SumGames - Lotteries


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     Lotteries are a form of gambling which involves the drawing of lots for a prize. According to Wikipedia the word stems from the Dutch word loterij, which is derived from the noun lot meaning fate or destiny, but there are many historical references to lotteries and dividing assets by lot, for instance Israel being divided among the tribes by lot. According to Richard Thaler (in The Winner’s Curse), The Sistine chapel and its paintings were supported by lotteries, the Italian lottery has been running continuously since 1530, and lotteries are played in over 100 countries.

     Lotteries are typically very negative sum games, whereby a relatively low percentage of the amount wagered is returned to the bettors. Part of the amount bet goes to cover costs of administering the game, but a larger percentage usually goes to support a governmental cause. For instance in my state, just over half the amount bet in the California Lottery goes into the prize pool, and about a third goes to public education.

     Because of the long odds and low payout, many have bluntly described lotteries as a "tax on stupid people," but there are reasonable explanations for why people play lotteries. For example they give people (usually temporary) hope of having wealth, and many people see them as their only option for raising their standard of living (despite ridiculously low probabilities). A terrific summary of the topic (including how lotteries compare to investing) was published by Professor Meir Statman titled Lottery Players/Stock Traders in the Jan/Feb 2002 issue of the Financial Analysts Journal (or see Lottery Traders). You can also read Statman's article in the Wall Street Journal titled The Mistakes We Make—and Why We Make Them (8/24/2009) and Statman also has a new book coming in November (available for pre-order) titled What Investors Really Want: Know What Drives Investor Behavior and Make Smarter Financial Decisions.

     Some quotes related to the discussion from Statman's FAJ article include ...

As Bernstein (1996) has noted, gambling draws more people than baseball parks or movie theaters, and gambling is also evident in the investment arena—and not just in the behavior of day traders.

Christiansen (1987) estimated that lottery winners receive, on average, only 49 cents of every dollar paid by all ticket buyers. So, the expected return of a lottery ticket is negative, a 51 percent loss. Lottery buying is a negative-sum game. Stock trading also is a negative-sum game. But whereas the frame of lottery-ticket buying as a negative-sum game is transparent, the frame of stock trading as the same game is opaque. As Treynor (1995, originally 1971) noted, people confuse the stock-holding game with the stock-trading game. The stock-holding game is a positive-sum game; buyers of stocks can expect to receive, on average, more than they spend. The stock-trading game, however, is a negative-sum game. In the absence of trading costs, management fees, and expenses, stock traders can expect to match the returns of an index of all stocks. But after trading costs are considered, they can expect to lag that index. Indeed, Barber and Odean (2000a) found that not only do stock traders, on average, lag the market but that the magnitude of the lag increases with the amount of trading.

Lotteries are a puzzle because, according to standard financial theory, people are averse to risk; they are willing to take risks only on investments that offer sufficiently high expected returns. So, why do people buy lottery tickets that offer high risk with negative expected returns? Trading is a puzzle because, as Milgrom and Stokey (1982) noted, a trader’s offer to trade should raise suspicion in fellow traders that the would-be trader has superior, perhaps inside, information. Rational traders should refuse to trade under such conditions, and no trading will take place.

Black (1986) and Treynor offered two solutions to the trading puzzle. First, perhaps traders think that they are all above average; they may all think that they have superior information or skill. Second, perhaps traders simply like to trade. Friedman and Savage had offered a third solution in the context of lotteries. “Men will and do take great risks to distinguish themselves, even when they know what the risks are,” Perhaps people trade stocks and buy lottery tickets because these games offer the only way of rising from the working class to the middle or the upper class. Is it wise to extinguish dreams that sell for a dollar?





Gary Karz, CFA
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