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The Review of Financial Studies
, Volume Advance Article – May 22, 2018

42 pages

/lp/ou_press/option-pricing-of-earnings-announcement-risks-ZI7B030P4z

- Publisher
- Oxford University Press
- Copyright
- © The Author(s) 2018. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.
- ISSN
- 0893-9454
- eISSN
- 1465-7368
- D.O.I.
- 10.1093/rfs/hhy060
- Publisher site
- See Article on Publisher Site

Abstract This paper uses option prices to learn about the equity price uncertainty surrounding information released on earnings announcement dates. To do this, we introduce reduced-form models and estimators to separate price uncertainty about earnings announcements from normal day-to-day volatility. Empirically, we find strong support for the importance of earnings announcements. We find that the anticipated price uncertainty is quantitatively large, varies across time, and is informative about the future return volatility. Finally, we quantify the impact of earnings announcements on formal option pricing models. Received April 13, 2017; editorial decision February 5, 2018 by Editor Stijn Van Nieuwerburgh. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online. Every quarter, the SEC requires public corporations to disclose a range of fundamental information via “earnings announcements.” These information releases are arguably the primary conduit for corporate communication to investors and often generate dramatic equity price movements as prices quickly impound new information. As an example, almost 20% of Google’s total equity price volatility occurs on the day following its quarterly earnings releases. Large literatures model earnings, study the theoretical pricing of earnings risks and the ex post response of equity prices to the information releases, both contemporaneously (earnings response coefficients) and with lags (e.g., post-earnings-announcement drift). Overall, earnings announcements and risks are key events driving equity returns and prices. This paper studies the pricing of earnings risk in option prices.1 These announcements generate fundamentally different risks compared to Brownian or Poisson risks in asset pricing models due to their predictable timing. To see this, Figure 1 graphs short dated option implied volatilities (IVs) for Intel Corporation with earnings announcement dates (EADs) marked with a circle. IVs increase predictably prior to and sharply decrease after earnings are announced (previously noted by Patell and Wolfson 1979, 1981). The goal of this paper is to incorporate earnings announcements and risks into option pricing models, to use option prices to extract option-implied ex ante information about the impact of earnings risks on equity prices, and to study the information content of these announcements. Figure 1 View largeDownload slide Short-term ATM implied volatility (Intel Corporation) This figure shows the implied volatility of Intel (INTC) calculated as the average of the put and call implied volatility of the contracts closest to at-the-money (moneyness is defined as $$K/F$$, where $$F$$ is the forward price of the underlying) for the shortest available option maturity. The sample period is from January 2000 to August 2015. Circles indicate EADs. Figure 1 View largeDownload slide Short-term ATM implied volatility (Intel Corporation) This figure shows the implied volatility of Intel (INTC) calculated as the average of the put and call implied volatility of the contracts closest to at-the-money (moneyness is defined as $$K/F$$, where $$F$$ is the forward price of the underlying) for the shortest available option maturity. The sample period is from January 2000 to August 2015. Circles indicate EADs. On the theoretical side, we specify new option pricing models building on Piazzesi (2000) with deterministically timed jumps on earnings dates with random sizes. This “earnings risk” model naturally generates the IV patterns seen in the data and motivates estimators of the ex ante equity price uncertainty associated with an earnings announcement, essentially the option implied price volatility associated with the news. A simplified version of our general model provides the intuition. Consider an extension of the Black-Scholes model with a single, predictably timed price jump occurring at time $$\tau_j$$ (the EAD) whose size is normally distributed with a volatility of $$\sigma_{j}^{\mathbb{Q}},$$ where $$\mathbb{Q}$$ is the risk-neutral probability. Equity prices are log-normally distributed, and option prices are given by a modification of the Black-Scholes formula. For an option with time to maturity $$T$$ and $$t<\tau_j\leq t+T$$, the IV at time $$t$$ is \begin{equation} \sigma_{t,T}=\sqrt{\sigma^{2}+{\left( \sigma_{j}^{\mathbb{Q}} \right) ^{2}}/T}, \end{equation} (1) where $$\sigma$$ is the diffusive volatility. This simple model delivers three general implications of earnings announcements: (1) IVs increase continuously and nonlinearly prior to an EAD (as $$T$$ decreases), (2) IV discontinuously falls after the announcement, and (3) the term structure of IV is downward-sloping prior to the announcement. The first two of these implications generate the distinctive pattern in Figure 1 and were previously noted in Patell and Wolfson (1981). We will mainly rely on the third implication for our empirical work. The central quantity is the earnings price volatility $$\sigma_{j}^{\mathbb{Q}},$$ the risk-neutral anticipated announcement volatility. This parameter is a reduced form, capturing the impact of all information released, not just current quarter earnings or forward guidance. Earnings risks naturally vary over time and across firms, and an intermediate goal is to develop easy-to-compute and accurate option-based estimators of this parameter for each EAD.2 Equation (1) can be used to develop ex ante estimators of $$\sigma_{j}^{\mathbb{Q}}$$ using options of different maturities (term structure estimators) and ex post estimators of $$\sigma_{j}^{\mathbb{Q}}$$ based on the post-announcement decrease in IV (time-series estimators).3 We also consider more general models incorporating stochastic volatility and Poisson-driven jumps in prices and perform a structural estimation. Given this theoretical framework, our main contributions are empirical. Using a broad data set of actively traded firms from 2000 to 2015, we characterize the information about earnings risks embedded in options. We first extend the initial work of Patell and Wolfson (1981) testing the impact of earnings announcements on option prices. Two of our tests are related to those in Patell and Wolfson (1979, 1981), but the third is new. These tests document strong evidence that earnings announcements affect option prices (consistent with Figure 1). Our next goal is to quantify earnings uncertainty. Using estimators derived from Equation (1), estimates indicate that earnings uncertainty is large, statistically significant, and varies across both firms and time. There is a strong business cycle pattern, with the level and cross-sectional variation in earnings risks increasing substantially in recessions. For our sample, the average earnings uncertainty ranges from roughly $$4\%$$–$$6\%$$ during pre- and post-crisis expansions to approximately $$10\%$$–$$11\%$$ at the height of the 2000–2002 or 2008–2009 recession, respectively. Cross-sectional earnings uncertainty dispersion increases in recessions, more than doubling from less than $$3\%$$ to over $$6\%$$. In terms of informational content, option-based estimates of earnings volatility are highly informative about future realized equity volatility: the ex ante estimates have a correlation of more than $$50\%$$ with realized price volatility after the announcement. This is close to what could maximally be expected given normal sampling errors in realized volatility. The cross-sectional correlation between option implied average earnings volatility and subsequent post-earnings daily equity volatility is roughly $$85\%$$. Earnings volatility estimates also provide incremental information in forecasting the following month’s equity volatility relative to diffusive IV (e.g., Christensen and Prabhala 1998; Lamoureux and Lastrapes 1993; Jiang et al. 2005). Another commonly used measure of firm-level uncertainty is the dispersion in analysts earnings forecasts, based on the idea that firms with higher earnings uncertainty are more difficult to analyze, which in turn generates a broader range of analyst forecasts. We find no significant relationship between dispersion of analysts forecasts with our measure, consistent with Diether, Malloy, and Scherbina (2002). We also find that in our sample the dispersion of analysts forecasts has no statistical ability to forecast post-earnings daily equity volatility. Next, we analyze the pricing of earnings announcement risks. For index options, there is strong evidence for volatility and/or Poisson drive jump risk premiums (see, e.g., Pan 2002; Broadie et al. 2007). Quantifying earnings volatility risk premiums is straightforward given precise estimates of $$\sigma_{j}^{\mathbb{Q}}$$ for each EAD, which can be compared to realized earnings volatility in a number of ways. One way compares averages of $$\sigma_{j}^{\mathbb{Q}}$$ to close-to-open equity return volatilities on EADs, which assumes all of the overnight price move is from earnings induced jumps. We also construct measures based on close-to-close returns, allowing for some “digestion” time for prices to adjust after the open, compute standardized returns (which are less sensitive to outliers), and analyze straddle returns. Every measure points to significant earnings jump risk premiums. Average option implied earnings day volatility is 8.22% for the full-sample compared to a realized announcement day volatility of 7.42%, a premium of 80 bps. Focusing only on close-to-open returns (assuming all of the effect occurs at the open), the average premium is 56 bps. Averages are sensitive to outliers, and the results are stronger using medians, trimmed estimates, or standardized returns. The risk premium is consistent with a significant systematic component in earnings risks: ex ante earnings volatility estimates are strongly related to historical equity beta, with a correlation of roughly 60% across firms. To connect earnings uncertainty risk premium estimates with economically interesting quantities, we compute at-the-money straddle returns on EADs. The straddle positions are opened prior to the EAD and closed the next day. The average (median) EAD straddle return is $$-8\%$$ ($$-10\%$$). We compute bootstrap returns to account for the fact that straddle returns are generally negative, and results confirm statistically significant straddle returns consistent with an economically significant earnings jump risk premium. These risk premium results are related to robust patterns of equity returns around earnings dates. First noted by Beaver (1968), there are positive average equity returns for firms announcing earnings (see also Cohen et al. 2007; Frazzini and Lamont 2007). Savor and Wilson (2016) provide a model-based explanation for the firm-level earnings announcement premium. Our results contribute to this literature by documenting a robust earnings jump volatility risk premium. Finally, we build continuous-time stochastic volatility (SV) models incorporating both randomly timed and earnings induced price jumps. These models allow us to quantify the impact of earnings via option pricing errors and the relative importance of EADs vis-a-vis SV and randomly timed jumps. Using IVs, we estimate the SV models for some of the largest firms in our sample: Amazon, General Electric, IBM, Intel, Microsoft, and Qualcomm. We again find strong earnings effects, which are strongest around EADs where pricing errors can be more than $$50\%$$ lower when incorporating earnings jumps. Pure SV models cannot fit term structure IV patterns observed around EADs, resulting in large pricing errors. For example, average pricing errors for AMZN the day prior to earnings are $$8.11\%$$, $$2.53\%$$, and $$3.82\%$$ for short, medium, and long term options, respectively, and fall to $$3.69\%$$, $$1.49\%$$, and $$1.70\%$$, respectively, when incorporating earnings announcements. Although there are only four EADs per year, overall option pricing errors fall on average by almost $$20\%$$. EADs are far more important than Poisson price jumps. Our results have other research implications. There is a growing literature using firm IVs, either directly or via a variance risk premium calculation, as regressors or for portfolio sorts. These procedures may be sensitive to EADs and factors such as option maturity that are unrelated to the research questions. For example, consider a firm with $$\sigma=25\%$$ and an average sized earnings jump volatility of 7.3%. From Equation (1), the IV of a 2-week option is almost 44% but only 32% for an option expiring in 6 weeks. Thus, for options spanning EADs, there is significant IV variation unrelated to fundamentals from maturity effects. An et al. (2014), for instance, sort stocks by changes in 30-day IVs, arguing that sharp increases in IV can be linked to informed trading. Our model suggests that firms with rapidly increasing IVs are also more likely to announce earnings. Similarly, Baltussen et al. (forthcoming) use short-term options and calculate the standard deviation of the IV over a calendar month. Our model suggests that firms with the highest volatility of IV are biased toward announcing firms, given the pattern of IVs around EADs, independent of fundamentals. We show empirically that earnings announcements increase the noise in the measurement of IV-based sort variables and provide guidance on how to minimize the impact of earnings announcement related time variation in IVs on cross-sectional studies. All of our implications generally apply to other predictable events including macroeconomic announcements and elections, referendums, summits or other scheduled meetings (e.g., OPEC semiannual meetings). As an example, consider the Brexit vote on June 23, 2016. Just prior to the vote, 1-month and 2-month USD/GBP currency IV was 28.21% and 21.51%, respectively. The term structure estimate of the Brexit impact on the USD/GBP exchange rate was 7.45%. The pound fell 7.6% on the day following the vote. A similar pattern occurred prior to the 2016 U.S. election. Kelly et al. (2016) analyze the impact of predictable national elections and global summits on option prices. 1. Incorporating Earnings Announcements in Equity Price Models 1.1 Stochastic volatility models This section incorporates earnings announcement risks into continuous-time SV models. The first step is a model of how earnings announcements impact equity prices. Earnings announcements normally occur outside of normal trading hours, either after the 4:00 p.m. market close or before the formal 9:30 a.m. open. We assume earnings induce a jump or discontinuity in the continuous-time price path. The jump assumption is intuitive, consistent with existing work analyzing macroeconomic announcement effects (e.g., Piazzesi 2005; Beber and Brandt 2006), consistent with statistical evidence identifying announcements as the cause of jumps in jump-diffusion models (Johannes 2004; Barndorff-Nielsen and Shephard 2006), and parsimonious.4 For earnings announced during normal market hours, Patell and Wolfson (1984) find the bulk of the price response occurs within the first few minutes. For earnings announced outside of normal market hours, Martineau (2017) argues earnings news arrives as a “jump”, with 80% of the price response occurring within the first few trades after news is released (see also Lee 2012). Formally, $$N_{t}^{d}$$ counts EADs prior to time $$t$$: $$N_{t}^{d}=\sum_{j} {\rm 1}\kern-0.24em{\rm I}_{\left[ \tau_{j}\leq t\right] }$$ where $${\rm 1}\kern-0.24em{\rm I}$$ is the indicator function and $$\tau_{j}$$ is an increasing sequence of predictable stopping times representing earnings announcements. The jump size, $$Z_{j}=\log\left( S_{\tau_{j}}/S_{\tau_{j-}}\right)$$, is distributed according to a known distribution, $$Z_{j}|\mathcal{F}_{\tau_{j}-}\sim\pi\left( Z_{j} ,\tau_{j}-\right)$$. In addition to earnings jumps, price jumps can arrive at random times $$\bar{\tau}_{j}$$ via a Poisson process $$\bar{N}_t$$ with intensity $$\bar{\lambda}_y$$ and jump size $$\bar{Z}_{j}$$. We do not consider other predictable events such as mid-quarter earnings updates, stock splits, or mergers and acquisitions although these do have interesting implications (see, e.g., Bester et al. 2013). We assume a square-root SV process, thus prices and variance processes solve: \begin{align} dS_{t} & =\left( \mu - \bar{\lambda}_y \psi_t \right) S_{t}dt+\sqrt{V_{t}} S_{t}dW_{t} \notag\\ &\quad +d\left( \sum\nolimits_{j=1}^{N_{t}^{d}}S_{\tau_{j}-}\left[ e^{Z_{j}}-1\right] \right) +d\left( \sum\nolimits_{j=1}^{\bar{N}_{t}}S_{\bar{\tau}_{j}-}\left[ e^{\bar{Z}_{j} }-1\right] \right), \nonumber\\ dV_{t} & =\kappa_{v}\left( \theta_{v}-V_{t}\right) dt+\sigma_{v} \sqrt{V_{t}}dW_{t}^{v},\nonumber \end{align} where $$\psi_t$$ is the random jump compensator, $$W_{t}$$ and $$W_{t}^{v}$$ are two standard Brownian motions with correlation $$\rho dt$$. This process is well defined in continuous time.5 The jump $$Z_{j}$$ captures the equity price response to the information released in the earnings announ