Calculation of rolling weights with initial weight at the first day-CodePudding

I have a DataFrame for weights and returns and I want to adjust the weights based on the returns one day before, except for the initial weights. The basic idea is that the weights are changing based on the returns.

I created an example with the weights, returns and the preferred rolling weights:

weights:
            01K W   02K W   03K W   04K W
Dates               
2021-01-01  0.0     0.2     0.3     0.5
2021-01-02  0.0     0.2     0.3     0.5
2021-01-03  0.5     0.2     0.3     0.0
2021-01-04  0.5     0.2     0.3     0.0
2021-01-05  0.5     0.0     0.2     0.3
2021-01-06  0.5     0.0     0.2     0.3

returns:
            01K W   02K W   03K W   04K W
Dates               
2021-01-01  0.01    0.01    -0.03   0.05
2021-01-02  0.02    0.02    0.04    -0.02
2021-01-03  0.03    -0.03   0.01    -0.02
2021-01-04  -0.03   0.01    0.02    0.03
2021-01-05  0.02    0.02    0.01    0.01
2021-01-06  0.01    -0.01   0.03    0.02

With these weights and returns, I try to calculate the rolling weights for 01K W as follows:

2021-01-03: 0.5 (initial weight) (ignore return on previous day)
2021-01-04: 0.515 = 0.5 * (1 0.03) (0.03=return on 2021-01-03)
2021-01-05: 0.4996 = 0.5 * (1 0.03) * (1-0.03)(-0.03=return on 2021-01-04)
2021-01-06: 0.5095 = 0.5 * (1 0.03) * (1-0.03) * (1 0.02)(0.02=return on 2021-01-05)

rolling_weights:
            01K W   02K W   03K W   04K W
Dates               
2021-01-01  0.0000  0.20000 0.30000 0.500
2021-01-02  0.0000  0.20200 0.29100 0.525
2021-01-03  0.5000  0.20604 0.30264 0.000
2021-01-04  0.5150  0.19986 0.30567 0.000
2021-01-05  0.4996  0.00000 0.20785 0.300
2021-01-06  0.5095  0.00000 0.20993 0.303

For reproducibility:

import pandas as pd
returns = pd.DataFrame({
    'Dates':['2021-01-01', '2021-01-02', '2021-01-03', '2021-01-04', '2021-01-05', '2021-01-06'],
    '01K W':[0.01, 0.02, 0.03, -0.03, 0.02, 0.01], 
    '02K W':[0.01, 0.02, -0.03, 0.01, 0.02, -0.01], 
    '03K W':[-0.03, 0.04, 0.01, 0.02, 0.01, 0.03], 
    '04K W':[0.05, -0.02, -0.02, 0.03, 0.01, 0.02]}) 
returns = returns.set_index('Dates')

weights = pd.DataFrame({
    'Dates':['2021-01-01', '2021-01-02', '2021-01-03', '2021-01-04', '2021-01-05', '2021-01-06'],
    '01K W':[0, 0, 0.5, 0.5, 0.5, 0.5], 
    '02K W':[0.2, 0.2, 0.2, 0.2, 0, 0], 
    '03K W':[0.3, 0.3, 0.3, 0.3, 0.2, 0.2], 
    '04K W':[0.5, 0.5, 0, 0, 0.3, 0.3]}) 
weights = weights.set_index('Dates')

Thank you very much for your suggestions.

CodePudding user response：

Multiply weights by partial (i.e. resets every time weights are zero) cumprod of returns that are zeroed at positions where weights are zero, and then shifted 1 position down:

weights_new = pd.DataFrame([weights[col]*(returns.where(weights!=0,0).shift(1).fillna(0) 1)[col].groupby(((returns.where(weights!=0,0).shift(1).fillna(0) 1)[col] == 1).cumsum()).cumprod() for col in weights.columns]).T