The dependence of belief dynamics on beliefs: implications for stock returns, with Ian Dew-Becker and Pooya Molavi, October 2024

This paper studies the implications of a simple theorem, which states that for arbitrary underlying dynamics, the cumulants of Bayesian beliefs have a recursive structure: the sensitivity of the mean to news is proportional to the variance; the sensitivity of the nth cumulant to news is proportional to the (n+1)th. The specific application is the US aggregate stock market, because it has a long time series of high-frequency data along with option-implied higher moments. The model qualitatively and quantitatively generates a range of observed features of the data: negative skewness and positive excess kurtosis in stock returns, positive skewness and kurtosis and long memory in volatility, a negative relationship between returns and volatility changes, and predictable variation in the strength of that relationship. Those results have a simple necessary and sufficient condition, which is model-free: beliefs must be negatively skewed in all states of the world. We show how to empirically measure belief moments nonparametrically.

Climate Transition Risks and the Energy Sector, with Viral Acharya, Stefano Pastore, Johannes Stroebel, Zhenhao Tan, and Tiffany Yong, January 2025

We build a general equilibrium model to study how climate transition risks affect energy prices and the valuations of different firms in the energy sector. We consider two types of fossil fuel firms: incumbents that have developed oil reserves they can extract today or tomorrow, and new entrants that must invest in exploration and drilling today to have reserves to potentially extract tomorrow. There are also renewable energy firms that produce emission-free energy but cannot currently serve non-electrifiable sectors of the economy. We analyze three sources of climate transition risk: (i) changes in the probability of a technological breakthrough that allows renewable energy firms to serve all economic sectors; (ii) changes in expected future taxes on carbon emissions; and (iii) restrictions on today’s development of additional fossil fuel production capacity. We show that the different transition risk—and, importantly, uncertainty about their realizations—have distinct effects on firms’ decisions, on their valuations, and on equilibrium energy prices. We provide empirical support for the heterogeneous effects of different transition risks on energy prices and stock returns of firms in different energy sub-sectors.

The Economics of Biodiversity Loss, with Theresa Kuchler, Johannes Stroebel, and Olivier Wang, March 2025

We explore the economic effects of biodiversity loss by developing an ecologically-founded model of how different species interact to deliver the ecosystem services that contribute to economic production. Ecosystem services are produced by combining several complementary ecosystem functions such as pollination and water filtration, which are each provided by several substitutable species. It follows that economic output is an increasing but concave function of species richness, and the economic cost of losing a species depends on: (i) how many redundant species remain within its ecosystem function, (ii) how critical the affected function is for overall ecosystem productivity, and (iii) the extent to which ecosystem services constrain economic output relative to other factors of production. We derive an expression for the fragility of ecosystems and economic output to further biodiversity loss, and decompose this fragility into within-function and across-function effects. Ecosystem fragility increases with both mean species losses as well as the imbalance of species losses across ecosystem functions. Consistent with the model, we show that empirical measures of biodiversity degradation and ecosystem fragility are reflected in market assessments of risk in the cross-section of countries, which we extract from the prices of credit default swaps. We conclude by embedding our model of ecosystem services production in an intertemporal planning problem and study optimal land use when land use raises output at the cost of reducing biodiversity.

Biodiversity Risk, with Theresa Kuchler, Johannes Stroebel, and Xuran Zeng, September 2024

Northwestern University Moskowitz Prize for sustainable finance research

Berkeley Haas Sustainable Business Research Prize

We explore the effects of physical and regulatory risks related to biodiversity loss on economic activity and asset values. We first develop a news-based measure of aggregate biodiversity risk and analyze how it varies over time. We also construct and publicly release several firm-level measures of exposure to biodiversity risk, based on textual analyses of firms’ 10-K statements, a large survey of financial professionals, regulators, and academics, and the holdings of biodiversity-related funds. Exposures to biodiversity risk vary substantially across industries in a way that is economically sensible and distinct from exposures to climate risk. We find evidence that biodiversity risks already affect equity prices: returns of portfolios that are sorted on our measures of biodiversity risk exposure covary positively with innovations in aggregate biodiversity risk. However, our survey indicates that market participants do not perceive the current pricing of biodiversity risks to be adequate.

Prediction When Factors are Weak, with Dacheng Xiu and Dake Zhang, March 2023

[Supplement]

In macroeconomic forecasting, principal component analysis (PCA) has been the most prevalent approach to the recovery of factors, which summarize information in a large set of macro predictors. Nevertheless, the theoretical justification of this approach often relies on a convenient and critical assumption that factors are pervasive. To incorporate information from weaker factors, we propose a new prediction procedure based on supervised PCA, which iterates over selection, PCA, and projection. The selection step finds a subset of predictors most correlated with the prediction target, whereas the projection step permits multiple weak factors of distinct strength. We justify our procedure in an asymptotic scheme where both the sample size and the cross-sectional dimension increase at potentially different rates. Our empirical analysis highlights the role of weak factors in predicting inflation, industrial production growth, and changes in unemployment.

What Drives Booms and Busts in Value?, with John Campbell and Christopher Polk, November 2023

[Online Appendix]

Value investing delivers volatile returns, with large drawdowns during both market booms and busts. This paper interprets these returns through an intertemporal CAPM, which predicts that aggregate cash flow, discount rate, and volatility news all move value returns. We document that indeed these shocks explain a large fraction of quarterly value returns over the last 60 years. We also distinguish between the intra-industry and inter-industry components of value, showing that the ICAPM explains the former better. Finally, we develop a novel methodology to perform this decomposition at the daily frequency, using it to interpret value returns during the Covid-19 pandemic.

The decline of the variance risk premium: evidence from traded and synthetic options, with Ian Dew-Becker, July 2024

The historical returns on equity index options are well known to be strikingly negative, with large negative CAPM alphas. That is typically explained either by investors having convex marginal utility over stock returns (e.g. crash/variance aversion) or by intermediaries demanding a premium for hedging risk. This paper shows that over the last 15 years, the returns of traded options have become significantly less negative, to the point that their CAPM alpha (and, relatedly, that of the variance risk premium) is now statistically indistinguishable from zero. We also build dynamically replicated, or synthetic, options, and show that over the period 1926–2022 they always had zero alpha. To explain these facts, the paper develops a model where the negative alpha of traded options between the late 80s and the early 2000s was driven by the risk that intermediaries in the options market had to bear; those alphas did not reflect the risk preferences of the average equity investor. Instead, synthetic options, based entirely on the price of the equity index, directly reflect the representative investor’s risk preferences: those show that the average investor never, over the last century, required high risk compensation for market downturns. Over time, as the quantity of risk borne by intermediaries declined, the risk premium of the traded options converged to those of the synthetic options. We provide empirical evidence on risk exposures of dealers consistent with the model.

A Quantity-Based Approach to Constructing Climate Risk Hedge Portfolios, with Georgij Alekseev, Quinn Maingi, Julia Selgrad and Johannes Stroebel, September 2024

Best Paper in Asset Pricing at the 2022 SFS Cavalcade

Two Sigma Award, Best Paper on Investment Management, 2022 WFA Meetings

We propose a new methodology to build portfolios that hedge climate change risks. Our quantity-based approach explores how mutual funds holdings change when the fund adviser experiences a local extreme heat event that shifts beliefs about climate risks. We use the observed trading behavior to predict how investors will reallocate their capital when "global" climate news shocks occur, which shift the beliefs and asset demands of many investors simultaneously and thus move equilibrium prices. We show that a portfolio that holds stocks that investors tend to buy after experiencing a local heat shock appreciates in value in periods with aggregate climate news shocks. Our quantity-based approach yields superior out-of-sample hedging performance compared to traditional methods of identifying hedge portfolios. The key advantage of the quantity-based approach is that it learns from cross-sectional trading responses rather than time-series price information, which is limited in the case of climate risks. We also demonstrate the efficacy and versatility of the quantity-based approach by constructing successful hedge portfolios for aggregate unemployment and house price risk.

Credit Default Swap Spreads and Systemic Financial Risk, April 2014

[Online Appendix]

Runner-up, Ieke van den Burg Prize for Research on Systemic Risk 2015

This paper measures the joint default risk of financial institutions by exploiting information about counterparty risk in credit default swaps (CDS). A CDS contract written by a bank to insure against the default of another bank is exposed to the risk that both banks default. From CDS spreads we can then learn about the joint default risk of pairs of banks. From bond prices we can learn the individual default probabilities. Since knowing individual and pairwise probabilities is not sufficient to fully characterize multiple default risk, I derive the tightest bounds on the probability that many banks fail simultaneously.

31. Nature Loss and Climate Change: the Twin-Crises Multiplier, with Theresa Kuchler, Johannes Stroebel, and Olivier Wang

      AEA Papers and Proceedings (2025), 115: 409-414

30. Four Facts about ESG Beliefs and Investor Portfolios, with Matteo Maggiori, Johannes Stroebel, Zhenhao Tan, Stephen Utkus, and Xiao Xu

Journal of Financial Economics (2025), 164

Northwestern University Moskowitz Prize for sustainable finance research (honorable mention)

29. Test Assets and Weak Factors, with Dacheng Xiu and Dake Zhang

Journal of Finance (2025), 80(1), 259-319

    [Code]

28. Recent Developments in Financial Risk and the Real Economy, with Ian Dew-Becker

Annual Review of Financial Economics (2024), 16 (4):1-22

27. Equity Term Structures without Dividend Strips Data, with Bryan Kelly and Serhiy Kozak

Journal of Finance (2024), 79 (6)

   [Data]

26. Cross-sectional uncertainty and the business cycle: evidence from 40 years of options data, with Ian Dew-Becker

  American Economic Journal: Macroeconomics (2023), 15 (2): 65-96

  [Data]

25. The effect of climate risks on the interactions between financial markets and energy companies, with Arthur van Benthem, Edmund Crooks, Eugenie Schwob and Johannes Stroebel 

  Nature Energy (2022), 7: 690–697 

24. Factor Models, Machine Learning, and Asset Pricing, with Bryan Kelly and Dacheng Xiu

  Annual Review of Financial Economics (2022), 14: 337-68

23. The Collateral Rule: Evidence from the Credit Default Swap Market, with Agostino Capponi, Allen Cheng, Chuan Du, and Richard Haynes

Journal of Monetary Economics (2022), 126: 58-86

22. Climate Change and Long-Run Discount Rates: Evidence from Real Estate, with Matteo Maggiori, Krishna Rao, Johannes Stroebel, and Andreas Weber

Review of Financial Studies (2021), 34(8): 3527-3571

RFS Editor's Choice Article

RFS Michael Brennan Best Paper Award Runner Up 2022

21. Asset Pricing with Omitted Factors, with Dacheng Xiu

 Journal of Political Economy (2021), 129(7): 1947-1990

Lead Article 

Best Paper Prize at the 2017 European Financial Association conference

  [Online Appendix] [Code]

20. The joint dynamics of investor beliefs and trading during the COVID-19 crash, with Matteo Maggiori, Johannes Stroebel and Stephen Utkus

PNAS (2021), 118(4) 

Previously circulated as "Inside the Mind of a Stock Market Crash"

19. Five Facts About Beliefs and Portfolios, with Matteo Maggiori, Johannes Stroebel, and Steven Utkus

American Economic Review (2021), 111 (5): 1481-1522

2021 AQR Insight Award (Distinguished Paper)

Best Behavioral Finance Paper, Midwest Finance Association Meetings 2020

Yuki Arai Faculty Research Prize for Finance 2019

[Online Appendix]

18. Climate Finance, with Bryan Kelly and Johannes Stroebel

 Annual Review of Financial Economics (2021), 13:15-36

17. Hedging macroeconomic and financial uncertainty and volatility, with Ian Dew-Becker and Bryan Kelly

 Journal of Financial Economics (2021), 142: 23-45

[Data] [Online Appendix]

16. Thousands of alpha tests, with Yuan Liao and Dacheng Xiu

Review of Financial Studies (2021), 34(7): 3456-3496

[Online Appendix] [Code]

15.  Taming the Factor Zoo: a Test of New Factors, with Guanhao Feng and Dacheng Xiu

  Journal of Finance (2020), 75(3): 1327-1370

[Online Appendix]

AQR Insight Award 2018, First Prize

14.  Uncertainty Shocks as Second-Moment News Shocks, with David Berger and Ian Dew-Becker

  Review of Economic Studies (2020), 87(1): 40-76

[Data] [Online Appendix]

     (Previous Title: "Contractionary Volatility or Volatile Contractions"?)

13.  Hedging Climate Change News, with Robert Engle, Bryan Kelly, Heebum Lee and Johannes Stroebel

  Review of Financial Studies (2020), 33(3): 1184-1216

[Data]

12.  An Intertemporal CAPM with Stochastic Volatility, with John Campbell, Christopher Polk and Bob Turley 

  Journal of Financial Economics (2018), 128(2): 207-233

Lead article

Fama-DFA Prize for the Best Paper Published in the Journal of Financial Economics (Asset Pricing), 2018

[Online Appendix]

11.  Excess Volatility: Beyond Discount Rates, with Bryan Kelly

  Quarterly Journal of Economics (2018), 133(1): 71-127

    Finalist, AQR Insight Award, 2016

    Napa Conference Best Paper Award, 2016

    [Online Appendix]

10.   The Price of Variance Risk, with Ian Dew-Becker, Anh Le and Marius Rodriguez

  Journal of Financial Economics (2017), 123(2): 225-250

Lead article

[Data] [Online Appendix]

9.   Asset Pricing in the Frequency Domain: Theory and Empirics, with Ian Dew-Becker

  Review of Financial Studies (2016), 29(8): 2029-2068

[Online Appendix] [Coverage: VoxEU]

8.   No-Bubble Condition: Model-Free Tests in Housing Markets, with Matteo Maggiori and Johannes Stroebel

  Econometrica (2016), 84(3): 1047-1091

[Online Appendix] [Reply] [Coverage: VoxEU]

7.   Systemic Risk and the Macroeconomy: An Empirical Evaluation, with Bryan Kelly and Seth Pruitt

  Journal of Financial Economics (2016), 119(3): 457-471

Lead article

Fama-DFA Prize for the Best Paper Published in the Journal of Financial Economics (Asset Pricing), 2016

Q-Group Roger F. Murray Prize (3rd prize), 2015

[Online Appendix] [Data] [Coverage: MoneyAndBanking.com; VoxEU; BFI]

6.   A Review of Long-Run Discounting: evidence from Housing Markets, with Matteo Maggiori

 Rivista di Politica Economica (2016), 4, 7-36 (not refereed)

5.   Very Long-Run Discount Rates, with Matteo Maggiori and Johannes Stroebel

  Quarterly Journal of Economics (2015), 130(1): 1-53

QJE Lead Article

QJE Editor's Choice article

Jacob Gold & Associates Best Paper Prize, ASU Sonoran Winter Finance Conference, 2014

NYU Glucksman Institute Faculty Research Prize for the Best Paper in Finance, 2015

[Online Appendix] [NBER WP Version] [Data]

[Coverage: Forbes ; Economist, May 2014 ; National Review ; NBER Digest ; VoxEU; Economist, April 2015]

4.   No News is News: Do Markets Underreact to Nothing?, with Kelly Shue

  Review of Financial Studies, (2014), 27(12): 3389-3440

Lead Article

RFS Editor's Choice article

Winner of the UBS Global Asset Management Award for Research in Investments, FRA Meeting 2012

[Coverage on Capital Ideas]

3.   Hard Times, with John Campbell and Christopher Polk

  Review of Asset Pricing Studies (2013), 3(1): 95-132

[Online Appendix]

2.   Intangible Capital, Relative Asset Shortages, and Bubbles, with Tiago Severo

  Journal of Monetary Economics (2012), 59: 303-317

[Online Appendix]

1.   Forced Sales and House Prices, with John Campbell and Parag Pathak

 American Economic Review (2011), 101(5): 2108–31

[Online Appendix] [Coverage at SeekingAlpha]