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What Are The Odds?


What Are The Odds?

Recently, Mega Millions mania has gripped the U.S. With a jackpot that eclipsed US$1.5 billion, there was a veritable scramble to purchase tickets before the final draw. When a prize pool reaches such an absurdly high level, we typically observe a change in ticket purchasing behaviour. This phenomenon has some takeaways for investors in the stock market.

The Mega Millions is an American lottery game that is offered in 44 states. In a relatively new Mega Millions formula that was introduced, players pick five numbers from 1 to 70, and a Mega number of 1 to 25. This pegs the odds of winning the Mega Millions jackpot at 1 in 302,575,350.

In the Mega Millions game, the jackpot increases when there is no top-prize winner. This creates an interesting dynamic: as the size of the jackpot increases, the incentive to chip in more money to participate in the next draw increases, given the opportunity to win an even higher prize amount.

Mega Millions has been described by Gordon Medenica, the lead director of Mega Millions Group, a lottery consortium, as reaching a “cultural phenomenon” once it enters the $200 million to $400 million jackpot range. Medenica also said that when jackpots approach the half-billion-dollar mark the need for state lotteries to advertise essentially becomes superfluous. Why is this?

What is typically observed is that as the jackpot grows to a very large number, even infrequent players will join in, perhaps by impulsively buying a ticket at a convenience store to avoid the fear of missing out. This helps the jackpot swell to even higher levels, and so the cycle repeats. Word of mouth spreads news of the abnormally large prize pool, and people feel genuine excitement in participating and having a shot at winning an enormous fortune.

The below chart helps illustrate the above-mentioned dynamic: as the jackpot increases beyond a certain threshold, the growth rate becomes exponential until the jackpot is eventually won.


Source: LottoReport.com; via Business Insider

The graph below shows the relationship between the size of the jackpot and the number of tickets sold. As we can see, smaller jackpot amounts garner relatively fewer ticket sales. In contrast, when the jackpot balloons, we see the number of tickets sold skyrocket, as many jackpot chasers pile in.


Source: LottoReport.com; via Business Insider

There are times where we see similar behaviour in the stock market. When a stock does very well, a number of psychological biases combine to potentially influence our behaviour, and drive a continuation of the stock price momentum on the upside.

The first is the fear of missing out – that is the feeling of regret or anxiety that ensues after we see a stock price run up and see others making money from that investment. The second is recency bias – that is, the phenomenon of someone more easily remembering events that have happened recently; as John Kenneth Galbraith put it, financial markets are characterised by “extreme brevity of the financial memory.”

Essentially, these cognitive flaws can cause investors to overweight the significance of recent stock price increases, and forget that stocks typically do not follow an uninterrupted upward path. An uncoupling of a stock from what its fundamentals would dictate is likely when a stock price goes fundamental off the back of speculative buying. Perversely, the stock price momentum can drive further buying, creating a speculative mania and heightening the risk of a permanent loss of capital.

Unlike the Mega Millions lotto, where there will eventually be a winner (or a number of winners that share the spoils), a runaway stock that has been inflated by speculation is unlikely to have a sanguine ending.


George joined MGIM in September 2015 as a Research Analyst. Prior to joining MGIM, George was an investment analyst at Private Portfolio Managers where he covered global equities across various industries, using a value investing framework. George’s prior experiences include equities research and investment banking roles at both Citi and Greenhill & Co.

This post was contributed by a representative of Montgomery Investment Management Pty Limited (AFSL No. 354564). The principal purpose of this post is to provide factual information and not provide financial product advice. Additionally, the information provided is not intended to provide any recommendation or opinion about any financial product. Any commentary and statements of opinion however may contain general advice only that is prepared without taking into account your personal objectives, financial circumstances or needs. Because of this, before acting on any of the information provided, you should always consider its appropriateness in light of your personal objectives, financial circumstances and needs and should consider seeking independent advice from a financial advisor if necessary before making any decisions. This post specifically excludes personal advice.

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