Thursday, November 26, 2009

Lottery tickets

Another comment on "The Black Swan". In the glossary on pages 308-309 Taleb defines:

Lottery-ticket fallacy: the naive analogy equating an investment in collecting positive Black Swans to the accumulation of lottery tickets. Lottery tickets are not scalable.

By scalable Taleb means having unlimited upside.

The analogy to lottery tickets is unwelcome to Taleb because he advocates a strategy of betting on long shots which you are hoping will pay off because of unexpected events ("Black Swans" in his terminology). This looks something like buying lottery tickets but buying lottery tickets is generally a stupid strategy. The reason is not because they don't have unlimited upside (the millionfold gains available in typical state lotteries are greater than are plausibly possible in most other venues) but because the tickets cost too much. The New York State lottery seems to return about 40% of the amount bet which I think is fairly typical. So if you could buy lottery tickets for 10 cents on the dollar they would be a fine investment.

Taleb believes markets don't properly price in the possibility of extreme events, Black Swans. This is plausible but there is a problem in trying to take advantage of such mispricing. Namely, as the example of lotteries shows, people like making long shot bets. So any particular long shot bet may be overpriced (as lottery tickets are). So you can't just blindly bet on long shots (lest you violate another of Taleb's precepts which is don't be the sucker) you have to locate good long shot bets. But Taleb doesn't offer much help in that regard.


  1. Hmm, I'm not so sure about this. If we're talking a "bar bet" where there's reason to believe that our ignorance is being actively taken advantage of, that's one thing.

    But if it's true that markets generally underassess extreme events, and one is considering betting on a random sample of them, the fact that some of this random sample might turn out to be bad bets if we spent enough time investigating them further doesn't necessarily mean that we should drop the deal or commence investigating the whole set.

    In practice it seems there is another useful dimension to probability which relates to knowledge level vs uncertainty in the probability, the cost of aquiring that knowledge, etc. I haven't run across a good treatment of it (and the above sloppy discussion certainly doesn't constitute one:-)

  2. Let me elaborate a little. Taleb contends people don't properly take into account rare extreme events. So for example the stock price of insurance company A may ignore the chance a category 5 hurricane will hit Miami next year causing A to go bankrupt. But shorting A's stock is not a pure play on the chance a hurricane will hit Miami as there are lots of other uncertainties affecting A's stock price. If the chance a hurricane will hit Miami is isolated in some sort of pure play instrument the price of that instrument may not underestimate the odds even though they are implicitly underestimated when combined with other uncertainties in the stock price of A. This makes betting on Black Swans more difficult than Taled indicates.

  3. I see. Thanks for the clarification.