not normally distributed log-returns

[Daniel Schmitt]

Hello,

I need to compare the returns of two different investment strategies. These returns are log returns and are measured for an investment period of
6 months (125 days)
12 months (251 days)
24 months (504 days)
When I try to test whether the two different return destributions are normally distributed or not, I get for one strategy (251 and 504 days) that the log returns are not normally
distributed but in case of 125 days they are. For the other strategy the log returns are always normally distributed.
Now I don't have a clue what to do? The returns are already log-transformed, so does it make sense to transformed them again?
Thanks for any help or comments in advanced.

[Jorge Eduardo Perez Perez]

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[Phil Bromiley]

I'm not sure why you'd double log transform something - I would think it would be very hard to interpret. If you really care about normality, you can try other transformations.

Many tests do not necessarily assume normality. In addition, while some may object, if you have a very large sample, you can often reject such normality hypotheses even if the deviations are modest. In such a case, a test assuming normality might be reasonable. At the most extreme, you can always do a non-parametric text.

[Attaullah Shah]

Though stocks returns are long known to have fat tails. However, like Phil pointed out, with large number of observation, even trivial deviation will make normality test to produce results in favor of non-normal distribution. It is better to use qnorm plot instead to check normality for getting a better idea about your data.