Political Calculations
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30 April 2019

Well over two years after Philadelphia's controversial tax on sweetened beverages distributed for retail sale within the city's limits first went into effect in January 2017, the Philadelphia Inquirer has conducted what it describes as the "first independent polling done about the tax". Here's a short summary of the results of its survey of registered voters in Philadelphia:

  • 62% describe the soda tax as either a failure or as a complete failure.
  • 55% want to see the tax repealed.

It's not surprising that roughly five out of eight Philadelphians view the city's soda tax as a failure. The Philadelphia Beverage Tax has chronically fallen short of the desired level of revenue that city officials were counting upon to fund pre-Kindergarten and community school programs and also to fund repairs and improvements to city-owned parks, recreation centers, and libraries. The following chart shows how far short the city's annual tax collections from its soda tax have fallen below its original revenue projections.

Philadelphia Soda Tax, Desired versus Actual Revenues in 2017 and 2018

In 2017, Wharton Business School Professor of Finance and Public Policy Robert Inman declared the Philadelphia Beverage Tax could be considered a success if it collected as little as 85% to 90% of the city's original annual revenue target of $92.4 million. It has clearly failed to pass that very low threshold for success during the first two years it has been in effect.

Beyond its fiscal failure, tax opponents have argued that the soda tax creates some really perverse incentives for city residents who support these programs, who must either choose to purchase and consume beverages perceived to be unhealthy or accept the programs they want will be starved of funds. We believe the twisted and hypocritical logic that tax supporters have used to justify the soda tax contributes to the widespread public perception of the tax's failure.

The Inquirer poll reveals that Philadelphians really do want the things that the city's 1.5 cent-per-ounce tax on naturally and artificially-sweetened beverages were meant to fund, with many indicating a willingness to dedicate other tax revenues to pay for them. The city's mayor, Jim Kenney, and several city council officials oppose the repeal of the Philadelphia Beverage Tax.

The tax will be an issue in the upcoming primary election for city mayor and city council positions in the heavily Democratic party-controlled city on 21 May 2019.

Previously on Political Calculations

We've been covering the story of Philadelphia's flawed soda tax on roughly a monthly basis from almost the very beginning, where our coverage began as something of a natural extension from one of the stories we featured as part of our Examples of Junk Science Series. The linked list below will take you through all our in-near-real-time analysis of the impact of the tax, which at this writing, has still to reach its end. For a general history of Philadelphia's soda tax, check out the Philadelphia Inquirer's timeline.

There are still aspects of the story we plan to develop, including the impact of the tax on city retailers and beverage distributors, several of whom have opened their books to the media during the past two years. We'll also get back to where our coverage started to review what two years of scientific study has determined about the effectiveness of soda taxes in reducing obesity rates, which are the main benefit claimed by soda tax supporters for imposing this particular kind of "sin" tax.

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29 April 2019

The S&P 500 (Index: SPX) was buoyed up to reach new record heights during the fourth week of April 2019, closing the week at a new all-time record high value of 2,939.88.

Overall, we find the level of the S&P 500 is consistent with investors focusing on the distant future quarter of 2020-Q1, which in our dividend futures-based model of how stock prices work, covers the period from 21 December 2018 through 20 March 2020, coinciding with the dividend futures contracts for that quarter.

Alternative Futures - S&P 500 - 2019Q2 - Standard Model with Annotated Redzone Forecast - Snapshot on 26 Apr 2019

The expectations for dividends to be paid out during this time also got a boost during the past week, rising from $14.55 per share to $14.65 per share according to the CME Group's estimates for S&P 500 quarterly dividend futures.

On the whole, aside from the better than expected economic and earnings news that boosted stock prices during the week, it was relatively quiet with the Fed's minions muzzled by a news blackout period ahead of its next two-day Federal Open Market Committee meeting on 30 April-1 May 2019, the news from which may affect investor expectations for potential future interest rate cuts.

Speaking of which, the CME Group's Fedwatch Tool indicates that investors are currently betting on a quarter point cut in the Federal Funds Rate taking place during 2018-Q4.

We'll find out later this week. In the meantime, here are the notable market-moving headlines we flagged during the fourth week of April 2019.

Monday, 22 April 2019
Tuesday, 23 April 2019
Wednesday, 24 April 2019
Thursday, 25 April 2019
Friday, 26 April 2019

Barry Ritholtz found six positives and six negatives for U.S. markets and the economy in his weekly bigger picture overview of the week's events.

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26 April 2019

It's Friday and, if we're being honest, it has been a really long week. So much so that probably the last thing you want to have to even think about right now is making dinner. Wouldn't it be a lot easier if you just ordered in some pizza instead?

Well, that's one problem solved, but now you have another. How much pizza should you order?

If you're like a lot of people, you also don't want to spend a lot of money on dinner, so you'll decide how much pizza to get by choosing from the options you have available among the latest coupons from your preferred pizza provider. Kind of like the following example from Pizza Hut (warning: this particular coupon has expired!)

Pizza Hut coupons, 2016 - Source: PrintableCoupons Blog - http://www.printablecouponsblog.com/get-your-pizza-hut-coupon/

After considering all these potential options, let's say for the sake of argument that you've narrowed in on the options at the top of the middle two columns, which you reckon will satisfy your pizza consumption plans: 2 medium one-topping pizzas for $21.49 or 1 large one-topping pizza for $13.99. Being the kind of person who wants to maximize the value you get for pizza dollar, which coupon should you use when placing your order?

That answer hinges on how much pizza there is in a medium versus a large pizza. Keeping with Pizza Hut's menu options, a medium pizza is 12-inches in diameter, while a large is 14-inches in diameter.

After becoming mentally exhausted after such a long week of work, you might conclude that with 2 medium pizzas, you will effectively have 24-inches of pizza diameter, which is 10 more than the 14-inch diameter large pizza, For just $7.50 more, the 2 medium pizza coupon might seem like its a better deal.

That would be true, if and only if that really gave you the equivalent of a 24-inch diameter pizza. In reality, you have two 12-inch diameter pizzas, which are much, much smaller than that. If you want to get the most pizza you can for the least dollars, you're going to need to do some math in choosing between these coupons.

We know it's Friday, and that math is the last thing you want to do right now, so we built a tool to do that bit of personal finance math for you! Just enter the coupon options and pizza size information in the following tool, and we'll take care of the rest. If you're accessing this article on a site that republishes our RSS news feed, please click through to our site to access a working version of the tool.

Pizza Coupon Input Data
Input Data Coupon Option #1 Coupon Option #2
Number of Pizzas
Pizza Size (Diameter)
Price With Coupon

Which Pizza Coupon Is the Better Deal?
Calculated Results Unit Cost
Pizza Coupon Option #1
Pizza Coupon Option #2
The Bottom Line

Using the default values, Coupon Option #2, the single large, one-topping pizza, will give you the best value for your pizza dollar. Meanwhile, if you play with the numbers and plug in the prices that apply for 3-topping pizzas, you'll find the outcome changes.

And because we don't want to think about it any more, we'll leave you with the following video, featuring consumers impressed by a large, 14-inch diameter pizza:

It's funny what you find at the intersection of hunger, geometry, and pizza coupons! Speaking of which, there has been a rather noisy debate about the math involved in settling a different aspect of this question elsewhere on the Interwebs, which directly inspired us to create this tool to tackle the problem from a personal finance angle!

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25 April 2019

If you saw the news headlines earlier this week, you already know that new home sales in the U.S. showed signs of a rebound in March 2019. If that preliminary indication holds through the next several months of revisions, that rebound is coming at a good time because the new home market in the U.S. has been on the verge of a correction.

That assessment is based on the trailing twelve month average of the market capitalization of new home sales in the U.S., which initially appears to have bottomed in February/March 2019 after having peaked in March 2018. Since then, the estimated market cap of new homes in the U.S. has fallen by roughly 9%.

Trailing Twelve Month Average New Home Sales Market Capitalization, Not Adjusted for Inflation and Adjusted for Inflation, January 1976 - March 2019

After adjusting for inflation to put the estimate market cap figures into terms of constant March 2019 U.S. dollars, the results of the math get slightly worse, with the magnitude of the decline crossing the correction threshold with a little over a 10% decline.

The results of those year-over-year comparisons are a bit easier to see in the next chart, where we've calculated the year-over-year growth rate of the U.S. new home market cap.

Year Over Year Growth Rate of Nominal and Inflation-Adjusted Trailing Twelve Month Average of New Homes Market Capitalization, January 2000 - March 2019

The bad news is the growth rate of the new home market cap is the most negative it has been since the first U.S. housing bubble began to deflate. The good news is that recent descent slowed in March 2019. We're in for several months of data updates and revisions before we can definitively determine if the new home market has really hit bottom.


U.S. Census Bureau. New Residential Sales Historical Data. Houses Sold. [Excel Spreadsheet]. Accessed 24 April 2019. 

U.S. Census Bureau. New Residential Sales Historical Data. Median and Average Sale Price of Houses Sold. [Excel Spreadsheet]. Accessed 24 April 2019. 

U.S. Department of Labor Bureau of Labor Statistics. Consumer Price Index, All Urban Consumers - (CPI-U), U.S. City Average, All Items, 1982-84=100 [PDF Document]. Accessed 10 April 2019. 


24 April 2019

Back in 2010, we introduced a new way to visualize how out of balance the U.S. government's spending had become with respect to the typical income earned by U.S. households.

To do that, we plotted the U.S. government's spending per household against median household income, but that wasn't all. We also estimated how high federal spending could be with respect to the household income measure to keep the government's budget in balance, which we featured as the "Zero Deficit Line".

Want to see how that looks with eight additional years of data? Here you go!...

U.S. Government Spending Per Household Versus Median Household Income, 1967-2017

The chart now covers a five decade long period from 1967 through 2017, where we're not yet able to present the data for 2018 because the U.S. Census Bureau won't publish its estimate of household income and median household income for that year until September (to be fair, they just collected that data last month!)

Although not as bad as in 2009, the U.S. government's spending is still pretty far out of whack, holding well above the level the Zero Deficit Line indicates would be affordable for typical American households.

But we notice that the ZDL isn't necessarily capturing the full story, which we can see when we plot the same U.S. government spending per household and the government's tax revenues per household against Median Household Income.

U.S. Government Spending and Tax Collections Per Household Versus Median Household Income, 1967-2017

The difference between the Zero Deficit Line and U.S. government spending per household isn't capturing the full extent to which that spending exceeds the levels that would be affordable for American households because tax revenues have not kept pace with the ZDL since 2015. That's mainly because of what the New York Times described as the "most important least-noticed economic event of the decade", which coincidentally had also escaped the contemporary notice of the New York Times, which was very heavily invested in boosting their preferred successor to President Obama at the time, for whom that real economic distress would be a defeating distraction.

Two years later, they finally acknowledged it and called it an "invisible recession", or a mini-recession, but it really wasn't all that invisible at the time it was happening if you knew where to look for it. It was very good news when it was finally clear it was ending.

The bad news however is that the lagging effect of that event on tax revenues means that the gap between excessive spending and the Zero Deficit Line has grown wider than it indicates. When the data for U.S. households in 2018 becomes available later this year, we'll revisit the ZDL again.


U.S. Census Bureau. Current Population Survey. Annual Social and Economic Supplement. Historical Income Tables. Table H-5. Race and Hispanic Origin of Householder -- Households by Median and Mean Income. [Excel Spreadsheet]. Issued 28 August 2018. Accessed 28 August 2018.

White House Office of Management and Budget. Historical Tables, Budget of the U.S. Government, Fiscal Year 2020. Table 1.1 - Summary of Receipts, Outlays, and Surpluses or Deficits (-): 1789-2024. [PDF Document]. Issued 11 March 2019. Accessed 11 March 2019.

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23 April 2019

Published last week, data for February 2019 saw the combined direct trade loss between the U.S. and China expand to $5.2 billion, as the trailing twelve month average of the value of trade between the two nations has shrunk as a result of the tariff war that began on 22 March 2018.

Combined Value of U.S. Exports to China and Imports from China, January 2008 - February 2019

Since the growth of trade between the U.S. and China over time tends to grow at a steady pace outside periods of economic recessions (such as in 2008-2009) or slowdowns (such as 2015-2016), that gap is what we measure when we compare the counterfactual of the trade growth that would likely have occurred between the two nations if the linear trend that existed before March 2018 continued without interruption with how the combined value of both nations' exports and imports to each other has evolved since the U.S.-China trade war began. For February 2019, that means the combined value of goods directly traded between the U.S. and China is nearly 9% less than would be the case if the two nations had avoided entering into their tariff war.

For the 12 month period from March 2018 through February 2019, that expanding gap represents an estimated cumulative reduction of $20.6 billion worth of direct annual trade between the U.S. and China.

The year-over-year growth rate of U.S. imports from China has dropped into negative territory in recent months, which in the absence of the trade war, would indicate a deterioration in the relative health of the U.S. economy. A similar pattern for the year-over-year growth rate of U.S. exports to China has existed since late 2017, coinciding with the Chinese economy's decline in relative health over that time.

Year Over Year Growth Rate of Exchange Rate Adjusted U.S.-China Trade in Goods and Services, January 1986 - November 2018

The impact of the tariff war between the U.S. and China has been to amplify these negative indications in the year-over-year growth rate measure.


Board of Governors of the Federal Reserve System. China / U.S. Foreign Exchange Rate. G.5 Foreign Exchange Rates. Accessed 17 April 2019.

U.S. Census Bureau. Trade in Goods with China. Accessed 17 April 2019.

U.S. Census Bureau. U.S. Trade Online. Accessed 17 April 2019. 


22 April 2019

If investors are in any rush to push the S&P 500 (Index: SPX) above the record high closing value of 2,930.75 it set back on 20 Setpember 2019, they didn't betray any sign of it during the Good Friday holiday-shortened third week of April 2019, as the index mainly drifted sideways during the week.

Alternative Futures - S&P 500 - 2019Q2 - Standard Model with Annotated Redzone Forecast - Snapshot on 19 Apr 2019

On the plus side, we've finally reached the end of our redzone forecast period, which we developed over 14 weeks ago. The following chart shows the seemingly remarkable result, where every daily closing value for the S&P 500 falls within the forecasted range.

Alternative Futures - S&P 500 - 2019Q2 - Standard Model with Annotated Redzone Forecast - 21 Dec 2018 to 18 Apr 2019

We say "seemingly remarkable" because we broke with our previous practice of simply drawing a red-shaded box indicating the forecast on the spaghetti forecast chart generated from our dividend futures-based model of how stock prices work that never changes over time, regardless of changes in future expectations. Here, because of the sheer amount of time we were seeking to bridge in compensating for the "echo" of past volatility that arises from our model's use of historic stock prices as the base reference points from which it projects into the future, we set our redzone forecast up this time to automatically update as future expectations changed.

Starting with the assumption that investors would largely be focused on 2019-Q1 over much of this period, and later on 2020-Q1 after 2019-Q1 came to an end, we anchored one end of our experimental redzone forecast range to the level of the S&P 500 at the close of trading on Friday, 11 January 2019. We then fixed the other end of the range to what our dividend futures-based model forecast projected the level of the S&P 500 would be on 22 April 2019, provided that investors would be setting stock prices in accordance with the future expectations associated with the distant future quarter of 2020-Q1.

As those future expectations have changed over the last 14 weeks, so has the trajectory of our redzone forecast range, which has continually fluctated from week to week. Fourteen weeks later, every single point of the actual trajectory of the S&P 500 falls within the range defined by how we introduced our assumptions back on 14 January 2019.

Fortunately, since we're now out of the period where the past volatility of stock prices affects the accuracy of our model, we can finally stop, where the model will better communicate how far forward in time investors are focusing as they set current day stock prices.

Meanwhile, for a week where the market didn't move very much, there was still quite a lot of noise for investors to absorb, as evidenced by the major market-moving headlines of the week.

Monday, 15 April 2019
Tuesday, 16 April 2019
Wednesday, 17 April 2019
Thursday, 18 April 2019

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18 April 2019

1929 Mercury Dime - Source: U.S. Commission of Fine Arts - https://www.cfa.gov/about-cfa/design-topics/coins-medals/mercury-dime

Have you ever found a U.S. dime minted before 1965 in your change?

We ask, because 1964 was the last year in which U.S. coins with a face value of 10 cents or more were produced by the U.S. Mint were mostly made out of silver [1]. During the next 10 years, the price of silver rose, then skyrocketed in the mid-to-late 1970s, giving Americans a strong incentive to pluck any these silver coins out of circulation [2] because they became worth more than their face values.

By the 1980s, it was extraordinarily rare to find any pre-1965 silver coin in your change. Today, it has become exceedingly rare.

But next week, it may become a just a bit more commonplace.

As part of National Coin Week, which runs from 21 April 2019 through 28 April 2019, coin dealers across the U.S. plan to return up to one million vintage or collectible coins back into circulation, where they may very well turn up in your change. What they hope will be The Great American Coin Hunt will be on!

Not all the coins they put back into circulation in this Willy Wonka-fashion will be silver. The dealers will release a variety of coins dating back as far as the 1800s into the wild, so to speak, where anyone paying cash and getting change back may be in for a neat surprise.

If that's you, happy hunting!


[1] Before 1965, U.S. dimes, quarters, and half-dollars were minted from an alloy known as "junk silver", which is 90% silver and 10% copper.

[2] For an anecdotal history of the disappearance of silver-based coinage in the U.S., check out this discussion thread at the Metal Detecting Forum.


17 April 2019

From time to time, we test out hypotheses that make for interesting discussion. For example, let's consider the impact of two recent 737 crashes on Boeing's stock price (NYSE: BA).

Here, we had the idea that if we compared Boeing's stock price with that of another company whose fortunes are closely tied to Boeing, we could perhaps get an indication of how investors are pricing the company's potential legal liability for the Lion Air Flight JT610 crash on 29 October 2018 in Indonesia, which killed 189 people, and the Ethiopian Airlines Flight ET302 crash on 10 March 2019, which killed 157 passengers and crew, by comparing Boeing's stock price with that of Spirit Aerosystems (NYSE: SPR). The following chart shows the trajectory of both companies' stock prices from 15 October 2018 through 12 April 2019, where we've also indicated the timing of the two crashes.

Boeing and Spirit Aerosystems' Stock Prices, 15 October 2018 through 12 April 2019

This comparison is particularly relevant because Spirit Aerosystems manufactures the fuselage of Boeing's 737 MAX aircraft. Our hypothesis was that because the cause of the two recent Boeing 737 MAX crashes have been attributed to faulty sensors and software malfunctions, Boeing's stock would show a relatively greater decline than Spirit Aerosystems, where because the fuselage is a mechanical structure, we reasoned that Spirit would only be exposed to reductions in Boeing's production of the 737 MAX, while Boeing would bear the additional burden of legal liability related to the two crashes linked to the sensor and software failures.

It sounds plausible, and in the initial reaction of both companies' stock prices to each crash, it also looks plausible, but there is some strange synchronization going on between the stock prices of the two companies, which you can see in the next chart as we've tracked each company's stock price as a percentage of the peak market closing values both companies simultaneously reached on 1 March 2019.

Boeing and Spirit Aerosystems' Stock Prices as Percentage of Their Peak Values (Both on 1 March 2019), 15 October 2018 through 12 April 2019

It's no surprise to find that the two companies' stock prices are closely synchronized to each other, with their changes over time typically falling within a few percentage points of each other. It's also not strange to see that Boeing's share price did indeed bear a heavier burden than Spirit Aerosystems' stock price did in the immediate aftermath of both 737 MAX crashes.

What is a bit strange is how they've gone about recoupling to each to other's performance after each crash event. Following the Lion Air crash, we find that Boeing's stock price surged after 27 November 2018 to catch up to the level of Spirit Aerosystems' stock within the matter of a week. Which kind of makes sense because at that time, it seemed that Boeing would avoid having exposure to any additional legal liability from that crash.

But that pattern was reversed after the Ethiopian Air crash, where Spirit Aerosystems' stock price was the one that moved to recouple with Boeing's relative stock price performance after 2 April 2019, which it did by dropping down to Boeing's level. We suspect that may have been speculation on the part of investors that production of the 737 MAX aircraft would be reduced as news that the grounding of the troubled aircraft would extend longer than expected emerged. Although Boeing had resisted it, the situation with so many aircraft on the ground and order cancellations forced its hand as the production cut announcement for the 737 MAX finally came on 8 April 2019.

Boeing should still has greater exposure to legal liability from the crashes, so it will be interesting to see how its relative stock price performance evolves over time as those costs become better quantified. As long as it does, we should see it as a persistent relative underperformance when compared with Spirit Aerosystems' stock price.

At least until the legal issues are finally in Boeing's rear view mirror. We'll see how that hypothesis works in practice.

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16 April 2019
Kal Visuals - Starbucks Coffee Cup at Unsplash

If you're a member of Starbucks (Nasdaq: SBUX) customer loyalty rewards program, the sad news today is that company's new rewards redemption scheme has gone into effect.

The reason why that's sad news is because the program's rewards have become much less generous. Previously, a rewards member could redeem 125 points (or stars) to get any item off Starbucks' menu for "free", with the best bang for the buck coming from redeeming points for either upgraded or high-priced menu items, such as handcrafted beverages, sandwiches and salads.

That changes today because the company is seeking to reduce its costs from financially literate rewards program members, who took advantage of the program's previous redemption terms to receive the maximum value they could from the points they accumulated through regular purchases and periodic promotional deals. Starbucks' new rewards program scheme makes redeeming points for higher-priced menu items more costly:

Starbucks is overhauling its rewards program so that customers will start earning rewards faster. Quicker access to freebies means the coffee chain is also essentially eliminating its Gold Level status by default.

Previously, you had to reach Gold Level — 300 stars — to be able to redeem a free drink or food item for an additional 125 stars. Starting April 16, customers can cash in their Starbucks stars as soon as they get them. Like before, 2 stars will be earned for every dollar spent....

For 25 stars you can ask for an extra shot of espresso, pump of flavor, or opt for any dairy substitute at no extra cost; 50 stars lets you walk out of your local Sbux with a brewed hot coffee, tea, or baked good, on the house; 150 means a free handcrafted drink, hot breakfast, or yogurt parfait; 200 stars, and lunch is on Starbucks. And if you ever make it to 400 stars without cashing in first, there's an option for "select merchandise" or packaged coffee.

But not all of Starbucks' Rewards stars are equal. In the following table, we did the math to identify where Starbucks' rewards members can get the biggest bang for their rewards points when redeeming them to buy the indicated items off of Starbucks' menu. If you're wondering about the particular items shown, most prices and items could be found for sale at Starbucks' first retail store, located across from Pike Place Market in Seattle, Washington, on 16 April 2019, while others may be found at other retail locations in the United States.

Relative Value of Starbucks New Rewards Redemption Scheme
Selected Menu Items Menu Cost for Item Reward Points Earned If Item Purchased Minimum Points to Redeem Item As Reward Number of Units Needed to Purchase to Earn Enough Points to Redeem Item As Reward
Shot of Flavored Syrup (Grande) $0.50 1.0 25 25.0
Hot Brewed "Grande" Coffee (Pike Place Roast) $2.45 4.9 50 10.2
Bakery: Butter Croissant $2.75 5.5 50 9.1
Bakery: Blueberry Scone $2.95 5.9 50 8.5
Bakery: Banana Nut Bread $3.15 6.3 50 7.9
Handcrafted Drink: Café Latte (Grande) $3.65 7.3 150 20.5
Handcrafted Drink: Café Mocha (Grande) $4.15 8.3 150 18.1
Sandwich: Ham & Swiss Panini $6.75 13.5 200 14.8
Sandwich: Turkey Pastrami Reuben $7.75 15.5 200 12.9
Salad: Grilled Chicken & Cauliflower Tabbouleh $9.45 18.9 200 10.6
1-lb Bag of Coffee: Pike Place Roast Whole Bean $12.95 25.9 400 15.4

We find that the sweet spot for redeeming Starbucks rewards for loyalty program members seeking maximum value has moved from the high-end of the company's menu offerings to the company's bakery goods. Not uncoincidentally, Starbucks' bakery goods tend to carry the highest profit margins of all the items on its menu, so that's a change that may benefit the company's bottom line.

Meanwhile, the strategy of up-sizing drinks would appear to continue providing greater value in redeeming reward points than ordering beverages in smaller volume cups. The values in the table above apply for "grande"-sized beverages, which fall in the middle of the beverage options on Starbucks' menu - "short" or "tall"-sized beverages would deliver less value than what these figures indicate, while "venti" or "trente"-sized drinks would deliver greater value for their new reward redemption value of 150 points. It is unclear at this time if Starbucks Rewards members would be required to redeem an additional 25 points to upgrade a Café Latte to a Café Vanilla Latte on top of the 150 points it will now take to purchase the base beverage (of any size) in Starbucks' new rewards scheme.

Update 11:25 AM Eastern: The 150 points for handcrafted beverages include the additional flavored shots - we've confirmed there is no additional point charge.

The worst deal, by far, would be to redeem points to add flavored syrups to their regularly ordered beverage by itself. We think the only reason anyone would voluntarily choose to do this would be to use up small totals of accumulated points that are at direct risk of expiring before they might otherwise be used.

The rewards program change seems primarily aimed at boosting Starbucks' profit margins, which have been declining since early 2017. Starbucks is expected to close 150 of its U.S. stores in 2019 to help boost its profitability in the U.S. At the same time, Starbucks has focused considerable attention on growing overseas, particularly in China. Starbucks' stock price has generally risen since mid-2018, largely on the strength of its international expansion.

Image Credit: unsplash-logoKal Visuals

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15 April 2019

The S&P 500 (Index: SPX) continued its upward trajectory in the second week of April 2019, where it is now within 24 points, or 1%, of its previous peak of 2,930.75 set back on 20 September 2019.

Alternative Futures - S&P 500 - 2019Q2 - Standard Model with Annotated Redzone Forecast - Snapshot on 12 Apr 2019

The thing that boosted the market the most during the week was the news on Friday, 12 April 2019 that China's exports to global markets has rebounded to a five-month high, suggesting relative improvements in the economic health of importing countries.

The same news story revealed that China's own imports have continued to decline however, indicating that nation's economy is still slowing. For stock markets, that bad news was offset in part by the ongoing expansion of the Chinese government's efforts to stimulate its economy, where there are indications they are gaining some traction.

Our roundup of those headlines, and other market-moving headlines, is straight ahead....

Monday, 8 April 2019
Tuesday, 9 April 2019
Wednesday, 10 April 2019
Thursday, 11 April 2019
Friday, 12 April 2019

How many positives and negatives for the U.S.' markets and economy did Barry Ritholtz find during the second week of April 2019? Click through to find out!...

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12 April 2019

We have recently breaking news from the world of maths, where David Harvey and Joris van der Hoeven have posted a new paper describing a computational method they developed that may have reached the theoretical speed limit for performing the multiplication of very large numbers.

In the following video, Harvey describes what that speed limit is, or rather, the minimum number of calculations required to reach the correct product for two large numbers that are being multiplied:

If the method is proven, it represents a large step forward in speeding the solution of large number multiplication by reducing the number of required calculations. We built the following tool to get a sense of how much smaller the theoretical limit of N log (N) [N multiplied by the natural logarithm of N] is when compared to the N² operations required by the traditional method of multiplying two numbers with the same number of digits. If you're reading this article on a site that republishes our RSS news feed, click here to access a working version of this tool!

Properties of Numbers Being Multiplied
Input Data Values
Number of Digits

Number of Operations Needed to Multiply Two Numbers
Calculated Results Values
Traditional Multiplication Method
Theoretical "Most Efficient" Method
Percentage Reduction

For the default example, where we're multiplying two numbers with 10,000 digits each, you can see why this development is exciting because it would be possible to reduce the number of individual operations needed to arrive at the product from 100,000,000 to 92,104, a computational efficiency gain of nearly 99.91%.

Which is to say that you can not only get to the answer much more quickly, you would also greatly reduce the amount of energy that computers consume in reaching the product of the two very large numbers being multiplied.

Writing at The Conversation, Harvey describes what he and van der Hoeven have achieved, where the secret to reaching the theoretical peak efficiency for multiplying very large integers is to use multidimensional Fast Fourier Transforms (FFTs):

A few weeks ago, Joris van der Hoeven and I posted a research paper describing a new multiplication algorithm that finally reaches the N log (N) holy grail, thus settling the “easy” part of the Schönhage–Strassen conjecture.

The paper has not yet been peer-reviewed, so some caution is warranted. It is standard practice in mathematics to disseminate research results before they have undergone peer review.

Instead of using one-dimensional FFTs — the staple of all work on this problem since 1971 — our algorithm relies on multidimensional FFTs. These gadgets are nothing new: the widely-used JPEG image format depends on 2-dimensional FFTs, and 3-dimensional FFTs have many applications in physics and engineering.

In our paper, we use FFTs with 1,729 dimensions. This is tricky to visualise, but mathematically no more troublesome than the 2-dimensional case.

If you want to find out more about FFTs, Better Explained has one of the gentler introductions to the math of Fast Fourier Transforms.

Meanwhile, Harvey recognizes the current generation of van der Hoeven's and his algorithm is limited in how it can be used effectively:

The new algorithm is not really practical in its current form, because the proof given in our paper only works for ludicrously large numbers. Even if each digit was written on a hydrogen atom, there would not be nearly enough room available in the observable universe to write them down.

On the other hand, we are hopeful that with further refinements, the algorithm might become practical for numbers with merely billions or trillions of digits. If so, it may well become an indispensable tool in the computational mathematician’s arsenal.

So it's not quite yet the perfect way to multiply, but it initially appears to be much closer than what anyone else has achieved, and with a little more work, could very well become the "perfect way to multiply" very big numbers!

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