Working Papers

Taming the Factor Zoo  (March 2017)
with Guanhao Feng and Dacheng Xiu

The asset pricing literature has produced hundreds of potential risk factors. Organizing this ``zoo of factors" and distinguishing between useful, useless, and redundant factors require econometric techniques that can deal with the curse of dimensionality. We propose a model-selection method that allows us to systematically evaluate the contribution to asset pricing of any new factor, above and beyond what is explained by a high-dimensional set of existing factors. Our procedure selects the best parsimonious model out of the large set of existing factors, and uses it as the control in making statistical inference about the contribution of new factors. Our inference allows for model selection mistakes, and is therefore more reliable in finite sample. We derive the asymptotic properties of our test and apply it to a large set of factors proposed in the literature. We show that despite the fact that hundreds of factors have been proposed in the last 30 years, some recent factors -- like profitability -- have statistically significant explanatory power in addition to existing ones. We confirm the effectiveness of our procedure to discriminate factors in a recursive and out-of-sample experiment, and show that it results in a parsimonious model with a small number of factors and high cross-sectional explanatory power, even as the pool of candidate factors has expanded dramatically.

with Dacheng Xiu
[MATLAB code[AFA Slides]

We propose a three-pass method to estimate the risk premia of observable factors in a linear asset pricing model, which is valid even when the observed factors are just a subset of the true factors that drive asset prices or they are measured with error. We show that the risk premium of a factor can be identified in a linear factor model regardless of the rotation of the other control factors as long as they together span the space of true factors. Motivated by this rotation invariance result, our approach uses principal components to recover the factor space and combines the estimated principal components with each observed factor to obtain a consistent estimate of its risk premium. Our methodology also accounts for potential measurement error in the observed factors and detects when such factors are spurious or even useless. The methodology exploits the blessings of dimensionality, and we therefore apply it to a large panel of equity portfolios to estimate risk premia for several workhorse linear models. The estimates are robust to the choice of test portfolios within equities as well as across many asset classes.

with David Berger and Ian Dew-Becker
(Replaces: "Contractionary Volatility or Volatile Contractions"?)

This paper provides new empirical evidence on the relationship between aggregate uncertainty and the macroeconomy. We identify uncertainty shocks using methods from the literature on news shocks, following the observation that second-moment news is a shock to uncertainty. According to a wide range of VAR specifications, shocks to uncertainty have no significant effect on the economy, even though shocks to realized stock market volatility are contractionary. In other words, realized volatility, rather than uncertainty about the future, is associated with contractions. Furthermore, investors have historically paid large premia to hedge shocks to realized volatility, but the premia associated with shocks to uncertainty have not been statistically different from zero. We argue that these facts are consistent with the predictions of a simple model in which aggregate technology shocks are negatively skewed. So volatility matters, but it is the realization of volatility, rather than uncertainty about the future, that seems to be associated with declines.

with Bryan Kelly

Finalist, AQR Insight Award, 2016
Napa Conference Best Paper Award, 2016

We document a form of excess volatility that is difficult to reconcile with standard models of prices, even after accounting for variation in discount rates. We compare prices of claims on the same cash flow stream but with different maturities. Standard models impose precise internal consistency conditions on the joint behavior of long and short maturity claims and these are strongly rejected in the data. In particular, long maturity prices are significantly more variable than justified by the behavior at short maturities. Our findings are pervasive. We reject internal consistency conditions in all term structures that we study, including equity options, currency options, credit default swaps, commodity futures, variance swaps, and inflation swaps.

with Matteo Maggiori, Johannes Stroebel, and Andreas Weber

Revise and Resubmit at the Journal of Political Economy

The optimal investment to mitigate climate change crucially depends on the discount rate used to evaluate the investment's uncertain future benefits. The appropriate discount rate is a function of the horizon over which these benefits accrue and the riskiness of the investment. In this paper, we estimate the term structure of discount rates for an important risky asset class, real estate, up to the very long horizons relevant for investments in climate change abatement. We show that this term structure is steeply downward-sloping, reaching 2.6% at horizons beyond 100 years. We explore the implications of these new data within both a general asset pricing framework that decomposes risks and returns by horizon and a structural model calibrated to match a variety of asset classes. Our analysis demonstrates that applying average rates of return that are observed for traded assets to investments in climate change abatement is misleading. We also show that the discount rates for investments in climate change abatement that reduce aggregate risk, as in disaster-risk models, are bounded above by our estimated term structure for risky housing, and should be below 2.6% for long-run benefits. This upper bound rules out many discount rates suggested in the literature and used by policymakers. Our framework also distinguishes between the various mechanisms the environmental literature has proposed for generating downward-sloping discount rates.

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.


  10.  An Intertemporal CAPM with Stochastic Volatility
with John Campbell, Christopher Polk and Bob Turley
[Online Appendix]

Journal of Financial Economics, forthcoming

This paper studies the pricing of volatility risk using the first-order conditions of a long-term equity investor who is content to hold the aggregate equity market rather than tilting towards value stocks and other equity portfolios that are attractive to short-term investors. We show that a conservative long-term investor will avoid such tilts in order to hedge against two types of deterioration in investment opportunities: declining expected stock returns, and increasing volatility. Empirically, we present novel evidence that low-frequency movements in equity volatility, tied to the default spread, are priced in the cross-section of stock returns. 

    9.  The Price of Variance Risk
with Ian Dew-Becker, Anh Le and Marius Rodriguez
[Online Appendix]

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

JFE Lead article

Between 1996 and 2014, it was costless on average to hedge news about future variance at horizons ranging from 1 quarter to 14 years. Only unexpected, transitory realized variance was significantly priced. These results present a challenge to many structural models of the variance risk premium, such as the intertemporal CAPM and recent models with Epstein–Zin preferences and long-run risks. The results are also difficult to reconcile with macro models in which volatility affects investment decisions. At the same time, the data allows us to distinguish between different disaster models; a model in which the stock market has a time-varying exposure to disasters and investors have power utility fits the major features of the variance term structure.

with Ian Dew-Becker
[Online Appendix[Coverage: VoxEU]

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

We quantify investors' preferences over the dynamics of shocks by deriving frequency-specific risk prices that capture the price of risk of consumption fluctuations at each frequency. The frequency-specific risk prices are derived analytically for leading models. The decomposition helps measure the importance of economic fluctuations at different frequencies. We precisely quantify the meaning of "long-run" in the context of Epstein-Zin preferences -- centuries -- and measure the exact relevance of business-cycle fluctuations. Last, we estimate frequency-specific risk prices and show that cycles longer than the business cycle -- long-run risks -- are significantly priced in the equity market.
with Matteo Maggiori and Johannes Stroebel
[Online Appendix[Coverage: VoxEU]

Econometrica (2016), 84(3): 1047-1091

We test for the existence of housing bubbles associated with a failure of the transversality condition that requires the present value of payments occurring infinitely far in the future to be zero. The most prominent such bubble is the classic rational bubble. We study housing markets in the U.K. and Singapore, where residential property ownership takes the form of either leaseholds or freeholds. Leaseholds are finite-maturity, pre-paid, and tradable ownership contracts with maturities often exceeding 700 years. Freeholds are infinite-maturity ownership contracts. The price difference between leaseholds with extremely-long maturities and freeholds reflects the present value of a claim to the freehold after leasehold expiry, and is thus a direct empirical measure of the transversality condition. We estimate this price difference, and find no evidence of failures of the transversality condition in housing markets in the U.K. and Singapore, even during periods when a sizeable bubble was regularly thought to be present.

with Bryan Kelly and Seth Pruitt
Journal of Financial Economics (2016), 119(3): 457-471

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

This article studies how systemic risk and financial market distress affect the distribution of shocks to real economic activity. We analyze how changes in 19 different measures of systemic risk skew the distribution of subsequent shocks to industrial production and other macroeconomic variables. We empirically explore this link in the US and Europe over several decades. We also propose dimension reduction estimators for constructing systemic risk indexes from the cross section of measures and demonstrate their success in predicting future macroeconomic shocks out of sample.
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

We estimate how households trade off immediate costs and uncertain future benefits that occur in the very long run, 100 or more years away. We exploit a unique feature of housing markets in the U.K. and Singapore, where residential property ownership takes the form of either leaseholds or freeholds. Leaseholds are temporary, pre-paid, and tradable ownership contracts with maturities between 99 and 999 years, while freeholds are perpetual ownership contracts. The price difference between leaseholds and freeholds reflects the present value of perpetual rental income starting at leasehold expiry, and is thus informative about very long-run discount rates. We estimate the price discounts for varying leasehold maturities compared to freeholds and extremely long-run leaseholds via hedonic regressions using proprietary datasets of the universe of transactions in each country. Households discount very long-run cash flows at low rates, assigning high present value to cash flows hundreds of years in the future. For example, 100-year leaseholds are valued at more than 10% less than otherwise identical freeholds, implying discount rates below 2.6% for 100-year claims.

with Kelly Shue

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

RFS Lead Article
Editor's Choice article
Winner of the UBS Global Asset Management Award for Research in Investments, FRA Meeting 2012

As illustrated in the tale of “the dog that did not bark,” the absence of news and the passage of time often contain information. We test whether markets fully incorporate this information using the empirical context of mergers. During the year after merger announcement, the passage of time is informative about the probability that the merger will ultimately complete. We show that the variation in hazard rates of completion after announcement strongly predicts returns. This pattern is consistent with a behavioral model of underreaction to the passage of time and cannot be explained by changes in risk or frictions.

    3.  Hard Times
with John Campbell and Christopher Polk
[Online Appendix]

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

We show that the stock market downturns of 2000–2002 and 2007–2009 have very different proximate causes. The early 2000s saw a large increase in the discount rates applied to profits by rational investors, while the late 2000s saw a decrease in rational expectations of future profits. We reach these conclusions by using a VAR model of aggregate stock returns and valuations, estimated both without restrictions and imposing the cross-sectional restrictions of the intertemporal capital asset pricing model (ICAPM). Our findings imply that the 2007–2009 downturn was particularly serious for rational long-term investors, whose losses were not offset by improving stock return forecasts as in the previous recession.

    2.  Intangible Capital, Relative Asset Shortages, and Bubbles
with Tiago Severo
[Online Appendix]

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

Purely technological factors can be a fundamental force behind the emergence of asset price bubbles in developed economies. We analyze an economy in which the produc- tion technology utilizes both physical and intangible capital, where the latter cannot be used as collateral for borrowing. Technological change, in the form of increased importance of intangible capital in production, sharpens the borrowing constraints of entrepreneurs, leading to a scarcity of high-yield assets relative to low-yield ones. This can create the conditions for asset bubbles. Additionally, due to the financial frictions, standard dynamic efficiency tests are not valid, and bubbles are not Pareto improving.

    1.  Forced Sales and House Prices
with John Campbell and Parag Pathak
[Online Appendix] [Coverage at SeekingAlpha]

American Economic Review (2011), 101(5): 2108–31
This paper uses data on house transactions in the state of Massachusetts over the last 20 years to show that houses sold after foreclosure, or close in time to the death or bankruptcy of at least one seller, are sold at lower prices than other houses. Foreclosure discounts are particularly large on average at 28% of the value of a house. The pattern of death-related discounts suggests that they may result from poor home maintenance by older sellers, while foreclosure discounts appear to be related to the threat of vandalism in low-priced neighborhoods. After aggregating to the zipcode level and controlling for regional price trends, the prices of forced sales are mean-reverting, while the prices of unforced sales are close to a random walk. At the zipcode level, this suggests that unforced sales take place at approximately efficient prices, while forced-sales prices reflect time-varying illiquidity in neighborhood housing markets. At a more local level, however, we find that foreclosures that take place within a quarter of a mile, and particularly within a tenth of a mile, of a house lower the price at which it is sold. Our preferred estimate of this effect is that a foreclosure at a distance of 0.05 miles lowers the price of a house by about 1%.

An Equilibrium Model of Institutional Demand and Asset Prices
by Ralph Koijen and Motohiro Yogo
AFA 2017

The Cross-Section of Currency Volatility Premia

by Pasquale Della Corte, Roman Kozhan, and Anthony Neuberger
AFA 2017

Climate Risks and Market Efficiency

by Harrison Hong, Frank Weikai Li and Jiangmin Xu
NBER Asset Pricing Meeting, November 2016

Volatility Managed Portfolios

by Alan Moreira and Tyler Muir
Paul Woolley Centre Conference (LSE) 2016

Linking Cross-Sectional and Aggregate Expected Returns
by Serhiy Kozak and Shri Santosh
SFS Cavalcade 2016

Systemic Default and Return Predictability in the Stock and Bond Markets

by Jack Bao, Kewei Hou and Shaojun Zhang
UBC WFC 2016

Nominal Exchange Rate Stationarity and Long-Term Bond Returns
by Hanno Lustig, Andreas Stathopoulos and Adrien Verdelhan
AFA 2016

Fear Trading
by Paul Schneider and Fabio Trojani
AFA 2016

Horizon-specific macroeconomic risks and the cross section of expected returns
by Martijn Boons and Andrea Tamoni
EFA 2015

Efficiency and Distortions in a Production Economy with Heterogeneous Beliefs
by Christian Heyerdahl-Larsen and Johan Walden
WFA 2015

Aggregate Tail Risk and Expected Returns
by David Chapman and Michael Gallmeyer
SFS Cavalcade 2015

Nominal term spread, real rate and consumption growth
by Anna Cieslak and Pavel Povala
MFA 2015

Business-cycle consumption risk and asset prices
by Federico Bandi and Andrea Tamoni
AFA 2015

Credit-induced booms and busts
by Marco Di Maggio and Amir Kermani
Tel Aviv Finance Conference 2014
The Credit Spread Puzzle - Myth or Reality?
by Peter Feldhütter and Stephen Schaefer
CEPR Asset Pricing Conference (Gerzensee) 2014

Preferred Habitats and Safe-Haven Effects: Evidence from the London Housing Market
by Cristian Badarinza and Tarun Ramadorai
Paul Woolley Centre Conference (LSE) 2014

Ambiguity Aversion and Household Portfolio Choice: Empirical Evidence
by Stephen Dimmock, Roy Kouwenberg, Olivia Mitchell and Kim Peijnenburg
Mitsui Finance Symposium (at U Michigan) 2014

Macroeconomic Variables and the Term Structure: Long-Run and Short-Run Dynamics
by Hitesh Doshi, Kris Jacobs and Rui Liu
USC Fixed Income Conference 2014

Estimates of the Size and Source of Price Declines Due to Nearby Foreclosures
by Elliot Anenberg and Ed Kung
HULM 2013 (at FRB Atlanta)

Treasury Liquidity, Funding Liquidity and Asset Returns
by Ruslan Goyenko
Oxford Asset Pricing Retreat 2013

The Asset Pricing Implications of Government Economic Policy Uncertainty
by Jonathan Brogaard and Andrew Detzel
McGill Global Asset Management Conference 2013

The pricing effects of ambiguous private information
by Scott Condie and Jayant Ganguli
MFA 2013

Foreclosure Externalities: Some New Evidence
by Kristopher Gerardi, Eric Rosenblatt, Paul Willen and Vincent Yao
HULM 2012 (at FRB Boston)

An Agent Based Model of the Household Sector
by Doyne Farmer and John Geanakoplos
AFA 2012

Term Structure of Credit Default Swap Spreads and Cross-Section of Stock Returns
by Bing Han and Yi Zhou
AFA 2012

CDS as Insurance: Leaky Lifeboats in Stormy Seas
by Eric Stephens and James Thompson
WFA 2011