ninja1024

the Jarque–Bera test is a simple stats test for normality based on the first 4 moments, along the lines of Bchad's recommendation but you'll need to compute the JB test statistic and compare it against a table rather than eye-balling skewness and kurtosis. There is plenty of info about it on the web. There are also other more involved statistical tests which can also be implemented easily just with a spreadhseet, just google "tests for normality"

the reason why you want to use log-return is because it is additive, i.e. the log-return over some time interval is equal to the sum of the log-returns over a partition of that time interval. under certain set of assumptions, the sum of a large number of i.i.d. random variables will be approximately gaussian (CLT). so the assumption that the log-return is normal is grounded in theory, it is not just an empirical exercise about finding the best distribution that fits your data