I got 50% just looking at the first two moments, and 75% looking at all of them. Which feels wrong. So I've probably made a mistake
GAT
75% I got just by setting it up in excel to optimise the expected log utility (weighted log of each outcome). That should account for all the moments. 50% I did just looking at the mean and standard deviation, and using the normal formula for that.
GAT
For the first two moments, I got radically different results.
S1 = 0.0575 ;
S2 = 0.043045 ;
k1 == s1/s2 = 1.33581136
If we use the alternative mean/variance form, the ratio is even bigger:
k1 ≈ s1/(s2 - s1^2) = 1.44695
I don't see how you got 50%.