Statistics Module

The statistics module contains the GRS function which computes the Gibbons, Ross, and Shanken (GRS) test for a factor model.

statistics

finance_byu.statistics.GRS(df, exret, factors)

Implementation of the Gibbons, Ross, and Shanken (GRS) test for a factor model.

Parameters:

df: pandas.core.frame.DataFrame

DataFrame containing a columns with excess returns and columns with factor returns.

exret: list

List of the variable / column names in df which are excess portfolio returns to be tested.

factors: list

List of the variable / column names in df which are factor returns.

Returns:

output: tuple(float,float,Regtable)

Tuple containing the GRS statistic, associated p-value, and Regtable with regression results for regressions of the form exret = alpha + summation(beta*factor) + e.

Example

>>> from finance_byu.statistics import GRS
>>> import numpy as np
>>> import pandas as pd
>>>
>>> n_periods = 1.0e2
>>>
>>> df = pd.DataFrame(np.random.random((int(n_periods),6)))
>>> df = df.rename(columns={0:'port1',1:'port2',2:'port3',3:'exmkt',4:'smb',5:'hml'})
>>> grsstat,pval,tbl = GRS(df,['port1','port2','port3'],['exmkt','smb','hml'])
>>> grsstat

29.257621230624505

>>> pval

1.8957078244964134e-13

>>> from tabulate import tabulate
>>> print(tabulate(tbl.render(),tablefmt='github',headers=tbl.render().columns))

|           | port1   | port2   | port3   |
|-----------|---------|---------|---------|
| Intercept | 0.431   | 0.574   | 0.452   |
|           | (4.78)  | (6.82)  | (5.14)  |
| exmkt     | -0.020  | 0.075   | 0.146   |
|           | (-0.19) | (0.79)  | (1.48)  |
| smb       | 0.094   | 0.051   | -0.135  |
|           | (0.91)  | (0.53)  | (-1.32) |
| hml       | 0.064   | -0.258  | 0.009   |
|           | (0.62)  | (-2.69) | (0.09)  |
| Obs       | 100     | 100     | 100     |
| Rsq       | 0.01    | 0.08    | 0.04    |