“Stock Embedding and Stock Association in Fund Holdings” — afternoon session, May 24, 2024
Q: The correlation of stock returns shows a structural break over the 2014–2023 historical period (Figure 4.10), so why doesn’t the Fama-MacBeth regression (Table 4.17) account for this structural change, and instead compute significance directly on the mean factor return over the entire history?
A: A structural break in the time series of pairwise stock return correlation doesn’t imply that the cross-sectional correlation between the anomaly factor and future returns also undergoes a structural change over time. Looking at the daily IC mean and cumulative IC (Figure 4.16), the cross-sectional correlation coefficient between the associated-momentum factor and future returns shows no obvious structural change over time. Since the factor serves as the explanatory variable and future returns as the dependent variable, their correlation coefficient is approximately the factor return; so when the daily IC is approximately stationary, a significance test can be run directly on the time-series mean of the factor return. In addition, a Newey-West adjustment was applied to the time-series variance during testing. That said, for greater rigor, one could also perform structural-break detection on the time-series distribution of daily IC before the Fama-MacBeth test, or perform structural-break detection on the time-series distribution of the estimated regression coefficients (i.e., the factor returns) during the test.
Q: How can you tell that the W2V similarity metric from the embedding model has better interpretability than the human-defined association metric?
A: The W2V similarity obtained from the embedding model shows a stronger monotonic relationship with stock market cap and industry characteristics (Figures 4.3–4.6): sorting all stocks in the market by market cap into five groups (or splitting into two groups by same-industry/different-industry), and computing the mean pairwise W2V similarity (or human-defined association) within each group, we find that W2V similarity decreases as market cap increases (and same-industry W2V similarity is higher), and the difference in average W2V similarity across groups is more pronounced than the difference in average human-defined association. Therefore, W2V similarity correlates more strongly with market cap and industry classification, and can be explained more readily by observable stock characteristics.
Q: Why do you believe the W2V-similarity-driven factor performs better?
A: In the factor evaluation, first, on the IC and ICIR metrics, the W2V-similarity-driven factor outperforms the human-association-driven factor, meaning the factor value correlates more strongly with future returns and with less volatility in that correlation, indicating stronger predictive power for the former. Second, sorting stocks each day into five groups by factor value and comparing the historical return performance of the highest-factor-value group, the lowest-factor-value group, and the benchmark index (CSI All Share), we find that the highest group consistently beats the overall market, and the highest-minus-lowest group achieves stable hedged performance. Across these portfolios’ historical performance — return, Sharpe ratio, drawdown, win rate, and so on — the W2V-similarity-driven factor outperforms the human-association-driven factor throughout, so it can be concluded that the W2V-similarity-driven factor performs better.
Q: Why did you model using the full universe of A-share mutual funds, rather than distinguishing between equity funds, hybrid funds, and bond funds?
A: During data processing, funds holding less than 20% of net asset value in A-shares, as well as funds holding fewer than 10 A-share stocks, were excluded. This, in a meaningful sense, filters down to funds that pay close attention to A-shares and invest prudently. This paper aims to use the embedding method to repeatedly exploit fund holdings data to extract stock-level characteristics from the perspective of institutional investors — characteristics that, in theory, arise from buy-side holding demand and collective shareholder decision-making, and that come more from broad coverage across institutional investors in general rather than from a small number of institutions specializing in some particular stock characteristic for targeted investment. In addition, this paper uses an unsupervised embedding model, and I did not want to introduce too much subjective, prior-driven filtering logic.
Q: Since the embedding model gives equal attention to all funds across the market, might it overweight small funds while underweighting the influence of the small number of large funds?
A: It might indeed, and this is exactly the limitation raised in the conclusion and outlook section of Chapter 5. However, within the embedding model, it would be easy to weight different funds by influence in the loss function, with influence proxied by fund size, historical performance, and so on. But choosing the proxy variable for the weighting would likewise introduce prior logic, undermining the generality of this paper’s research topic. Based on my understanding of actively managed funds, relatively unimportant small funds tend to follow and imitate the holding behavior of larger, more influential funds — active fund managers have a tendency to herd together — and a small fund that goes its own “maverick” way is also more likely to be weeded out by the market precisely because its buying and selling diverges from that of large capital. So weighting small and large funds equally does not necessarily mean the influence of large funds is underweighted.
Q: You suggest the model learns the views embedded in active funds’ holding behavior. If one invested based on these views, wouldn’t that mean converging with the investment behavior of public mutual funds? Public funds want to grow their AUM to earn management fees, and may concentrate their holdings in a small number of heavyweight stocks — is it wise to follow public fund holdings?
A: It wouldn’t converge with public fund behavior. What the model learns is the stock associations embedded in fund holdings, which helps uncover a more diversified set of related stocks. If a stock is found to have historically underperformed relative to other highly-associated stocks, that more likely suggests the stock’s market price is undervalued — the model’s value lies precisely in discovering associated stocks and holding the ones that are “underpriced relative to their peers,” rather than buying stocks that funds have already piled heavily into. This paper holds that what’s embedded in public fund holdings is, more than anything, the fundamentals and competitive landscape that fund managers derive through their own analysis; so the stock associations the model identifies are, more than anything, similarities in the fundamentals, business operations, and growth potential of listed companies. Around these similarities, finding companies with the same kind of fundamentals but undervalued is why the associated-momentum factor can remain consistently effective. So investing based on the model’s characterization of company associations is not necessarily following public fund behavior — it could also be filling in the “blind spots” of public funds, complementing their holdings in a way that helps promote market efficiency.