Wednesday, February 2, 2011

Generating truly random numbers... always harder than you think. Always, always, always.

This comes under the category of "lessons that people generally know are true, but frequently have to re-learn the hard way". Such is the case of Mohan Srivastava, who successfully created algorithms to predict winning scratch lottery tickets.

One thing that's not discussed in the article, however, is why this isn't necessarily arbitraged. Mr Srivastava says that he figured out that his hourly wage from doing it just wasn't high enough. This confirms in my mind that he's a smart dude.

But let me suggest another reason, which relates directly to mispricing in financial markets.

It would be damn hard to convince a newsagent to let you come in day after day, look at 50 lottery tickets, buy only 7 of them, cash in the winnings and repeat. In fact even just doing it once marks you as highly suspicious. They might let you do it one day, suspecting that you're just a kook. But once they see you doing it multiple times, they'll do one of a couple of obvious things:

1. Stop selling to you.
2. Wait until you pick the tickets you want, then keep those tickets for themselves.
3. Call the lottery ticket office and tell them that something funny is going on.

Why would they do this? It's obvious - if one customer is taking all the winning lottery tickets, then selling only losing tickets to the other customers will cause fewer of them to come back to your store, hence less cash for you.

It's not enough to find mispriced assets. You've got to find mispriced assets that people will keep selling to you at the wrong price, even as you increase your volume of purchases.

Lottery tickets, sadly, are not such a case.

The story also tells you something else very good about mispricing. Arbitrage is likely to exist in markets where there are the fewest people looking for arbitrage. That's Grossman and Stiglitz (1980). So what's an example of a market that's populated only by imbeciles?  The lottery! The classic stupidity tax.

As a result, if you're the smartest guy playing the lottery by an order of 2 standard deviations (as Mr Srivastava probably was), there might actually be mispricing. In S&P 500 stocks where you're trading against Goldman? Yeah, not so much.

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