the mathematics are simple: steemdollars are traded up to 30% more on external exchanges.
But also steem itself is traded 30% more on external exchanges.
Why is this so?
Its because the peg - internal conversion from steemdollars to steem takes one week average of the currenct steem to dollar price, which is 30% below the current steem price.
this is so mainly to dont make it easy to manipulate the peg though the price feed providers.
So with just trading in and out steemdollars you cannot make a win.
the only win you can make is if the peg - internal steem conversion rate - is less then 30% below the current steem price.
in this case you can directly internally convert your steem dollars to steem and then sell the new created steem on external exhanges to steem dollars. the steem dollars you can then convert again to steem and so on untill you can make some win with it.
good luck and have fun!
UPDATE: Oh in this case it could also be the other way round, you have to convert internally steem to steemdollars and then sell them on an external exchange to for example bitcoins. then buy with the bitcoins steem on an external exchange so on and so on. sadly steem seems to miss an ability to internally convert steem to steem dollars, so we most likely just have to wait until the 100% steem inflation per year (currently even 5000%) brings downs the steem price to one steem dollar or below. so im sorry in this case, you cannot do anything to correct the steem dollar price, except waiting for the steem inflation to take place and bring the price down again :)
I think that's what I said. scratches head
I never said there was arbitrage, per se, only that there is a premium price for SBD on the exchanges for authors who are interested in cashing out at a higher rate than what they expected.