Your Exchange could keep your CC's in storage for you. Many offer "cold storage" which simply means your coins are kept "offline" until you indicate that you wish to make a move with them. You can find quite a few news stories of Exchanges being hacked, and many coins stolen. Think about your coins being in something such as a banking account at the Exchange, but remember your coins are digital only, and How do I protect my crypto? that blockchain transactions are irreversible. Unlike your bank, these Exchanges do not need deposit insurance, so know that hackers are always available trying everything they could to find your Crypto Coins and steal them. Exchanges generally offer Password protected accounts, and many offer 2-factor authorization schemes - something to seriously consider to be able to protect your account from hackers.