning)
In [182]:
import numpy as np
import pandas as pd
from pylab import mpl, plt
import statsmodels.formula.api as smf
import statsmodels.api as sm
plt.style.use('seaborn')
mpl.rcParams['font.family'] = 'serif'
%matplotlib inline
In [2]:
import os
os.getcwd()
Out[2]:
'/content'
In [120]:
filename = 'https://raw.githubusercontent.com/cyrus723/my-first-binder/main/factsets_etf.csv'
In [121]:
data = pd.read_csv(filename)
In [122]:
data.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 1893 entries, 0 to 1892 Data columns (total 8 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ticker 1893 non-null object 1 name 1893 non-null object 2 issuer 1893 non-null object 3 exp 1893 non-null float64 4 nav 1893 non-null float64 5 aum 1893 non-null float64 6 class 1893 non-null object 7 beta 1893 non-null float64 dtypes: float64(4), object(4) memory usage: 118.4+ KB
In [123]:
data['scaled_aum'] = np.log(data['aum'])
In [124]:
data['aum_million'] = data['aum'] / 1000000
In [125]:
data.head()
Out[125]:
| ticker | name | issuer | exp | nav | aum | class | beta | scaled_aum | aum_million | |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | SINV | ETFMG Prime 2X Daily Inverse Junior Silver Min... | ETFMG | 1.0 | 11.9 | 115432.0 | Equity | -2.1 | 11.656437 | 0.115432 |
| 1 | B621WX | WisdomTree Short AUD Long EUR | WisdomTree | 0.0 | 30.2 | 156868.0 | Currency | -0.2 | 11.963160 | 0.156868 |
| 2 | B68GS4 | WisdomTree Long EUR Short USD | WisdomTree | 0.0 | 29.8 | 166949.0 | Currency | 0.1 | 12.025444 | 0.166949 |
| 3 | *CINC.B | CI DoubleLine Income USD Fund Unhedged | CI Financial Corp. | 1.0 | 17.7 | 176787.0 | Fixed Income | -0.3 | 12.082701 | 0.176787 |
| 4 | B68GSP | WisdomTree Long JPY Short USD | WisdomTree | 0.0 | 29.0 | 203339.0 | Currency | -0.1 | 12.222630 | 0.203339 |
In [126]:
data.tail()
Out[126]:
| ticker | name | issuer | exp | nav | aum | class | beta | scaled_aum | aum_million | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1888 | BDR7WS | Hanwha ARIRANG S&P500 ETF(H) | HANWHA LIFE INSURANCE Co., Ltd. | 0.0 | 17574.9 | 4.420000e+11 | Equity | 0.7 | 26.814576 | 442000.0 |
| 1889 | BMJJF5 | Hanwha Arirang SYNTH-MSCI Emerging Markets ETF(H) | HANWHA LIFE INSURANCE Co., Ltd. | 1.0 | 10002.4 | 7.400000e+11 | Equity | 0.8 | 27.329916 | 740000.0 |
| 1890 | BG8FBY | Hanwha ARIRANG KTB 3Y Futures ETF | HANWHA LIFE INSURANCE Co., Ltd. | 0.0 | 51743.0 | 7.540000e+11 | Fixed Income | 0.0 | 27.348658 | 754000.0 |
| 1891 | B7W7BH | Hanwha ARIRANG Dividend ETF | HANWHA LIFE INSURANCE Co., Ltd. | 0.0 | 12555.7 | 2.030000e+12 | Equity | 0.8 | 28.339057 | 2030000.0 |
| 1892 | B76Y8C | HANWHA ARIRANG 200 ETF | HANWHA LIFE INSURANCE Co., Ltd. | 0.0 | 35505.7 | 6.610000e+12 | Equity | 1.0 | 29.519605 | 6610000.0 |
Summary Statistics¶
In [127]:
data.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 1893 entries, 0 to 1892 Data columns (total 10 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ticker 1893 non-null object 1 name 1893 non-null object 2 issuer 1893 non-null object 3 exp 1893 non-null float64 4 nav 1893 non-null float64 5 aum 1893 non-null float64 6 class 1893 non-null object 7 beta 1893 non-null float64 8 scaled_aum 1893 non-null float64 9 aum_million 1893 non-null float64 dtypes: float64(6), object(4) memory usage: 148.0+ KB
In [128]:
data.describe().round(2)
Out[128]:
| exp | nav | aum | beta | scaled_aum | aum_million | |
|---|---|---|---|---|---|---|
| count | 1893.00 | 1893.00 | 1.893000e+03 | 1893.00 | 1893.00 | 1893.00 |
| mean | 0.55 | 994.99 | 8.829291e+09 | 0.66 | 18.42 | 8829.29 |
| std | 0.96 | 7030.29 | 1.620810e+11 | 0.67 | 2.55 | 162081.01 |
| min | 0.00 | 0.00 | 1.154320e+05 | -4.90 | 11.66 | 0.12 |
| 25% | 0.00 | 20.30 | 1.878199e+07 | 0.30 | 16.75 | 18.78 |
| 50% | 0.00 | 29.50 | 8.541894e+07 | 0.70 | 18.26 | 85.42 |
| 75% | 1.00 | 54.70 | 4.387002e+08 | 1.00 | 19.90 | 438.70 |
| max | 20.00 | 108546.70 | 6.610000e+12 | 4.40 | 29.52 | 6610000.00 |
In [129]:
data.aggregate([min,
np.mean,
np.std,
np.median,
max]
).round(2)
Out[129]:
| ticker | name | issuer | exp | nav | aum | class | beta | scaled_aum | aum_million | |
|---|---|---|---|---|---|---|---|---|---|---|
| min | *ARB | 15 FiCAS Active Crypto ETP | 21Shares AG | 0.00 | 0.00 | 1.154320e+05 | Alternatives | -4.90 | 11.66 | 0.12 |
| mean | NaN | NaN | NaN | 0.55 | 994.99 | 8.829291e+09 | NaN | 0.66 | 18.42 | 8829.29 |
| std | NaN | NaN | NaN | 0.96 | 7030.29 | 1.620810e+11 | NaN | 0.67 | 2.55 | 162081.01 |
| median | NaN | NaN | NaN | 0.00 | 29.50 | 8.541894e+07 | NaN | 0.70 | 18.26 | 85.42 |
| max | ZIG | iShares eb.rexx Government Germany UCITS ETF (DE) | Zacks Investment Management | 20.00 | 108546.70 | 6.610000e+12 | Fixed Income | 4.40 | 29.52 | 6610000.00 |
In [131]:
data.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 1893 entries, 0 to 1892 Data columns (total 10 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ticker 1893 non-null object 1 name 1893 non-null object 2 issuer 1893 non-null object 3 exp 1893 non-null float64 4 nav 1893 non-null float64 5 aum 1893 non-null float64 6 class 1893 non-null object 7 beta 1893 non-null float64 8 scaled_aum 1893 non-null float64 9 aum_million 1893 non-null float64 dtypes: float64(6), object(4) memory usage: 148.0+ KB
In [132]:
data2 = data.groupby(by='class').mean()
data2
Out[132]:
| exp | nav | aum | beta | scaled_aum | aum_million | |
|---|---|---|---|---|---|---|
| class | ||||||
| Alternatives | 1.820513 | 21.320513 | 1.186542e+08 | 0.235897 | 17.267977 | 118.654158 |
| Asset Allocation | 0.965517 | 395.551724 | 3.299403e+09 | 0.544828 | 17.414796 | 3299.403427 |
| Commodities | 0.412162 | 175.028378 | 1.406693e+09 | 0.477027 | 17.345794 | 1406.693136 |
| Currency | 1.032967 | 758.836264 | 2.028511e+08 | 0.648352 | 16.333805 | 202.851121 |
| Equity | 0.569337 | 852.437812 | 1.261168e+10 | 0.868906 | 18.660249 | 12611.676815 |
| Fixed Income | 0.257576 | 1957.354293 | 4.164261e+09 | 0.168434 | 18.875313 | 4164.260947 |
In [138]:
data['class'] = data['class'].replace(['Asset Allocation','Fixed Income' ], ['Asset_Allocation', "Fixed_Income"])
In [143]:
data2 = data.groupby(by='class').mean()
data2
Out[143]:
| exp | nav | aum | beta | scaled_aum | aum_million | |
|---|---|---|---|---|---|---|
| class | ||||||
| Alternatives | 1.820513 | 21.320513 | 1.186542e+08 | 0.235897 | 17.267977 | 118.654158 |
| Asset_Allocation | 0.965517 | 395.551724 | 3.299403e+09 | 0.544828 | 17.414796 | 3299.403427 |
| Commodities | 0.412162 | 175.028378 | 1.406693e+09 | 0.477027 | 17.345794 | 1406.693136 |
| Currency | 1.032967 | 758.836264 | 2.028511e+08 | 0.648352 | 16.333805 | 202.851121 |
| Equity | 0.569337 | 852.437812 | 1.261168e+10 | 0.868906 | 18.660249 | 12611.676815 |
| Fixed_Income | 0.257576 | 1957.354293 | 4.164261e+09 | 0.168434 | 18.875313 | 4164.260947 |
In [144]:
data3 = data.rename({'class': 'asset_class'}, axis=1, inplace=False)
In [145]:
data.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 1893 entries, 0 to 1892 Data columns (total 10 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ticker 1893 non-null object 1 name 1893 non-null object 2 issuer 1893 non-null object 3 exp 1893 non-null float64 4 nav 1893 non-null float64 5 aum 1893 non-null float64 6 class 1893 non-null object 7 beta 1893 non-null float64 8 scaled_aum 1893 non-null float64 9 aum_million 1893 non-null float64 dtypes: float64(6), object(4) memory usage: 148.0+ KB
In [146]:
data3.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 1893 entries, 0 to 1892 Data columns (total 10 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ticker 1893 non-null object 1 name 1893 non-null object 2 issuer 1893 non-null object 3 exp 1893 non-null float64 4 nav 1893 non-null float64 5 aum 1893 non-null float64 6 asset_class 1893 non-null object 7 beta 1893 non-null float64 8 scaled_aum 1893 non-null float64 9 aum_million 1893 non-null float64 dtypes: float64(6), object(4) memory usage: 148.0+ KB
In [149]:
data4 = pd.get_dummies(data3, columns=['asset_class'])
In [150]:
data4.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 1893 entries, 0 to 1892 Data columns (total 15 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 ticker 1893 non-null object 1 name 1893 non-null object 2 issuer 1893 non-null object 3 exp 1893 non-null float64 4 nav 1893 non-null float64 5 aum 1893 non-null float64 6 beta 1893 non-null float64 7 scaled_aum 1893 non-null float64 8 aum_million 1893 non-null float64 9 asset_class_Alternatives 1893 non-null uint8 10 asset_class_Asset_Allocation 1893 non-null uint8 11 asset_class_Commodities 1893 non-null uint8 12 asset_class_Currency 1893 non-null uint8 13 asset_class_Equity 1893 non-null uint8 14 asset_class_Fixed_Income 1893 non-null uint8 dtypes: float64(6), object(3), uint8(6) memory usage: 144.3+ KB
Regression Analysis¶
In [157]:
data5 = data4[['exp',
'scaled_aum',
'beta',
'asset_class_Alternatives',
'asset_class_Commodities',
'asset_class_Currency',
'asset_class_Equity',
'asset_class_Fixed_Income']].dropna()
In [158]:
data5.describe()
Out[158]:
| exp | scaled_aum | beta | asset_class_Alternatives | asset_class_Commodities | asset_class_Currency | asset_class_Equity | asset_class_Fixed_Income | |
|---|---|---|---|---|---|---|---|---|
| count | 1893.000000 | 1893.000000 | 1893.000000 | 1893.000000 | 1893.000000 | 1893.000000 | 1893.000000 | 1893.000000 |
| mean | 0.552034 | 18.423791 | 0.658162 | 0.020602 | 0.078183 | 0.048072 | 0.613312 | 0.209192 |
| std | 0.964520 | 2.549140 | 0.665928 | 0.142086 | 0.268530 | 0.213975 | 0.487120 | 0.406839 |
| min | 0.000000 | 11.656437 | -4.900000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 25% | 0.000000 | 16.748409 | 0.300000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 50% | 0.000000 | 18.263078 | 0.700000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 |
| 75% | 1.000000 | 19.899327 | 1.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 |
| max | 20.000000 | 29.519605 | 4.400000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
In [159]:
data6 = data5.loc[data5['exp'] <= 3]
In [160]:
data6.describe()
Out[160]:
| exp | scaled_aum | beta | asset_class_Alternatives | asset_class_Commodities | asset_class_Currency | asset_class_Equity | asset_class_Fixed_Income | |
|---|---|---|---|---|---|---|---|---|
| count | 1883.000000 | 1883.000000 | 1883.000000 | 1883.000000 | 1883.000000 | 1883.000000 | 1883.000000 | 1883.000000 |
| mean | 0.506638 | 18.426578 | 0.659480 | 0.018056 | 0.078598 | 0.047796 | 0.614976 | 0.210303 |
| std | 0.583454 | 2.550354 | 0.666672 | 0.133190 | 0.269182 | 0.213391 | 0.486730 | 0.407632 |
| min | 0.000000 | 11.656437 | -4.900000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 25% | 0.000000 | 16.748837 | 0.300000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| 50% | 0.000000 | 18.263078 | 0.700000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 |
| 75% | 1.000000 | 19.901608 | 1.000000 | 0.000000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 |
| max | 3.000000 | 29.519605 | 4.400000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |
In [ ]:
In [161]:
data7 = data6[['exp', 'scaled_aum']].dropna()
In [162]:
pd.plotting.scatter_matrix(data7,
alpha=0.2,
diagonal='hist',
hist_kwds={'bins': 35},
figsize=(10, 6));
# plt.savefig('../../images/ch08/fts_11.png');
In [163]:
data7 = data6[['exp', 'beta']].dropna()
In [164]:
pd.plotting.scatter_matrix(data7,
alpha=0.2,
diagonal='hist',
hist_kwds={'bins': 35},
figsize=(10, 6));
# plt.savefig('../../images/ch08/fts_11.png');
In [ ]:
OLS Regression¶
In [165]:
reg = np.polyfit(data6['exp'], data6['scaled_aum'], deg=1)
In [166]:
ax = data6.plot(kind='scatter', x='scaled_aum', y='exp', figsize=(10, 6))
ax.plot(data6['scaled_aum'], np.polyval(reg, data6['scaled_aum']), 'r', lw=2);
# plt.savefig('../../images/ch08/fts_12.png');
In [183]:
formula = 'exp ~ scaled_aum + beta + asset_class_Commodities+ asset_class_Currency+ asset_class_Equity +asset_class_Fixed_Income'
results = smf.ols(formula, data6).fit()
print(results.summary())
OLS Regression Results
==============================================================================
Dep. Variable: exp R-squared: 0.203
Model: OLS Adj. R-squared: 0.201
Method: Least Squares F-statistic: 79.80
Date: Wed, 18 May 2022 Prob (F-statistic): 4.58e-89
Time: 23:41:37 Log-Likelihood: -1442.8
No. Observations: 1883 AIC: 2900.
Df Residuals: 1876 BIC: 2938.
Df Model: 6
Covariance Type: nonrobust
============================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------------------
Intercept 2.2168 0.101 21.937 0.000 2.019 2.415
scaled_aum -0.0697 0.005 -14.250 0.000 -0.079 -0.060
beta 0.0669 0.020 3.335 0.001 0.028 0.106
asset_class_Commodities -0.6271 0.069 -9.024 0.000 -0.763 -0.491
asset_class_Currency -0.1260 0.078 -1.618 0.106 -0.279 0.027
asset_class_Equity -0.4496 0.058 -7.785 0.000 -0.563 -0.336
asset_class_Fixed_Income -0.6544 0.061 -10.670 0.000 -0.775 -0.534
==============================================================================
Omnibus: 210.403 Durbin-Watson: 1.932
Prob(Omnibus): 0.000 Jarque-Bera (JB): 363.791
Skew: 0.752 Prob(JB): 1.01e-79
Kurtosis: 4.541 Cond. No. 207.
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Correlation¶
In [171]:
data2.corr()
Out[171]:
| exp | nav | aum | beta | scaled_aum | aum_million | |
|---|---|---|---|---|---|---|
| exp | 1.000000 | -0.626718 | -0.445960 | -0.164197 | -0.559892 | -0.445960 |
| nav | -0.626718 | 1.000000 | 0.335254 | -0.191956 | 0.633204 | 0.335254 |
| aum | -0.445960 | 0.335254 | 1.000000 | 0.587259 | 0.730016 | 1.000000 |
| beta | -0.164197 | -0.191956 | 0.587259 | 1.000000 | -0.105800 | 0.587259 |
| scaled_aum | -0.559892 | 0.633204 | 0.730016 | -0.105800 | 1.000000 | 0.730016 |
| aum_million | -0.445960 | 0.335254 | 1.000000 | 0.587259 | 0.730016 | 1.000000 |
In [179]:
X = data6[['scaled_aum', 'beta','asset_class_Commodities','asset_class_Currency','asset_class_Equity','asset_class_Fixed_Income']]
y = data6['exp']
In [184]:
X_ols = sm.add_constant(X)
model = sm.OLS(y, X_ols).fit()
print(model.summary())
OLS Regression Results
==============================================================================
Dep. Variable: exp R-squared: 0.203
Model: OLS Adj. R-squared: 0.201
Method: Least Squares F-statistic: 79.80
Date: Wed, 18 May 2022 Prob (F-statistic): 4.58e-89
Time: 23:41:41 Log-Likelihood: -1442.8
No. Observations: 1883 AIC: 2900.
Df Residuals: 1876 BIC: 2938.
Df Model: 6
Covariance Type: nonrobust
============================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------------------
const 2.2168 0.101 21.937 0.000 2.019 2.415
scaled_aum -0.0697 0.005 -14.250 0.000 -0.079 -0.060
beta 0.0669 0.020 3.335 0.001 0.028 0.106
asset_class_Commodities -0.6271 0.069 -9.024 0.000 -0.763 -0.491
asset_class_Currency -0.1260 0.078 -1.618 0.106 -0.279 0.027
asset_class_Equity -0.4496 0.058 -7.785 0.000 -0.563 -0.336
asset_class_Fixed_Income -0.6544 0.061 -10.670 0.000 -0.775 -0.534
==============================================================================
Omnibus: 210.403 Durbin-Watson: 1.932
Prob(Omnibus): 0.000 Jarque-Bera (JB): 363.791
Skew: 0.752 Prob(JB): 1.01e-79
Kurtosis: 4.541 Cond. No. 207.
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:117: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only x = pd.concat(x[::order], 1)
In [ ]:
In [185]:
beta = np.linalg.inv(X_ols.T.dot(X_ols)).dot(X_ols.T.dot(y))
pd.Series(beta, index=X_ols.columns)
Out[185]:
const 2.216848 scaled_aum -0.069728 beta 0.066850 asset_class_Commodities -0.627084 asset_class_Currency -0.126001 asset_class_Equity -0.449633 asset_class_Fixed_Income -0.654390 dtype: float64