Sunday, September 15, 2013

Trading the Lottery

My friends and kin divide swiftly into two distant camps when I mention the lottery.

Those in one camp say, with the great force, that the lottery is a fool's game because of the odds against winning are so great.

The others say, with a wistful smile, that they set aside a dollar or two each Friday to buy a ticket, and maybe $5 when the jackpot is up.

Those in the first camp no doubt put all of their retirement savings in a money-market fund paying 0.4% interest each year because they don't like risk.

Those in the second most likely buy a stock on impulse because they heard from a friend that Jim Cramer mentioned it on his show Mad Money.

Regular readers of Private Trader know that my style of trading lies in neither camp. I want numbers before making a trade. I want to make a rational decision. I want to know the reward/risk ratio.

Happily, a lottery ticket can be treated as something to trade, just as much as a share of AAPL.

A lottery ticket, in a way, resembles a long stock option spread, bought for a premium. It has a known maximum gain and maximum loss, and it has an expiration date, when it becomes worthless.

The lottery ticket does options one better in that it has known odds of success. The best options can do in that regard is to provide implied volatility that can be applied the stock price in order to calculate a range that will contain 68.2% of transactions over a designated time period.

In the case of a lottery ticket, the jackpot is the maximum gain, and the cost of a ticket is the maximum loss. The reward risk ratio is the jackpot vs. the ticket price.

In the case of Powerball, for example, the present jackpot is $400 million. The cost of a ticket is $2. So the reward/risk ratio is 400,000,000:2, which reduces to 200,000,000:1.

Another way of thinking of it is to ask: How much of a reward do I get per chance, or per "odd" in the odds calculation?

That answer comes by dividing the reward by the denominator of the odds. In the case of Powerball this week, the jackpot is $400,000,000, the cost of a ticket is $2, and so the reward is $200,000,000. The odds of winning Powerball are 175,223,510:1.

The cost of a chance, then, is $200,000,000 / 175,223,510, or $1.14.

On the spreadsheet I use to track such things, I call that figure the "odds-adjusted index", or just the "index" for short, and write it without the dollar sign.

An odds-adjusted index of 1.14 is actually quite good for the big multi-state games. That's because no one has won Powerball for awhile and so the jackpot is high. Compare that to Mega Millions, where the index is only 0.74.

Note that the index changes with each drawing, rising if no one wins and that jackpot is increased, and falling if there are winners and the jackpot is reset to its base.

The index is how I determine whether a lottery ticket is worth buying. An index greater than 1.00, as in Powerball this week, means that the reward is greater than my risk when adjusted for the odds. An index of less than 1.00 means that my reward is substandard by that same criteria.

I've found that the single-state game in my home state, Oregon, is in fact the besst play.

Oregon Megabucks has a jackpot that resets to $1 million when someone wins, and then gradually climbs with each drawing. Today it stands at $7.8 million, with odds of 1:6,135,756.

The cost of a chance is 50 cents, so the odds-adjusted index comes in at 2.54, which is higher than I've ever seen the multi-state games reach.

Some would say that $7.8 million is small potatoes compared to the $400 million Powerball jackpot. And so it is. But honest, $7.8 million would change my life so dramatically that the additional $392.2 million is fairly redundant.

I also did similar calculations for raffles that the Oregon Lottery occasionally offers. The 1st prize is $1 million with odds of 1:250,000 and a $10 ticket price. The odds-adjusted index is only 0.40. The 2nd prize index is even worse, at 0.08.

One way to think of a lottery or a raffle is as a giant roulette wheel. The more numbers you cover for each spin of the wheel, the greater your chances of winning.

In the case of Powerball, the roulette wheel has 175,223,510 slots.

In trading lotteries, it makes far more sense to buy a month's worth of tickets for one drawing, rather than dribbling it out over four Fridays, as in the practice of the second group above. An even better strategy would be for the player to buy 52 tickets on his or her birthday.

Of course, that strategy makes it harder to catch the maximum index, when the jackpot is at its highest. The great unknown in any lottery is whether someone will win any given drawing, reducing the jackpot to its base

My compromise strategy is to buy lottery tickets when the odds-adjusted index is above a certain level. I play the Oregon Megabucks, because it has the highest index of the games available to me, and I play it when the index is 3.00 or higher.

When the index has reached my play point, I buy 40 chances a week, picking at random which of the three weekly drawings to play. So it costs me $20 a week to play, and that gives me 12 weeks of plays with an annual lottery budget of $240.

My $240 budget is clearly arbitrary, as is the $20 per week and the 3.00 minimum index. Others will make different choices. And I might, as well. An index greater than 1.00 is a rarity for the big-money multi-state games, so I might change my rules and start playing Powerball or Mega Millions when their index rises to such heights.

Of course, most people don't live in Oregon. Other states have other lotteries with different jackpots, odds and ticket prices, and therefore different indexes. Here's an example of my spreadsheet that you can copy and use for your own calculations.

That's my take on the lottery. I find it to be a useful addition to my trading vehicles that costs little and gives exposure to huge returns.

Note: In contrasting lottery tickets with stock options, I referred to the number 68.2%. This comes from statistics and refers to the one standard deviation boundaries, which are expected to contain 68.2% of whatever is being studied. Putting it another way, given an item (a trade or whatever), there is a 68.2% chance that it will appear within those boundaries.

Tim Bovee, Private Trader tracks the analysis and trades of a private trader for his own accounts. Nothing in this blog constitutes a recommendation to buy or sell stocks, options or any other financial instrument. The only purpose of this blog is to provide education and entertainment.
No trader is ever 100 percent successful in his or her trades. Trading in the stock and option markets, and buying lottery tickets, is risky and uncertain. Each trader must make trading decision decisions for his or her own account, and take responsibility for the consequences.

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