本研究立基於Ali與Hirshleifer (2020) 的有限注意力框架，該文獻將動能溢出效應(Momentum Spillover) 歸因於共同分析師覆蓋所建立的資訊傳遞渠道，並證實關聯公司報酬(Connected-Firm Return, CFRET) 具備顯著的股價預測能力。本研究將此架構拓展至由ETF持股所構成的隱性網絡，探討ETF共同持股是否能產生類似於共同分析師網絡的連結效應，並檢驗由此網絡建構的CFRET是否同樣具備預測力。
實證資料涵蓋2017年4月至2024年12月、每月平均約700檔（樣本末約1,071檔）美國股票型ETF的每日持股明細。我們採用源自自然語言處理的GloVe(Global Vectors) 模型，試圖從高維度的共現矩陣中學習股票的低維表示向量。然而，分析發現原始GloVe向量的主成分嚴重受到「個股的ETF持有普及度」（即一檔股票被多少ETF持有）與市值等共同因子主導，未能有效反映真實的同儕聯繫。
為克服此一問題，我們使用Mu與Viswanath(2018)的“All-but-the-Top” 幾何修正法，透過移除向量均值與前幾大主成分來濾除市場雜訊。本研究在81個有效月份的樣本上，將上述架構加以嚴格檢驗與分解，獲得三項主要發現。
第一，幾何修正的真正價值在於讓「誰是同儕」這個問題有明確、可區分的答案。原始GloVe 向量呈現嚴重各向異性：任取兩檔股票，其平均餘弦相似度高達0.90、近99%互為正鄰居，亦即幾乎全市場都算「同儕」，使「關聯公司」失去鑑別力。經“All-but-the-Top” 修正後，正鄰居比例降至約50%，同儕才真正被區分出來；連帶使CFRET對「要取多少鄰居」(Top-K)此一人為選擇變得穩健，而原始向量的訊號則隨此選擇劇烈擺盪。
第二，捕捉領先－滯後(Lead-Lag)效應的條件式雙重排序策略，可產生約2.7%的月度報酬（夏普比率約1.3）、Fama-French五因子Alpha約2.4%（t=3.28）；但本研究發現，此報酬約三分之二實源於一個未被五因子模型涵蓋的「普及度溢酬」（依ETF持有普及度排序之多空組合，月均風險調整後Alpha達2.0%，t=2.85，且幾乎全數來自最低普及度分位的顯著負Alpha），而非純粹的共持風格連結。
第三，以「訊號正交化」與「組內中性化」兩種互補設計完全控制普及度後，CFRET 的單變量排序在所有修正等級仍然顯著：訊號正交化下每月約0.7%至1.0%（t介於2.0 與2.9 之間），組內中性化結果同向，且其利潤幾乎完全集中於「同儕表現極差」的放空端，與有限注意力假說下負面資訊延遲擴散的預期一致；雙重排序的時機增量則在剝離普及度後不再顯著，顯示其主要透過普及度通道實現。據此，本研究將ETF 隱性網絡的定價效果區分為兩條可分離的通道：一是與「個股的ETF持有普及度」相伴隨的報酬成分（普及度溢酬），二是扣除普及度後、源自共同持股關聯的資訊擴散成分，後者為本研究欲捕捉之核心效應。至於各通道的成因（例如被動資金需求或資訊擴散），本研究不作因果論斷，留待後續研究。

This study builds on the limited-attention framework of Ali and Hirshleifer (2020), which attributes momentum spillover to the information-transmission channels created by shared analyst coverage and shows that the resulting connected-firm return (CFRET) significantly predicts stock returns. We extend this framework to the implicit network formed by ETF co-holdings, asking whether common ETF ownership produces linkage effects analogous to those of the shared-analyst network, and whether a CFRET constructed from this network carries comparable predictive power.
Our empirical data cover daily holdings of, on average, roughly 700 U.S. equity ETFs per month (about 1,071 near the end of the sample) from April 2017 to December 2024. We employ the GloVe (Global Vectors) model from natural language processing to learn low-dimensional stock representations from the high-dimensional co-occurrence matrix. We find, however, that the leading principal components of the raw GloVe vectors are dominated by common factors such as “ETF popularity” (how frequently a stock is held) and market capitalization, so the raw vectors fail to reflect genuine peer linkages.
To address this, we apply the “All-but-the-Top” geometric refinement of Mu and Viswanath (2018), which removes the common mean vector and the leading principal components to filter out market-wide noise. Over the 81 valid sample months, we subject the framework to a rigorous test and decomposition, obtaining three main findings.
First, the real value of the geometric refinement is that it makes the question “who is a peer” well defined and discriminating. The raw GloVe vectors are severely anisotropic: the average pairwise cosine similarity reaches 0.90 and nearly 99% of stock pairs are positive neighbors—that is, almost the entire market qualifies as a “peer,” stripping “connected firms” of any discriminating power. After the “All-but-the-Top” refinement, the share of positive neighbors falls to about 50%, so peers become genuinely distinguishable; this in turn makes CFRET robust to the arbitrary choice of how many neighbors (Top-K) to include, whereas the raw-vector signal swings wildly with that choice.
Second, a conditional dual-sort strategy that captures the lead-lag effect generates a monthly return of about 2.7% (Sharpe ratio about 1.3) and a Fama-French five-factor alpha of about 2.4% (t = 3.28); however, our decomposition shows that roughly two-thirds of this return stems from an “ETF popularity premium” not spanned by the five-factor model (a long-short portfolio sorted on ETF popularity earns a monthly risk-adjusted alpha of 2.0%, t = 2.85, almost all of which comes from the significantly negative alpha of the least-held decile rather than any positive alpha on the most-held one), rather than from a pure co-holding linkage.
Third, after fully stripping out popularity with two complementary designs (signal orthogonalization and within-group neutralization), the univariate CFRET sort remains significant at every refinement level: 0.7% to 1.0% per month under signal orthogonalization (t between 2.0 and 2.9), with the within-group sort pointing the same way. The profits concentrate almost entirely in the short side, where peers have performed worst, consistent with the delayed diffusion of negative information under limited attention; the timing increment of the dual sort, by contrast, does not survive the purge, indicating that it operates mainly through the popularity channel. Accordingly, this study reinterprets the pricing effect of the implicit ETF network as two separable channels: a passive-demand-driven “popularity-intensity channel” and an information-diffusion-driven “co-holding spillover channel,” the latter being the core effect this study seeks to capture; we make no causal claims about the origin of either channel, leaving that to future research.

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