Security Analyst Recommendations and Stock Returns 541 j=1 to ni1 analysts who have outstanding recommendations for the firm on that day and dividing by ni1.Formally, A-1= 1n-1 一∑Ar-1 (1) 几ir-1=1 Using these average ratings,each covered firm is placed into one of five portfolios as of the close of trading on date r-1.The first portfolio consists of the most highly recommended stocks,those for which 1sA1.5;the second is comprised of firms for which 1.5 <A2;the third contains firms for which 2<A2.5;the fourth is comprised of firms for which 2.5 <A-13;and the fifth portfolio consists of the least favorably rec- ommended stocks,those for which Ai>3.8 After determining the composition of each portfolio p as of the close of trading on date r-1,the value-weighted return for date r is calculated. Denoted by Rpr for portfolio p,this return is given by: (2) where x-1=the market value of equity for firm i as of the close of trading on date r-1 divided by the aggregate market capitalization of all firms in portfolio p as of the close of trading on that date, Rir=the return on the common stock of firm i on date r,and npr-1=the number of firms in portfolio p at the close of trading on date T-1. There are two reasons we value weight rather than equally weight the se- curities in each portfolio.First,an equal weighting of daily returns(and the implicit assumption of daily rebalancing)leads to portfolio returns that are severely overstated.?Second,a value weighting allows us to better capture the economic significance of our results,as the individual returns of the s Five portfolios are chosen so as to achieve a high degree of separation across firms in the sample while retaining sufficient power for our tests.The cutoffs,although somewhat arbitrary, are set so that only the bottom portfolio contains firms whose consensus ratings corresponded to hold or sell recommendations,due to the relative infrequency of such ratings.Qualitatively similar results are obtained for our main analysis when(1)the cutoffs for portfolios 1,2,3,and 4 each year are set equal to the 20th,40th,60th,and 80th percentiles,respectively,of the prior year's distribution of consensus recommendations,and(2)the first portfolio includes only firms with an average rating of one. This problem arises due to the cycling over time of a firm's closing price between its bid and ask (commonly referred to as the bid-ask bounce).For a more detailed discussion,see Blume and Stambaugh(1983),Barber and Lyon (1997),Canina et al.(1998),and Lyon,Barber,and Tsai(1999)
j 5 1 to nit21 analysts who have outstanding recommendations for the firm on that day and dividing by nit21. Formally, AN it21 5 1 nit21 ( j51 nit21 Aijt21. ~1! Using these average ratings, each covered firm is placed into one of five portfolios as of the close of trading on date t 2 1. The first portfolio consists of the most highly recommended stocks, those for which 1 # AN it21 # 1.5; the second is comprised of firms for which 1.5 , AN it21 # 2; the third contains firms for which 2 , AN it21 # 2.5; the fourth is comprised of firms for which 2.5 , AN it21 # 3; and the fifth portfolio consists of the least favorably recommended stocks, those for which AN it21 . 3.8 After determining the composition of each portfolio p as of the close of trading on date t 2 1, the value-weighted return for date t is calculated. Denoted by Rpt for portfolio p, this return is given by: Rpt 5 (,i51 npt21 xit21 Rit, ~2! where xit21 5 the market value of equity for firm i as of the close of trading on date t 2 1 divided by the aggregate market capitalization of all firms in portfolio p as of the close of trading on that date, Rit 5 the return on the common stock of firm i on date t, and npt21 5 the number of firms in portfolio p at the close of trading on date t 2 1. There are two reasons we value weight rather than equally weight the securities in each portfolio. First, an equal weighting of daily returns ~and the implicit assumption of daily rebalancing! leads to portfolio returns that are severely overstated.9 Second, a value weighting allows us to better capture the economic significance of our results, as the individual returns of the 8 Five portfolios are chosen so as to achieve a high degree of separation across firms in the sample while retaining sufficient power for our tests. The cutoffs, although somewhat arbitrary, are set so that only the bottom portfolio contains firms whose consensus ratings corresponded to hold or sell recommendations, due to the relative infrequency of such ratings. Qualitatively similar results are obtained for our main analysis when ~1! the cutoffs for portfolios 1, 2, 3, and 4 each year are set equal to the 20th, 40th, 60th, and 80th percentiles, respectively, of the prior year’s distribution of consensus recommendations, and ~2! the first portfolio includes only firms with an average rating of one. 9 This problem arises due to the cycling over time of a firm’s closing price between its bid and ask ~commonly referred to as the bid-ask bounce!. For a more detailed discussion, see Blume and Stambaugh ~1983!, Barber and Lyon ~1997!, Canina et al. ~1998!, and Lyon, Barber, and Tsai ~1999!. Security Analyst Recommendations and Stock Returns 541
542 The Journal of Finance larger and more important firms will be more heavily represented in the aggregate return than will those of the smaller firms.This may,however, bias against finding evidence of abnormal returns,as markets are likely to be most efficient for the largest securities. For each month in our sample period,the daily returns for each portfolio p,Rpr,are compounded over the n trading days of the month to yield a monthly return,Rpt: Rt=Π(1+Rpr)-1. (3) r=1 In addition to these five portfolios,we construct two other portfolios.The first additional portfolio consists of all covered firms on each date r(those that have an outstanding rating from at least one analyst in the Zacks data- base on that day)and the second portfolio consists of neglected firms on that date (those firms on the CRSP daily returns file that do not have any out- standing analyst ratings on that day).10 The composition of each of these two portfolios is recalculated every day,because firms gain or lose analyst cov- erage over time. B.Performance Evaluation To determine whether profitable investment strategies exist with respect to analysts'consensus recommendations,we begin with a simple calculation of market-adjusted returns for each of our constructed portfolios.It is given by Rpt-Rt for portfolio p in month t,where Rmt is the month t return on the CRSP NYSE/AMEX/Nasdag value-weighted market index.We next cal- culate three measures of abnormal performance for each portfolio.First,we employ the theoretical framework of the Capital Asset Pricing Model(CAPM) and estimate the following monthly time-series regression: Rpt-Rn=ap+Bp(Rmt-Rr）+∈pt (4) where Rt=the month t return on treasury bills having one month until maturity,11 @p=the estimated CAPM intercept (Jensen's alpha), B=the estimated market beta,and ept=the regression error term. This test yields parameter estimates of ap and Bp 10 Because the academic version of the Zacks database does not include the recommenda- tions of all brokerage houses,it is possible that some of the "neglected"firms are actually covered by one or more analysts.To the extent this is true,our test for differences in returns between neglected and covered firms is less powerful. This return is taken from Stocks,Bonds,Bills,and Inflation,1997 Yearbook
larger and more important firms will be more heavily represented in the aggregate return than will those of the smaller firms. This may, however, bias against finding evidence of abnormal returns, as markets are likely to be most efficient for the largest securities. For each month in our sample period, the daily returns for each portfolio p, Rpt, are compounded over the n trading days of the month to yield a monthly return, Rpt: Rpt 5 )t51 n ~1 1 Rpt! 2 1. ~3! In addition to these five portfolios, we construct two other portfolios. The first additional portfolio consists of all covered firms on each date t ~those that have an outstanding rating from at least one analyst in the Zacks database on that day! and the second portfolio consists of neglected firms on that date ~those firms on the CRSP daily returns file that do not have any outstanding analyst ratings on that day!. 10 The composition of each of these two portfolios is recalculated every day, because firms gain or lose analyst coverage over time. B. Performance Evaluation To determine whether profitable investment strategies exist with respect to analysts’ consensus recommendations, we begin with a simple calculation of market-adjusted returns for each of our constructed portfolios. It is given by Rpt 2 Rmt for portfolio p in month t, where Rmt is the month t return on the CRSP NYSE0AMEX0Nasdaq value-weighted market index. We next calculate three measures of abnormal performance for each portfolio. First, we employ the theoretical framework of the Capital Asset Pricing Model ~CAPM! and estimate the following monthly time-series regression: Rpt 2 Rft 5 ap 1 bp~Rmt 2 Rft ! 1 ept , ~4! where Rft 5 the month t return on treasury bills having one month until maturity,11 ap 5 the estimated CAPM intercept ~Jensen’s alpha!, bp 5 the estimated market beta, and ept 5 the regression error term. This test yields parameter estimates of ap and bp. 10 Because the academic version of the Zacks database does not include the recommendations of all brokerage houses, it is possible that some of the “neglected” firms are actually covered by one or more analysts. To the extent this is true, our test for differences in returns between neglected and covered firms is less powerful. 11 This return is taken from Stocks, Bonds, Bills, and Inflation, 1997 Yearbook. 542 The Journal of Finance