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?

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    $\begingroup$ 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. $\endgroup$ Apr 13, 2019 at 17:02
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    $\begingroup$ 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? $\endgroup$
    – Alex C
    Apr 13, 2019 at 17:13

1 Answer 1


No, you should expect them to be different. For example, consider -10% and +10%. 1.1*0.9 = 0.99 -> -1% return vs 0% if you use addition.


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