Calculation of floating weights based on weight and return DataFrame-CodePudding

I have two DataFrames; returns and weights and I try to combine them to a floating_weights DataFrame. The idea behind is that I want to dynamically adjust the weights in period t with the return in period t-1. So the weights increase, if there are positive returns and vice versa.

Here I created a simple example:

weights:
    Dates       01K W   02K W   03K W   04K W
0   2021-01-01  0.0     0.2     0.3     0.5
1   2021-01-02  0.0     0.2     0.3     0.5
2   2021-01-03  0.5     0.2     0.3     0.0
3   2021-01-04  0.5     0.2     0.3     0.0
4   2021-01-05  0.5     0.0     0.2     0.3
5   2021-01-06  0.5     0.0     0.2     0.3


returns:
Dates           01K W   02K W   03K W   04K W
0   2021-01-01  0.01    0.01    -0.03   0.05
1   2021-01-02  0.00    0.02    0.04    -0.02
2   2021-01-03  0.03    -0.03   0.01    -0.02
3   2021-01-04  -0.03   0.01    0.02    0.00
4   2021-01-05  0.02    0.02    0.01    0.01
5   2021-01-06  0.01    -0.01   0.03    0.02

The floating_weights DataFrame is based on the normal weights adjusted with the returns from the previous period:

floating_weights (2021-01-01, 02K W): 0.2 (start with normal weight)

floating_weights (2021-01-02, 02K W): 0.202 = 0.2 * (1 0.01)

floating_weights (2021-01-03, 02K W): 0.206 = 0.2 * (1 0.01) * (1 0.02)

floating_weights (2021-01-04, 02K W): 0.19986 = 0.2 * (1 0.01) * (1 0.02) * (1-0.03)

The floating_weights would look like this.

    Dates       01K W   02K W   03K W   04K W
0   2021-01-01  0.0000  0.20000 0.30000 0.500
1   2021-01-02  0.0000  0.20200 0.29100 0.525
2   2021-01-03  0.5000  0.20604 0.30264 0.000
3   2021-01-04  0.5150  0.19986 0.30567 0.000
4   2021-01-05  0.4995  0.00000 0.20785 0.300
5   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, 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, 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 the help!

CodePudding user response：

We can use cumprod to calculate the cumulative returns, then shift and multiply the cumulative returns with the weights dataframe to get the desired result

r = returns.add(1).cumprod().shift()
floating_weights = weights.mul(r, fill_value=1)

If you want to reset the cumprod every time the weight is assigned to zero, in such case we have to consider each column separately

floating_weights = weights.copy()

for col in weights:
    g = weights[col].eq(0).cumsum()
    r = returns[col].add(1).groupby(g).cumprod()
    floating_weights[col] = weights[col].mul(r.shift(1), fill_value=1)

>>> floating_weights

               01K W     02K W     03K W  04K W
Dates                                          
2021-01-01  0.000000  0.200000  0.300000  0.500
2021-01-02  0.000000  0.202000  0.291000  0.525
2021-01-03  0.500000  0.206040  0.302640  0.000
2021-01-04  0.515000  0.199859  0.305666  0.000
2021-01-05  0.499550  0.000000  0.207853  0.300
2021-01-06  0.509541  0.000000  0.209932  0.303