Gaming the Float: How Managers Respond to EPS-based Incentives

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A Appendix We show that a drop in analyst coverage decreases the probability of meeting the earnings forecast. Consider a firm with s shares outstanding and net income uniformly distributed [−e, e]), where e is in dollars. Assume that each analyst issues a forecast that is independently drawn from a uniform distribution over [−e, e]), and that the consensus forecast is the sample mean. With infinite analysts, the forecast equals the mean and there is no variance. In this benchmark case the forecast is unbiased and has no noise, and the probability that the firm meets earnings forecasts is s 200e . For simplicity, we compare to the case in which there is only one analyst. The variance in the estimate will therefore be much higher than the benchmark case (the variance of the sample mean is decreasing in N). Because the variance is higher, the probability of meeting the forecast is lower. The intuition for this is straightforward. If the forecast is relatively close to the mean, then P r(meet) = is close to one of the tails of the distribution, then P r(meet) < s 200e . But if the forecast s 200e . No matter where the forecast is, the target size around the forecast is always ± s 200 , but integrating over this range results in different probabilities depending on where in the distribution the forecast is. When the forecast deviates from the mean, the result is a lower probability simply because the outcomes in the tails are less likely to occur. With probability 1 − With probability P r(meet) = s 200e the forecast will be close enough to the mean such that P r(meet) = s 200e . s 400e the forecast will be on the left tail of the uniform distribution such that in expectation 3s 800e . Because the forecast is unbiased the effect is the same on the right tail. Therefore, with a noisy, unbiased forecast: E[P r(meet)] = (1 − s 200e ) s 200e + 2( s 400e ) 3s 400e = s 200e (1 − s 800e ). We can compare this probability to the case in which the forecast is not noisy (infinite analysts). It is easy to show that if the manager prefers the same Pr(meet), shares need to increase in response to a drop in analyst coverage. Using s ∗ to denote the shares in the case of a forecast without noise, then s 200e (1 − s 800e ) = s∗ 200e → s > s∗ . The result shown above assumes analysts are unbiased. It can be shown that an increase in forecast bias has the same qualitative effect. Intuitively, integrating over the ± s 200 range results in a lower probability when the forecast is farther away from the mean. In this way an increase in bias has an effect similar to an increase in forecast variance. 31
Page 1 and 2: Gaming the Float: How Managers Resp
Page 3 and 4: earnings will choose more shares ou
Page 5 and 6: targets. Managers change the target
Page 7 and 8: it does not increase as the firm’
Page 9 and 10: meeting that forecast. This leads t
Page 11 and 12: 2.2 Time series determinants of sha
Page 13 and 14: ealized but before they are reporte
Page 15 and 16: A and incentive compensation in Pan
Page 17 and 18: elationship between incentive compe
Page 19 and 20: the view that increases in forecast
Page 21 and 22: In columns 2 and 3, we measure our
Page 23 and 24: atypical amount. In Table 9, we rep
Page 25 and 26: price levels observed in the data.
Page 27 and 28: management tools. 27
Page 29: De Angelis, D. and Y. Grinstein (20
Page 33 and 34: Figure 1: Example of the relationsh
Page 35 and 36: Figure 3: Median Shares Outstanding
Page 37 and 38: Table 2: Determinants of Shares Out
Page 39 and 40: Table 4: Shares Outstanding: First
Page 41 and 42: Table 6: Changes in Shares Outstand
Page 43 and 44: Table 8: Changes in Shares and Acco

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