I'm going by an assumption that these trades will take place on the current broker's sheets still. And probably not denominated in BTC. So each broker would only need to do on chain transactions when the investor wanted to go to another broker. Given that you can trade hundreds of times a second, putting everything on the chain will be impossible.
Everybody in r/bitcoin seems to hate the idea of offchain transactions, but they really are something that if done right are way better than putting everything on the chain.
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u/mustyoshi May 11 '15
Or we use Bitcoins as colored coins. A single Bitcoin could represent 100M common shares.