Discussion of Information Uncertainty and Post-Earnings-Announcement-Drift

Journal of Business Finance & Accounting, 34(3) & (4), 434 438, April/May 2007, 0306-686X doi: 10.1111/j.1468-5957.2007.02031.x Discussion of Information Uncertainty and Post-Earnings-Announcement-Drift Lakshmanan Shivakumar The post-earnings-announcement drift has been the longest-standing anomaly in the finance and accounting literature. Several decades after this anomaly was first identified by Ball and Brown (1968), the strategy remains profitable. It has also withstood a variety of methodological checks. Although the anomaly violates the semi-strong form of market efficiency, Francis, LaFond, Olsson and Schipper (2007) (FLOS hereafter) argue that this need not imply investors irrationality, as stock-return predictability rationally arises under a learning model. FLOS test the validity of rational learning models as an explanation for the post-earnings-announcement-drift by examining the empirical implications of this hypothesis. FLOS draw three implications from the learning hypothesis. Their first hypothesis is that initial reaction to earnings surprise will be more muted, the larger is the information uncertainty about underlying earnings. This is because Bayesian investors place less weight on noisier (i.e., more uncertain) earnings information and more weight on their priors, making them under-react to new information. The testable prediction from this hypothesis is that the greater the information uncertainty, the smaller will be the magnitude of initial market reaction to earnings surprises. The second hypothesis is that, if information uncertainty gives rise to the post-earningsannouncement-drift, then it must be greater in firms with higher post-earningsannouncement-drift. As firms with extreme earnings surprises are the firms with most drift, they should also be firms with the most information uncertainty. The last hypothesis is that, controlling for earnings surprises, abnormal returns associated with the post-earnings-announcement-drift are larger for firms with higher information uncertainty. This hypothesis essentially states the consequences of hypothesis 1. That is, if initial under-reaction to earnings surprises is larger for firms with greater information uncertainty, as stated in hypothesis 1, then the subsequent corrections, which cause the post-earnings-announcement-drift, should also be larger for firms with greater information uncertainty. In addition to the above three implications of the learning hypothesis, FLOS conduct two additional analyses. First, they study the relation between their findings and those of The author is from the London Business School. He thanks Jennifer Francis, Per Olsson, Peter Pope and Katherine Schipper for helpful comments. Address for correspondence: Lakshmanan Shivakumar, London Business School, Regent s Park, London NW1 4SA, UK. e-mail: LShivakumar@london.edu Journal compilation C 2007 Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. 434

DISCUSSION OF POST-EARNINGS-ANNOUNCEMENT-DRIFT 435 Mendenhall (2004), who shows that post-earnings-announcement-drift exists because of limits of arbitrage. Mendenhall (2004) uses idiosyncratic volatility to proxy for arbitrage limits. As idiosyncratic volatility is likely to be correlated with information uncertainty, FLOS examine whether the findings of the two studies are related. Second, they extend their findings for the post-earnings-announcement-drift to other market anomalies, namely the value-glamour anomaly and the accrual anomaly. Using accruals quality to proxy for information uncertainty, FLOS provide evidence consistent with all three implications derived from the rational learning model. Also, they find that accrual quality subsumes the relation documented by Mendenhall (2004) between idiosyncratic volatility and post-earnings-announcement-drift, implying that post-earnings-announcement-drift is not due to arbitrage limits preventing informed investors from taking advantage of market inefficiencies. Finally, they show that the proxy for information uncertainty has discriminative power for payoffs associated with trading strategies based on accruals and value-glamour anomalies. FLOS make a useful contribution to our understanding of the anomalies. Most studies interpret predictability of stock returns, including the predictability based on past earnings surprises as in the post-earnings-announcement-drift anomaly, as evidence of investor irrationality. However, Brav and Heaton (2002) argue that such predictability is also consistent with rational learning by investors in an uncertain environment. The current paper derives empirical implications from the Brav and Heaton (2002) argument and provides evidence consistent with it. Its results imply that the post-earnings-announcement-drift would exist even if investors were not naïve or irrational. But, having said that, the paper s results do not rule out alternative behavioral explanations for the drift anomaly. In fact, its results are equally supportive of behavioral and rational learning models. Thus, even though its evidence suggests that drift can exist in a world with rational investors, it does not help us discriminate between behavioral and rational explanations. 1 In Section 1, I discuss issues pertaining to the background literature and to hypotheses development. In Section 2, I discuss issues relating to the empirical implementation and Section 3 concludes and provides suggestions for future research. 1. ISSUES RELATING TO MOTIVATION AND HYPOTHESES DEVELOPMENT FLOS motivate their study by stating that prior literature reaches different conclusions about how information uncertainty affects stock price under-reaction. In particular, FLOS note that Liang (2003) shows a negative relation between changes in uncertainty and the under-reaction to earnings announcements, whereas Zhang (2006) finds a positive relation between under-reaction and information uncertainty. This difference in predictions is surprising, as both Liang (2003) and Zhang (2006) derive their implications from Daniel et al. (1998). However, there is a simple resolution for this apparent difference. Whereas both Zhang (2006) and FLOS focus on the level of information uncertainty before an event such as an earnings announcement, Liang s (2003) arguments are based on changes in information uncertainty from before to after an earnings announcement. A larger resolution of information uncertainty 1 Brav and Heaton (2002) claim that no empirical study can ever distinguish between behavioral and rational explanations as the empirical predictions from these two explanations are identical.

436 SHIVAKUMAR is likely to occur at earnings announcement when the initial uncertainty about earnings is low, because low uncertainty would allow investors to weight newly released earnings information more heavily. Consequently, if stock price under-reactions are positively correlated with initial information uncertainty, they are likely to be negatively correlated with changes in information uncertainty around the event of interest. For this reason, I believe neither the arguments nor the evidence in the prior literature on the role of information uncertainty is contradictory, and that the results in the current paper are in line with both Liang (2003) and Zhang (2006). The paper presents three hypotheses that are derived from the rational learning models for the drift anomaly. In the null form, the hypothesis is that information uncertainty is unrelated to post-earnings-announcement-drift. The paper does not present or discuss this null hypothesis. In particular, are there any formal models that explain apparent stock under/over-reactions without predicting a link between the under/over-reaction and information uncertainty? Most popular theories for stock market anomalies, rational or otherwise (e.g., Daniel et al., 1998 and 2001; Hirshleifer, 2001; and Brav and Heaton, 2002) seem to rely upon information uncertainty. Given this, it would be useful to know which theories, if any, can be downgraded as relatively weak in explaining the anomalies based on the paper s evidence. The paper s second hypothesis is that, if information uncertainty causes the drift, then stocks in the extreme UE deciles should have greater information uncertainty than the non-extreme deciles, as the drift is observed primarily in the extreme UE deciles. This, however, need not be the case. To give an example, consider two firms with the same level of information uncertainty: one firm has an extremely positive earnings surprise and the other has little or no earnings surprise (and so will be in the non-extreme UE decile). If information uncertainty causes the market to under-react to unexpected earnings, then the under-valuation will be larger for the firm with positive earnings surprise, because a large proportion of the good news has not been reflected in this firm s stock price. In other words, even if information uncertainty is the same across the earnings-surprise portfolios, extreme earnings-surprise portfolios will still have greater drift than non-extreme earnings-surprise portfolios. Thus, even though the paper finds information uncertainty to be higher for the extreme UE deciles, it is not an implication of the uncertainty-based explanation for post-earnings-announcementdrift. The more reasonable explanation for the observed relation between information uncertainty and extreme deciles is that the proxy used for information uncertainty (namely, volatility of accruals residual from the Dechow-Dichev model) rather than the actual information uncertainty, is correlated with earnings volatility. This causes extreme earnings surprise portfolios to have a disproportionately larger number of firms with high residual-accrual volatility. 2. ISSUES RELATING TO SAMPLE AND EMPIRICAL IMPLEMENTATION In order to compute their proxy for information uncertainty, FLOS require firms to have seven years of past data for inclusion in the final sample. Moreover, they require firms to have data on analysts forecasts. These requirements bias their sample towards the relatively larger firms. Bernard and Thomas (1989) show that post-earnings-announcement-drift is substantially lower for larger firms. Consistent with the bias towards larger firms in the FLOS sample, Table 2 shows that postearnings-announcement-drift is about 0.84% per month for the unrestricted sample,

DISCUSSION OF POST-EARNINGS-ANNOUNCEMENT-DRIFT 437 whereas it is only 0.49% per month for the sample with information uncertainty data. The substantial difference between the samples of firms with and without data on information uncertainty raises concerns about the generalizabiltiy of the paper s results. Information uncertainty is measured as the residuals of the accruals in the Dechow and Dichev (2002) model. The Dechow Dichev model has been developed to capture the role of accruals in mitigating timing and matching problems in cash flows. However, companies additionally use accruals to report losses in a timely manner. Ball and Shivakumar (2006) show that this timely loss-recognition role of accruals implies a nonlinearity in the Dechow Dichev model, and that a failure to consider such non-linearity can lead researchers to incorrectly interpret more volatility in accruals as indicating lower-quality accruals, when in fact the greater accrual volatility arises from timely loss recognition, a positive attribute of accrual reporting. Since both economic gains and economic losses are equally important in stock valuation, one might argue that a symmetric accrual model is more appropriate for identifying value-relevant information as opposed to identifying information that is relevant for contracting or monitoring purposes and as a result, argue against the use of non-linear accrual models in studies that deal with valuation, such as FLOS. However, in reality, firms recognize economic losses in a more timely manner than economic gains, partly due to the asymmetric costs of recognizing economic gains and economic losses (Basu, 1997; and Ball and Shivakumar, 2006). Thus, even in the context of stock valuation, accrual models that capture value-relevant information should consider the empirical fact that, in reality, reported accruals provide more timely information to investors about economic losses than about economic gains. At the least, it would be useful to examine the consequences of allowing for asymmetric reporting of losses in the accruals model. 3. CONCLUSIONS FLOS provide interesting and useful evidence on the relation between information uncertainty and stock market anomalies. By using a novel measure for information uncertainty derived from earnings, the paper confirms evidence in the prior literature that information uncertainty is a reason for the apparent stock market under- and over-reactions to earnings surprises. Although the paper derives its hypotheses from a model of rational learning, its results are consistent with models based both on rational learning and on investors cognitive biases. While Brav and Heaton (2002) present one possible reason why information uncertainty delays price adjustment to news, there are several other possible explanations for the link between information uncertainty and the delay in price adjustment, even within a rational paradigm. For instance, information uncertainty increases information asymmetry across investors, leading to higher transaction costs. The transaction costs act as frictions that prevent informed investors from arbitraging and delay price adjustments to new information (Chordia et al., 2006). It would be a useful exercise for future research to establish the precise link between information uncertainty and stock price formation in capital markets. Another fruitful area for research is the extension of FLOS to an international context in order to explain cross-country differences in postearnings-announcement-drift (see Hong, Lee and Swaminathan, 2003). The results in FLOS suggest that, the poorer the accounting quality in a country, the greater will be the drift in that country.

438 SHIVAKUMAR REFERENCES Ball, R. and P. Brown (1968), An Empirical Evaluation of Accounting Numbers, Journal of Accounting Research, Vol. 6, pp. 159 78. and L. Shivakumar (2006), The Role of Accruals in Asymmetrically Timely Gain and Loss Recognition, Journal of Accounting Research, Vol. 44, No. 2, pp. 207 42. Basu, S. (1997), The Conservatism Principle and Asymmetric Timeliness of Earnings, Journal of Accounting & Economics, Vol. 24, pp. 3 37. Bernard, V.L. and J.K. Thomas (1989), Post-Earnings-Announcement Drift: Delayed Price Response or Risk Premium, Journal of Accounting Research, Vol. 27, pp. 1 35. Brav, A. and J.B. Heaton (2002), Competing Theories of Financial Anomalies, Review of Financial Studies, Vol. 15, No. 2, pp. 575 606. Chordia, T., A. Goyal, G. Sadka, R. Sadka and L. Shivakumar (2006), Liquidity and Post- Earnings-Announcement Drift, Working Paper (London Business School). Daniel, K., D. Hirshleifer and A. Subrahmanyam (1998), Investor Psychology and Security Market Under- and Overreactions, Journal of Finance, Vol. 53, pp. 1839 86. (2001), Overconfidence, Arbitrage, and Equilibrium Asset Pricing, Journal of Finance, Vol. 56, pp. 921 66. Dechow, P. and I. Dichev (2002), The Quality of Accruals and Earnings: The Role of Accrual Estimation Errors, The Accounting Review, Vol. 77, Supplement, pp. 35 59. Francis, J., R. LaFond, P. Olsson and K. Schipper (2007), Information Uncertainty and Post- Earnings-Announcement-Drift, Journal of Business Finance & Accounting, Vol. 34, Nos. 3&4, pp. 403 33. Hirshleifer, D. (2001), Investor Psychology and Asset Pricing, Journal of Finance, Vol. 56, No. 4, pp. 1533 97. Hong, D., C. Lee and B. Swaminathan (2003), Earnings Momentum in International Markets, Working Paper (Cornell University). Liang, L. (2003), Post Earnings Announcement Drift and Market Participants Information Processing Biases, Review of Accounting Studies, Vol. 8, pp. 321 45. Mendenhall, R. (2004), Arbitrage Risk and Post-Earnings-Announcement Drift, Journal of Business, Vol. 77, pp. 875 94. Zhang, F. (2006), Information Uncertainty and Stock Returns, Journal of Finance, Vol. 61, pp. 105 37.