The Elasticity of Quantitative Investment
Review of Financial Studies (lead article and editor's choice)
Presentations: University of Utah, University of Washington, Yale, Purdue, London Business School, Boston University, Brigham Young University Economics Department, Brigham Young University Finance Department, Indiana University
What is the demand elasticity of statistical arbitrageurs that invest according to the advice of modern cross-sectional asset pricing models? Thirteen models from the literature exhibit strikingly inelastic demand, in contrast to classical models that rely on statistical arbitrageurs to create elastic market demand for assets. This inelasticity arises from the difficulty of trading against price changes. A quantitative equilibrium model shows that aggregate demand remains inelastic even with these statistical arbitrageurs in the market.
Why Do Portfolio Choice Models Predict Inelastic Demand? (with Mahyar Kargar and Jiacui Li) [published paper]
Journal of Financial Economics
Presentations: NBER LTAM, AFA, MFA, Maryland Young Scholars, UConn Finance Conference, Wabash Finance
Classical asset pricing models predict that optimizing investors exhibit extremely high demand elasticities, while empirical estimates are significantly lower—by three orders of magnitude. To reconcile this disparity, we introduce a novel decomposition of investor demand elasticity into two key components: “price pass-through,” which captures how price movements forecast returns, and “unspanned returns,” reflecting a stock’s lack of perfect substitutes. In a factor model framework, we show that unspanned returns become significant when models include “weak factors.” Classical models overestimate demand elasticity by assuming both very low unspanned returns and high price pass-throughs, assumptions that are inconsistent with empirical evidence.
The Limits of Factor Model Spanning (with Fahiz Baba-Yara and Brian Boyer)
R&R at the Review of Financial Studies
Presentations: Wharton Micro Finance Seminar, Craig Holden Memorial Conference, Red Rock Finance Conference, Indiana University, Brigham Young University
We investigate the extent to which modern academic machine learning models agree on which factors are priced in the cross-section of returns. We find that models disagree to a surprising extent. The majority of average returns attributed to factor exposure by any given model is generally deemed pure-alpha by other models. We provide a theoretical model with many predictors that provides an impossibility theorem for creating a consensus model using machine learning and available data.
Classical Versus Demand System Asset Pricing
Classical asset pricing (CAP) models often assume that asset demand is linear in log prices, while demand system asset pricing (DSAP) relies on near-isoelastic demand. Although isoelastic demand arises from a particular coefficient restriction—and exotic alternatives like cosine demand are possible—it fits the data better than a CAP model. CAP models predict similar percentage price impacts across stocks of very different sizes, whereas DSAP predicts smaller impacts for larger stocks, consistent with observed demand curves. I show that DSAP demand better matches the data by measuring price multipliers across the size distribution.
Do Households Matter for Asset Prices? (with Samuli Knüpfer, Jens Soerlie Kvaerner, Bahar Sen Dogan, and Petra Vokata)
Presentations: European Finance Association, Midwest Finance Association
Contrary to the common assertion that households have little impact on stock prices, we find their relevance is of first order. We quantify their impact using an assetdemand system applied to the complete ownership data for all Norwegian stocks from 2007 to 2020. Households contribute the most to stock market volatility relative to their market share. Even in absolute terms, they come second, surpassed only by institutional investors. Our granular data on households reveal a strong factor structure in household demand: The demand of the rich is distinct from less affluent investors, accounts for the bulk of volatility attributable to households, tilts away from ESG, and is informative about future firm fundamentals. We conclude by using the demand system to measure the profits one can make from trading on household demand shocks.
Rewriting Expected Returns (with Xiao Han, Stanislav Sokolinski, and Andrea Tamoni)
We develop a novel, equilibrium-based framework that systematically measures how investor flows can "rewrite returns" by re-pricing the cross-section of stocks. Our methodology enforces market clearing while providing a near-closed-form, economically intuitive approximation of how flows-both where they originate and where they land-ultimately shape asset returns. To illustrate its application, we apply our method to the classic value and momentum anomalies, showing that sufficiently large reallocations from growth to value funds could wipe out the value premium while substantially boosting momentum. In contrast, similarly sized inflows from a more diversified source-such as households, who hold both growth and value stocks-induce less extreme effects. In practice, extreme reallocation scenarios far exceed typical fund flow levels, explaining why certain anomalies persist despite their theoretical fragility. The transparent nature of our approximation provides a computationally efficient tool for "what-if" experiments and can assist researchers, policymakers, and practitioners in gaining clearer insights into how capital flows affect asset prices.
Is Asset Demand Elasticity Set at the Household or Intermediary Level? (with Ehsan Azarmsa)
Presentations: SFS Cavalcade, Yiran Fan Memorial Conference, AFA Annual Meeting
Household-based and intermediary-based asset pricing models disagree about the elasticity of the allocations to intermediaries. Household-based models (e.g., Lucas (1978); Campbell and Cochrane (1999); Bansal and Yaron (2004)) focus on households’ risk-return trade-offs, implying that the allocation to intermediaries is so elastic that renders the intermediaries’ portfolio behavior irrelevant. In contrast, intermediary-based models (e.g., He and Krishnamurthy (2013); Koijen and Yogo (2019); Haddad and Muir (2021)) emphasize households’ inelastic allocations, leading to drastically different pricing predictions. We shed light on this discrepancy by examining households’ allocations to intermediaries and estimating their price elasticity in the 13F data of institutional holdings. In a variance decomposition exercise, we find that households primarily respond to intermediaries’ excess demand for stocks by rebalancing their direct stock holdings, while their allocation to intermediaries exacerbates the demand pressure by about 10%. Consistent with theory, allocations to some intermediary types, such as mutual funds and investment advisors, exhibit a negative and significant relationship with the price of their portfolio assets. However, the elasticity of these allocations is not large enough to have a first-order impact on the aggregate demand elasticity for assets. Our results support the central premise of intermediary-based asset pricing models: households do not reallocate enough to eliminate mispricings induced by intermediary-level frictions.
Good Variance, Bad Variance: Cash-Flows, Discount Rates, and the Risk-Return Relationship (with Brandon Bates, Brian Boyer, and Tyler Shumway)
We decompose conditional variance into the sum of two components: one driven by uncertainty about cash-flow growth, or bad variance, and a second driven by uncertainty about discount rates, or good variance. We develop a simple theoretical model with time-varying second conditional moments and document empirical evidence that suggests bad variance earns a risk premium that is statistically and economically significant, whereas good variance does not. In out-of-sample tests we find that bad variance dominates other predictors of market returns and can help identify the gap between the lower bound of Martin (2016) and the actual market risk premium.
Profit Puzzles and the Fall of Public-Firm Profit Rates (with Alexandre Sollaci and James Traina)
Presentations: Indiana University, Federal Reserve Bank of San Francisco, International Monetary Fund, NBER SI Macroeconomics and Productivity
Why have US aggregate profit rates increased while financial market rates decreased since 1980? We propose a mismatch hypothesis: Profit rates in the national accounts track the return on capital for all firms, while financial market rates track the cost of capital for public firms only. We show public-firm profit rates halved since 1980, matching trends in financial markets and suggesting low market power. Nonfinancial domestic private-firm profit rates doubled, suggesting high market power or risk. Size and sector differences cannot explain the divergence, though intangible-intensity might. Our results indicate substantial biases in extrapolating public-firm trends to the aggregate economy.
Why Do Betas Fail? The Limits of Factor Models in High-Dimensional Settings (with Alejandro Lopez-Lira)
We develop a model featuring a high-dimensional state space, numerous assets, and rational risk-averse investors with incomplete information about covariances and expected returns. The model is able to explain several high-dimensional cross-sectional asset pricing puzzles. First, the capital asset pricing model (CAPM) fails because as the number of assets increases, average pricing errors grow because investors cannot fully recover the covariance matrix, even without considering uncertainty about expected returns. Moreover, since investors have different priors regarding the high-dimensional covariance matrix, the risk prices associated with common factors' exposures (betas) are also attenuated, with the consequence that it is beneficial to hedge systematic risk. Furthermore, investors having different priors about return predictability via characteristics leads to a zoo of anomalies. Finally, our model features the emergence of numerous high Sharpe ratio strategies that are not spanned by each other.
Mispricing and the Elasticity of Quantitative Investment
What happens to mispricing when statistical arbitrageurs, investing with prominent factor models from the literature, enter the market? This question is addressed with counterfactual experiments using an asset demand system methodology. Mispricing increases or marginally decreases when these models are used to manage capital counterfactually. This indicates that it is either quite difficult to eliminate mispricing or there are serious empirical shortfalls in modern factor models.
A Demand System Approach to Residential Housing Supply (with Darren Aiello, Mahyar Kargar, Jason Kotter, and Gregor Schubert)
Investment Mandates and Diversification (with Xiao Han, Lars-Alexander Kuehn, and Wenyu Wang)
Predictable Downturns (inactive)
Eugene Fama stated in his Nobel Prize lecture that “there is no statistically reliable evidence that expected stock returns are sometimes negative” (2013). However, various theoretical models such as Barberis et al. (2015) and Barlevy and Veronesi (2003) imply that expected stock returns are sometimes negative. This paper provides evidence that expected excess aggregate stock market returns are sometimes negative, and that portfolios composed of the most liquid stocks have predictable downturns as well. This paper presents a forecasting model that relies exclusively on ex-ante information to predict stock market downturns only when the day-prior confidence of a downturn is relatively high, and shows that the average excess return on days which are predicted to be downturns by the forecasting model is -13.9 basis points. Volatility and classic factor return variables alone are sufficient to predict downturns in the sample and are the most powerful downturn predictors. A market timing portfolio using these ex-ante predictions generates a risk-adjusted return of 3.5 basis points per day, annualized to an average 8.8% risk-adjusted return.