Category Archives: stock market

How Gamestop’s Stock Price Was Squeezed

The story of how Gamestop (NYSE: GME) went from a value of $11.01 per share on 13 November 2020 to reach $325.00 per share on 29 January 2021 has become a stock market legend.

It has also become the subject of a fascinating academic study, where a new paper by Lorenzo Lucchini, Luca Maria Aiello, Laura Alessandretti, Gianmarco De Francisci Morales, Michele Starnini and Andrea Baronchelli investigated how social media contributed to the short squeeze that made GME into *the* prototype meme stock.

If you're not familiar with the story, here's the paper's summary of how the GME short squeeze was made, in which Reddit's r/wallstreetbets (WSB) plays a prominent role (we've added the bullet list formatting to make it easier to follow):

GameStop (GME) is a US video game retailer which was at the centre of the short squeeze in January 2021. The timeline of the events around the squeeze is summarized in table 1, and it unfolded as follows.

  • In 2019, Reddit user u/DeepFuckingValue entered a long position on GME, i.e. he bought shares of the GME stock, and started sharing regular updates in WSB.
  • On 27 October 2020, Reddit user u/Stonksflyingup shared a video explaining how a short position held by Melvin Capital, a hedge fund, could be used to trigger a short squeeze.
  • On 11 January 2021, GME announced a renewed Board of Directors, which included experts in e-commerce. This move was widely regarded as positive for the company, and sparked some initial chatter on WSB.
  • On 19 January, Citron Research (an investment website focused on shorting stocks) released a prediction that GME’s stock price would decrease rapidly.
  • On 22 January, users of WSB initiated the short squeeze.
  • By 26 January, the stock price increased more than 600%, and its trading was halted several times due to its high volatility. On that same date, business magnate Elon Musk tweeted ‘Gamestonk!!’ along with a link to WSB.
  • On 28 January, GME reached its all-time intra-day highest price, and more than 1 million of its shares were deemed failed-to-deliver, which sealed the success of the squeeze. A failure to deliver is the inability of a party to deliver a tradable asset, or meet a contractual obligation; a typical example is the failure to deliver shares as part of a short transaction.
  • On 28 January, the financial service company Robinhood, whose trading application was popular among WSB users, halted all the purchases of GME stocks.
  • On 1 and 2 February, the stock price declined substantially.

By the end of January 2021, Melvin Capital, which had heavily shorted GameStop, declared to have covered its short position (i.e. closed it by buying the underlying stock). As a result, it lost 30% of its value since the start of 2021, and suffered a loss of 53% of its investments, i.e. more than 4 billion USD.

While the paper's summary indicates a substantial decline in value, we'll point out that since it peaked at $325 per share, GME bottomed at $40.69 per share on 18 February 2022 before climbing back up to $300 per share on 8 June 2021, before dropping back toward the middle of that range. The following chart shows its stock price history:

GME Stock Price History: 12 October 2020 - 14 April 2022

That's all the "what happened", but it's the "why it happened" we find fascinating. The authors identify one key element in the postings of the WSB redditors that established their credibility, separating their postings from the ordinary run of the mill comments that dominate discussions on many other stock investing discussion sites, which they describe in the paper's introduction:

In this paper, we analyse discussions on WSB from 27 November 2020 to 3 February 2021 (table 1) and investigate how they translated into collective action before and during the squeeze that was initiated on 22 January and lasted until 2 February. Motivated by recent theoretical [10,11] and experimental [12] evidence that minorities of committed individuals may mobilize large fractions of a population [10,1315] even when they are extremely small [16], we investigate whether committed users on WSB had a role in triggering the collective action. To this aim, we operationalize the commitment of a user as an exhibited proof that the user has financial stakes in the asset.

We won't keep you in suspense. Here's the summary of what they found:

We show that a sustained commitment activity systematically pre-dates the increase of GameStop share returns, while simple measures of public attention towards the phenomenon cannot predict the share increase. Additionally, we also show that the success of the squeeze operation determines a growth of the social identity of WSB participants, despite the continuous flow of new users into the group. Finally, we find that users who committed early occupy a central position in the discussion network, as reconstructed by WSB posts and comments, during the weeks preceding the stock price surge, while more peripheral users show commitment only in the last phases of the saga.

The last part is to say that the early influencers who effectively established their credibility continued to be influential within the network. We think that continued influence is attibutable to their success, which had the short squeeze of GME's stock not occurred, would have led other WSB participants to discount the information value of their postings. People with opinions about a company's investment worthiness are a dime a dozen on a stock discussion board, but people who back up their talk with hard evidence of their bets that go on to pay off were granted credibility.

Much of the authors' study focuses on the dynamics between this "core" group of GME redditors and others who were on the periphery of the investing activity, which they describe as a "behavioural cascade" event. The core group attained a critical point of credibility, sweeping up peripheral redditors who transitioned from observers to participants as the short squeeze cascaded into a legendary event.


As for the hedge fund that lost billions on its attempted short of GME, the firm is considering returning what's left of the capital it controls to its remaining investors as its future with its current structure is in doubt. The fund lost 39% of its capital in 2021, with another 21% of losses to date in 2022. It's management would launch a new fund to replace it.


Lorenzo Lucchini, Luca Maria Aiello, Laura Alessandretti, Gianmarco De Francisci Morales, Michele Starnini and Andrea Baronchelli. From Reddit to Wall Street: the role of committed minorities in financial collective action. Royal Society Open Science. Volume 9, Number 4. 6 April 2022. DOI: 10.1098/rsos.211488.

150 Years of Historic Yields for the S&P 500

With over 95% of the earnings data for the fourth quarter of 2021 now reported, we thought it might be a good time to visualize the historic yields for the S&P 500 (Index: SPX). The following chart presents the trailing year earnings and dividend yields for the index over the past 150 years, from January 1871 through December 2021.

Historic Yields for the S&P 500, January 1871 through December 2021

For December 2021, we find the earnings yield for the S&P 500 is 4.70%, which places it within the middle of the range it has fallen during the past thirty years. The index' dividend yield however is 1.46%, which comes within a few tenths of a percent from its all-time low recorded at the peak of the Dot-Com Bubble in August 2000.

At this point in 2022, both measures of the relative valuation of the S&P 500 have risen as the value of the index has fallen throughout the year to date.

Dividends by the Numbers in January 2022

The U.S. stock market started January 2022 on a strong footing for dividend paying stocks. The market's dividend metadata for the month reveals both month-over-month and year-over-year improvement, although the year-over-year data is skewed by the impact of the coronavirus pandemic.

Let's dive straight into our summary of January 2022's dividend metadata!

  • In January 2022, a total of 5,159 U.S. firms declared dividends during the month. That's down 172 from December 2021's total of 5,331, but is up 3,693 year-over-year from January 2021's coronavirus pandemic low.
  • Just 59 publicly traded companies announced they would pay an extra, or special, dividend in January 2022. That's 109 fewer than the previous month and 54 fewer than January 2021's count of 113.
  • There were 198 dividend increases declared in January 2022, and increase of 53 from the 145 announced in December 2021. That's 24 more than had been recorded a year earlier in January 2021.
  • 17 firms announced they would reduce their dividends in January 2022, just two less than the number recorded in December 2021. Compared to January 2021 however, the month's total is 15 less.
  • No companies announced they would suspend or omit making dividend payments in January 2022, unchanged from December 2021's level, and three fewer than the number of companies taking that action a year earlier in January 2021.

The following chart puts January 2022's data for dividend rises and cuts into visual context with the preceding eighteen years worth of monthly U.S. stock market data:

Number of Public U.S. Firms Increasing or Decreasing Their Dividends Each Month, January 2004 through January 2022

At the beginning of January 2022, we find the U.S. stock market is carrying the momentum of its previous year of strength. We would be remiss however if we didn't point out that this data, and in particular, the number of dividend decreases each month, provides a near real-time indicator of the relative health of the U.S. economy, but one that slightly lags behind it.

That's to say that what lies ahead for 2022 may be very different from what the market experienced in 2021.

The Groundhog Day Stock Market Anomaly

Should you, as an investor, let a groundhog decide when to buy stocks in the U.S. stock market?

To many rational investors, that sounds completely crazy. But if you believe investors are irrational, and you happened to have seen a recent paper presented in Finance Research Letters, you might just consider it. Here's the conclusion from the paper by Savva Shanaev, Arina Shuraeva, and Svetlana Federova:

This study has discovered a new calendar anomaly on the United States stock market associated with the prognostications of Punxsutawney Phil on the Groundhog Day. Across 1928–2021, the S&P 500 substantially appreciated subsequent to Phil’s “prediction” of an early spring, while the returns were moderately negative after he “predicted” a long winter. The difference in buy-and-hold abnormal returns two weeks after the Groundhog Day is a statistically and economically significant 1.85%, establishing the importance of the Groundhog Day superstition to investor sentiment and market performance. There is a seemingly puzzling positive anticipation effect to an early spring prognostication equalling 1.14% over the two weeks prior to the announcement that implies either informed trading or, more likely, rational investors exploiting their awareness of the superstition and weather forecasts. The results are robust in subsamples, when controlled for a wide range of other calendar anomalies, as well as to time-varying risk premia and conditional heteroskedasticity.

The findings have implications for academics and stock market participants. For individual and institutional investors, this study has identified an exotic yet moderately profitable trading strategy. For empirical finance researchers, it has highlighted the nuanced idiosyncratic nature and persistence of calendar anomalies, showing that country-specific superstitions can have notable market specific effects. While some anomalies can have no explanations consistent with the efficient market hypothesis – like Friday the 13th effect or, indeed, the Groundhog Day effect established in this paper – they seem to exist, hence the market truly is that irrational.

In the study, the authors reviewed daily U.S. stock market data extended back to 1928, which includes 18 years in which Punxatawney Phil did not see his shadow, signaling both an early end to winter and an opportune time to invest in the U.S. stock market. That opportune time is defined as the period covering the 11 trading days preceding Groundhog Day (2 February) each year, through the 10 trading days following it.

We wanted to confirm their results for ourselves, so we tapped Yahoo! Finance's historical data for the S&P 500 (Index: SPX). This database contains daily trading data for the index beginning in January 1950, where the period since contains 17 of the 18 Groundhog Days where Punxatawney Phil did not see his shadow to predict an early spring. The following chart suggests Shanaev, Shuraeva, and Federova may be onto something....

The Groundhog Day Stock Market Anomaly, 1950-2021

For all years since 1950 where Punxatawny Phil saw his shadow, forecasting a long winter, the average value of the S&P 500 ten trading days after Groundhog Day was barely changed from its value eleven trading days before it. But in the 17 years where Punxatawny Phil did not see his shadow, predicting an early end to winter, the value of the S&P 500 rose an average 3.0% above its pre-Groundhog Day anomaly value.

So are you ready to start taking investing advice from the world's most famous groundhog? Before you do, you may want to consider the following video:

As with any scientific hypothesis, it takes only one bit of contrary evidence to debunk it. In this case, all we need to do is show that instead of being irrationally influenced by the weather prognostications of a burrowing rodent, investors in any one of the years in which Punxatawney Phil saw no shadow were instead motivated by rational considerations to bid up stock prices.

We chose 2020. The year the coronavirus pandemic would negatively impact the world's economy. The year that saw billions of people deal with the irrational fear of a deadly spreading virus amplified by responses of public officials that were often even more irrational. A year in which irrationality would seem to have abounded like no other in recent history!

The next chart shows how the S&P 500 evolved during 2020's Groundhog Day anomaly window, which covers the trading days from 16 January 2020 through 18 February 2020:

The Groundhog Day Stock Market Anomaly, 2020

So far, it seems to check the boxes for irrational behavior the Groundhog Day anomaly. We see Groundhog Day fell on a Sunday, so we set our Day 0 as Monday, 3 February 2020. We visually confirm that the preceding trading day of Friday, 1 February 2020 saw the S&P 500 bottom at 97.2% of its pre-anomaly window value. It began rising on 3 February 2020, proceeding to end the anomaly window period at 101.6% of its pre-anomaly period value after peaking at 101.9% on the seventh day after Groundhog Day.

But that doesn't consider what other information investors were considering during this period, much less what parts of that information were driving the stock market. For that, we tapped our own archives, where the clues to indicate investors were actually behaving very rationally were built into the headlines of our weekly recaps of the S&P 500's activity:

What we describe as a Lévy flight event corresponds to the decline of the index' value during the early part of the Groundhog Day anomaly window, which then combined with the realization that China's response to the epidemic would negatively affect the outlook for U.S. businesses. On 3 February 2020, U.S. stock prices rebounded slightly from that low based on strong U.S. manufacturing data with a small boost from tech stocks.

But what really caused stock prices to surge came on Tuesday, 4 February 2020, when China's central bank signaled they would initiate major stimulus programs to offset the negative economic impact of the spreading pandemic. The U.S. Federal Reserve also acted to boost liquidity in U.S. money markets at this time, but that was a much smaller act than the stimulus rolling out in China. U.S. stock prices remained elevated through the end of this period as Fed officials sought to boost confidence in the U.S. economy.

Most of that positive response would dissipate as the seriousness of the coronavirus pandemic became more apparent by the end of February 2020, but if you follow the links above to see the contemporary news headlines, there was nothing pointing to the prospects of an early spring that would affect the trajectory of the S&P 500 during the Groundhog Day anomaly window. Unless, of course, the Bank of China's officials took their policy direction from Punxatawney Phil. Whose 2020 weather prediction for an early srping also turned out to be wrong, as indicated by this late April 2020 photo....

Groundhog didn't like the late April snow (she was in the middle of nest building when it hit). by Ralph Katieb via Unsplash -

The following video clip provides better advice for those irrational enough to follow the life advice of groundhogs:

Update: According to Punxatawny Phil, there will be no Groundhog Day-related stock market rally in 2022!


Savva Shanaev, Arina Shuraeva, Svetlana Federova. The Groundhog Day stock market anomaly. Finance Research Letters. DOI: 10.1016/ 22 December 2021.

Yahoo! Finance. S&P 500 Historial Prices. [Online Database]. Accessed 1 February 2022.

Image credit: Photo by Ralph Katieb on Unsplash

Another View of the Bottom Dropping Out of the S&P 500

When we say the bottom dropped out of the S&P 500 (Index: SPX) last week, what does that really mean?

It seems obvious that we're referring to the decline in stock prices, but there's much more to it than that. After all, the stock market has weeks when its value rises and has weeks when its value falls from the previous week, but we don't claim the bottom has dropped out of the index every time the latter situation happens. What makes the trading week ending 21 January 2022 different?

It wasn't the rate at which stock prices declined. On no single day of the holiday-shortened trading week did the S&P 500 drop by more than 2% of their previous day's closing value, the volatility threshold we use for any given day's trading to qualify as being interesting.

Nor did the overall 8.3% decline of the index since its 3 January 2022 record high qualify as interesting, falling less than the 10% threshold that it would take to qualify as a correction in stock prices according to professional traders. By both these definitions, what happened in the Nasdaq composite index (Index: COMP) during the past three weeks qualifies as interesting, but not so much for the more diverse S&P 500.

Instead, our observation has a lot to do with how stock prices were behaving in recent months. Here, let's start with the latest update to our chart showing the S&P 500's periods of relative order and chaos, which now covers the full 30-year period from December 1991 through December 2021.

S&P 500 Average Monthly Index Value vs Trailing Year Dividends per Share, December 1991 to December 2021

According to a long-standing set of technical definitions we developed, here's how we define when a period of order exists in the market:

Order exists in a market whenever the change in the price of assets in the market are closely coupled with the change in the income that might be realized from owning or holding the assets, within a band of approximately normal variation about a central tendency.

In the case of the stock market, the assets are stocks, the price of which is given by the value of the S&P 500 index. The income that might be realized from owning or holding the assets are dividends, represented in the chart by the index' trailing year dividends per share.

When we refer to these two things being closely coupled, we mean when both the value of the S&P 500 and the index' trailing year dividends per share are either rising or falling together in a general trend. When that coupling exists, the variation of stock prices about a mean trend line can be approximately described by a normal distribution.

Looking at the most recent period of our 30-year chart, we see the period from March 2021 through December 2021 could reasonably qualify as a period of order according to our definition. Both stock prices and dividends per share have both been rising during these months.

Our next chart zeroes in on this period with daily data, where we confirm a close coupling exists in the period from 30 June 2021 through the end of 2021 and into January 2022.

S&P 500 Index Value vs Trailing Year Dividends per Share, 31 March 2021 to 21 January 2022

We've added statistical control chart-style thresholds to the chart to visualize a statistical hypothesis test. Here, when stock prices fall within three standard deviations of the mean trend, order can be said to exist for the S&P 500. Once stock prices fall outside that range indicated by the red dashed lines, we reject the hypothesis that order exists in the market.

On 21 January 2022, we see the level of stock prices drop below that key statistical threshold. We confirm order has broken down for the S&P 500 in this analytical approach and has done so by breaking through the lower limit of the range we would expect to find stock prices had the short established period of relative order in the U.S. stock market not broken down. This backward-looking approach confirms the similar assessment we arrived at using a forward-looking model.

To put it more colorfully, the bottom has dropped out of the S&P 500.

And now you know why we can say that! Now the question has become "is what happened on 21 January 2022 an outlier event and the trend still holds, or has it truly broken down?" We'll learn the answer to that question as early as this week.

Previously on Political Calculations