No, you were correct, arithmetic mean of returns is not standard in finance. If it was, financial crashes would be much worse. They do arithmetic means of "log

No, you were correct, arithmetic mean of returns is not standard in finance. If it was, financial crashes would be much worse. They do arithmetic means of "log returns" because 1/n sum(log(r)) = log(product(r)^(1/n)). That is, in log world, the arithmetic mean is the geometric mean.