Abstract
The main purpose of this paper is to analyze the time patterns of individual analysts’ relative accuracy ranking in earnings forecasts using a Markov chain model. Two levels of stochastic persistence are found in analysts’ relative accuracy over time. Factors underlying analysts’ performance persistence are identified and they include analyst’s length of experience, workload, and the size and growth rate of firms followed by the analyst. The strength and the composition of these factors are found to vary markedly in different industries. The findings support the general notion that analysts are heterogeneous in their accuracy in earnings forecasts and that their superior/inferior performance tends to persist over time. An analysis based on a refined measure of analysts’ forecast accuracy ranking that strips off firm-specific factors further enhances the empirical validity of the findings. These findings provide a concrete basis for researchers to further explore why and how analysts perform differently in the competitive market of investment information services.
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Notes
A discussion that relates analysts’ accuracy in earnings forecasts to their ability in recommending stocks that generate superior returns is given in Loh and Mian (2006). It is seen to suggest the significance of information contents in earnings forecasts that apply to equity valuation.
There are several possible explanations for such findings. They include: (1) lack of extensive database, (2) primitive nature of statistical analysis as constrained by the computer facilities available at that time, and (3) the wide spread belief at that time in the implausibility of the existence of superior analysts in an efficient market.
Use of ranking statistics in the study of performance persistence arises naturally. For instance, Carhart (1997) uses it in the study of mutual fund performance.
References for Markov chains can be found in Grimmet and Stirzaker (2001), Chap. 6.
It is similar to the actuarial table for life expectancy conditional on a person’s current age. The conditional probability of survival shifts as the person’s current age increases, but not in a monotonic fashion.
This finding applies to both superior and inferior performers. Our results are somewhat different from those reported in Sinha et al. (1997). In the latter work, it was found that while superior performance persists, inferior performance does not.
Only 1% of analyst-firm combinations in the I/B/E/S database have forecasts recorded at more than 90 days prior to the end of the fiscal quarter.
We recognize that a forecast made closer to the end of the quarter for which an earnings forecast is made may be based on more newly available information and thus result in better accuracy. For that reason, in our measuring system, an analyst can gain an edge by postponing the forecast as long as possible. However, a forecast made later in the designated quarter is less useful to the analyst’s clients and can be detrimental to the analyst’s job evaluation. An analyst is expected to provide the forecast within a reasonable time window, usually within the first 2 months of the fiscal quarter. The fact that a definite majority of analysts in our sample (over 75%) made their first forecast for the quarter during the first 2 months of the quarter confirms this contention.
An in-depth investigation, conducted by the present authors, of analysts’ timing of quarterly earnings forecasts reveals that only a small percentage of analysts (about 3%) have more than 50% of their quarterly earnings forecasts made later than 30 days prior to the end of the fiscal quarter. These analysts often carry a heavy forecasting workload because they follow a large number of firms. We also note that few analysts have a preset narrow time range in which they made all, or a majority of, their forecasts. Instead, they made forecasts at varying times in the quarter over the sample years and for different firms. In that sense, the 60-day window that we use to rank analysts’ forecast accuracy does not run a significant risk of generating biased results in favor of chronically late forecasters. To narrow or divide the time window further will unduly reduce the available data points and make analysis difficult and less reliable. It will take another special study to devise a mechanism to adjust the effects of timing differences across a spectrum of analysts and firms.
The time point t − 1 in our context here is actually a fraction of a calendar quarter prior to the quarter end point t. This is because we take the first forecast of an analyst within 3 months, but more than 30 days prior to the time point t.
Our definition of the AFE here is just one of the several possible measures used to rank analysts’ accuracy in earnings forecasts. We have examined advantages and disadvantages of several measures that have been employed in the literature. In the end, we chose to use the definition provided above, in conjunction with a carefully chosen winsorization scheme, for the main analysis in this paper. In a later section, we also conduct a robustness study based on another measure of relative forecast accuracy.
The “transient” factors may include pure luck, big earnings surprises, occasional information advantages, irregularity in firms’ accounting treatments, etc. The “long-lasting” factors may involve analysts’ information gathering skills, analytic capacity, workload, in-depth understanding of the industry and firm being followed, etc.
We also note that the value of standard deviation of the AFEs (not shown in the table) is strikingly parallel to the corresponding mean value in both industry and year dimensions, due to the positive correlation between them.
Recognizing that the overall dataset pools together analysts who follow different industries, and hence involves rankings of AFEs from heterogeneous groups, we present the results in Table 1 mainly to illustrate our analytical procedure. Results from analysis on individual industries are to follow.
Missing observations can happen for various reasons, such as switching to other roles as research director, money manager or investment officer in asset management firms, firm executive, or exiting the profession in pursuit of other interests. It can also result, in a small number of cases, from our data trimming schemes outlined in Sect. 2.
When an analyst covers firms in more than one industry, the analyst is counted as a distinct analyst in each of the industries. For that reason, the analyst’s performance in each of the different industries is ranked separately competing against analysts in that particular industry.
In an earlier version of this paper, we produced results in a format similar to Table 2 for nine Morningstar Investment Style groups. The reason for doing so is to determine whether, after separating firms into more homogeneous groups by their capitalization size and P/B ratio, the average quintile ranking scores deviate in a significant way from the median value, 3.0, in successive observation years. The results, not shown here for economy of space, behave with even stronger degree of departure from the pure chance model compared with the case with the 13 industries as shown in Table 2.
We first constructed the expected frequency table under \( H_{0}^{{(1{\text{st}})}} \) as described in Sect. 3. We then calculated the quantity \( \chi^{2} = \sum\nolimits_{i = 1}^{5} {\sum\nolimits_{j = 1}^{6} {\left[ {{{\left( {f_{ij}^{(o)} - f_{ij}^{(e)} } \right)^{2} } \mathord{\left/ {\vphantom {{\left( {f_{ij}^{(o)} - f_{ij}^{(e)} } \right)^{2} } {f_{ij}^{(e)} }}} \right. \kern-\nulldelimiterspace} {f_{ij}^{(e)} }}} \right]} } \), where \( f_{ij}^{(e)} \)is the expected number of observations in the cell at the i-th row and j-th column, and \( f_{ij}^{(o)} \)is its observed counterpart. The degrees of freedom for the χ2 statistic is (5 − 1) × (6 − 1) = 20. (Since the frequencies on the 6th row are estimated values as explained in Sect. 3, we exempt them from the test.) The number of observations in each cell used in the calculation of the χ2 statistic here is set equal to one half of the observations we actually count. This is to allow for the overlapping nature of our moving window. In this particular circumstance, the (first) observation year of this cycle overlaps with the formation year in the next cycle. The true number of independent observations is not exactly known, but it should be between 50 and 100% of the number of observations that we actually count. To make the matter simple and to be on the conservative side, we use the lower bound, that is, one half. Specifically, the number of observations used in the test statistic is equal to n × 5 × (14/2) = 35 n, where n is the number of analysts in a quintile, averaged over the fourteen formation years (1988–2001), and the number “5” is because there are five quintiles in a dataset. The number “14” in the expression above is because of the fourteen formation cycles in our sample—altogether, it is 267.6 × 35 = 9,366, the number of estimated independent observations for the overall dataset. In Table 4, we apply the same calculation procedure to each of the thirteen industries, with the value of n replaced by the average quintile group size for that particular industry.
The degrees of freedom in the test is (6 − 1) = 5. The numbers of (independent) observations are estimated to be 4n, 3n, 3n, and 3n for year 2, 3, 4, and 5 respectively, where n is the average number of analysts in a quintile over the 14-year cycle. Again, these estimates are on the conservative side.
The motivation for using the last three sample years, 2004–2006, was mainly that they are relatively recent and are more relevant to current conditions. We also noted that Regulation FD (fair disclosure) became effective on 10/23/2000 and may have altered analysts’ relative performance in earnings forecasts compared with the period prior to it. For that reason, our study reported below is seen to have incorporated the impact of the new regulation and may provide insights into the factors that affect analysts’ performance in the new regulatory environment.
From our analysis presented in Sect. 6, we recognize that the influences of the transient factors have a half-life span in most cases much less than 0.35 years. The variable SCORE-A as defined above is predominantly driven by the long-lasting factors.
We skipped the first quarter of 1984 because of the absence of some necessary records in the I/B/E/S database in that very first quarter.
The other score variable SCORE-R is for a different ranking score system to be explained in the next section.
Heretofore, our analysis is based on the 5% two-sided significance level on the t-statistic which is near the normal distribution given the large sample size as indicated on the column with the caption “N”.
The reader is referred to Clement (1999), Jacob et al. (1999), Mikhail et al. (1997, 2003), Ghosh and Whitecotton (1997), Abarbanell and Lehavy (2003), and Stickel (1992) for the findings related to FN, SB and AE. A lone finding about the effect of ASIZE is reported in Brown (1997). A similar finding in a foreign country is also documented by Ho (2004). The variable FGR is new in this study.
We note that the enactment of the Regulation FD starting in October 2000 may have reduced the importance of analyst’s experience, which may in part proxy for an analyst’s connection with corporate executives whose firms the analyst follows. The uncertain economy in the early 2000s in the aftermath of the burst of the high tech bubble in the stock market may also have affected the usefulness of analysts’ past experience.
The reader is referred to Johnson and Wichern (2002), Chap. 11, for detailed methodological explanations of this analysis.
A same measure is employed by Clarke and Subramanian (2006, p. 92, Eq. 11), in a study of herding behaviors among analysts in earnings forecasting.
A different standardized measure of forecasting accuracy is proposed by Clement (1999) and used by Jacob et al. (1999), in which the absolute values of forecast errors of individual analysts for firm k in year t are normalized (i.e., divided) by the average absolute forecast error from all participating analysts in the same firm and year. This measure has the tendency to magnify the accuracy differences among analysts because a large proportion (about 50%) of quarterly earnings forecast errors in our sample are within a small range of ± 3 cents per common stock share. Further, more than 10% of all forecast errors in our sample are exactly zero, which renders the normalization infeasible in many cases. In summary, such a normalization process could produce serious distortions. Because of these concerns, we did not pursue a measure of accuracy along that line.
In Sect. 2 we state that only firms with four or more participating analysts in a quarter immediately prior to the quarter in question, as listed in the original I/B/E/S database, are included in our sample for that quarter. But other trimming criteria, such as that an analyst will have to provide quarterly forecasts for at least ten quarters for the firm, further reduced the number of qualified analysts in our sample. This explains why we have a substantial number of firms with three or fewer qualified analysts.
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Acknowledgments
The authors gratefully acknowledge receipt of research supports from Lubar School of Business at the University of Wisconsin-Milwaukee and Department of Business at Missouri Western State University. These supports include access to the databases used in this paper.
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Hsu, D., Chiao, CH. Relative accuracy of analysts’ earnings forecasts over time: a Markov chain analysis. Rev Quant Finan Acc 37, 477–507 (2011). https://doi.org/10.1007/s11156-010-0214-z
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DOI: https://doi.org/10.1007/s11156-010-0214-z