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Gambling on the Martingale Strategy

Suppose for a minute that you just wagered 25 cents on the outcome of a coin flip with a friend. The coin flip happens, you call "heads" while it's in the air, but after it falls, it comes up "tails". You've lost.

Your friend offers you the chance to go again. You take it, but you double the size of your bet to 50 cents. The coin is flipped and you call "tails", but it comes up "heads" and you lose again. Now, you're down 75 cents. Your friend offers you another chance to play.

Once again, you take it. But once again, you double the size of your bet, raising it to one dollar (or 100 cents, if you prefer). This time, the outcome of the coin toss matches your call, and you win. You've gone from 75 cents in hole to a net gain of 25 cents compared to when you started playing.

You may not realize it, but you've been using the martingale system (or strategy) in choosing the size of your bets. The strategy was first put forward by French mathematician Paul Lévy, who realized that one winning bet was all that was needed to turn around and fully reverse the outcome of a series of losing bets. Of course, the catch is that you have to have sufficient resources to weather the losses while you're racking up losing bets and realistic odds of eventually winning your wager to make it work for you, but if you want to learn more about the mathematical insight behind it, check out the following 19 minute Numberphile video featuring Tom Crawford.

If you're ready to head to the casino after seeing the video, you can rest assured you will not see any games where you have a 50% chance of winning or losing. There are some games that come close to those odds, but the potential rewards will be less.

With some modifications, you could apply the system to investing, but you'll find that approach has many of the same limitations:

Drawbacks of the Martingale Strategy

  • The amount spent on trading can reach huge proportions after just a few transactions.
  • If the trader runs out of funds and exits the trade while using the strategy, the losses faced can be disastrous.
  • There is a chance that the stocks stop trading at some point in time.
  • The risk-to-reward ratio of the Martingale Strategy is not reasonable. While using the strategy, higher amounts are spent with every loss until a win, and the final profit is only equal to the initial bet size.
  • The strategy ignores transaction costs associated with every trade.
  • There are limits placed by exchanges on trade size. Therefore, a trader does not receive an infinite number of chances to double a bet.

Don't forget that time is one of the transaction costs you pay. So are opportunity costs, because you may have other, better things to do with your stake that you are passing up by trying to come out just slightly ahead in continuing to play the same game you started losing.

Environmental Arguments Against the Penny

2021 Lincoln Penny Observse and Reverse - Source: U.S. Mint

As of 2019, roughly one third of polled Americans favor abolishing the penny.

That's still a minority, since over half of Americans responding to that poll favored keeping the penny circulating in the U.S. economy. But with inflation rising and the penny falling in value, the economics for keeping the penny in use are changing. From that perspective alone, it might soon be worth revisiting whether the U.S. Mint should continue stamping out the millions of copper-plated zinc discs it does each year.

That would follow the example of Canada. We learned a lot of economic arguments in favor of abolishing the penny from that country's "Godfather of the Ban-the-Penny Movement".

But we hadn't encountered an environmental argument against the lowest value U.S. coin in circulation until the American Council on Science and Health's Josh Bloom did some back-of-the-envelope math to quantify some of that impact.

Here's a portion of that discussion:

Pennies are not only a nuisance (stores hate them), but they are also an environmentally harmful nuisance. Here are a few facts that support this.

  • The melt value of a zinc penny is one-half of a cent.
  • Even so, according to the US Mint, it costs about 2.4 cents to make one penny.
  • In 2013 alone, this cost taxpayers $105 million.
  • Since 1982, 327 billion pennies have been minted.
  • A zinc penny weighs 2.5 g.
  • Doing the math, 327 billion pennies weigh 1.8 billion pounds
  • Tractor-trailer trucks can transport 80,000 pounds.
  • Given these figures, it required 22,500 full trucks to transport all the pennies that were minted since 1982.
  • A full tractor-trailer truck gets about 5 mpg.
  • Assuming that your average penny must travel 1,000 miles from the mint to wherever it is going (pure guess), it has taken 4.5 million gallons of fuel just to transport all the pennies that have been minted since 1982.
  • One gallon of diesel fuel produces 23.8 pounds of carbon dioxide when burned.
  • So, by simply hauling around all the stupid useless pennies since 1982, 107 million pounds of carbon dioxide has been emitted, plus who knows how much diesel pollution.
  • A whole bunch of zinc is being mined for no good reason. The mining itself causes more pollution.
  • About two-thirds of pennies don't even circulate. They are either thrown out or sitting around in jars.
  • Other countries have dropped the penny and started rounding off to the nearest five cents. It worked out just fine.
  • Some of this math may be correct.

And, these (very) rough calculations do not include the energy needed to mine the zinc ore, transport it to a smelter, purify the ore, transport the purified zinc to the mint, and then make it into pennies.

And that doesn't consider that most the world's zinc, including that used to make U.S. pennies since 1982, is mined in China before being shipped overseas, which also adds to the coin's carbon footprint.

We think the changing economics of pennies will have more impact on whether it makes sense to stop minting them than the environmental case. Exit question: how many people have already begun hoarding the copper pennies minted in 1982 and earlier the way people harvested silver coins out of general circulation after they stopped being minted in 1964?

References

Bloom, Josh. If Cash Is No Longer King What Does That Make Stupid Pennies? American Council on Science and Health. [Online Article]. 16 July 2021.

U.S. Mint. H.I.P. Pocket Change Kids Site: Penny. [Online article]. 2021.

Previously on Political Calculations

2010’s Worst Paying College Degrees Ten Years Later

In 2010, U.S. compensation and data software firm Payscale identified the 10 lowest paying college degrees for those starting their first jobs in their fields after graduation. We wondered how on the mark that list was, so we tapped Payscale's 2020 data for starting wages by college major to see if things got relatively better or worse for today's graduates in those fields.

The results are shown in the following chart. The original 2010 data is shown in blue and the newer 2020 data is shown in green. In between, in orange, we've adjusted the 2010 starting salary data for inflation to be in terms of 2020 U.S. dollars to make those older salaries directly comparable to the actual starting pay for graduates in the listed fields in 2020.

Starting Pay for 2010's Worst Paying College Degrees

After adjusting for inflation, we see only two degrees where the actual starting pay for graduates in 2020 is ahead of 2010's inflation-adjusted level: Athletic Training and Elementary Education. Horticulture comes close to breaking even, so to speak, and the remaining fields would appear to have become even less rewarding.

Of these less rewarding degrees, Culinary Arts presents the biggest gap between 2010's inflation adjusted pay and 2020's actual starting pay, followed by Special Eduation and Paralegal Studies.

In 2010, Payscale also indicated what an individual holding these degrees could expect to make at a mid-career point, some 10 or more years after graduation. Since it's 10 years later, we thought it would be especially interesting to see how 2020's actual mid-career pay compares with 2010's inflation-adjusted mid-career pay. Our results are shown in the next chart:

Mid-Career Pay for 2010's Worst Paying College Degrees

Once again, the fields of Culinary Arts and Athletic Training come out the furthest ahead after accounting for inflation, but Theology graduates also gained more income than would have been expected based on 2010's inflation-adjusted pay.

Most the other fields saw their 2010 graduates making something within a several percent of their 2010 peers' inflation adjusted pay, with one big exception, which looks like it is in error.

According to Payscale's 2020 survey data, individuals holding degrees in Special Education with 10 or more years of experience saw the average mid-career pay in their field collapse. At $54,500, it is just $700 higher than 2010's non-inflation adjusted pay, some $9,800 below what adjusting the mid-career income for 2010 would predict.

The Bureau of Labor Statistics indicates the median pay for Special Education teachers was $61,420 per year in 2019, which is more in line with Payscale's 2010 inflation-adjusted mid-career income figure.

We sampled other income data for other fields, which appears to be in line with Payscale's surveyed reults, so the 2020 mid-career pay figure for Special Education degree holders appears to be an outlier.

Overall, it appears most of 2010's lowest paying degrees for college graduates turned out to be as bad for pay 10 years later as 2010's data suggested they would be.

Absence of Discounts Confirms Tomato Soup Inflation

Campbell's Condensed Tomato Soup has long been our favorite way to visualize the effects of inflation over time in the U.S. economy. That's because the product is defined by its iconic packaging, a No. 1 size steel can that contains the same amount of condensed tomato soup as it did when the product was first introduced to the public in the late 1800s.

This relative stability in packaging however means Campbell Soup (NYSE: CPB) cannot hide the price increases is passes along to its customers through shrinkflation, which many other food producers exploit by keeping the same prices on their goods, but diminishing the amount of goods within them. When inflation drives up the costs of what they have to pay to make and transport their goods to consumers, Campbell's must increase their prices to compensate.

That's what's happening now. Campbell Soup has confirmed it is increasing prices across its product lines:

Get ready to add a few dollars to your monthly canned soup budget, because thanks to rising supply chain costs, Campbell’s is planning to raise its prices. On Wednesday, Campbell’s announced its last-quarter earnings were weaker than the company had expected. Compared to the same time period last year, profits had fallen 5% to $160 million.

“Our results were impacted by a rising inflationary environment, short-term increases in supply chain costs, and some executional pressures,” said CEO Mark Clouse....

Clouse assured investors that the company is taking steps to recover from the slump, including a new pricing strategy, which will roll out over the current quarter (which ends in early August). Across the company portfolio Campbell’s net sales decreased 14% over the last quarter, so expect this pricing strategy to affect more than just canned soup—Swanson broth, Pop Secret popcorn, Cape Cod chips, Pace salsa, Snyder’s of Hanover pretzels, V8 juice, Prego tomato sauce, SpaghettiOs, and Pepperidge Farm are all owned by Campbell’s.

Whether or not you, personally, will be paying more for these products is yet to be seen. Though retailers will be paying more for Campbell’s products, it’s ultimately up to them whether or not to absorb the higher costs, or pass them onto consumers.

The markup between wholesale and retail prices give retailers some flexibility in how they might choose to pass their increased costs along to consumers. And that is where we can show how that works, because we've tracked the prices consumers have paid for Campbell's Condensed Tomato Soup since the product rolled out onto grocery store shelves in the late 1800s.

Unit Price per Can of Campbell's Condensed Tomato Soup at Discounted Sale Pricing, January 1898 - July 2021

For products like Campbell's Condensed Tomato Soup, retailers pass along their cost increases to consumers by offering fewer and smaller discounts. This marketing strategy lets them hold their shelf prices relatively stable, but only until inflationary pressures rise enough to force retailers to increase their shelf price. Once they do, their higher markups allow them to regain the ability to offer larger discounts.

You can see that dynamic playing out in this chart as prices have periodically stepped upward in 5 to 10 cent intervals since the U.S. government ended its failed attempt to stop inflation through price controls in 1974. As prices have risen, deep discounting becomes much less common and eventually the low prices consumers were once able to pay becomes a thing of the past.

In 2021, the price of Campbell's Condensed Tomato Soup is converging near a shelf price of $1.00 per 10.75 ounce can. In July 2021, the trailing twelve month average discounted sale price is $0.95 per can, which has fallen from a seasonal peak of $0.99 per can in December 2020 thanks largely to some unique pandemic-driven supply and demand dynamics. We think we'll start seeing higher retail shelf prices in the very near future to confirm the permanence of 2021's inflation.

The S&P 500 Clocks High Before Retreating in Week 2 of July 2021

The S&P 500 (Index: SPX) started the trading week strong, reaching a record high close of 4,384.63 on Monday, 12 July 2021 before losing steam and retreating through much of the rest of the week. The index closed the week at 4,327.16.

That's generally consistent with the dividend futures-based model's projections for investors focusing their attention on 2022-Q1 in setting current day stock prices.

Alternative Futures - S&P 500 - 2021Q3 - Standard Model (m=-2.5 from 16 June 2021) - Snapshot on 16 Jul 2021

While the model looks forward to a sideways to slowing rising run over the next several weeks if investors keep their focus on 2022-Q1, it also indicates the risk of a 5% decline should investors have reason to shift their attention back to the current quarter of 2021-Q3.

Whether that happens will depend much on what happens with the outlook for inflation in the U.S. economy, which continues to play an outsized role in the news influencing investors' expectations.

Monday, 12 July 2021
Tuesday, 13 July 2021
Wednesday, 14 July 2021
Thursday, 15 July 2021
Friday, 16 July 2021

Looking for additional markets and economics news? Check out Abnormal Returns, in which Tadas Viskanta provides a daily roundup of links to interesting news and analysis.