Option Pricing of Earnings Announcement Risks
Andrew Dubinsky (GSAM)
Michael Johannes (Columbia)
Andreas Kaeck (Sussex)
Norman Seeger (Amsterdam)
Derivatives and Volatility Conference
NYU Stern, 2017
US Steel on Tuesday
“US Steel is diving after reporting a loss for the first quarter of
2017 on Tuesday. The adjusted $0.83 per share loss was far
below analysts expectations of earnings of $0.35 per share.
Additionally, the company whiffed on revenues, generating
$2.73 billion versus expectations of $2.95 billion.”
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Earnings announcements matter. A lot.
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Earnings announcements are priced in options
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This paper
Extend traditional models to incorporate earnings announcements, use options
to learn from options about earnings induced price volatility, to understand how
earning risks are priced in options and to study their information content.
Contributions:
1. Models: Build stochastic volatility models incorporating earnings announcements.
2. Impact: document earnings announcements have a first order impact on option prices (extending
early work by Patell and Wolfson)
3. Estimates: estimate and characterize earnings induced price volatility, both in the time series and
cross-section.
4. Information and pricing: understand the predictive content of earnings volatilities and earnings
jump risk premia.
5. Calibrate formal stochastic volatility option pricing models to understand the relative importance
of earnings announcements.
*** Laboratory to understand predictable events, but results apply to many other
events like such as macro economic announcements. Suggests a different view of
‘volatility:’ a sequence of important predictable events.
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Earnings announcements
Every quarter, firms are required by the SEC to report
“earnings.” These almost always occur outside of trading hours
(BMO or AMC)
– These announcements include accounting information (income & cash
flow statements, balance sheet, etc.) but also informal “soft” information,
forecasts, and often Q&A with management.
Major determinant of asset return volatility.
– E.g., 20% of Google’s total volatility occurs on the 4 days after earnings.
– Related to many interesting return anomalies: e.g., post-earnings
announcement drift.
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Earnings announcements matter.
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Incorporating earnings announcement risks
Consider first a simple model for intuition
– Let
count the number of earnings announcements prior to time t.
–
is the random jump size induced by an EAD at time
:
~
,
)
μ
∑
1
Notables
– Arrival times are fully predictable. Volatility as a sequence of events.
– One shot event: hard to learn about jumps from P-measure (1 data point)
– Can add stochastic volatility, random jumps (we do).
– Return volatility on day of/after EAD:
.
– Earnings ‘jump’ is a reduced form model of earnings information.
Standard accounting regression:
-
)+
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Option pricing
Option prices: equity prices are log-normal, thus Black-Scholes like formula
holds.
For an option expiring in T days, where t<
<t+T, the annualized implied
volatility (IV) at time t is
,
– Option pricing implications
• IV’s increase prior to earnings announcements.
• IV falls discontinuously after an earnings announcement
• The term structure of IV decreases with maturity (negatively sloped term structure)
*** The first two of these were noted by PW (1979, 1985). They worked in volatilities
instead of variances.
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General patterns are easily confirmed (formal tests in paper)
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How to extract/estimate EAD price jump volatility?
The simple model provides a number of ways to estimate EAD
volatility. Two primary approaches:
1. Compare pre and post announcement volatility (time series)
,
and
,
2. Use the term structure of implied volatility (term structure)
,
and
,
Like an ‘implied’ earnings price jump volatility estimator. In the paper
– Discuss how stochastic volatility affects estimators: minor impact, largely robust.
– Argue term structure is more robust and less noisy than time series (though
empirically highly correlated).
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Simple, robust event risk estimators
An advantage of these estimators are their simplicity: don’t need a formal SV
model, etc. Can apply to any event.
Brexit
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Simple, robust event risk estimators
An advantage of these estimators are their simplicity: don’t need a formal SV
model, etc. Can apply to any event.
Brexit: GBP/USD implied volatilities the day prior to Brexit
– 1 month: 28.21%, 2 months: 21.51%
– Term structure estimator:
=7.5%
– Spot GBP/USD dropped 10% the next day.
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Data
Standard data sources
– OptionMetrics post 2000. Close prices, careful to average call and put
prices to avoid synchronicity issues
– EADs: Thomson Reuters, IBES, and Compustat (manually search
disagreements on LexisNexis).
Screens
– Select 50 most actively traded firms by option $ volume each year.
– Slightly unbalanced panel.
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Results: earnings jump volatility estimates
In the paper, we report firm specific and pooled estimates. A
few representative firms:
Notes
– Strong time series variation: Apple’s std. deviation about 3%.
– Magnitudes: largely determined by transparency of firm: firms whose
earnings are more easily discerned have lower volatility. E.g., WMT vs.
NFLX.
– Correlation with time series estimator: across firms, 93%.
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Time series behavior
Earnings uncertainty and cross-sectional dispersion increases in
recessions
Significantly correlated with CAPM betas: systematic components.
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0
2
4
6
8
10
12
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Earnings uncertainty
Average Std Dev
Results: Predictive information in options
Are options informative about future realized volatility?
– Cross-sectional correlation at firm level: 85%. Highly informative.
– Correlations are at maximally expected levels given normal noise in 1-
day realized volatility.
Pooled
– Significant, no evidence that analyst dispersion is informative.
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Variance risk premiums
Strong evidence for macro market variance and jump risk premia:
– Indices, long term bonds, FX markets, commodity markets (intuively, IV-RV>0).
– Hard to tell if volatility or jump risk.
– Evidence for earnings announcement volatility jump premium?
Why volatility premia for individual firm volatilities?
– Capital constrained intermediaries
– Systematic components: strong correlation between
and CAPM β. (similar
reason why positive announcement premia at firm level)
Consider multiple measures of variance risk premia
– Compare
to various measures of
.
– Standardized realized returns by option implied volatility
– Compute announcement day straddle returns
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Results: Jump volatility risk premium
Uniform evidence that implied EAD jump volatility is greater
than subsequent return volatility (Qvol>Pvol)
– Average standardized returns are less than 1
– P-Vol is always less than Q-vol (CC-close-to-close)
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Jump volatility risk premium results
Uniform evidence that implied EAD jump volatility is greater
than subsequent return volatility (Qvol>Pvol)
– Average standardized returns are less than 1
– P-Vol is always less than Q-vol (CC-close-to-close)
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Straddle returns
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Straddle returns are highly significant: -8%/EAD.
SV option pricing model implications
Consider a general SV model
Main question: How important are earnings announcements for
pricing the full cross-section of options? Focus on pricing errors.
Data and calibration approach
– Focus on 6 most liquid firms. 9 options by moneyness (DOTM, OTM, ATM) and
maturity (S/M/L) for 16 years.
– Computations: 150K numerical inversions for objective function evaluation.
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Option pricing summaries
Results for Intel
– SVEJ (SV with earnings jumps) and SVJEJ (SVJ with earnings jumps)
Huge conditional improvement around EADs, large overall
improvement (15-20%). Far more important than random jumps.
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Conclusions, implications, and future directions
Earnings announcements are first order important for option prices,
and option prices are highly useful for learning about future earnings
induced price volatility.
Important note of caution: individual firm options are quite different
from index options.
– Many papers are now using option IV’s to generate trading strategies for equities.
Since much of IV variation loads on EADs, these trading strategies will too
Event risk is most important at a firm level, but still very important for
macroeconomic markets. Other events?
– Macroeconomic events (FOMC, employment, etc.)
– Market specific events (crop reports, oil inventory announcements)
– Political events: Kelly, Pastor, and Veronesi (2015)
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