by Chris Godfrey, Sessional Lecturer at the ICMA Centre where his many research interests include Behavioural Finance.
Last week, the world was seized with the spectacle of long lines of Americans queuing to buy tickets for the Powerball lottery, spurred on by the prospect of winning the largest jackpot in history.
The eventual advertised annuity value of the jackpot was an enormous $1.586 billion, driven up by a series of rollovers from previous draws in which no ticket won a jackpot, and by the frenetic buying of tickets. Prior to the previous draw on Saturday 9 January, California Lottery spokesman Mike Bond had reported ticket sales of $2.8 million per hour, against the usual average of $1 million a day, but the craze continued when this draw resulted in a 19th successive rollover: on the afternoon of Wednesday’s draw, the Massachusetts State Lottery reported that they were selling $37,615 worth of tickets every minute.
But how do we explain the long lines of those queuing up to buy tickets, sometime reaching spectacular lengths?
Behavioural finance may be able to help. One of the first questions this subject area wrestles with is why some people both buy insurance and also take part in lotteries, so that they were sometimes apparently risk-averse (paying to avoid financial risk) and sometimes actively risk-seeking (taking on gambles where, on average, they would consistently lose).
One of the insights of Kahneman and Tversky, who went on to win the Nobel Prize for Economics, was that people judge events not in relation to their actual probabilities, but by their perceptions of their probabilities, and that they tend to overweight extremely unlikely events while underestimating the likelihood of more common events. We see this in many other areas of life: news stories about the risks from vanishingly unlikely events, such as plane crashes, gain far more traction and cause much greater public anxiety than stories about much more common risks, such as road accidents. They also noticed that we find it increasingly difficult to assess changes in probabilities as they become increasingly remote: we may have a good intuitive feel of the difference between a probability of 1 in 5 and 1 in 10, but we find it much more difficult to assess the difference between a probability of 1 in a million and 1 in two million. When, in October 2015, the operators of the Powerball lottery changed the jackpot odds from 1 in 175,223,510 to 1 in 292,201,338 in order to increase the maximum payout, we’re simply not well equipped to assimilate that it means that the chances of a winning ticket had just gone down by 40%.
Even if people know that they will lose money on the Powerball lottery on average, once behavioural finance comes into play, the chance at the jackpot makes it feel like a good deal.
Since we tend to perceptively overweight the likelihood of highly improbable outcomes, we can show that behavioural biases will lead people to accept gambles where they will lose, on average, provided there is a small chance of a sizeable jackpot payoff; in statistical terms, behavioural investors will accept investments which are strongly positively skewed even if they have a negative expected return. This has been suggested as one reason why shares in companies which are very nearly bankrupt stay higher than we might expect, since a small number do indeed go on to make dramatic recoveries. This is compounded by skewed perceptions of how often people actually have won in the past, what Kahneman and Tversky call “availability”; the mental image of winning is made easier by the massive publicity given to lottery winners and lottery operators’ advertising efforts.
The psychological effect of the huge jackpot also, surely, had an effect: not only do lottery sales increase as rollovers pile up, but a rollover which sells more tickets for one draw will also sell more tickets for subsequent draws, so that the avalanche of sales for the Powerball lottery draw on the previous Saturday itself could be said to have contributed to the even larger wave of lottery mania on the Wednesday. Social networks, also, surely played their part: a pair of fascinating studies from Finland found that people were more likely to buy the shares and the cars that those near them had bought previously, and a study on the Dutch postcode lottery found that lottery players were more likely to have other lottery players as immediate neighbours than non-players.
Heart over head
Relevant, too is the way in which people tend to divide up spending and income into different budgetary compartments, so that people may be buying lottery tickets out of the imaginary budget they have allocated to Entertainment, whereas they wouldn’t want to out of the imaginary budget they’ve marked for Pensions; Behavioural Finance calls this “Mental Accounting.”
Beyond these calculations, however, we need to consider that the lottery jackpot itself forms a psychological object of desire, or “phantastic objects,” onto which wishful thinking is projected, and toward which those taking part are moved by emotion rather than by any kind of calculation. In case we think of only lottery punters being subject to these forces, this has been argued to underpin the exuberance of the dot com bubble and the erstwhile appeal of hedge funds. Doubtless, we Behavioural Finance researchers will be studying the data from last week’s lottery for some time to come.
If you found this story interesting, you can study Behavioural Finance as a Masters degree at the ICMA Centre, part of the triple-accredited Henley Business School. Find out more about the MSc Behavioural Finance here: icmacentre.ac.uk/courses/msc-behavioural-finance
 Amos Tversky and Daniel Kahneman, ‘Advances in Prospect Theory: Cumulative Representation of Uncertainty’, Journal of Risk & Uncertainty 5, no. 4 (October 1992): 297–323.
 Nicholas Barberis and Ming Huang, ‘Stocks as Lotteries: The Implications of Probability Weighting for Security Prices’, American Economic Review 98, no. 5 (1 December 2008): 2066–2100.
 Jennifer Conrad, Nishad Kapadia, and Yuhang Xing, ‘Death and Jackpot: Why Do Individual Investors Hold Overpriced Stocks?’, Journal of Financial Economics 113, no. 3 (September 2014): 455–75, doi:10.1016/j.jfineco.2014.04.001.
 Amos Tversky and Daniel Kahneman, ‘Judgment under Uncertainty: Heuristics and Biases’, Science 185, no. 4157 (1974): 1124–31.
 Ian Walker and Juliet Young, ‘An Economist’s Guide to Lottery Design’, The Economic Journal 111, no. 475 (2001): F700–722.
 Sophie Shive, ‘An Epidemic Model of Investor Behavior’, Journal of Financial & Quantitative Analysis 45, no. 1 (February 2010): 169–98.
 Mark Grinblatt, Matti Keloharju, and Seppo Ikäheimo, ‘Social Influence and Consumption: Evidence from the Automobile Purchases of Neighbors’, Review of Economics and Statistics 90, no. 4 (17 October 2008): 735–53, doi:10.1162/rest.90.4.735.
 Peter Kuhn et al., ‘The Effects of Lottery Prizes on Winners and Their Neighbors: Evidence from the Dutch Postcode Lottery’, The American Economic Review 101, no. 5 (2011): 2226–47.
 Richard Thaler, ‘Mental Accounting and Consumer Choice’, Marketing Science 4, no. 3 (1985): 199.
 David Tuckett and Richard Taffler, ‘Phantastic Objects and the Financial Market’s Sense of Reality: A Psychoanalytic Contribution to the Understanding of Stock Market instability1’, International Journal of Psychoanalysis 89, no. 2 (April 2008): 389–412.
 David Tuckett and Richard Taffler, ‘A Psychoanalytic Interpretation of Dot.com Stock Valuations’, SSRN Scholarly Paper (Rochester, NY: Social Science Research Network, 1 March 2005), http://papers.ssrn.com/abstract=676635.
 Arman Eshraghi and Richard Taffler, ‘Hedge Funds and Unconscious Fantasy’, Accounting, Auditing & Accountability Journal 25, no. 8 (19 October 2012): 1244–65, doi:10.1108/09513571211275461.
2 Comments Add yours
The Powerball jackpot is also a good example of the limits to arbitrage. There are *only* 292.2 million possible combinations in the lottery and each ticket costs $2. Thus you could have guaranteed winning the jackpot of $1.56 billion (as an annuity or $930 billion if taken as a lump sum – plus winnings from smaller prizes) simply by buying a ticket for every set of numbers at a cost of only $584.4 million – netting a risk-free profit of nearly $1 billion. Of course, if there were multiple winners sharing the jackpot (in fact, there were three), then you would lose money on the trade (plus the effect of taxes etc).
There was also a more practical obstacle, however – namely that there is no way to automate the process of buying lottery tickets. Each pay slip has space for 5 sets of numbers, so you would need to fill in 58.44 million. Each of these has to be paid for and returned individually at a participating store. Allowing 3 seconds for each transaction, it would have taken 2.92 million minutes/48,700 hours/2,029 days/5.6 years for one person to buy enough tickets – or you would have had to employ 507 people working full-time for the four days between lottery draws (although, even at a generous minimum wage of $15 per hour, this would only come to $730,500).
Even if trades look profitable in theory, they cannot always been applied in the real world.
(for the background to the calculations, see http://blogs.wsj.com/economics/2016/01/12/how-to-guarantee-yourself-the-jackpot-in-the-biggest-lottery-ever-in-theory-anyway/)
Strangely enough, there is some evidence that this has been attempted before: an Australian syndicate attempted to buy every ticket in a 1992 Virginia lottery. As you predict, they came up against physical limitations and failied to purchase 2 million of the total 7 million combinations, and it’s unclear whether they actually succeeded in hitting the jackpot.
I’m more intrigued as to how they coordinated the number-picking: this being 1992, how did they ensure that their decentralised ticket buying operation bought every combination of numbers exactly once?