Measuring Risk Information

• Published date: 01 May 2022
• Author: KEVIN C. SMITH,ERIC C. SO
• Date: 01 May 2022
• DOI: http://doi.org/10.1111/1475-679X.12413

DOI: 10.1111/1475-679X.12413

Journal of Accounting Research

Vol. 60 No. 2 May 2022

Printed in U.S.A.

Measuring Risk Information

KEVIN C. SMITH∗AND ERIC C. SO†

Received 5 November 2020; accepted 27 September 2021

ABSTRACT

We develop a measure of how information events impact investors’ expecta-

tions of risk. The measure is broadly applicable and simple to implement.

We derive it from an option-pricing model, where investors anticipate an an-

nouncement that simultaneously conveys information on the announcer’s

expected future cash flows and risk profile. We empirically implement the

measure using firms’ earnings announcements, showing that it closely aligns

with our model’s predictions and offers strong forecasting power for firms’

risk profiles, costs of capital, and future investments. We further highlight

pitfalls of using simple changes in option-implied volatilities to study infor-

mation gleaned from earnings announcements. Finally, we apply our mea-

sure to study disclosure regulation, the efficacy of text-based proxies, and

market-wide events, which we use to illustrate our measure’s uses, and illu-

minate its potential limitations.

JEL codes: G10, G11, G12, G14, M40, M41

Keywords: risk uncertainty; earnings announcements; implied volatility;

cost of capital; risk disclosure

∗Graduate School of Business, Stanford University; †Sloan School of Management, Mas-

sachusetts Institute of Technology

Accepted by Philip Berger. Wethank an anonymous reviewer, Judson Caskey (discussant),

Tim de Silva, Tim Gray, Matt Lyle, Xu Jiang, and seminar participants at Boston College,

Boston University, the Massachusetts Institute of Technology, Santa Clara University,Stanford

University, and University of Toronto for helpful feedback and suggestions. We further thank

participants from the Journal of Accounting Research conference for many helpful comments.

An online appendix to this paper can be downloaded at http://research.chicagobooth.edu/

arc/journal-of-accounting- research/online-supplements.

375

© 2021 The Chookaszian Accounting Research Center at the University of Chicago Booth School of

Business

376 k. c. smith and e. c. so

1. Introduction

Information is frequently impounded into stock prices in the form of dis-

crete, anticipated events, such as earnings announcements, press releases,

investor conferences, SEC filings, and policy announcements. Research on

the impact of these events typically focuses on the information they con-

tain regarding expected future cash flows. Yet, in many cases, these events

simultaneously provide information that changes investors’ expectations of

risk, which we refer to as risk information. For example, investors may learn

about the scope of firms’ risky investments, their financial liquidity, expo-

sures to risk factors, and/or changes in their operational strategy.

Our study is motivated by the importance of quantifying the risk infor-

mation contained in these events. Expectations of risk play a central role

in most research settings studied by financial economists. For example, the

severity and nature of risk influences decisions over debt contracting, com-

pensation design, information acquisition, and portfolio choice. Therefore,

characterizing and quantifying risk information gleaned from information

events is an important step toward understanding how and why interactions

among economic agents evolve over time. We derive a measure of an antic-

ipated event’s risk information content, implement it empirically, and run

a battery of tests that yield support for its efficacy.

As an example of how information events can provide information on

risk, consider Facebook’s earnings announcement in July 2018. This an-

nouncement commanded national headlines in part because it triggered

a single-day stock price drop of 19% when providing information on risk

in addition to information on cash flows.1Despite beating analysts’ earn-

ings forecasts, Facebook warned of heightened risks associated with privacy

controls, concerns over user growth, and the fallout from the Cambridge

Analytica scandal.2

Studying risk information conveyed by events like Facebook’s announce-

ment poses a challenge: How can researchers calibrate the risk informa-

tion when the events also provide information on the level of future cash

flows? Standard measures of the information content of an announcement

based on stock prices cannot be used to quantify risk information for

at least two reasons. First, under prevailing asset-pricing theory, expected

stock returns are independent of firm-specific risks. Second, stock returns

(as well as bond returns) are jointly and simultaneously influenced by infor-

mation on expected cash flows and risk-factor exposures, which precludes

1See for example, Castillo [2018], Price [2018], and Phillips [2018].

2Earnings announcements can also reduce investors’ expectations over risk. Take, for ex-

ample, Raytheon’s earnings announcement in February 2019, in which the company noted

greater stability in their projected sales to the U.S government and an increase in capital

returned to investors via dividends and buybacks. Our approach suggests that this announce-

ment lowered investors’ expectations of risk equivalent in magnitude to ∼25% of the diffusive

variance expected over the month following the announcement.

measuring risk information 377

using stock returns to distinguish these two types of information. To mea-

sure risk information, we turn our attention to option markets, which en-

able researchers to directly observe investors’ expectations of the firm’s fu-

ture return variance.

We begin with an option-pricing model in which investors observe an an-

ticipated information event that contains information on both the mean

and variance of the firm’s future payoffs. The model’s central output is

our measure of risk information, denoted as RiskInfot, which captures how

the event impacts investors’ expectations of the future return variance

over the tdays following its release. Following the “event-study” approach,

RiskIn fotmeasures the event’s impact on investor beliefs by focusing on

changes in market prices in a short window around the announcement.3

Specifically, RiskInfotis based on the change in the return variance im-

plied by options that mature tdays after the announcement. The link be-

tween this change and risk information is intuitive: Because the option-

implied variance captures investors’ beliefs regarding the future return

variance, its change around the event should capture how the event af-

fected investors’ beliefs about this variance.

However, our model shows that the change in the implied variance

would exhibit a systematic downward bias if directly used as a metric of

risk information. The reason is that, in expectation, option-implied vari-

ances predictably drop after the release of anticipated news events, regard-

less of whether these events contain risk information (Patell and Wolfson

[1979], Dubinsky et al. [2019]). The intuition is that, because these events

move prices, investors expect them to generate heightened return volatil-

ity, which causes the option-implied variance to rise prior to their release.

After these events pass, volatility is no longer elevated, and thus the option-

implied variance drops to its typical level, on average.

Our model shows that, to measure risk information, one simply needs

to adjust the change in the implied variance on the event date for this ex-

pected decline. Moreover, for any given event, this expected decline can

be measured and adjusted for using the difference in the implied vari-

ances from short- and long-dated options just prior to its release. Intuitively,

the magnitude of the expected decline depends upon the amount of re-

turn variation investors expect the event to create. Furthermore, when in-

vestors expect the event to create greater return variation, the short-term

implied variance rises relative to the long-term implied variance because

3This event-study approach distinguishes our measure from other potential measures of

risk information, such as annual changes in textual attributes, changes in realized volatility

or the cost of capital surrounding the announcement, or discount-rate changes derived from

return decompositions (as in Vuolteenaho [2002], Penman and Zhu [2014]). By using short-

horizon changes in market prices, our measure isolates only the novel information that in-

vestors learn from the event. In contrast, for example, changes in volatility surrounding an

announcement could occur even when investors do not learn from the event. Similarly, dis-

cussions of risk factors may reflect sources of risk already known to investors.