# Daily returns to monthly basic question [closed]

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!

## closed as off-topic by amdopt, Helin, skoestlmeier, Daneel Olivaw, LocalVolatilityOct 26 '18 at 14:31

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – amdopt, Helin, skoestlmeier, Daneel Olivaw, LocalVolatility
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• Yes, the compounded return is 2.12%. 2.31% is just a summation of the returns column... – amdopt Oct 25 '18 at 15:48

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