I think the actual problem there is the contract cap—going to all this work results in something like $120 [Edit: on further calculation, I think it’s actually much lower, like $30, assuming you don’t have other gambling winnings to offset.] in reward, which is likely not worth the hassle. If you could put in 10x the money and 10x the return without a corresponding increase in the hassle, then it might be worth it.
We can work out the bounds on the error created by the arbitrage in the absence of contract caps. A wrinkle is that for US tax law you can combine all gambling winnings and losses over the course of the year, so if you bought $2k of Trump on BetFair and $6k of Clinton on PredictIt, the $10k you get back would have $8k subtracted from it, and you only need to pay taxes on your $2k of winnings. But from BetFair’s point of view, your profit is $8k, and you need to pay the profit fee on $8k and the withdrawal fee on $10k. (BetFair’s fee structure is monstrously complicated, so I’m going to pretend they have PredictIt’s fee structure.) Since the profit fees and withdrawal fees apply before the income tax, and the income tax only multiplicatively reduces the profit, we’ll just determine the difference in probabilities that leads to the exchange giving you back more money than you put in, as positive profit will still be positive profit after taxes when it might not be after fees. (I’m also assuming no deposit fees, but you can just roll those into the price of the contracts.)
So suppose you have two mutually exclusive and exhaustive options, whose prices on the two exchanges are (going with the example) c and t. As this is an opportunity for arbitrage, let’s assume c+t<1-y, and c>t. (We’ll eventually solve for y, which tells us how much the probabilities need to be off for there to be an arbitrage opportunity.)
Suppose x wins. We lose (1-x)*.1 to the profit fee, leaving .9+.1x to be hit by the withdrawal fee of 5%, leaving .855+.095x as the gain. We need .855+.095x > c+t for this to be profitable.
If we’re highly risk averse, we pick x to be the cheaper of the two (t). That gives us .855 + 0.095t > c + t, and we can immediately observe .855 + 0.095t = 1 - y, which tells us that y = .145-.095t.
Which is basically what we would have gotten if we multiplied the fees together; the only interesting thing is that the lowest probability assignment (in this example, BetFair’s 20% on Trump) affects the bounds, such that disparities need to be higher when the more extreme probability is more extreme (because the profit fee cuts deeper).
I think the actual problem there is the contract cap—going to all this work results in something like $120 [Edit: on further calculation, I think it’s actually much lower, like $30, assuming you don’t have other gambling winnings to offset.] in reward, which is likely not worth the hassle. If you could put in 10x the money and 10x the return without a corresponding increase in the hassle, then it might be worth it.
We can work out the bounds on the error created by the arbitrage in the absence of contract caps. A wrinkle is that for US tax law you can combine all gambling winnings and losses over the course of the year, so if you bought $2k of Trump on BetFair and $6k of Clinton on PredictIt, the $10k you get back would have $8k subtracted from it, and you only need to pay taxes on your $2k of winnings. But from BetFair’s point of view, your profit is $8k, and you need to pay the profit fee on $8k and the withdrawal fee on $10k. (BetFair’s fee structure is monstrously complicated, so I’m going to pretend they have PredictIt’s fee structure.) Since the profit fees and withdrawal fees apply before the income tax, and the income tax only multiplicatively reduces the profit, we’ll just determine the difference in probabilities that leads to the exchange giving you back more money than you put in, as positive profit will still be positive profit after taxes when it might not be after fees. (I’m also assuming no deposit fees, but you can just roll those into the price of the contracts.)
So suppose you have two mutually exclusive and exhaustive options, whose prices on the two exchanges are (going with the example) c and t. As this is an opportunity for arbitrage, let’s assume c+t<1-y, and c>t. (We’ll eventually solve for y, which tells us how much the probabilities need to be off for there to be an arbitrage opportunity.)
Suppose x wins. We lose (1-x)*.1 to the profit fee, leaving .9+.1x to be hit by the withdrawal fee of 5%, leaving .855+.095x as the gain. We need .855+.095x > c+t for this to be profitable.
If we’re highly risk averse, we pick x to be the cheaper of the two (t). That gives us .855 + 0.095t > c + t, and we can immediately observe .855 + 0.095t = 1 - y, which tells us that y = .145-.095t.
Which is basically what we would have gotten if we multiplied the fees together; the only interesting thing is that the lowest probability assignment (in this example, BetFair’s 20% on Trump) affects the bounds, such that disparities need to be higher when the more extreme probability is more extreme (because the profit fee cuts deeper).