Is there no value in defending the definition of a word? Arbitrage originally meant expected profits with zero risk of loss. Now some people say they also want to use it to mean expected profits with non-zero risk of loss. Okay, then why not just say "expected profits" (or "edge" as traders would call it) since you've eliminated the distinction that makes the term meaningful in the first place? I mean, would you say that the AGI I'm building in my basement is "Friendly" just because I expect it to do good things, even though it also might paperclip the universe 2% of the time?
Pure arbitrage pretty much never exists. There is almost always non-zero risk of loss. Arbitrage transactions invariably have some execution risk, though with very liquid markets and electronic trading it may be arbitrarily small. Generally the liquid markets with the fastest trading are those that will offer the least arbitrage opportunities though so in reality greater profits almost always come at the cost of increased execution risk. It doesn't seem a huge stretch to extend the concept to statistical arbitrage - you're never really going from zero risk to risk, you're just increasing from a very small risk to a larger risk and going from very reliable price correlations to less reliable ones.
I've noticed something very curious on Intrade markets for 2012 Republican Presidential Nominee - Ron Paul gets 3.5% of getting a nomination - a value that's clearly (and spare me EMH here) wishful thinking of Ron Paul supporters more than any genuine estimate.
And this brings me to a question - if prediction markets overestimate chance of winning of some rare case, how can I profit from that? Naively if I know true chance is 1%, I win $3.5 99% of the time, and lose $97.5 1% of the time, for expected payoff of $2.5. But my maximum loss is 39x higher than my expected profit, and I won't be getting any money out of it for three more years.
I'd need to bet significant amount to earn any money out of it, and that would require accepting 39x as high maximum loss. No reasonably prediction market would accept this kind of leverage without some collateral, nor could I get any reasonable loan for it at rates that would make this arbitrage profitable.
The only way I can think of would be convincing someone with plenty of money that I'm right, and have him provide me with collateral for some (probably very high) portion of the payoff. But if results depend on my ability to convince rich people, that's not prediction market! None of this is a problem for people trying to artificially pump estimates for Ron Paul - they'll just take the loss, and write it off as marketing expense.
None of these problems occur if some position is vastly overestimated, like 60% estimate if I know true value to be 40% - this would be a cheap bet - maximum loss of $40 for expected profit of $20, and people who want to pump it need to take about as much risk as people who want to bring it back to the true value, not a lot more.
I'm confused. Is there some nice way to arbitrage this, or is this an inherent weakness of prediction markets and we should only trust positions they pick as leaders, not chances of their long tail?