Do Analysts’ EPS Forecasts Obey Benford’s Law? An Empirical Analysis
Abstract
Benford’s law gives the expected frequencies of digits in tabulated data. In this study, I investigate the extent to which a sample of analysts’ earnings per share (EPS) forecasts obey Benford’s law. I conduct Benford’s law’s second digit and last-two digits tests on a sample of analyst EPS forecasts of S&P 500 firms from 1998 to 2018. Overall, I find that analysts’ EPS forecasts obey Benford’s law’s second digit test but do not obey the last-two digits test. These findings suggest that while analysts do not engage in number invention, they do engage in rounding when making EPS forecasts.
References
Alali, F., & Romera, S. (2013). Benford's law: Analyzing a decade of financial data. Journal of Emerging Technologies in Accounting, 10(1), 1-39. https://doi.org/10.2308/jeta-50749
Archambault, J., & Archambault, M. (2011). Earnings management among firms during the pre-sec era: A Benford's law analysis. Accounting Historian's Journal, 38(2), 145-170. https://doi.org/10.2308/0148-4184.38.2.145
Benford, F. (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, 78, 551-572.
Cheong, F. S., & Thomas, J. (2016). Management of reported and forecast EPS and the extent to which investors adjust. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2830725 https://doi.org/10.2139/ssrn.2830725
Dechow, P., & You, H. (2012). Analysts' motives for rounding EPS forecasts. The Accounting Review, 87(6), 1939-1966. https://doi.org/10.2308/accr-50226
Diekmann, A. (2007). Not the first digit! Using Benford's law to detect fraudulent scientific data. Journal of Applied Statistics, 34(3), 321-329. https://doi.org/10.1080/02664760601004940
Drake, P. D., & Nigrini, M. J. (2000). Computer assisted analytical procedures using Benford's Law. Journal of Accounting Education, 18(2), 127-146. https://doi.org/10.1016/S0748-5751(00)00008-7
Durtschi, C., Hillison, W., & Pacini, C. (2004). The effective use of Benford's law to assist in detecting fraud in accounting data. Journal of Forensic Accounting, 5(1), 17-34.
Earle, T. C. (2009). Trust, confidence, and the 2008 global financial crisis. Risk Analysis: An International Journal, 29(6), 785-792. https://doi.org/10.1111/j.1539-6924.2009.01230.x
Eckel, N. (1982). An EPS forecasting model utilizing macroeconomic performance expectations. Financial Analysts Journal, 38(3), 68-77. https://doi.org/10.2469/faj.v38.n3.68
Ferran, E., Moloney, N., Hill, J., & Coffee, Jr., J. (2012). The regulatory aftermath of the global financial crisis. Cambridge University Press. https://doi.org/10.1017/CBO9781139175821
Giles, D. E. (2007). Benford's law and naturally occurring prices in certain eBay auctions. Applied Economics Letters, 14(3), 157-161. https://doi.org/10.1080/13504850500425667
Günnel, S., & Tödter, K. H. (2009). Does Benford's law hold in economic research and forecasting? Empirica, 36(3), 273-292. https://doi.org/10.1007/s10663-008-9084-1
Herrmann, D., & Thomas, W. (2005). Rounding of analyst forecasts. The Accounting Review, 80(3), 805-823. https://doi.org/10.2308/accr.2005.80.3.805
Hill, T. P. (1995). Base-invariance implies Benford's law. Proceedings of the American Mathematical Society, 123(3), 887-895. https://doi.org/10.1090/S0002-9939-1995-1233974-8
Hong, H., & Kubik, J. D. (2003). Analyzing the analysts: Career concerns and biased earnings forecasts. The Journal of Finance, 58(1), 313-351. https://doi.org/10.1111/1540-6261.00526
Hrazdil, K., Trottier, K., & Zhang, R. (2013). A comparison of industry classification schemes: A large sample study. Economics Letters, 118(1), 77-80. https://doi.org/10.1016/j.econlet.2012.09.022
Jordan, C., & Clark, S. (2011). Detecting cosmetic earnings management using Benford's law. The CPA Journal, 81(2), 32-37.
Judge, G., & Schechter, L. (2009). Detecting problems in survey data using Benford's Law. Journal of Human Resources, 44(1), 1-24. https://doi.org/10.1353/jhr.2009.0010
Lang, M, & Lundholm, R. (1996). Corporate disclosure policy and analyst behavior. The Accounting Review, 74(4), 467-492.
Mikhail, M., Walther, R., & Willis, R. (1997). Do security analysts improve their performance with experience? Journal of Accounting Research, 35, 131-157. https://doi.org/10.2307/2491458
Newcomb, S. (1881). Note on the frequency of the use of the different digits in natural numbers. American Journal of Mathematics, 4(1), 39-40. https://doi.org/10.2307/2369148
Nigrini, M. J. (1996). A taxpayer compliance application of Benford's law. The Journal of the American Taxation Association, 18(1), 72.
Nigrini, M. J. (2012). Benford's law: Applications for forensic accounting, auditing, and fraud detection. John Wiley & Sons. https://doi.org/10.1002/9781119203094
Nigrini, M. J. (2020). Forensic analytics: Methods and techniques for forensic accounting. John Wiley & Sons.
Nigrini, M. J., & Miller, S. J. (2009). Data diagnostics using second-order tests of Benford's law. Auditing: A Journal of Practice and Theory, 28(2), 305-324. https://doi.org/10.2308/aud.2009.28.2.305
Nigrini, M. J., & Mittermaier, L. J. (1997). The use of Benford's law as an aid in analytical procedures. Auditing: A Journal of Practice and Theory, 16(2), 52-67.
Sambridge, M., Tkalčić, H., & Jackson, A. (2010). Benford's law in the natural sciences. Geophysical Research Letters, 37(22), 1-5. https://doi.org/10.1029/2010GL044830
Sedor, L. (2002). An explanation for unintentional optimism in analysts' earnings forecasts. The Accounting Review, 77(4), 731-753. https://doi.org/10.2308/accr.2002.77.4.731
Walther, B., & Willis, R. (2013). Do investor expectations affect sell-side analysts' forecast bias and forecast accuracy? Review of Accounting Studies, 18(1), 207-227. https://doi.org/10.1007/s11142-012-9204-9
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