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A stochastic model of superstardom: evidence from institutional investor's All-American Research Team.

Raymond A.K. Cox [a],[*]

Robert T. Kleiman [b]

Abstract

In this paper, we investigate the superstar phenomenon in the security analysis industry through an analysis of the probabilistic mechanism by which security analysts are selected for inclusion in Institutional Investor's All-American Research Team (II AART). Specifically, we examine whether the statistical distribution of the number of first team appearances by security analysts conforms to the Yule distribution, which implies that luck rather than differential talent explains success. This is an important issue since an analyst's position on the AART is an important determinant of the individual's pay and reputation. Our research results reject the Yule distribution. Thus, consistent with previous empirical studies by Stickel [Stickel, S. E. (1992). Reputation and performance among security analysis. J Finance 47, 1811-1836; Stickel, S. E. (1995). The anatomy of the performance of buy/sell recommendations. Financ Anal J 51, 25-39] and Brown and Chen [Brown, L. D., & Chen, D.M. (1991). How good is the All-A merican Research Team in forecasting earnings. J Bus Forecast 9, 14- 18], we find that selection to the AART can be attributed to skill rather than luck. [C] 2000 Elsevier Science Inc. All rights reserved.

Keywords: Superstardom; Security analysts; Yule

A constant question investors face is: Does the past performance of security analysts merit the compensation they receive? Recent data (Institutional Investor, October 1996) indicates analysts earning well over $500,000 per year with many in excess of $1,000,000 a year and as much as $5,000,000 (including stock). This event is an example of the so-called superstar phenomenon, wherein a relatively small number of people dominate the activities in which they are engaged and earn enormous amounts of income.

Extraordinary incomes earned by superstars may be driven by an allocative equilibrium in which markets reward talented people with increasing returns to ability.. Or perhaps, the superstar phenomenon has nothing to do with the differential talent of individuals. If, on the other hand, the source of their high incomes is not their talent, the skewness in income distributions caused by the phenomenon may be perceived as inequitable.

Rosen (1981) suggests that much of the superstar phenomenon can be explained by convexity of sellers' revenue functions since the convex revenue function implies that the distribution of rewards is more skewed than. the distribution of talent (i.e., small differences in talent are magnified into disproportionate levels of success). In a similar vein, MacDonald (1988) presents a dynamic version of Rosen's superstar model using a popular music performing artist illustration. He shows that in equilibrium only the young enter the occupation and earn low incomes playing to small crowds, and only the successful stay on. Overall, there are few stars in the industry but as a group they serve a large fraction of the audience and earn an even larger share of the rewards. Another illustration of the superstar phenomenon is in the sport of golf. If a golfer is, on average, but one stroke better than other competitors then a disproportionate number of tournament championships would be won by said athlete.

In this paper, we view the superstar phenomenon in the context of a probabilistic mechanism underlying the selection of security analysts to Institutional Investor's All-American Research Team (II AART). The II AART is chosen as a measure of reputation of the security analyst. An analyst's position on the AART is an important determinant of his pay and reputation. According to Kover (1997), the typical pay differential between a first-team analyst and an also-ran was approximately $1 million per annum. However, some analysts contend privately that the list is little more than a popularity contest and does not reflect actual differences in talent.

To test the superstar phenomenon, this study employs a stochastic model of Yule (1924) and Simon (1955). Our findings show that the probability distribution implied by the stochastic model does not describe the empirical data in the security analysis industry. Thus, our results support the notion that the most successful security analysts achieve such results due to their proficiency as opposed to mere chance or luck. Our empirical results endorse the theory of superstardom advanced by Rosen (1981) and MacDonald (1988).

The remainder of the paper is organized as follows. In the following section, we review previous studies of the performance of Wall Street brokerage analysts. In Section 2, we introduce the stochastic model advanced by Yule (1924) and Simon (1955) as a possible description of the superstar generating process. Section 3 describes the data and presents empirical results. The paper ends with a brief summary and concluding remarks.

1. Previous literature on the security analysis process

Security analysts are among the most significant information intermediaries in the capital markets. These individuals generally work within the research departments of investment banks and cover a group of companies within a particular industry. They regularly collect and process large amounts of information provided by corporations and data vendors and then disseminate the processed data to investors and money managers. In particular, many institutional investors rely on the earnings forecasts and stock recommendations prepared by the security analyst community.

Studies in the field of finance on the output of security analysts have focused on the information content and accuracy of their earnings forecasts. Early examinations of the accuracy of the annual earnings per share forecasts of security analysts by Brown and Rozeff (1980), O'Brien (1987, 1990), and Butler and Lang (1991) suggested the absence of analysts who could provide more accurate earnings forecasts over multiple year periods. However, controlling for the recency of the forecasts, Sinha et al. (1997) found analysts classified as "superior" in estimation periods also generally remained superior in holdout periods. Similarly, Mikhail et al. (1997) found a statistically significant decline in the absolute value of analyst forecast errors as firm specific experience increases. Thus, analysts improve their forecasting accuracy with firm specific experience.

Two studies specifically examined the ability of members of II's AART to forecast earnings per share. Brown and Chen (1991) found evidence of the earnings forecast superiority of the II AART compared to the consensus of security analysts from the Zacks Investment Research database. In another study, Stickel (1992) documented that members of Institutional Investor's All American Research Team had smaller average annual earnings forecast errors than did non-team members.

The buy and sell recommendations of Wall Street brokerage house analysts are also of interest to institutional fund managers. Stickel (1992) found the higher the II AART ranking, the greater the impact of the analyst's buy/sell recommendations on temporary stock-price movements. In a complementary article, Stickel (1995) found similar results for the 1988 to 1991 time period. On the other hand, Womack (1996) provided evidence that stock prices are significantly influenced by changes in analysts' recommendations, not only at the immediate time of the announcement of the change, but also in subsequent months. Finally, Milchail et al. (1997) found that the stock recommendations of more experienced analysts were not more profitable than those from less experienced analysts.

Another stream of recent research has focused on the process that security analysts use to arrive at their ratings for a given security. Stickel (1992) suggests that analysts use ambiguous and complex information, methodology, and judgements to arrive at their ratings (buy, sell, or hold) for a given security. On the other hand, Hayward and Boeker (1998) and Michaely and Womack (1998) found that analysts at investment banks that undertake corporate finance deals for a client rate that company's common stock more favorably than do peer analysts. [1] However, Hayward and Boeker note that the positive bias is moderated by the rating assigned the analyst in Institutional Investor's annual survey of all-star analysts. More prestigious analysts issue lower ratings suggesting that analysts who have strong positions vis-a-vis their corporate finance departments seek to provide independent recommendations. Thus, the tendency of all-star analysts to offer more objective advice may result in differential levels of perf ormance among analysts.

Taken as a whole, prior empirical work suggests that members of the II AART provide superior earnings per share forecasts than do non-team members and have a greater influence on stock price movements. Previous research also suggests that there is evidence of some analysts who consistently provide more accurate earnings forecasts over multiple year periods. Finally, prior studies indicate that while more experienced analysts issue more accurate earnings forecasts, they do not necessarily provide superior stock price recommendations.

2. A stochastic model of superstardom

The Rosen-MacDonald theory of superstar centers on an implicit comparison of success relative to the differences in talent. In this section, we show a model of the phenomenon of superstars that does not require differential talents among individuals using the stochastic model of Yule (1924) and Simon (1955). Simon suggests that a variety of sociological, biological, and economic phenomena are driven by certain probability mechanisms. Specifically, he shows that a wide range of empirical data (e.g., distributions of incomes by size, distributions of cities by population, distributions of biological genera by number of species, and distributions of scientists by number of papers published (see Chung and Cox, 1990)) conforms well to a class of distributions which can be obtained from stochastic processes similar to those yielding negative binomial or log series distributions. This class of distributions is given by (see Simon, 1955, p. 426):

f(i) = [psi]B(i,[rho] + 1), (1)

where [psi] and [rho] are constants and B(i,[rho] + 1) is the beta function of i and [rho] + 1, i.e.,

B(i,[rho] + 1) = [[[integral].sup.1].sub.0] [[lambda].sup.i-1][(1 - [lambda]).sup.[rho]] d[lambda] = [lceil](i)[lceil]([rho] + 1)/[lceil](i + [rho] + 1), 0 [less than] i; 0 [less than] [rho] [less than] [infinity]. (2)

Since the class of distributions represented by expression (1) was first derived by Yule (1924), the distribution carries his name. Since Yule's model does not require the assumption of differential talents among individuals (that is, luck explains success) data fitting the distribution would suggest the superstar phenomenon could exist among individuals with equal talent in their field of endeavor.

The stochastic process that would lead to the Yule distribution can be characterized as follows. Because the main thrust of this paper is to examine whether the Yule distribution can explain the relative frequency of brokerage analysts' selection to II AART, we portray the process in such a context. For simplicity, and without loss of generality, suppose that each team position is vied for by the same number of individuals, n. [2] Further assume all team positions are selected sequentially and assigned to one successful security analyst. After the last team position is chosen for a given year, the selection process repeats itself to select a new team the following year. If the following two assumptions describe the probability of being selected to the AART the process may be characterized by the Yule distribution.

Assumption 1 The probability that team k + 1 selects an individual to the team who was already on exactly i of the k previous teams is proportional to i. In other words, the probability of a security analyst being selected to the team is proportional to the number of teams the individual was previously chosen for.

Assumption 2 There is a constant probability, [delta], that an analyst is selected for team k + 1 who was not yet chosen for any previous k teams. An alternative way of stating this assumption is that the probability of a security analyst who has never served on the team being chosen for the team is the same for all such security analysts.

In spirit, the process implied by these assumptions is similar to the superstar generating process suggested by Adler (1985). Adler argues that consumers minimize the cost of searching for information by choosing the most popular artists. In the current context the probability mechanisms underlying the superstar generating process proposed by Adler can be summarized as follows. Suppose that selectors of the team believe at first that all security analysts are equally likely to become stars, and that each selector picks one security analyst at random. Assume further that selectors live n periods and revise their prior distributions after each period. If there were a slight majority of judges that select a security analyst as their choice, that security analyst would eventually become a star since after each period of time a security analyst had a market share of selectors only marginally larger than everybody else. This share would increase steadily, and ultimately the security analyst becomes a star.

In the following sections, we examine empirically whether the above assumptions are a realistic representation of the process creating superstars in the security analysis industry. Ultimately, the reasonableness of these assumptions can only be judged by the prescriptive power of the Yule distribution. As a result, we examine whether the Yule distribution can explain the cross-sectional distribution of the number of times an individual is selected to the II AART first team.

3. Data and empirical results

The measure of superstardom used in this study is the number of selections to the first team of the AART. The selection to the II AART is done by confidentially surveying the directors of research and chief investment officers of over 2000 major money management institutions. These money managers are asked to evaluate security analysts in four of their primary activities: (1) stock recommendations, (2) earnings forecasts, (3) written reports, and (4) overall performance. Rankings are determined by using the numerical score each analyst receives, and scores are tallied by taking the number of votes awarded to an individual analyst and weighting them based on the size of the voting institution. The identities of the survey respondents and the institutions that employ them are kept confidential to ensure their continuing cooperation in the survey.

Note that two of the four ratings criteria -- the earnings forecasts and stock recommendations of security analysts -- have been extensively examined in previous empirical work, and these studies suggest that AART members demonstrate superior performance with respect to these criteria. Thus, on the basis of prior research, we would expect that the Yule distribution should be rejected since the prior work indicates differences in talent among security analysts.

Data for the present study were obtained from II AART first team lists compiled and reported annually in H, for the years 1972 through 1996, which contains 328 AART security analysts. The number of analysts on the first team has varied from 26 in 1972 to 81 in l996. [3] Table 1 shows a list of the top 50 most successful security analysts, based on first team AART appearances, and the industry followed by each analyst.

To examine the distribution of AART first team appearances by security analysts, we employ the Yule distribution. Simon (1955) suggests the Yule distribution provides a good fit to numerous empirical phenomena especially when the value of p is equal to one. Here we assume as an empirical approximation that the probability that team k + 1 selects a security analyst who has not yet been chosen to the previous k teams is small ([delta] [approximate] 0) so that [rho] is close to one. In this case the Yule distribution can be approximated by

f(i)=1/i(i+1) [sigma]f(i) = 1, (3)

where f(i) may be interpreted as the number of security analysts with i AART selections. Thus the number of security analysts with one AART selection is given by

f(1) = 1/1(1 + 1) 0.500. (4)

In a similar manner the number with two and three selections is given by

f(2) = 1/2(1 + 2) = 0.167 (5)

f(3) = 1/3(1 + 3) = 0.083. (6)

Table 2 shows the frequency of security analysts by the number of AART team selections. Among security analysts who have been selected at least once to the AART, 95 (28.96%) individuals have been selected only once, 66 (20.12%) individuals have been selected twice and, 37 (11.28%) individuals have three selections. It is interesting to note that only 41 (12.50%) have more than seven selections, while only 14 (4.27%) security analysts have more than 12 AART selections, revealing a high concentration by top security analysts.

The fourth and fifth columns of Table 2 show the actual and predicted proportion of security analysts with various numbers of AART selections, respectively. Casual observation of these columns leads one to suspect that the Yule distribution does not accurately describethe distribution of security analysts named to the AART. To more rigorously test the observation we apply a [[chi].sup.2] goodness-of-fit test to the data in these columns. Since the [[chi].sup.2] test requires that the predicted number of observations in each category be at least five we use only the observations where the actual number of AART selections is less than or equal to eleven or more (predicted number of security analysts is 13.448). The [[chi].sup.2] statistic Q is

Q = [[[sigma].sup.9].sub.j=1] [([Actual.sub.j] - [Predicted.sub.j]).sup.2]/[Predicted.sub.j] = 113.57. (7)

Since the [[chi].sup.2] statistic is greater than [[[chi].sup.2].sub.[alpha] = 0.05] = 23.209 we reject the hypothesis that the Yule distribution with [rho] = 1 generates the observations. Thus, our results are contrary to the superstar theory advanced by Adler (1985) but consistent with that of Rosen (1981) and MacDonald (1988).

We also perform an alternative test of the Yule distribution. Note first that [lceil](i)/[lceil](i + c) [approximate] 1/[i.sup.c] for any constant c when i is much greater than c (Titchmarsh, 1939, p. 58). Thus distribution (1) can be approximately written as:

f(i) = [psi][lceil]([rho] + 1)[i.sup.-([rho] + 1)] where [rho] = 1/(1 - [delta]). (8)

Since f(i) = [psi][lceil]([rho] + 1)[1.sup.-([rho] + 1)] = [psi][lceil]([rho] + 1), distribution (3) can be rewritten as:

f(i) = f(1)[i.sup.-([rho] + 1)], (9)

which upon rearrangement yields

f(i)/f(1) = [i.sup.-([rho] + 1)]. (10)

Finally, taking the log of both sides of Eq. (10), we obtain

log[f(i)/f(1)] = -([rho] + 1)log(i). (11)

This modified specification of the Yule distribution is tested by applying the following regression model to the frequency distribution data in Table 2:

log[f(i)/f(1)] = [alpha] + [beta]log(i) + [epsilon], (12)

where f (i) is the proportion of security analysts with i AART selections, f (1) is the proportion of individuals with one AART selection, and [epsilon] is an error term. If the Yule distribution with [rho] = 1 describes the data generation process then [alpha] should be insignificant and [beta] should be statistically minus two. The regression results with standard errors of the coefficients in parenthesis are:

log[f(i)/f(1)] = 0.3910 - 1.728log(i)

Standard error 0.1491 0.1551

t - statistic 2.62 1.75

Adjusted [R.sup.2] = 0.880, F = 124.19 (13)

The constant term [alpha] is statistically significant from zero at a 5% level. However, while the coefficient of log(i) is not significantly different from -2 for a two-tail test at the 5% level it is at the 10% level.

An alternative specification is to force the intercept term [alpha] to be zero in the equation. As a result, the equation becomes:

log[f(i)/(1)] = [beta]log(i) (14)

and running the regression results in:

log[f(i)/(1)] = -1.348log(i)

Standard error = 0.0634

t - statistic = -10.29

Adjusted [R.sup.2]= 0.831 F = 88.45 (15)

Thus, the results show that, indeed, the Yule distribution is not an accurate explanation of distribution of the number of AART selection by security analysts. [4] In other words, this distribution is not the result of the Yule distribution stochastic process. Since this process assumed equal talent among security analysts, the rejection of this model would lead to the conclusion that security analysts have differential proficiency. Thus, the selection of security analysts to the AART appears to be based on skill, rather than luck.

4. Summary and concluding remarks

Casual empiricism suggests that there exists a marked skewness in the distribution of output and earnings among individuals in various social-economic fields. Several recent studies have examined this so-called superstar phenomenon, and suggested that much of this phenomenon can be explained by imperfect substitutions among different sellers and increasing returns to ability.

In this study, we examine, the superstar phenomenon as an implication of probabilistic mechanisms by which research directors choose the II AART of security analysts. Specifically, we investigate whether a stochastic process similar to that yielding negative binomial or log series distributions (i.e., the Yule Distribution) represents the process generating the superstar phenomenon in the security analysis field.

In choosing the AART, selectors are asked to consider four factors: (1) stock recommendations, (2) earnings forecasts, (3) written reports, and (4) overall performance. Previous empirical studies by Brown and Chen (1991) and Stickel (1992, 1995) have documented the superiority of the II AART in two of the four categories -- stock recommendations and earnings forecasts. Given these findings, we would expect that an empirical test should reject the Yule distribution if there is no systematic bias in naming analysts to the AART.

Consistent, with prior empirical research on the AART, we find that the Yule Distribution is not an accurate explanation of the distribution of the number of AART appearances of security analysts. Thus, our results are contrary to Adler's (1985) work, and support the Rosen (1981) and MacDonald (1988) theory that the superstar phenomenon results from differential talent (rather than luck) among individuals. Moreover, these results are also compatible with Sinha et al.'s (1997) findings that differences exist in security analysts' expost forecasting accuracy and those of Mikhail et al. (1997) that security analysts improve their forecast accuracy with experience.

(a.) Department of Finance, Central Michigan University, Sloan Hall 324, Mt. Pleasant, MI 48859, USA

(b.) Oakland University, Rochester, MI, USA

(*.) Corresponding author. Tel.: +1-517-774-4714; fax: +1-517-774-6456.

E-mail address: raymond.cox@cmich.edu (R.A. Cox).

(1.) Analysts do not generate investment banking revenues directly. Instead, they provide support services to two major groups -- (1) investors who pay commissions to banks through their orders to buy and sell securities and (2) the bank's corporate finance group who produce revenues from underwriting and arranging financing for their corporate clients. Since corporate finance contributes significantly more to the bank's revenues than does commissions from equity sales to investors, security analysts may face a potential conflict of interest between the best interests of investors and the desires of the corporate finance department to issue "favorable" ratings on securities issued by their clients.

(2.) There are a number of security analysts chosen each year for the All-American Research Team broken down by ranked team (first, second, third and runners-up) and by industry.

(3.) The number of individuals on the team has steadily increased as the number of industries regularly followed by Wall Street brokerage firms has grown.

(4.) We reran the aforementioned test of the Yule distribution using only those 26 industries that were included in the II AART surveys each year over the 1972 through 1996 time period. These results also support the rejection of the Yule distribution and are available from the authors upon request.

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Author:Cox, Raymond A. K.; Kleiman, Robert T.
Publication:Review of Financial Economics
Article Type:Statistical Data Included
Geographic Code:1USA
Date:Jan 1, 2000
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