# Should the sum of daily returns be close to monthly returns

I am calculating value-weighted returns with monthly dividends reinvested and for some reason when I sum the daily returns some are a little bit off with monthly returns.

Is this normal?

• well, are you using arithmetic returns or logarithmic returns? A basic fact from the properties of logarithm is that a total log return is the sum of daily returns, $$\log (X_n/X_0)=\sum_{k=1}^n \log(X_k/X_{k-1}).$$ This is not true for arithmetic, it is a slightly more complicated multiplicative formula. – Nap D. Lover Apr 13 at 17:02
• You give very little detail of what you are doing. Where do your returns come from? Are you saying that using CRSP monthly vs daily returns you get different results? – Alex C Apr 13 at 17:13