“Anomalies, Roll’s Critique, and Proxy Error” Job Market Paper, semifinalist for the best paper in investments at the FMA 2023.

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Anomalies generate alphas. Roll (1977) notes that alphas contain two parts: the CAPM alpha and a bias resulting from the assets that are omitted from the equity market proxy. However, the size of the bias is not well understood. I develop a formal test that uses no arbitrage conditions to quantify the bias. I find that 12 of 99 documented anomalies have statistically significant bias, which range from .6% to 1.5%, annualized. I show that adding an anomaly as an additional factor, to make a new proxy, reduces the biases across anomalies only when the added anomaly had a significant bias. My test highlights that Roll’s Critique has sizable implications for asset pricing. In addition, the test can help classify whether an anomaly has substantial exposure to assets omitted from the equity market proxy. The test also provides a new proxy that may be closer to the CAPM market.

“Tax Loss Harvesting and Momentum” (with Richard Sias)

Evidence (e.g., Novy-Marx, 2012) that most stock return momentum arises from intermediate term (e.g., returns are more strongly related to returns over months -7 to -12 than -1 to -6) is inconsistent with most models of stock return momentum. We hypothesize that tax-loss selling may play a role in explaining these patterns. Consistent with our hypothesis we find that December and January exhibit a robust pattern with regard to the cross-sectional dependence of returns. Namely, December is positively cross-correlated with past months and January is negatively cross-correlated with past months and this pattern extends back more than one year.

“Factor Tilts or Active Tilts – Does Your Fund Look for the Value Factor or Value Investments?” (with Richard Sias)

We present a new decomposition of mutual funds activeness that partitions each funds’ active bets into factor exposure versus security selection. Empirically, we find that mutual funds have strongly moved from factor strategies to security selection over our sample from 2002 to 2014. Specifically, the amount of the managers’ portfolio that is unexplained by the factors is increasing over this sample period. The time series of factor tilts also provides evidence of whether mutual fund trading has reduced or eliminated known anomalies or whether the anomalies disappeared on their own. We find evidence consistent both with mutual funds trading to reduce anomalies as well as exacerbating anomalies. Funds in aggregate have a tilt toward long Asset Turnover (reducing the anomaly) as well as short Value (exacerbating the anomaly). In addition, the dispersion in tilts toward these factors increases over time.

“Sorting the Sources of Economic and Statistical Significance in Asset Pricing Tests: a GRS Decomposition into PCA Factors”

I show that an anomaly’s economic significance (average squared alphas) and statistical significance (Gibbons, Ross, and Shanken (1989) GRS F-scores) can be decomposed across the principal factors (eigenvectors of the residual covariance matrix). While an anomaly may be both economically and statistically significant, it does not imply that there exists a principal factor that is both economically and statistically significant. I examine the statistical and economic significance of the documented anomalies via the principal factors. Consistent with PCA factor models, such as Kozak, Nagel, and Santosh (2018), large eigenvalue principal factors carry most of the economic significance across anomalies. However, most of the statistical significance is carried by small eigenvalue principal factors, which is corroborated by the GRS test rejection of Kozak, Nagel, and Santosh (2018)'s PCA factor model. Qualitatively, the statistical and economic significance come from different principal factors. I propose a test to examine which of the principal factors bear significant contributions to GRS F-scores and average squared alphas. Both metrics only receive significant contributions from the principal factors with the largest and smallest eigenvalues. If large eigenvalue principal factors represent risk factors and small eigenvalue principal factors represent mispricing, then anomalies reveal the existence of priced omitted risk factors and mispricing.