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Alice’s Adventures in the Wonderful Looking Glass World of Prediction Markets

November 30, 2011

When Alice journeyed through the looking glass, Lewis Carroll tells us, she came across a Queen who claimed to be “one hundred and one, five months and a day.” “I can’t believe that!” said Alice. “Can’t you?” the Queen said in a pitying tone. “Try again: draw a long breath and shut your eyes.” Alice laughed. “There’s no use trying”, she said: “one can’t believe impossible things.” “I daresay you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half-an-hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast.”

Well, there’s not space enough to consider six impossible things here, but let’s think of one, and it’s a big one. It’s the idea that market prices, be it the stock market or the Betfair market or any other person-to-person betting market, already incorporate and fully reflect all available information. And so you can’t beat the market, unless you get lucky. Economists call this idea the ‘efficient market hypothesis’ and such a world as ‘informationally efficient.’

Now there’s a problem with this ‘looking glass’ world because in it nobody has an incentive to gather information. Why? Because information acquisition is costly and would add nothing to what can be obtained by simply looking at market prices. But if nobody acquires costly information, no trading will take place. And if nobody trades, what drives the market prices to incorporate and reflect all available information, i.e. what keeps the markets efficient? It’s called the ‘information paradox’, first formalized in a paper published by Sanford Grossman and Joseph Stiglitz in 1980, called ‘On the Impossibility of Informationally Efficient Markets.’ The same applies if information is costless to obtain but there are trading costs. In the real world, of course, there are both information and trading costs, and we have a paradox in spades. But still we are told that the market is informationally efficient. Welcome to the looking glass world of modern financial economics!

So is there a solution to the paradox? Consider the case of a betting market about the age of the looking glass queen. Let’s say nobody knows but lots of people are making guesses, some better informed than others, and betting looking glass money on the basis of these guesses. The queen just hasn’t been telling. Now she has told Alice, and the market will be settled later in the day when she tells the same to the whole world, one in which impossible things really are believed. Well, Alice has a little bit of time to place her bets before the rest of the world get to know the truth and if she’s clever she’ll bet enough to drive the market to the conclusion that the queen really is one hundred and one, five months and a day. And when the queen announces this is so, everyone will believe her. Alice will be rich, in a looking glass kind of way, and the queen will be not a day older. And the market will be efficient once again! And I think to myself, What a Wonderful World!

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