Daily returns to monthly basic question [closed]

Question

I am currently a little bit puzzled. I am trying to compute the monthly returns from a set of data.

30-Sep-18   175.9790658  Performance
29-Sep-18   175.9790658 0.000%
28-Sep-18   175.9790658 0.000%
27-Sep-18   174.9712013 0.576%
26-Sep-18   175.4530194 -0.275%
25-Sep-18   173.5249863 1.111%
24-Sep-18   173.6253172 -0.058%
23-Sep-18   175.9311682 -1.311%
22-Sep-18   175.9311682 0.000%
21-Sep-18   175.9311682 0.000%
20-Sep-18   171.6433724 2.498%
19-Sep-18   170.5624874 0.634%
18-Sep-18   167.1542002 2.039%
17-Sep-18   164.9153843 1.358%
16-Sep-18   168.1403232 -1.918%
15-Sep-18   168.1403232 0.000%
14-Sep-18   168.1403232 0.000%
13-Sep-18   167.0250094 0.668%
12-Sep-18   162.2830264 2.922%
11-Sep-18   163.2663355 -0.602%
10-Sep-18   163.7415407 -0.290%
09-Sep-18   166.8650865 -1.872%
08-Sep-18   166.8650865 0.000%
07-Sep-18   166.8650865 0.000%
06-Sep-18   165.9631283 0.543%
05-Sep-18   168.6782507 -1.610%
04-Sep-18   172.9814277 -2.488%
03-Sep-18   171.6316528 0.786%
02-Sep-18   172.3265548 -0.403%
01-Sep-18   172.3265548 0.000%
31-Aug-18   172.3265548 0.000%

For calculating the monthly performance (X2/X1)-1 has been used giving us a performance of 2.12% but the sum of individual daily returns is 2.31%

I don't see where discrepancy could come from is it because of the compounding? Are there perhaps any papers on this subject to read up on since google was to no avail.

Thanks for the help advance and kind regards!

Answer 1

it's the difference between $\sum_{i=1}^n \frac{X_i}{X_{i-1}} -1$ and $\frac{X_n}{X_0}-1$ and has nothing to do with your data integrity

Answer 2

Returns are cumulated, not summed. Run a cumulative product on your performance column (this looks like a pandas DataFrame; pandas has build in functions for that), which is the actual monthly return you are looking for.

Whether or not this is 2.12% is up to the integrity of your data set.