More Bitcoins trade off the chain than on exchanges. The biggest deals are done off the books, not on exchanges, for obvious reasons.
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If you talk to guys in the know, like Charlie Shrem, you'll find out that there are massive cash buyers buying Bitcoins off the chain everyday. Given Bitcoin is so illiquid, driving the price down (or up) is an easy task, especially for professional Wall Street traders.
Are you saying that bitcoins are being transfered by simply providing the private key to an address? I'm not understanding your suggestion that btc is being traded/bought "off the chain". I assume you mean the transaction is not seen on the blockchain?
Right. You're a miner and you wanna sell 1,000 Bitcoins. I send you the cash (or we use a middle man Broker like Shrem) cause we're both reputable people and you send me the BTC. There's an obvious transaction for the simple transfer in the ledger [in the blockchain] but that's it.
The market price isn't affected at all by your huge sale to me unless I choose to dump it all at once to push the price down.
If you watch interviews with guys like Barry Silbert and other big buyers you'll see that they rarely buy any BTC on exchanges. They buy from early adopters, miners and pools. Off The Chain transactions and they get a bulk discount rate.
Given bicoin is so illiquid it wouldn't be difficult to use this mechanism to consistently drive the price down.
But don't fret, just as easily as Bitcoin can be manipulated down, it can even more easily be manipulated up. The media will definitely get behind this next massive pump.
Edit: Coinbase does mostly OTC transactions from what I've read. It's a pretty common practice.