Probability of outlier events for laplace distribution

I've read that the laplace distribution is better for forecasting purposes than the normal distribution due to it better accounting for fat tails. However, when I run the numbers in matlab, laplace ends up with skinnier tails than a normal distribution. Am I doing anything wrong? Here is the code:

%laplace distribution

a = laprnd(755,100000,0,0.0034);
for x = 1:length(a)
rets(x) = prod(1+a(:,x))-1;
end

[sum(rets>.0419)/length(rets),sum(rets<-.1688)/length(rets)]

ans =

0.3122    0.0264

%Normal Distribution

j = normrnd(0,0.0034,755,100000);
for y = 1:length(j)
retsj(y) = prod(1+j(:,y))-1;
end

[sum(retsj>.0419)/length(retsj),sum(retsj<-.1688)/length(retsj)]

ans =

0.3151    0.0267