No, the coins are safest in your wallets on your pc/laptop what ever you choose.. Try and make an offline wallet if possible or keep them on a huge mem stick with a backup of your wallets data. Unfortunately to trade w have to send the coins to the exchange. This is where it becomes unsafe. I think all exchanges should get lost and close. they are all crap. why someone doesn't just create a program that allows people to exchange their coins without the need of anyone owning the exchange.

like the bitcoin itself and earn commission for the exchanges for keeping the program running like us miners do, keeping a ledger on their systems that cant be hacked and exchangable from the wallets themselves.