**Can The Meme Stock Index Act As An Equity Risk Forecasting Mechanism?**

#### Trading and Investing

THREE KEY TAKEAWAYS – The authors construct a meme stock index to predict selling and buying signals in the market. The index can correctly predict sell-offs in the S&P 500 that occur 9-days later with 88.89% accuracy.

– The index performs great with a 101.5% annualized risk-free return but an 81.43% volatility. The Sharpe Ratio for this portfolio is 1.247. The Sharpe Ratio is not very high, but it’s decent since we are investing in meme stocks with high volatility.

– The authors conclude that the change in the beta of the meme stock index is a useful indicator for market selling prediction but not buying prediction.

**Abstract**

“Meme Stocks” are stocks that experience extreme price increases in short time periods as a result of attention/hype generated on social media and online forums (most notably Reddit and Twitter). Since the price increase of these stocks is artificial (relying on the fever of the Internet) and not dependent on the actual performance of the company, these price spikes are typically followed by an inevitable crash. The objective of this paper is to analyze whether the performance of meme stocks can be used to predict movements in the S&P 500 and even the stock market crash of 2022.

Our approach is to construct a meme stock index using the top meme stocks (e.g. GameStop, AMC) and then utilize a machine learning model to predict buy and sell signals based on the beta of the index. Overall, our meme stock index is able to correctly predict buy/sell signals 57.38% of the time. More importantly, our meme stock index is able to correctly anticipate sell-offs that will take place 9-days later 88.89% of the time. Thus, it can become determined that our Meme Stock index was able to predict sell-offs in the S&P 500 in 9-day time frames with a very high degree of confidence.

We would like to thank Dr. Giuseppe Paleologo for this idea. Without his guidance, none of this would have been possible.

**2. Introduction**

**2.1 History of Meme Stocks**

A meme stock refers to the shares of a company that have gained a cult-like following online and through social media platforms. These online communities can go on to build hype around a stock through narratives and conversations elaborated in discussion threads on websites like Reddit and posts to followers on platforms like Twitter and Facebook.

The meme stock movement unofficially started in the summer of 2020 when most people were stuck at home during the first few months of the pandemic. Looking for something to do and a way to turn some of that extra free time into money, many people turned to the stock market and social media for ideas. The meme stock movement frenzy officially took off in January 2021, with GameStop (GME), the first meme stock, experiencing a stock price increase of 100 times over several months despite the company itself experiencing poor performance. AMC and Blackberry soon experienced huge growths in share price shortly after GameStop’s initial explosion, with stock prices increasing by 10 and 3 times, respectively (Gobler). Many stocks that experienced similar rapid growths in short time spans, as a result of increased online/social media hype, were deemed meme stocks (“Meme Stock”).

**2.2 Purpose of this research **

We conducted this research because we believe that there exists some relationship between meme stocks and the market (S&P 500). We wanted to explore the possibility of using meme stocks to predict buy and sell signals in the market. To do this, we constructed a meme stock index that includes 18 of the most popular meme stocks. We believe that a diversified meme stock index can help us better examine the relationship between meme stocks and the market.

**3. Data**

Our data encompasses the adjusted close price of the top 18 meme stocks from 31st December 2020 to 29th April 2022. These stocks are:

- AMC
- Advanced Micro Devices
- Amazon
- BlackBerry
- Bed, Bath & Beyond
- GameStop
- Intel
- BitNile Holdings
- Nio
- Nokia
- Palantir
- PayPal
- Snapchat
- Sundial Growers
- Spotify
- Tilray
- Tesla
- Workhorse Group

We believe that data prior to the start of 2021 would be redundant since the meme stocks frenzy only started in January 2021. Moreover, we believe that expanding our time period into the first half of 2022 would provide us with a deeper insight into correlations between the performance of meme stocks and the S&P 500 since global markets have been experiencing huge, prolonged falls since the start of 2022. In addition, we also used the adjusted close price of the S&P 500 from the same time period. After extracting the adjusted close prices for each meme stock and the S&P 500, we then determined their day-to-day price changes. This step is a crucial prerequisite for the allocation of weights in the construction of our meme stock index.

Figure 1: Dataset containing the adjusted close prices of each meme stock

Figure 2: The dataset on the top contains the adjusted close prices of the S&P500 and the dataset on the bottom contains the daily returns of the S&P 500

**4. Index construction and analysis**

**4.1 Analyzing the Sharpe Ratio to construct Meme Stock index**

The Sharpe Ratio is one of the most widely used formulae for calculating risk-adjusted return. The greater a portfolio’s Sharpe ratio, the better its risk-adjusted performance.

To construct our index, we used a portfolio randomizer to generate 10000 random portfolios each with different weightings for each meme stock. For each random portfolio, we calculated the returns, standard deviation, and returns/standard deviation. We then chose the portfolio with the best Sharpe Ratio to be our meme stock index. To find the portfolio with the best Sharpe Ratio, we identified the portfolio with the maximum returns/standard deviation value which would giveus the best return to risk ratio. The Sharpe ratio for this portfolio is 1.013 (“Meme Stock”).

**4.2 CAPM model**

We use CAPM to test our portfolio. The alpha in the CAPM model is 90.85% which is very high. The beta is 1.156. We believe it’s because the portfolio randomization helped us to select a portfolio with a relatively low beta but a high alpha.

**4.3 Alpha**

Alpha (α) is a term used in investing to describe an investment strategy’s ability to beat the market or its “edge.” Alpha is thus also often referred to as “excess return” or “abnormal rate of return,” which refers to the idea that markets are efficient, and so there is no way to systematically earn returns that exceed the broad market as a whole. Furthermore, alpha is often used in conjunction with beta (the Greek letter β), which measures the broad market’s overall volatility or risk, known as systematic market risk.

**4.4 Beta**

Beta (β) is a measure of the volatility or systematic risk of a security or portfolio compared to the market (S&P 500). Stocks with betas higher than 1.0 are more volatile than the S&P 500.

The portfolio/index’s beta changes over time (“What Is Beta in Finance, and How Is It Calculated?”).

**4.5 **Fama and French model

We use Fama and French models to test our portfolio. The alpha is 5.91%. The beta for market risk-free return is 0.37, for SMB is 2.5, and for HML is -0.21. SMB accounts for publicly traded companies with small market caps that generate higher returns, while HML accounts for value stocks with high book-to-market ratios that generate higher returns in comparison to the market. It is reasonable that our meme stock portfolio has a high positive beta with small companies, but a negative beta with value stocks.

**5. Initial Exploration of the Meme Stock Index as an indicator for S&P 500 movements **

After constructing our meme stock index, the next step was to check if the performance of the meme stock index can be an effective indicator of S&P 500 movements; is there a relationship between the performance of meme stocks and the movements of the S&P500?

To determine if our index can produce effective indication signals, we compared the rolling beta for our index with that of the S&P 500 since beta is a measure of the volatility of a portfolio/index in comparison to the S&P500. Our goal here was to observe whether significant changes in rolling beta relativity could be used as an effective signal of how S&P500 price will move. To test this, we experiment with different linear regression windows (30 and 60 days), different rolling beta windows (1, 3, 5), and different thresholds for determining the percentage change that would constitute a “significant change” in rolling beta relativity (Pipis). Daily returns were used to construct the linear regression windows of 30 and 60 days. Excess daily returns were not used.

We then calculated the beta for each day from the different linear regression windows. Next, to construct our rolling beta windows, we first subtracted the present day beta value from the beta value that was produced *n* days later, where *n *is the size of the rolling window. We then found the absolute value of the beta change and then divided this value by the size of the rolling window to calculate the relative beta change for each rolling window size. This relative beta change is a percentage change that represents the mean daily relative beta for each rolling window size. For example:

Let *n *= 3,

- Firstly, Day T Beta Value = 1
- Secondly, Day T+1 Beta Value = 2
- Thirdly, Day T+2 Beta Value = 4
- Fourthly, Day T+3 Beta Value = 3
- In addition, Total Beta Change = T+3 – T = 3 – 1 = 2
- Lastly, Relative beta for rolling window of size 3 for Day T+3 = Total Beta Change/3 = 2/3 = 0.667

Next, we ran various trials to determine the absolute beta change value that should be used as our minimum threshold to produce the most effective indication results of a relationship between the meme stock index and the S&P500. We ran these trials by plotting the price of the S&P500 and then plotting vertical bars on top of the S&P500 price curve, where each vertical bar represents a date where the absolute beta change value is above a certain threshold (e.g. 30%). We then observed the curve to see if sharp changes in the price of the S&P500 curve (denoted by a peak or trough) followed after each vertical bar (and before another vertical bar) in a consistent manner.

After testing various combinations of the aforementioned parameters (linear regression windows, rolling beta windows, significant change thresholds), we determined that beta relativity changes of 30% or greater were most effective in generating indication signals. Our tests proved that beta relativity changes that have a magnitude of 30% or greater are effective in producing indication signals that the S&P500 will experience significant movements soon. This is evidenced by our graphs below that demonstrate that a peak or trough is almost always preceded by a relative beta change of 30% or greater.

Moreover, we found that there were only 2 instances where the rolling beta relativity between the two indexes failed to be an effective indicator of S&P 500 movements. These are the 2 instances:

- 60-day Linear Regression Window and 3-day rolling beta window
- 60-day Linear Regression Window and 5-day rolling beta window

Figure 3: Graph displaying points of relative beta changes of 30% or greater (yellow vertical bars) and the S&P 500 price over time for a 30-Day Regression and Rolling Beta window of 1-Day combination.

Figure 4: Graph displaying points of relative beta changes of 30% or greater (yellow vertical bars) and the S&P 500 price over time for a 30-Day Regression and Rolling Beta window of 3-Days combination

Figure 5: Graph displaying points of relative beta changes of 30% or greater (yellow vertical bars) and the S&P 500 price over time for a 30-Day Regression and Rolling Beta window of 5-Days combination

Figure 6: Graph displaying points of relative beta changes of 30% or greater (red vertical bars) and the S&P 500 price over time for a 60-Day Regression and Rolling Beta window of 1-Day combination

As a result, based on these graphs, we have sufficient reason to believe that the performance of our meme stock index can be effective in producing signals that indicate a significant movement in the S&P 500 is coming. Furthermore, as can be seen in each of the graphs, the S&P 500 crash that took place in early 2022 is always directly preceded (by no more than a couple of weeks) by a relative rolling beta change of greater than 30%. Thus, our initial exploration suggests that there is great potential in the ability of meme stocks to predict sell-offs in particular.

**6. Predictivity Exploration with Machine Learning**

The final step of our research was to be able to confidently determine whether our meme stock index and meme stocks ultimately can become used to predict movements in the S&P 500. To do this, we attempted to utilize gradient boosting to predict buy/sell signals in the S&P 500 based on relative rolling beta change.

To predict buy/sell signals, we used the relative rolling beta changes to predict price changes instead. We implemented an 80/20 train-test split where we trained our model on the initial 80% of the data and then tested our model’s precision on the final 20% of the data. Since our data became arranged in chronological order, this meant that we would be predicting future values based on data from the past.

Furthermore, to ensure our price change data could become effectively inputted into our gradient boosting model, we had to perform feature engineering by using one-hot encoding:

a value of 0 associated with every negative price change, while a value of 1 associated with every positive price change. In our context, 0s represent sell signals while 1s represent buy signals.

Based on the relative rolling beta changes, our gradient boosting model would then predict either a 0 (signaling a sell) or a 1 (signaling a buy). For each initial linear regression and rolling beta window combination, we then tested various rolling windows for calculating price changes. We tested different rolling price change windows because we wanted to identify the time frame that we can expect movements in the S&P500 price to take place according to changes in the rolling beta of the meme stock index. The rolling price change window sizes we tested ranged sequentially from 1-day to 45-days.

To evaluate the performance of each combination, we used a confusion matrix since it can reflect the recall, precision, specificity, and accuracy of our model. In addition, we supplemented our evaluation with an accuracy score calculation. Of all our tests, we found that the combination of a 30-day linear regression window, 1-day rolling beta, and 9-day rolling price change enabled us to produce the best performing initial model. To improve our model’s performance, we then tuned the appropriate hyperparameters until we were able to optimize the model’s recall, specificity, precision, and accuracy. For our gradient boosting model, we used and experimented with 3 hyperparameters: max_depth, min_child_weight, and n_estimators. The max_depth values we tuned ranged from 3-15. The min_child_weight values we tuned ranged from 1-100. The n_estimators values we tuned ranged from 50-1000. We found that the most optimal hyperparameters were:

With these hyperparameters, we found that there were 16 instances where our model correctly predicted a sell signal and 2 instances where our model falsely predicted a sell signal. As a result, our model was able to correctly predict a sell signal 88.89% of the time. When predicting buy signals, we found that our model has a recall rate of 44.19% (19 instances where the model correctly predicted a buy signal over the total number of instances where the model predicted a buy signal). These values shown in our model’s confusion matrix below:

Figure 7: Confusion matrix showing our buy/sell predictions versus the actual actions of the S&P 500

In addition, our model also managed to achieve an accuracy rate of 57.38%.

**7. Conclusion**

The objective of this paper was to analyze whether the performance of meme stocks can be used to predict movements in the S&P 500. Based on our results, it appears that meme stocks have a very high degree of effectiveness in predicting sell signals. Since we decided to use a rolling price change window of 9-days for our final model, our results demonstrate that our meme stock index was able to correctly predict sell-offs in the S&P 500 that take place 9-days later 88.89% of the time.

However, with regards to predicting buy signals, our meme stock index performed significantly worse. When predicting buy signals, our model produced more false predictions than correct predictions (as evidenced by 19 correct buy signal predictions to 24 false buy signal predictions). The fact that the recall rate was 44.19%, and below the 50% threshold, communicates that meme stocks are terrible at predicting buy signals since they are even worse than making predictions based on random chance (or the flip of a coin). As a result, this shows that our meme stock index is not effective at predicting buy signals in the S&P 500.

**In conclusion, the performance of our meme stock index reveals that meme stocks have the potential to be used for predicting sell-offs in the S&P 500 that take place in 9-day time frames. **

On the other hand, it appears that meme stocks are not effective predictors of buy signals in the S&P 500. However, a significant limitation in our research was that our model’s training timeframe was very limited (beginning of 2021 to the beginning of 2022). This was due to the fact that the meme stocks phenomenon has only existed since January 2021. Thus, it is uncertain how effective meme stocks can still be in predicting sell-offs in the S&P 500 should the fever of meme stocks dissipate. Additionally, since meme stocks depend entirely on the attention/hype of the internet, the concept of meme stocks may very well disappear as quickly as they arrived. With this in mind, it is uncertain if the predictive prowess of meme stocks will continue into the future.

As of now, these limitations are contingent on a very important question: are meme stocks here to stay, or are they simply a flash in the pan?

**References:**

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“What Is Beta in Finance, and How Calculated?”* Investopedia*, 30 June 2022, www.investopedia.com/terms/b/beta.asp.

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“Fama and French Three Factor Model Definition: Formula and Interpretation” *Investopedia*, 31 May. 2022, https://www.investopedia.com/terms/f/famaandfrenchthreefactormodel.asp#:~:text=The%20Fama%20French%203%2Dfactor,Kenneth%20French%20in%20the%201990s.

Gaffney, Cynthia. “How to Calculate the Expected Return of a Portfolio Using CAPM.” *Pocketsense*, 19 Apr. 2017, https://pocketsense.com/calculate-expected-return-portfolio-using-capm-2745.html.

Gobler, Erin. “What Is a Meme Stock?” *The Balance*, The Balance, 31 Oct. 2021, https://www.thebalance.com/what-is-a-meme-stock-5118074.

Pipis, George. “Stocks Market Beta with Rolling Regression.” *Predictive Hacks*, 30 Jan. 2021, https://predictivehacks.com/stocks-market-beta-with-rolling-regression/.

**Can The Meme Stock Index Act As An Equity Risk Forecasting Mechanism?**

By:

Maximus Ong, Zhijiang Chen & Alexander Fleiss