Arbitrage?

Dear friends,

I was taking a look at a piece on political betting when I noticed the wildly divergent prices listed for betting on Michael Gove as next Conservative leader. I read the blog because it is interesting to see people's opinions on what is going to happen next. Often the rationalisations reveal much more than the predictions.

I am a bit iffy on how to figure with odds, but it seems to me that when you can place the same bet in two different places for much the same rate of return, it violates the no arbitrage condition from finance. It should be possible to immediately place a bet on both outcomes of different sizes, so that whatever the outcome one is able to make money.

For example, in the post one bookie offers a bet on Michael Gove promising £16 for every £1 bet that he is the next leader. If I have this right that is in addition to getting the £1 you paid back. So for instance if the bet had been 1/1 it would mean if you bet £1 and were successful, you would get your £1 back and another £1 for it to make friends with. For the bet to be worth the same as £1 then, the first bookie needs the chances of Michael Gove becoming the next leader to be one in seventeen. Of course they will try to cushion that so they can have a profit margin. Another bookie estimated the odds of this occurring at one in eight, which translated in funny betting language as 7/1, in contrast to the previous bookie's 16/1.

So, let's imagine for a moment that the conservative leadership election is tomorrow. I put £14 on Gove not becoming leader with the bookie with the 7/1 odds and I put £1 on Gove becoming leader with the bookie with the 16/1 odds. That means until the results are announced I am £15 out of pocket. I am not worried though. If Gove does not become leader, I get £2 from the 7/1 bet, as well as the £14 I put on that back. That adds up to £16, meaning I turn an impressive profit of £1. If Gove does become the leader of the Conservatives, then I win £16 from my bet there, as well as getting back the £1 I put on it, thus making a total profit of £2. Not amazing figures, admittedly, but barring the risk of bookies going bankrupt or the political system collapsing it seems like a sure thing.

Of course, there isn't actually a leadership election tomorrow, it is probably quite a way off. That means that any profits you are able to make this way are vulnerable to inflation, as the money you get out is worth less than the money you put in before, even though it exceeds it nominally. Much better to ask the bookies if they are willing to bet in gold, or rare pokémon cards.

I wonder if bookies have something to prevent people making this kind of bet. I imagine not, it does not sound like that would be legal. It is standard practice for political betters to have bets on both sides, but this is normally done in response to fluctuations in the betting markets, which in politics is very volatile.

This has been a different one for me. Hope it has been of some interest.

All the best,
Caleb