To arbitrage properly, in your example, one would need to hold a 10 BTC position on BTC-e and a $24,200 position on Coinbase/GDAX. When the spread between exchanges becomes favorable, execute a buy on GDAX and a sell on BTC-e simultaneously. Then one would have to wait however many days it will take to receive a wire from BTC-e's bank, and deposit the funds (minus profit) back to GDAX. The other thing you didn't mention, that would also have to be factored in, is withdrawal fees and SWIFT fees that may be collected by any of the banks involved (including intermediaries that the USD withdrawal wire gets routed through).
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