arithmetic mean of log returns that starts and ends with the same price in a time series

quick question: arithmetic mean of log returns that starts and ends with the same price in a time series

say a stock time series starts at t0 price 100 fluctuates in between the time series and ends at tx 100. arithmetic mean of log returns is 0, correct?

I ask this bc R seems to suggest otherwise or result in conflicting results.

• Does the asset in question pay dividends or not? If not and you start at $P_0$ and end up at $P_n=P_0$ then indeed the sum of log returns will be zero and so will the mean of log returns. If there are dividends then you may have made a positive return. – noob2 Mar 21 at 22:10
• Hi: Note that the comment of @noob2 holds for log returns also. In fact, I don't think anything that the OP said hinges on the returns being arithmetic. – mark leeds Mar 21 at 23:13
• Thanks guys for the quick mental check – charlie090 Mar 22 at 12:39