Event studies: A methodology review

Originally developed as a statistical tool for empirical research in accounting and finance, event studies have since migrated to other disciplines as well, including economics, history, law, management, marketing, and political science. Despite the elegant simplicity of a standard event study, variations in methodology and their relative merits continue to attract attention in the literature. This paper reviews some of the fundamental topics in short‐term event study methodology, with an attempt to add new perspectives to some pressing topics.     

Consistent estimation of cross-sectional models in event studies

Event studies often include cross-sectional regressions of announcementeffects on exogenous variables. If the event is voluntary andinvestors are rational, then standard OLS and GLS estimatorsare inconsistent. Consistent ML estimators are constructed fora cross-sectional model of horizontal mergers relating announcementeffects to exogenous characteristics of firms and industries.The OLS and ML estimates differ dramatically for bidders butnot for targets. The evidence suggests that manager of bidders,but not targets, have valuable private information about thepotential synergies from proposed mergers.     

An Investigation of Event Study Methodologies with Clustered Events and Event Day Uncertainty

The specification and power of mean-adjusted, market and quadratic models in event studies using OLS, Patell, Jaffe and GLS are examined. Simulation is used with security and portfolio returns to capture different cross correlations. The market model is always superior in specification and power compared to the mean-adjusted and quadratic models. The use of OLS with the market model is supported in the absence of clustered events and event day uncertainty, whereas use of Jaffe with the market model is supported in the presence of these problems.     

Dynamic Asset Allocation with Event Risk

Major events often trigger abrupt changes in stock prices and volatility. We study the implications of jumps in prices and volatility on investment strategies. Using the event-risk framework of Duffie, Pan, and Singleton (2000), we provide analytical solutions to the optimal portfolio problem. Event risk dramatically affects the optimal strategy. An investor facing event risk is less willing to take leveraged or short positions. The investor acts as if some portion of his wealth may become illiquid and the optimal strategy blends both dynamic and buy-and-hold strategies. Jumps in prices and volatility both have important effects.     

The Pricing of Event Risks with Parameter Uncertainty

Financial instruments whose payoffs are linked to exogenous events, such as the occurrence of a natural catastrophe or an unusual weather pattern depend crucially on actuarial models for determining event (e.g., default) probabilities. In many instances, investors appear to receive premiums far in excess of these modeled actuarial probabilities, even for event risks that are uncorrelated with returns on other financial assets. Some have attributed these larger spreads to uncertainty in the probabilities generated by the models. We provide a simple model of such parameter uncertainty and demonstrate how it affects rational investors' demand for event risk exposures. We show that while parameter uncertainty does indeed affect bond spreads, it does not tend to increase spreads by much. Indeed, the spread increases due to parameter uncertainty in our numerical examples are on the order of only 1–2 basis points. Moreover, in many instances, including those that have the most sensible correlation settings, parameter uncertainty tends to decrease the size of bond spreads. We therefore argue that parameter uncertainty does not appear to be a satisfactory explanation for high event-risk returns.     

Good-Deal Option Price Bounds for a Non-Traded Event with Stochastic Return: A Note

Cochrane and Sa'a-Requejo (2000, Journal of Political Economy) proposed the good-deal price bounds for the European call option on an event that is not a traded asset, but is correlated with a traded asset that can be used as an approximate hedge. One remarkable feature of their model is that the return on an event process explicitly appears in the option price bounds formula, which offered a contrast with the standard option pricing model. We show that the good-deal option price bounds on a non-traded event are obtained as a closed-form formula, when the return on an event is governed by a mean reverting process.     

Robust estimation with flexible parametric distributions: estimation of utility stock betas

The distributions of stock returns and capital asset pricing model (CAPM) regression residuals are typically characterized by skewness and kurtosis. We apply four flexible probability density functions (pdfs) to model possible skewness and kurtosis in estimating the parameters of the CAPM and compare the corresponding estimates with ordinary least squares (OLS) and other symmetric distribution estimates. Estimation using the flexible pdfs provides more efficient results than OLS when the errors are non-normal and similar results when the errors are normal. Large estimation differences correspond to clear departures from normality. Our results show that OLS is not the best estimator of betas using this type of data. Our results suggest that the use of OLS CAPM betas may lead to erroneous estimates of the cost of capital for public utility stocks.     

Investigating the leverage effect in commodity markets with a recursive estimation approach

This paper investigates the presence of the leverage effect in commodities, in comparison with financial markets. The EGARCH model with a Mixture of Normals distribution (EGARCH-MN) is used to capture (i) heavy tails and skewness in the conditional returns, and (ii) leverage effects and time-varying long-term component in the volatility specification. Besides, the estimation strategy relies on an innovative recursive (REC) method, which allows disentangling the leverage effect from the unconditional skewness as an empirical result. When applied to a broadly diversified dataset of assets during 1995–2012, the EGARCH-MN models offers state-of-the-art specifications with leverage and fat-tailed skewed densities, that allow to contrast the specific characteristics of commodities with traditional assets (equities, bonds, FX).     

An Event Option Pricing Model with Scheduled and Unscheduled Announcement Effects

There is considerable evidence supporting the time-varying distribution of asset returns. There is also ample evidence that scheduled announcement events such as money supply announcements (in the case of foreign exchange), earnings announcements (in the case of stocks), and crop reports (in the case of commodities), as well as random unscheduled events, can affect the level and volatility of asset returns. This study provides an Event Model for European call options which explicitly addresses effects of these two classes of events. This specification requires estimation of more parameters, but it could provide a more accurate basis for pricing options than previous Poisson jump-diffusion models. Parametric analysis shows that the standard models under price the options relative to the Event Model. The Event Model may be particularly useful in pricing short-term deep out-of-the-money options when scheduled events are present in the market.     

Mortgage prepayment with an uncertain holding period

A discrete-time-option pricing model is developed to value a mortgage and its embedded prepayment option when the effective life of the mortgage is a random variable with a probability distribution of known parameters. The model can be applied when the borrower's ex ante expectation of his tenure follows any probability distribution bounded to the left at zero. The Gamma distribution is used to illustrate the model.The pricing model is further applied to determine the conditions under which financially motivated prepayment is optimal. The results show that the certainty model understates the Interest Rate Differential needed to justify prepayment (IRD) for short Expected Holding Period (EHP) borrowers and overstates the IRD for long EHP borrowers. When the EHP is relatively long, the certainty model provides relatively good estimates of IRD during the beginning years of the mortgage life. Under most other conditions, the estimates of the certainty holding period model are biased.     

Nonparametric estimation for a stochastic volatility model

Consider discrete-time observations (X _{? δ} )_1≤?≤n+1 of the process X satisfying $dX_{t}=\sqrt{V_{t}}dB_{t}Consider discrete-time observations (X _{ℓ δ} )_{1≤ℓ≤n+1} of the process X satisfying dX_t=?{V_t}dB_tdX_{t}=\sqrt{V_{t}}dB_{t} , with V a one-dimensional positive diffusion process independent of the Brownian motion B. For both the drift and the diffusion coefficient of the unobserved diffusion V, we propose nonparametric least square estimators, and provide bounds for their risk. Estimators are chosen among a collection of functions belonging to a finite-dimensional space whose dimension is selected by a data driven procedure. Implementation on simulated data illustrates how the method works.     

Fully modified estimation with nearly integrated regressors

I show that the test procedure derived by Campbell and Yogo [2006. Journal of Financial Economics 81, 27–60] for regressions with nearly integrated variables can be interpreted as the natural t-test resulting from a fully modified estimation with near-unit-root regressors. This clearly establishes the methods of Campbell and Yogo as an extension of previous unit-root results and shows that the optimality of their test is valid under more general assumptions than those given in the original paper.     

Event study with imperfect competition and private information: earnings announcements revisited

Although prior research documents that prices respond to earnings announcements, only a little of the price variation is explained by these announcements. To further investigate the properties of the information environment around these announcements we use NYSE TAQ data and compute the maximum likelihood estimates (MLEs) of the primitive parameters of a Kyle (Econometrica 53(6):1315–1336, 1985) type model within and around earnings announcement windows. These include the precision of fundamentals given only public information, the precision of private signals, and the variance of uninformed liquidity trading (noise). We find that liquidity noise is higher while the precision of beliefs given only public information is lower within an earnings announcement window. The precision of private information is higher in an event window, consistent with greater information acquisition to try and interpret a public announcement. We also document that Kyle’s λ is higher in an event window, showing an overall increase in information asymmetry. Our overall findings suggest that the earnings announcement window is distinguished from the preceding and subsequent windows not by being a period with more public information but as a period with different public information.     

Optimal policies of call with notice period requirement

When an American warrant or a convertible bond is called by its issuer, the holder is usually given a notice period to decide whether to sell the derivative back to the issuer at the call price or to exercise the conversion right. Several earlier papers have shown that such notice period requirement may substantially affect the optimal call policy adopted by the issuer. In this paper, we perform theoretical studies on the impact of the notice period requirement on issuer’s optimal call policy for American warrants and convertible bonds. We also examine how the optimal call policy of the issuer interacts with holder’s optimal conversion policy.     

Improving Tests of Abnormal Returns by Bootstrapping the Multivariate Regression Model with Event Parameters

Parametric dummy variable-based tests for event studies usingmultivariate regression are not robust to nonnormality of theresidual, even for arbitrarily large sample sizes. Bootstrapalternatives are described, investigated, and compared for caseswhere there are nonnormalities, and cross-sectional and time-seriesdependencies. Independent bootstrapping of residual vectorsfrom the multivariate regression model controls type I errorrates in the presence of cross-sectional correlation, and surprisingly,even in the presence of time-series dependence structures. Theproposed methods not only improve upon parametric methods, butalso allow development of new and powerful event study testsfor which there is no parametric counterpart.     

Turkish bank efficiency: Bayesian estimation with undesirable outputs

This paper analyzes the productivity and efficiency of Turkish banks from 2002 to 2010. We obtained estimates of efficiency, productivity growth and efficiency growth using a Bayesian stochastic frontier approach and focused on accounting for Non-Performing Loans (NPLs) for use in our model. Specifically, we introduce NPLs as a bad output in an input distance function, and estimate a system of non-linear equations subject to endogeneity. We confirm that the productivity growth of Turkish banks was positive over the period of this study, which was mainly due to the improvement in technology, while efficiency growth continued to be negative over the same period. Methodologically, we also prove that not accounting for NPLs in estimating the frontier model might seriously distort the efficiency and productivity results. The study also provides measures of shadow prices for NPL and discusses the results in terms of several interesting trends in Turkish banking. Finally, the paper provides efficiency and productivity comparisons between domestic and foreign banks.