Seeing how much the ratio of gem obtained per gold can vary, I wonder if I can make some gold by buying gems when prices are low and selling them when prices are high. My question is are there any exchange fee that would make such transactions not profitable ?
There's no exchange fee, but there's a rather huge margin.
Take a look at the graph for trading gems on spidy, and adjust the sliders down the bottom to get a feel for how the price has changed over the past.
As you can see, if you'd bought during that dip on 19 September 2014, you could've got 100 gems for about 10g68s25c. If you'd then waited for the optimum time to sell, you could've got about 12g69s92c on 04 March 2015... i.e. about 2g per 100 gems.
So, yes, you can make money by buying and selling at the right time, but you'd better be willing to wait a heck of a long time to make it worth your while.
If you ask me, there are heaps of ways to make more money more easily. The only time I'd recommend this option is if you're going to be away from the game for a longer time and have a lot of gold sitting around, because, over time, the price will always increase quite a bit. Short term, though, I think you're wasting your money and your time checking the price (you'd be kicking yourself if you'd missed that peak or that trough). Notice the difference between the upper and lower parts of the graph - that's the margin, and where the seller (i.e. ArenaNet) makes their money (and you lose yours if you try to play the market).