Category Archives: data visualization

What Does Bitcoin Look, Walk, and Quack Like?

Duck, by Ross Sokolovski via Unsplash -

What is the best way to think about what Bitcoin (BTC-USD) is as an investment?

We've already demonstrated what it isn't. Bitcoin isn't "Gold 2.0". We know that's true because Bitcoin doesn't act like gold (KITCO: Live Gold Price), which rises in value whenever inflation forces real interest rates to fall. If anything, we found changes in the value of Bitcoin is almost completely independent of inflation-adjusted interest rates. If gold were a duck, Bitcoin wouldn't look, walk or quack anything like it.

Which then raises the question: what does Bitcoin look, walk and quack like?

We think Bitcoin looks, walks, and quacks like a non-dividend paying stock.

The thing that put us onto that line of thought was a recent headline: Bitcoin’s correlation with the Nasdaq 100 index reaches a new all-time high.

To be highly correlated with something is akin to looking, walking and quacking like it. So we put that proposition to the test, tracking the relationship between Bitcoin and the Nasdaq Composite Index (NASDAQ: COMP.IND), which is a broader measure of the stocks that trade on the NASDAQ stock exchange. The following chart shows what we found after we mapped the available data we have for the historic value of Bitcoin against the value of the Nasdaq Composite Index over the same period of time, from 17 September 2014 through 20 May 2022.

Bitcoin Value vs NASDAQ Composite Index, 17 September 2014 - 20 May 2022

In the chart, we see that Bitcoin's value has two distinct phases. One before the NASDAQ Composite index exceeded $10,000 in value, which was generally linear outside of a bubble-like period from October 2017 through November 2018. One after the NASDAQ exceeded $10,000 in value, coinciding with when Bitcoin began gaining institutional backing and its value with respect to the index took on power law characteristics. It both cases though, outside short periods where changes in its valuation decoupled from changes in the value of the stock index, Bitcoin has a generally tracked along with the NASDAQ, rising and falling with it in a positive relationship.

That makes it very much like a non-dividend paying stock, especially during the period after it began gaining significant institutional backing. We know that from the exponent of the power law relationship that exists between Bitcoin and the Nasdaq Composite Index during this period, which represents the ratio of the exponential growth rates of Bitcoin and that of the Nasdaq index, which includes dividend-paying stocks.

In doing that, Bitcoin is very much looking, walking, and quacking like a volatile non-dividend paying stock, which shares those characteristics. Unless and until it starts acting differently, that's perhaps the best way for investors to think about Bitcoin's qualities as an investment.


Federal Reserve Economic Data. NASDAQ Composite Index. [Online Database (Text File)]. Accessed 20 May 2022.

Yahoo! Finance. Bitcoin USD (BTC-USD), 14 September 2014 through 21 April 2022. [Online Database]. Accessed 20 May 2022.

Previously on Political Calculations

Image credit: Photo by Ross Sokolovski on Unsplash.

What Should the Value of the S&P 500 Be?

Since the S&P 500 (Index: SPX) peaked at 4,796.56 on 3 January 2022, the index has dropped by 18.2% of that record high value. But that simple observation raises a question. What should the value of the S&P 500 be?

We have a couple of interesting ways to approach answering that question, the first of which relies upon how investors set the average level of the index with respect to its trailing year dividends per share during periods of relative order in the U.S. stock market. The following chart illustrates the five major periods of order the S&P 500 has experienced since December 1991, which have been periodically interrupted by periods of relative chaos.

S&P 500 Average Monthly Index Value vs Trailing Year Dividends per Share, December 1991-May 2022 (through 18 May 2022)

In the chart, we show the mathematical relationships that have applied during those relative periods of order, which connects the average monthly value of stock prices (y) with the level of the index' trailing year dividends per share (x). We've built the following tool to do the related math to see how investors would set the value of the S&P 500 for the period of order you select for the trailing year dividends per share you enter. If you're accessing this article on a site that republishes our RSS news feed, you may need to click through to our site to access a working version of the tool.

Alternate S&P 500 Valuation Criteria
Input Data Values
Relative Period of Order
Trailing Year Dividends per Share

Projected S&P 500 Index Value
Estimated Results Values
Index Value Corresponding to Selected Period of Order

Using the default selection of the most recent period of order, which lasted from December 2018 through February 2020, until the arrival of the coronavirus pandemic initiated a period of chaos for the U.S. stock market, we find that with May 2022's estimated $62.90 for trailing year dividends per share, the corresponding value of the S&P 500 would be $3,777.

Or rather, that's what the math suggests would be a reasonable level for the S&P 500 had that relative period of order continued to the present. Since that value is below the current level of the index, this result suggests stock prices still have room to fall, but it's important to note that this level is neither a ceiling nor a floor. It simply represents the mean to which stock prices would revert during this particular previous relative period of order.

That mean level is visualized as the extended trajectory for this relative period of order in the chart above, where you can see the chaotic impact the arrival of the coronavirus pandemic had in March 2020, followed by the bubble inflated by the COVID stimulus programs of 2020 and President Biden's inflation-generating American Rescue Plan Act stimulus program of March 2021. That bubble entered its deflation phase after December 2021, which is still underway today.

With more than one previous relative period of order to choose from, there's a lot of room for interpretation. Other selectable options, such as the one for the early 1990s, may suggest the S&P 500 is greatly undervalued for the dividends per share you enter. One of the cool things about this tool is you can do the math for any level of trailing year dividends per share you choose, so you can find out how stock prices could alternatively been set during the days of the Dot Com Bubble, if that's your area of interest, or during any of the other periods in between. Go ahead and take the tool for a test drive to explore the world of alternate S&P 500 valuations!

Can you project where the S&P 500 could go during periods of chaos?

We know what you're thinking. Wouldn't it be nice if you could project what a reasonable level for the S&P 500 would look like during periods of chaos for the stock market? It would indeed, and we have you covered there as well.

Alternative Futures - S&P 500 - 2022Q2 with m=-2.5 from 20210616 - Snapshot on 20220518

If you know what the expectations are for changes in the growth rate of dividends at different points of time in the future, and you know how far into the future investors are focusing their forward-looking attention as they set current day stock prices, you can reasonably project the level for the S&P 500 even during periods of chaos in the stock market. It has been possible since April 2009 and became practical to accomplish after November 2009, when the CBOE introduced modern quarterly dividend futures for the S&P 500.

The Largest U.S. Trade Deficit in U.S. History

In March 2022, the United States imported far more goods than it exported, breaking its previoius record for its monthly trade deficit by a wide margin. We thought the occasion of the new record provided an interesting data visualization opportunity, so let's start with the overall summary:

The Largest Monthly Trade Deficit in U.S. Histsory, March 2022

The U.S. exported $179.5 billion worth of goods in March 2022, while importing $297.0 billion. That makes for a monthly trade deficit of $117.5 billion, which is 14.2% larger than the previous record of $102.9 billion set in November 2021.

Because we regularly follow trade between the U.S. and China, we broke out the portions of each of these categories that are attributable to that portion of the U.S.' overall trade with respect to the rest of the world. We find that U.S. exports to China accounted for 7.5% of that total. U.S. imports from China accounted for nearly 16.0% of all it imported from around the world. Netting these numbers out, we find that the U.S.' trade with China accounted for 28.9% of its entire recorded trade deficit in goods for the month.

We decided to dig deeper into the U.S. Census Bureau's trade data to see what it was that added the most to the U.S.' record high trade deficit in March 2022. Those results are presented in the following interactive chart, for which you may need to click through to our site to get the big picture. Hover your cursor over the dots in the chart to get the related surplus (+) or deficit (-) in millions of U.S. dollars.

The biggest portion of the U.S.' record March 2022 trade deficit was in the category for electric machinery. The second largest portion was for heavy mechanical machinery. (Note: nuclear reactors are included in the title for the official category, but this particular class of goods was a very small contributor to the U.S.' trade deficit in March 2022!) The third largest category covers vehicles, which is mostly accounted for by imports of foreign-made automobiles and trucks. The large number of imports recorded during the month may be attributable to progress finally being made in unloading the backlog of large container ships that queued up in large numbers outside U.S. seaports during 2021.


U.S. Census Bureau. Trade in Goods with World, Not Seasonally Adjusted. Last updated: 4 May 2022. Accessed 4 May 2022.

Bitcoin Is Not Gold 2.0

It's not often we can use math to definitively shut down a claim being made to pitch an investment, but here we are.

The pitch involves the cryptocurrency Bitcoin (BTC). The claim, most famously made by the Winklevoss brothers in 2017, is that "Bitcoin is Gold 2.0". Here's a more recent clip of the brothers repeating their pitch on CNBC on 10 July 2019:

While they may be among the most prominent pitchmen for Bitcoin, they're far from alone in claiming Bitcoin has gold-like investing properties. Here's a selection of articles we turned up from 2013 through 2022 where analysts have made similar claims:

Let's address the elephant in the room. For Bitcoin to be Gold 2.0, it needs to share gold's top investing characteristic: it needs to provide an effective hedge against inflation by rising in value as inflation reduces real yields. Gold, or as BTC enthusiasts would describe it, Gold 1.0, does exactly that when real interest rates fall and become negative as the rate of inflation grows to exceed nominal interest rates. Here's the chart we featured in previous analysis showing the price of gold doing just that, rising in value as real interest rates decline in value and vice versa.

Gold Spot Price vs Inflation-Indexed Market Yield of 10-Year Constant Maturity U.S. Treasury, 2 January 2007 - 17 March 2022

Now, here's a chart that presents the value of Bitcoin with respect to the same data for the inflation-adjusted yields of 10-year Constant Maturity U.S. Treasuries over the period from 17 September 2014 through 21 April 2022, covering nearly the entire period where we can identify that the claim that "Bitcoin is Gold 2.0" has been prominently made. Spoiler alert: Bitcoin is not Gold 2.0!

Gold Spot Price vs Inflation-Indexed Market Yield of 10-Year Constant Maturity U.S. Treasury, 2 January 2007 - 17 March 2022

The chart of Bitcoin's "relationship" with real yields looks like something that could have been created on an Etch-a-Sketch. The value of BTC either moves sideways or up-and-down.

That observation aside, we see three main periods for Bitcoin's valuation history in this chart:

  1. 17 September 2014 to 7 October 2020. The price of Bitcoin in U.S. dollars has virtually no relationship with real interest rates, despite substantial changes in their value during this period. In math terms, the slope of the trendlines whenever real interest rates are changing in value is nearly equal to zero, because the value of Bitcoin isn't changing with them.
  2. 8 October 2020 - 6 January 2022. This is the period when the biggest changes in the valuation of Bitcoin has occurred, and we find that while Bitcoin's value has ranged all over the map from nearly $11,000 to a peak of $67,567 during this second period, it's matched against very little change in real interest rates. In math terms, the effectively vertical movement in Bitcoin's valuation is not defined with respect to changes in real interest rates. In practical terms, whatever moved Bitcoin prices during this time was unconnected to how inflation affected interest rates.
  3. 7 January 2022 - 21 April 2022. Shown as the green circles on the chart, we find once again there is little change in the value of Bitcoin even though real interest rates have substantially changed. Just like in the first period, the value of Bitcoin shows little to no, or dare we say, zero connection to changes in real interest rates.

For the record, we're just the latest to conclude that Bitcoin is not Gold 2.0, though perhaps the first to show it using tools available to middle and high school algebra students. Here is other analysis that finds Bitcoin lacks gold's most attractive investing properties for extra credit reading:

With respect to changes in inflation-adjusted interest rates, we've demonstrated the value of Bitcoin either moves sideways or up-and-down with little rhyme or reason, making it very different from how gold has performed during the period of their shared existence. Bitcoin is not Gold 2.0.

Previously on Political Calculations


Federal Reserve Economic Data. Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity, Inflation-Indexed. [Online Database (Text File)]. Accessed 22 April 2022.

Yahoo! Finance. Bitcoin USD (BTC-USD), 14 September 2014 through 21 April 2022. [Online Database]. Accessed 22 April 2022.

Visualizing the Character Density of Classic Books

A good book can be a very good thing. Turning the pages of an engaging story filled with entertaining characters is always time well spent.

That's why we were pleasantly surprised to find the following chart out on the Datawrapper River, which visually ranks the character density of fifteen books known for having lots of characters. Most are considered literary classics, some are not. More on that in a bit, here's the chart:

Perhaps the least surprising book in the list is War and Peace. Tolstoy's work is notorious not just for being really long, but also for having a ton of characters. We would have predicted it would rank at or near the top, and at second, it does.

The most surprising title, but perhaps less so when we think more about it, is Harry Potter and the Philosopher's Stone, sold in the U.S. with the title Harry Potter and the Sorcerer's Stone. The first book of the Harry Potter series introduces a lot of characters in establishing its world in a comparatively short 352 pages, but not quite as many per 100 pages as Tolstoy did in War and Peace.

And then there's Antigua: The Land of Fairies, Wizards and Heroes, which is only available in an electronic Kindle version and blows Tolstoy's War and Peace out of the water, nearly doubling its character density.

It also seems as far from a classic work of literature as you can get. The titles we didn't recognize were contributed by the 372 Pages We'll Never Get Back podcast, whose hosts are reading books they're pretty sure they're going to hate. Which sounds like the book club we badly needed back in school just to make it through some of the 'masterpieces' being pushed by overly enthusiastic literature teachers. Going by the titles they've covered, they're having a lot of fun.