### Stefano Giglio

Professor of Finance, Yale School of Management

NBER Faculty Research Fellow

CEPR Research Affiliate

## Working Papers

**Asset Pricing with Omitted Factors**, with Dacheng Xiu, May 2018

(Formerly titled: "Inference on Risk Premia in the Presence of Omitted Factors")

*Best Paper Prize at the 2017 European Financial Association conference*

Standard estimators of risk premia in linear asset pricing models are biased if some priced factors are omitted. We propose a three-pass method to estimate the risk premium of an observable factor, which is valid even when not all factors in the model are specified or observed. We show that the risk premium of the observable factor can be identified regardless of the rotation of the other control factors, as long as they together span the true factor space. Motivated by this rotation invariance result, our approach uses principal components of test asset returns to recover the factor space and additional cross-sectional and time-series regressions to obtain the risk premium of the observed factor. Our estimator is also equivalent to the average excess return of a mimicking portfolio maximally correlated with the observed factor using appropriate regularization. Our methodology also accounts for potential measurement error in the observed factor and detects when such a factor is spurious or even useless. The methodology exploits the blessings of dimensionality, and we therefore use a large panel of equity portfolios to estimate risk premia for several workhorse factors. The estimates are robust to the choice of test portfolios within equities as well as across many asset classes.

**The Collateral Rule: An Empirical Analysis of the CDS Market**, with Agostino Capponi, Allen Cheng and Richard Haynes, November 2017

We study the empirical determinants of collateral requirements in the cleared credit default swap (CDS) market: how margins depend on portfolio risks and market conditions, and what the implications are for theoretical models of collateral equilibrium. We construct a novel data set containing CDS portfolios and margins posted by all participants to the main CDS clearinghouse, ICE Clear Credit, covering 60% of the U.S. market. We show that margins are much more conservatively set than under the standard Value-at-Risk (VaR) rule typically employed in this market, according to which one-week portfolio losses should exceed the posted collateral 1% of the time. We find that the frequency of these exceedances is heterogenous across market participants, indicating that variables other than VaR must determine margins. Our analysis suggests that extreme tail risk measures have a higher explanatory power for observed collateral requirements than the standard VaR, which depends mostly on the volatility of the loss distribution rather than on the extreme left tail. This finding is consistent with endogenous collateral theories such as Fostel and Geanakoplos (2015), in which extreme events dominate in determining collateral. The dependence of collateral requirements on extreme tail risks induces potential nonlinearities in margin spirals, dampening small shocks and amplifying large ones. We also provide empirical evidence that aggregate risks and participants’ funding costs play a prominent role in the determination of collateral requirements, consistent with many theoretical models of equilibrium with financial frictions like Brunnermeier and Pedersen (2009).

**How do investors perceive the risks from macroeconomic and financial uncertainty? Evidence from 19 option markets**, with Ian Dew-Becker and Bryan Kelly, October 2017

This paper studies the pricing of shocks to implied and realized volatility using options in 19 different markets, covering financials, metals, energies, and agricultural products. The markets are directly related to the state of the macroeconomy and financial markets, and investors can use the options to separately hedge shocks to real uncertainty and to the realization of volatility. Historically, realized volatility has earned a robustly negative risk premium, indicating that high macroeconomic volatility is associated with high marginal utility. However, models are driven by forward-looking conditional variances, which can be proxied by implied volatility. Over the same period, the cost of hedging shocks to implied volatility in commodity markets has been negative: portfolios with returns that are positively correlated with shocks to implied volatility have earned positive average returns. That result is inconsistent with the view that periods of high uncertainty, as measured by forward-looking implied volatility, are “bad” states of the world with high marginal utility. The result is, however, potentially consistent with models in which uncertainty is high in periods of high innovation.

**Taming the Factor Zoo**, with Guanhao Feng and Dacheng Xiu, August 2017

*AQR Insight Award 2018, First Prize*

[Slides]

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 to systematically evaluate the contribution to asset pricing of any new factor, above and beyond what a high-dimensional set of existing factors explains. Our methodology explicitly accounts for potential model-selection mistakes, unlike the standard approaches that assume perfect variable selection, which rarely occurs in finite sample and produces a bias due to the omitted variables. We apply our procedure to a set of factors recently discovered in the literature. We show that several factors – such as profitability and investments – have statistically significant explanatory power beyond the hundreds of factors proposed in the past. In addition, we show that our risk price estimates and their significance are stable, whereas the model selected by simple LASSO is not.

**Uncertainty Shocks as Second-Moment News Shocks**, with David Berger and Ian Dew-Becker, January 2017

(Replaces: "Contractionary Volatility or Volatile Contractions"?)

[Option-implied volatility data]

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.

**Climate Change and Long-Run Discount Rates: Evidence from Real Estate**, with Matteo Maggiori, Krishna Rao, Johannes Stroebel, and Andreas Weber,** **March 2018

*Revise and Resubmit at the Journal of Political Economy*

We explore what private market data can tell us about the appropriate discount rates for valuing investments in climate change abatement. We estimate the term structure of discount rates for real estate up to the very long horizons relevant for investments in climate change abatement. The housing term structure is downward sloping, reaching 2.6% at horizons beyond 100 years. We also show that real estate is exposed to both consumption risk and climate risk. We explore the implications of these new data using a tractable asset pricing model that incorporates important features of climate change. Climate change is modeled as a rare catastrophic event, the probability of which increases with economic growth. Economic activity partially mean reverts following a climate disaster, capturing the ability of the economy to adapt. As a result, short-run cash flows are more exposed to climate risk than long-run cash flows, allowing us to match the observed housing term structure. The model and data provide simple yet powerful guidance for appropriate discount rates for investments that hedge climate disaster risk. The term structure of these discount rates is upward-sloping but bounded above by the risk-free rate. For extremely far horizons at which we do not observe the risk-free rate, the estimated long-run discount rates for housing (a risky asset) provide an upper bound that becomes tighter with maturity. This suggests that the appropriate discount rates for investments in climate change abatement are low at all horizons, substantially below those conventionally used for valuing these investments and for determining the social cost of carbon.

**Credit Default Swap Spreads and Systemic Financial Risk**, April 2014

*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.

## Publications

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

** Journal of Financial Economics**, forthcoming

10. **Excess Volatility: Beyond Discount Rates**, with Bryan Kelly

** Quarterly Journal of Economics **(2017), 133(1): 71-127

* Finalist, AQR Insight Award, 2016*

* Napa Conference Best Paper Award, 2016*

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

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

*JFE Lead article*

8. **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]

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

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

[Online Appendix] [Coverage: VoxEU]

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

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

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

*JFE Lead article*

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

[Online Appendix] [Data (US and International Measures)] [Coverage: MoneyAndBanking.com; VoxEU; BFI]

* *

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] [Rents Worksheet] [Data Summary] [NBER WP Version]

[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

*RFS Lead Article*

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

3.** Hard Times**, with John Campbell and Christopher Polk

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

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

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

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

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