Thursday, 14 February 2008

Supermarket queues and arbitrage

A fairly common way to describe how arbitrage works in share prices is to compare it to supermarket queues. Here for example is Tim Harford's version in The Undercover Economist:

"Which queue is quickest? The simple answer is that it's just not worth worrying about. If it was obvious which queue was the quickest, people would already have joined it, and it wouldn't be the quickest any more. Stand in any queue and don't worry about it. Yet if people really just stood in any queue, then there would be predictable patterns that an expert shopper could exploit; for example, if people start at the entrance and work their way across the store, the shortest queue should be back near the entrance. But if enough experts knew that, it wouldn't be the shortest any more. The truth is that busy, smart, agile and experienced shoppers are a bit better at calling the fastest queues and can probably average a quicker time than the rest of us. But not by much."

Though I agree with the general thrust of this, I actually think supermarket queues function a bit differently. For example, those of you who do play Runaround when it comes to supermarket queues must have had the experience where you have switched to a shorter queue only for the one you were originally in move more quickly and you end up worse off. Given our loss averse disposition that experience must have an emotional cost. If it happens a few times you might even start to think that it 'always' happens to you (because you remember the pain when it does more than the pleasure when it doesn't). And that might cause you to stop switching queues altogether.

Secondly, sometimes there is a reason why shoppers already in a queue decide not to join an obviously shorter one. This might be because the shorter line appears to be moving more slowly because of someone inexperienced on the till. Or maybe a customer is having a dispute with the person on the till that is taking up time. This might lead new entrants to join the 'wrong' queue, particularly if their queue decisions are driven by mathematical models...

Conversely it may lead others to not join shorter queues because they believe that they are shorter because existing queue members have knowledge they do not, which may say something about our desire for social proof. In fact you do see these things happen quite a lot in the queues for ATMs. Quite often people will join a queue behind one ATM when another is free, presumably because they make the assumption that the free one is broken, otherwise someone would use it.

All of which points to arbitrage not actually working that effectively in the queue scenario. Now I'm not an expert on the formation of share prices, but it strikes me that if arbitrage can be floored by some fairly important bits of wonky human behaviour in supermarket and ATM queues, it probably happens in stockmarkets to an even greater degree. So it's risky to bank on rational and efficient prices. As Keynes famously said: "The markets can remain irrational longer than you can remain solvent."

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