Just don't kid yourself.

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Resist the Powerball Temptation

Noah Smith is a Bloomberg View columnist. He was an assistant professor of finance at Stony Brook University, and he blogs at Noahpinion.
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With the Powerball lottery jackpot at record levels, the nation’s attention is riveted on tonight’s drawing. Everyone is weighing in on whether it makes economic sense to play the lottery. In terms of pure expected value, playing the lottery is a bad bet -- in fact, it really has to be, since if the house weren’t guaranteed to win, the lottery wouldn’t be offered in the first place. So why do people seem so willing to throw away their money?

One answer is “the pleasure of fantasy.” When Greg Ip of the Wall Street Journal took a Twitter poll asking why people play Powerball, this was the most common answer. And it makes sense. When you have a lottery ticket in your hand that might be worth hundreds of millions of dollars, dazzling new possibilities open up -- a new house, fancy cars, a life of leisure and the end of financial insecurity for you, your family and your friends. Just imagining those possibilities might be fun, even if the rational part of your brain knows that they are incredibly remote. The lottery ticket might therefore be an accessory to fantasizing -- much like a video game or a good book.

Whatever the reason, it turns out that the desire to make lottery-like bets is fairly universal. In financial terms, assets that offer worse than average returns for a slightly increased chance of a huge payoff are said to have positive skewness. Quite a lot of research shows that people prefer to invest in this type of asset, even in their retirement accounts.

For example, Alok Kumar of the University of Miami has shown that individual investors like to buy stocks that have a positive skewness -- so-called lottery stocks. The finding confirms the results of an earlier study by Todd Mitton and Keith Vorkink of the Marriott School at Brigham Young University. Even in the laboratory, experimental subjects show a preference for assets with big but unlikely payoffs.

The next question we should ask is whether this desire is rational or not. After all, lottery stocks, like lotteries, perform poorly on average. An asset that had a higher chance of a huge win without doing worse most of the time would be a free lunch, and in financial markets there are few of those. Indeed, individual investors who go for lottery stocks do worse on average, just as we might expect.

If lottery stock preference is due to fantasy, like the kind Ip describes with real lotteries, then it’s a very expensive fantasy. Spending $2 on a Powerball ticket is one thing, but when people are spending substantial percentages of their retirement savings buying lottery stocks, they’re probably spending too much -- especially since even the most optimistic scenario for lottery stocks is a much smaller payoff than winning Powerball.

It’s here that we turn to behavioral finance and the prospect theory of decision-making, brainchild of the Nobel-winning economic psychologist Daniel Kahneman. Prospect theory has many elements, but one of these is called probability weighting. This describes people’s tendency to behave as if very small probabilities are bigger than they actually are.

For example, imagine that your doctor tells you that you have a 0.01 percent chance of dying in an operation. That’s a tiny chance -- one in 10,000. But your brain, unable to accurately conceive of such a tiny amount, inflates it, so that a 0.01 percent chance might sound about the same as a 0.5 percent chance -- big enough to deter some people from undergoing a potentially important operation. Thus, according to the theory, people drastically overweight the chance of rare events. Another theory, known as salience theory, says that people tend to do this even more when the outcome involved is either very good or very bad.

So people who buy Powerball tickets and invest in lottery stocks may be mentally inflating the odds of winning. They know that the chance is small, but they still think it’s a lot larger than it really is.

Researchers such as Kumar have found that the demographic groups most likely to invest in lottery stocks are lower-income people and minorities. These groups, with lower levels of education, might be more susceptible to the subtle cognitive distortion of probability weighting.  Those groups are also more likely to play the lottery itself.

Therefore, lotteries, and lottery stocks, might be more than harmless fantasy. They might also be taking advantage of the cognitive illusions and biases of less-educated, less-well-informed individuals, making money for the government at these vulnerable people’s expense. Those are also the very people who can least afford to lose money on long-shot bets. So lotteries -- and lottery stocks -- tend to function as a kind of tax on the poor.  

It might therefore be ethical to restrict lottery participation to those who are sufficiently educated to understand the loss they will probably take, and wealthy enough to afford it. This is what we do for risky investment like hedge funds. Alternatively, we could cap the amount of lottery tickets poor people are allowed to buy. Of course, this would generate much less revenue for governments that offer lotteries, so don’t bet on that happening.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.

To contact the author of this story:
Noah Smith at nsmith150@bloomberg.net

To contact the editor responsible for this story:
James Greiff at jgreiff@bloomberg.net