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January 16, 2017

The second week of January 2017 proved to be yet another disappointment for those focused on the Dow Jones Industrials (NYSE: DJI) and its now month-long quest to finally reach the magical 20,000 milestone, even as the Nasdaq index (Nasdaq: IXIC) hit a new record high.

Meanwhile, the S&P 500 in Week 2 of January 2017 kept bouncing along just below its week old all-time record high. Not that any of that was in any way unexpected....

Alternative Futures - S&P 500 - 2017Q1 - Standard Model with Connected Dots Between 29 December 2016 and 14 February 2017 - Snapshot on 13 January 2017

It was a week in which the news to which investors reacted had very little impact on the overall course of the S&P 500. The headlines below are what stood out to us as significant during the week that was.

Monday, 9 January 2017
Tuesday, 10 January 2017
Wednesday, 11 January 2017
Thursday, 12 January 2017
Friday, 13 January 2017

Barry Ritholtz summarized the positives and negatives reported for the U.S.' economy during Week 2 of January 2017.

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January 13, 2017

In our final post of 2016, in which we reviewed the biggest math-related stories of that year, and in particular, a story about the first statistically significant demonstration of Zipf's Law, we discussed why the story was important to the development of artificial intelligences (AIs):

While not much more than an interesting finding now, that Zipf's Law appears to hold across such a large body of human language will have applications in the development of artificial intelligence, particularly for machine understanding of human language. That next generation Amazon Echo, Google Home, or whatever mobile voice recognition app will be on your mobile devices in the future will get better at understanding and communicating with you as a result. More practically, because technology will be better able to replicate the patterns inherent in human writing, movie producers have moved one step closer to realizing their long-held dream of being able to replace all those annoying and costly human screenwriters with automated script writers, where audiences won't be able to tell the difference for most Hollywood productions.

That day is closer than you think, as an experiment between two AIs named Vladimir and Estragon, who happen to have been manufactured by Google, appear to have fallen in love. As you can see in the following video clip, the dialogue between the two Google Home units is approaching the emotional depth of what might pass muster as the script for a sequel to a recent blockbuster romance.

According to Core77, they have also discussed tacos, where with additional technological development, it wouldn't be hard to anticipate that dialogue worthy of Nora Ephron cannot be far behind.

At the very least, that's something to think about now that we're well into the entertainment industry's award season. The world of the future will be far stranger than most people alive today appreciate!

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January 12, 2017

Median new home sale prices in the United States are continuing their slow climb, at least according to data that the U.S. Census Bureau released in late December 2016, where since September 2015, median sale prices have generally risen by $5.32 for every $1 increase in median household income.

U.S. Median New Home Sale Prices vs Median Household Income, December 2000 - November 2016

We can see that slower growth trend more clearly by focusing on how median new home sale prices have evolved over time in recent years, which are shown in the following chart from July 2012 onward.

Trends in Trailing Twelve Month Average of Median U.S. New Home Sale Prices, July 2012 through November 2016

As a quick recap of what has been happening in the more recent trends, since September 2015, median new home sale prices in the U.S. have been escalating at an average rate of $938 per month, which is about 38% of their rate of inflation of $2,476 per month during the year from July 2012 through July 2013, when a number of Wall Street investment firms were snapping up thousands of homes out of foreclosure each month, which worked to constrain the available supply for home buyers, who were shunted into the new home market.

From July 2013 through September 2015, median new home sale prices rose at an average clip of $1,511 per month, as the pace of investor activity slacked off, before largely dissipating after September 2015, which allowed the relative supply of new homes to increase, as regular home buyers could once again purchase existing homes without being outbid.

And that's where we find ourselves now, as the new home sale price data has yet to take the effect of rapidly rising mortgage rates in November and December 2016 into full account. The next several months will be interesting to see how that factor plays into the prices of new homes sold.


Sentier Research. Household Income Trends: November 2016. [PDF Document]. 29 December 2016. [Note: We have converted all the older inflation-adjusted values presented in this source to be in terms of their original, nominal values (a.k.a. "current U.S. dollars") for use in our charts, which means that we have a true apples-to-apples basis for pairing this data with the median new home sale price data reported by the U.S. Census Bureau.]

U.S. Census Bureau. Median and Average Sales Prices of New Homes Sold in the United States. [Excel Spreadsheet]. Accessed 29 December 2016.


January 11, 2017

According to SlickCharts, as of 6 January 2017, there are 506 companies whose stocks make up the S&P 500 stock market index. According to Standard and Poor, 418 of those companies pay dividends. And according to Google Finance, which provided the raw data for each of those companies, the following chart shows the approximate stock prices with respect to the indicated annual dividends for each those 418 firms as of 6 January 2017.

Price per Share vs Annual Dividends per Share, 418 S&P 500 Dividend Paying Stocks (6 January 2017)

After making this chart, we couldn't help but notice the four companies that appear in the upper left corner of the chart, whose very high stock prices and very low projected annual dividends per share make them outliers when compared to nearly all the other data points in the chart. So we went the extra mile and recalculated the power law relationship we found between annual dividends per share and the stock prices for the 414 other companies of the S&P 500 that pay dividends to their shareholders.

Price per Share vs Annual Dividends per Share, 414 of 418 S&P 500 Dividend Paying Stocks (6 January 2017)

The four dividend paying firms whose stocks and dividends per share that we excluded from this second chart are: Cigna Corporation (NYSE: CI), Pioneer Natural Resources Company (NYSE: PXD), Global Payments Inc. (NYSE: GPN), and Cooper Companies Inc. (NYSE: COO).

Having established a considerably stronger correlation by excluding the share prices and annual dividends per share of these four S&P 500 companies, we now have a way to assess how a given company's share price compares to its dividend paying peers, where you can use the tool below to see what share price might be considered to be typical for a S&P 500 that pays the amount of annual dividends per share that you enter. If you're accessing this article that republishes our RSS news feed, please click here to access a working version of the following tool.

Dividends per Share Data
Input Data Values
Annual Cash Dividends per Share

Estimated Share Price Results
Calculated Results Values
Estimated "Typical" Share Price for S&P 500 Company

There's a lot that goes into whether or not a given firm's stock price might be considered to be high or low with respect to the "typical" share price that our tool above calculates. A growth stock may have a small dividend, where the company's owners are choosing to direct its earnings and available free cash flow toward investments that promise to rapidly boost the firm's revenues or increase its share of the markets in which it operates, which therefore tend to have high share prices with respect to whatever dividends they might pay.

Regardless of its share price, if a company doesn't pay dividends, it's technically a growth stock, even if it was a firm that previously paid dividends but stopped because of some form of economic distress, where you can identify the firms that fall into the latter category their very low prices per share. In January 2017, there were 88 non-dividend paying firms in the S&P 500 that collectively account for 15% of the S&P 500's total market capitalization.

Value stocks and income stocks, on the other hand, are often firms whose growth prospects are more limited, where the owners of the company have chosen to draw a regular income through cash dividend payments that are supported by the firm's earnings and cash flow. Compared to growth firms, the stocks of value and income firms tend to have considerably lower stock prices with respect to their dividends per share - mainly because of their slower growth prospects, but also in part because they are actively pulling market value out of the company whenever they make dividend payments to their shareholders.

Telling which kind of company is which can be challenging, but that's where a tool like the one we just created above might be useful. At the very least, it can give you something a bit more tangible to go on than you can usually find in mainstream media reporting on the topic!

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January 10, 2017
Starbucks Rewards Logo - Source: https://www.starbucks.com/card/rewards

The modern age of airline frequent flyer programs have been around since May 1981, when American Airlines (Nasdaq: AAL) revamped an earlier version of the concept for its customers as a marketing tool in its AAdvantage program. In return for choosing to fly on AA, customers were awarded with free flights once they had flown a given number of miles on the airline's flights. The program was remarkably successful and soon other airlines began copying AA's modern version of the customer loyalty program.

Recognizing the marketing potential of the airlines' frequent flyer programs, other businesses such as credit card companies started getting into the act and began cross-promotions with the airlines' frequent flyer programs, which benefited members of the programs because they could now accumulate additional frequent flyer miles toward gaining rewards without having to pay for an expensive ticket to fly somewhere. In some cases, they could even accumulate frequent flyer miles at a considerable discount compared to what it would cost to accumulate the miles by flying, which provided a cheaper and more rapid way to realize the benefits of the airlines' frequent flyer programs.

Like airlines with their frequent flyer programs, and flashing forward to the current day, Starbucks (Nasdaq: SBUX) has a rewards program aimed at boosting their revenues from their frequent customers. The Starbucks Rewards program provides the incentive of providing a free beverage or food item from its in-store menus to the members of its loyalty program whenever they accumulate 125 stars.

After you collect 125 Stars, you can choose to redeem them for a free food or drink item (excluding alcoholic beverages and multi-serve items) at any time before they expire - either choose to redeem a Reward in your mobile App when using Mobile Order & Pay or ask your barista when you are paying at a participating store.

Once your Reward is redeemed, 125 Stars will be removed from your Star balance. You can continue to earn a free Reward for every 125 Stars you accumulate. For example, if you have 250 Stars and have not redeemed your free Reward, you are eligible to redeem two free Rewards.

Not all Starbucks locations redeem free Rewards. Company-operated stores are able to honor the Rewards, but some kiosk locations (often those inside another facility like grocery stores) cannot. We hope to continue to increase the number of participating locations.

You can redeem your free reward at any Teavana® store or Evolution Fresh™ kitchen.

Under normal circumstances, members of Starbucks' Rewards programs accumulate 2 stars for every $1 they spend at Starbucks (or 1 star for each 50 cents), which means that "free" drink or food item can be had after they have spent $62.50.

Periodically however, Starbucks' marketing team makes it possible for members of Starbucks' Rewards program to accumulate lots of stars at a considerably discounted price. Starbucks' Star Dash Challenge promotions award increased numbers stars in return for in-store purchases during set week-long periods of time, such as the one that began on 4 January 2017 that will run through the end of today, 10 January 2017, where a rewards program member could net up to a total of 200 stars, netting 75 stars once they've made 5 individual purchases, and then if they make 2 more individual purchases before the deadline runs out, they can accumulate an additional 125 stars, which enough to redeem a single food or drink item reward all by itself.

Starbucks Star Challenge - December 2016 - 200 Stars Earned

That kind of promotion is where savvy Starbucks Rewards members can maximize the bang for their bucks.

Since these promotional stars are based on individual purchases rather than the dollar amount of those purchases, rewards program members can "purchase" their reward at a highly discounted price by simply buying the lowest price items on Starbucks' menu to count toward their individual purchases. Like an airline frequent flyer member using alternate ways of accumulating miles to lower the cost of reaching the reward of a free flight at a reduced cost, Starbucks' Rewards members can do the same thing to acquire their desired "free" food or beverage at a considerably lower cost than they otherwise would have to pay.

Checking in at our local Starbucks store location, we found that the lowest price item that we could buy was the petite vanilla bean scone, where an individual scone would cost $1.25. The second-lowest cost item was the plain bagel, with a unit cost of $1.50.

Doing the math, purchasing 5 petite vanilla bean scones would cost $6.25 (ignoring any applicable sales tax for now), which means that if we committed to participating in Starbucks' Star Dash promotion, it would drop the cost of each star we might accumulate to 8.3 cents - an 83% discount. If opting for the plain bagel instead, the cost would be $7.50, or 10 cents per star accumulated through five bagel purchases. [Since sales taxes vary by location, we'll leave that particular math to you, but we'll note that taking sales taxes into account will increase the cost of each star you might buy through Starbucks Star Dash promotion.]

Where things get interesting is when considering whether to take the plunge of making the additional two purchases for the additional 125 stars that might be gained through the current promotion. For petite scone buyers, those additional 125 points could be purchased for $2.50, where each star costs just 2 cents each - a 96% discount with respect to their regular cost. Bagel buyers would pay $3.00 for those 125 points, or 2.4 cents per star.

When you consider that most individual items on Starbucks' menu - the ones that rewards program members would be most likely to redeem in exchange for their "stars" - cost in excess of $4.00 each, making it through to this point in Starbucks Star Dash promotion can represent an attractive proposition for Starbucks' frequent customers.

Starbucks Rewards Promotional Cups - Source: https://news.starbucks.com/news/rewards-automatic-gold

But the real question is whether you can realize an extra benefit beyond that. The people for whom participating in Starbucks Star Dash promotions make the most sense are those who would ordinarily consume the items that they might buy expressly for the purpose of racking up stars at the lowest cost, where the additional cost they might have in participating in the program would really represent a smaller incremental cost over what they would ordinarily pay for the same items they're buying from Starbucks to rack up points in the promotion.

For example, in the case of Starbucks' plain bagels, a consumer of bagels who might ordinarily (and regularly) pay 50 cents per bagel from a grocery store would really only be paying Starbucks an additional $1.00 out of their pocket for each bagel they would be consuming anyway, where after accounting for offsetting their cost of a bagel, they would basically just be paying Starbucks an out-of-pocket cost of $1.00 to toast it and to also supply them with pads of butter to enjoy them with it (we're afraid Starbucks charges extra for cream cheese, but we discovered that pads of Kerrygold Butter are included with the cost of their toasted bagels).

That offsetting cost then would drop their incremental cost of participating in Starbucks' Star Dash promotion to just 6.7 cents per star for the first 5 bagel purchases, which would then drop to just 1.6 cents per accumulated star for their next 2 bagel purchases during the period of the Star Dash Challenge promotion - nearly a 97% discount.

No matter how great the discount however, there is little question that rewards program members would be spending more at Starbucks than they otherwise might, so whether participating in the promotion makes financial sense is more a matter of whether or not you value what you're getting in return.

We'll leave the exercise of how to maximize the benefits of whatever "free" food or beverage item that you might then redeem in exchange for your accumulated Starbucks Rewards stars, and frequent purchases, up to you!


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Welcome to the blogosphere's toolchest! Here, unlike other blogs dedicated to analyzing current events, we create easy-to-use, simple tools to do the math related to them so you can get in on the action too! If you would like to learn more about these tools, or if you would like to contribute ideas to develop for this blog, please e-mail us at:

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