Forecasting tomorrow's change in Tesla holders could be worth money to a broker. This paper offers evidence that the count is partly predictable. Turning that forecast into a hedge for fractional-share inventory requires three assumptions: holder counts stand in for fractional flow, every holder trades one share, and activity moves with price. The last assumption already runs into trouble in the paper's Figures 8 and 10. For airlines and biotech before 2020, the correlations approach −0.5.
From holder counts to a trading forecast
Erlwein-Sayer, Kepezkaya, Packham and Petukhina begin with a problem brokers actually face. Exchanges reject fractional orders, leaving brokers to net customer fractions internally and hold the remainder themselves. A forecast of tomorrow's retail flow would let the broker position ahead of it: overhedge expected buying and underhedge expected selling.
Robintrack supplies the target. It recorded the number of Robinhood accounts holding each of 8,392 stocks hourly from May 2018 to August 2020. The authors turn those observations into daily changes. They then join them to Yukka news-sentiment, ESG and risk scores, Bloomberg spreads and volume, and Yahoo returns. The matched sample contains 561 stocks. Within each of 11 industries, they use k-means to group stocks by the 120-day rolling correlation between activity and returns, producing 22 clusters. They choose the stock closest to each centroid and add AAPL, AMZN, MSFT and TSLA, bringing the total to 26.
A separate single-layer LSTM forecasts each stock. Its input is five days of 24 features, all lagged one day. The model is refit daily using the trailing 125 trading days and predicts one day ahead. The authors compare three feature sets: the full set, features selected by a random forest, and a set excluding sentiment and risk scores. A rolling ARIMAX uses the same features as a benchmark. LSTMs outperform ARIMAX, and the paper says sentiment "improves LSTM performance in most cases". A classification LSTM supplies flow-direction predictions, which feed a stylised exercise in inventory PnL.
Does the target capture fractional trading?
Holder counts combine whole-share and fractional owners without recording the shares or dollars they trade. As the paper acknowledges, Robinhood does not separate those owners. The paper dates the launch of Robinhood's fractional trading to December 2019. Yet training ends on 1 July 2019 and validation on 23 October 2019. Feature selection and every hyperparameter were therefore fixed using a platform that had no fractional trading.
Daily refits eventually include post-launch observations. But the 125-day window continues to carry pre-launch history for months into the test period, and the test window's first five weeks also precede the launch. Appendix B lists different boundaries (train 06/2018 to 11/2019). Either account puts the end of training before fractional trading began on Robinhood.
The LSTM advantage is clearer than the sentiment advantage
The nonlinear model justifies its place. TSLA's all-features RMSE before March 2020 is 3355.64, compared with 10111.03 for ARIMAX. After February, the best LSTM records an RMSE of 2950.15 for AAPL against 3525.44, and 6405.61 for TSLA against 8225.75. The evidence supports the paper's "almost all stocks" claim. Its later wording, "across all representative stocks", goes too far. On ASM after February, ARIMAX's MAE of 69.16 beats every LSTM variant; the best LSTM reaches 71.50. The comparison also gives the LSTM the best of three variants against a single ARIMAX.
Sentiment delivers less. Before March, it improves forecasts for AAPL, AMZN and MSFT. AAPL's selected-feature MAE is 884.03 versus 997.76 without sentiment; AMZN's is 454.01 versus 485.41. For MSFT, the all-features MAE is 1057.26 against 1294.38. Our count of MAE across the tables nevertheless puts the sentiment-free set first for 9 of 26 stocks before March and 10 of 26 afterward. During COVID, when news-driven flow should count most, excluding sentiment wins for AMZN (1490.65 vs 1620.90) and TSLA (3803.97 vs 3870.07). Some wins attributed to sentiment are barely distinguishable at the reported precision: RIG has 16.42 against 16.43, while TSLA's pre-March MAE is 1733.15 against 1735.99.
The design tilts the comparison toward sentiment. Two of the three variants include it, so selecting the minimum favours that side even if the sentiment features contribute nothing. We did not find a Diebold-Mariano or comparable test of the differences. The panel regressions account for 4.1% to 7.1% of total variance. Their sentiment coefficients also move around: dropping collinear regressors changes the negative-news coefficient from −2.137 to +1.467. The rolling ARIMAX coefficients show sign changes consistent with that panel reversal. Discussing those changes, the authors write that this "cautions against a structural interpretation of individual sentiment coefficients".
Inventory PnL depends on intraday drift
In the inventory exercise, the broker buys h = λ times predicted activity at the open. Customers execute at the open-close midpoint; the broker closes its position at the close. Daily PnL is −h·o + q(o+c)/2 + (h−q)c, or, after simplification, (c−o)(h − q/2).
A broker holding no inventory loses half of q times the open-to-close move when customers buy on rising days. Holding inventory helps only when predicted flow and intraday returns have the same sign. The authors explicitly assume this positive correlation. The exercise depends on it. Yet the paper's rolling correlations between flow and price approach −0.5 for several stocks in 2018-2019. Those correlations measure close-to-close returns, whereas the PnL uses open-to-close returns. They suggest a problem without directly testing the required relationship.
The formula includes neither spreads nor costs.
Position size raises a separate objection. Per-stock residual exposure, the paper says, "is bounded by less than one share". The exercise nevertheless scales h to the entire predicted change in holders and assumes each holder trades exactly one share. It therefore tests a dealer's willingness to warehouse retail flow, exposing the broker to a larger and different risk than the residuals from fractional trading.
The authors describe the exercise as "highly stylised", citing "the unavailability of information of actual customer trading times and quantities." Their conclusion acknowledges the gap again: "More precise information on actual trading activity would allow for more detailed analyses of high-priced stocks". It still says that forecast-based inventory building "lead to promising results for risk management purposes". They also acknowledge that "setting inventory equal to the trading activity forecast is generally too aggressive." Fair enough. Their exceptions deserve attention, though: average PnL declines for TSLA and BABA, and the 5% quantile deteriorates for TSLA, BABA and MSFT. Among the four highest-priced stocks, the group they identify as most relevant to fractional brokers, two (BABA, MSFT) appear on those lists. We found no dollar magnitudes in the text. The results are presented in a figure.
Where does the directional signal hold?
The direction forecasts provide the strongest evidence, with large differences between stocks. Over 181 daily signals, AMZN and TSLA produce permutation p-values below 0.2% on both the random and shifted tests. MSFT records 71.4% and 12.2%; AAPL records 34.2% and 6.2%. The paper itself describes MSFT as a poor performer. Its statement that accuracy is "significantly greater than 50% for each stock." is hard to reconcile with that result.
The tests have different nulls. Permutation preserves the number of long and short signals, controlling for class imbalance; a fixed 50% benchmark leaves that imbalance untreated. MSFT can exceed 50% accuracy and still lose to shuffled sequences with the same long/short mix 71.4% of the time. Simply predicting the majority direction is consistent with that outcome.
We could not test these findings ourselves. Robintrack ceased collecting data in August 2020, and we have neither a retail holder-count panel nor broker residual-inventory data. Public prices cannot recover the target.
The directional evidence holds for two of four mega-caps (AMZN and TSLA, p below 0.2%). The magnitude forecasts outperform an ARIMAX whose TSLA RMSE was three times the LSTM's. Establishing the hedging claim requires a broker's actual fractional residuals and PnL that pays the spread. We would take the risk-management claim seriously if forecast-sized pre-positioning reduced 95% VaR on those real residuals after that spread.
For now, the paper makes a good case for running that pilot.