To capture time series dynamics that capture, for example, momentum patterns, we compute historical returns using the pct_change(n_periods), that is, returns over various monthly periods as identified by lags. We then convert the wide result back to long format using .stack(), use .pipe() to apply the .clip() method to the resulting DataFrame and winsorize returns at the [1%, 99%] levels; that is, we cap outliers at these percentiles.

Finally, we normalize returns using the geometric average. After using .swaplevel() to change the order of the MultiIndex levels, we obtain compounded monthly returns for six periods ranging from 1 to 12 months:

outlier_cutoff = 0.01
data = pd.DataFrame()
lags = [1, 2, 3, 6, 9, 12]
for lag in lags:
    data[f'return_{lag}m'] = (monthly_prices
                           .pct_change(lag)
                           .stack()
                           .pipe(lambda x: x.clip(lower=x.quantile(outlier_cutoff),
                        upper=x.quantile(1-outlier_cutoff)))
                           .add(1)
                           .pow(1/lag)
                           .sub(1)
                           )
data = data.swaplevel().dropna()
data.info()

MultiIndex: 521806 entries, (A, 2001-01-31 00:00:00) to (ZUMZ, 2018-03-
                             31 00:00:00)
Data columns (total 6 columns):
return_1m 521806 non-null float64
return_2m 521806 non-null float64
return_3m 521806 non-null float64
return_6m 521806 non-null float64
return_9m 521806 non-null float64
return_12m 521806 non-null float6

We can use these results to compute momentum factors based on the difference between returns over longer periods and the most recent monthly return, as well as for the difference between 3 and 12 month returns as follows:

for lag in [2,3,6,9,12]:
    data[f'momentum_{lag}'] = data[f'return_{lag}m'].sub(data.return_1m)
data[f'momentum_3_12'] = data[f'return_12m'].sub(data.return_3m)