Returns to E/P Strategies, Higgledy-Piggledy Growth,’ Forecast Er - PDF document

Returns to E/P Strategies, Higgledy-Piggledy Growth,’ Forecast Errors, and Omitted Risk Factors“E/P effect” remains an enigma.Russell J. Fuller, Lex C. Huberts, and Michael J. LevinsonHigh E/P (low P/E) investing has been a popular investmentstrategy for many years. A numdocument that high E/P strategies have historically generated,on average, above-normal returns. Some examples are Basu[1983], Goodman and Peavey and Jaffe, Keim, andWesterfield [l989]. 989]. also find positiveabnormal returns associated with high E/P stocks, but they findvalue to priceratios (B/P) and abnormal returns.One rationale offered as to why high E/P strategies mwork comes out of studies describing what is referred to as“Higgledy Piggledy Growth” (see Little [1966], Brealey [1967,Brealey [1967,)that earnings changes appear to be randomly distributed over with future earnings changes. This implies that As we note in our 1992 interpretation of Higgledy Piggledy Growth is that fearnings growth cannot be forecast at all! If this is true, and ifone assumes a simple model where stock prices are solely afunction of future earnings growth, then high E/P the same for all stocks. Consequently, by investing in high E/P’ earnings, and they setBecause many generated positive alphas and, if so, why. Specifically, weWe also explore whether “omitted risk factors” might accountfor any abnormal returns associated with high E/P investing.We find that high E/P stocks did generate positive alphas.abnormal returns. The “E/P effect” remains an enigma.in our 1992 article and are more fully described there. In impact look-ahead and survivorship biases can have onfinancial studies.)Each year the earnings-to-price (E/P) ratio for eachcompany is determined by dividing fiscal year EPS by thestock price as of the following March 31. For example, for1973 and a company with a December 31 fiscal year, the E/Pratio is determined by dividing its 1972 EPS by its March 31,1973, price. In order to reduce the influence of outliers, wetypically use the median rather than the mean of the variableexamined.A minimum market capitalization screen is used to insurethat the stocks in the sample are representative of those fromwhich institutional investors are likely to choose.2 The numberof stocks that meet the market capitalization requirement andhave the necessary earnings data ranges from 887 stocks in1973 to 1,179 stocks in 1990. Thus, one might think of thesample as representing (approximately) the top 1,000 stocks interms of market capitalization for each year of the study.For each year, stocks are ranked by E/P ratio and assignedstocks with the highest E/P ratios for that year; the fifthin each industry, containing the highest 20% of each industry in terms of E/P ratios, and so on. Thus, for the industry- stocks, but also but this occurs relatively infrequently. Because the use ofdiversification results in a narrower range of E/P ratios across— the range for the non-diversified quintiles is (Hi E/P)(Lo E/P)All StocksQ1Q2Q3Q4Q5 Avg. E/P0.0980.1630.1240.0980.0730.022Avg. P/E10.26.18.110.213.744.9 (Hi E/P)(Lo E/P)All StocksQ1Q2Q3Q4Q5 Avg. E/P0.0990.1480.1150.0980.0780.039Avg. P/E10.16.78.710.212.825.6 portfolio excess returns are then regressed against the excess68EXHIBIT 2Estimates of AlphaER(Qi)t = A + B ´ ER (All Stocks, Eqwtd)t (Hi E/P)(Lo E/P)Q1Q2Q3Q4Q5Q1 - Q5 A3.4%2.5%0.3%-1.6%-4.7%8.0%t(A)4.344.940.61-2.84-5.50 Q1Q2Q3Q4Q5Q1 - Q5 A4.7%3.1%-1.1%-3.1%-3.8%8.5%t(A)2.773.18-1.41-2.94-2.41 Q1Q2Q3Q4Q5Q1 - Q5 A4.0%3.1%-0.2%-2.0%4.7%8.7%t(A)3.383.57-0.29-2.21-3.20 Q1Q2Q3Q4Q5Q1 - Q5 A1.7%1.3%2.2%0.4%-5.7%7.4%t(A)1.931.692.490.43-4.30quintile, defined as the median return for the quintile minus the monthly T-bill Thus, it appears that Q1 outperformed the sample as aNotice that for each of the three different subperiods listed— the t-performance of “value” stocks during the 1985-1991 period.It is well-known that the market capitalization of a firm’sequity (firm size) is a major freturns. Consequently we returns are actually just a proxy for the size effect.y for the size effect.)Exhibit 3 reports the results for the regression over theentire time period, but excluding the January months. Notice that while the estimated alpha for Q1 is reduced from 3.4% to2.4% (Hi E/P)(Lo E/P)Q1Q2Q3Q4Q5Q1 - Q5 A2.4%2.5%0.6%-1.0%-4.7%7.1%t(A)3.255.131.23-1.81-5.42monthly T-bill return, against the excess return for an equally-weightedThe findings we report in Exhibits 2 and 3 are consistentwith most of the previous studies on E/P strategies. Thus, ifpositive alphas is true, the next question is “why?” What are ’ earnings changes are close toclose to zero, however, it could still be the case that multi-yearearnings growth rates are positively correlated. One might alsoConsequently, for this article we extend this line of analysisining the correlation between past four-year EPSgrowth rates and subsequent (future) four-year growth rates.For example, for E/P quintiles formed at the end of March1976 (denoted 7603), each company’s with that same company’s growth rate over the subsequent four Q1Q2Q3Q4 760371-75 & 75-79-0.0740.0000.111-0.212-0.126-0.051770372-76 & 76-800.015-0.0990.227-0.0630.0920.017780373-77 & 77-810.008-0.0320.1070.1060.067-0.095790374-78 & 78-820.007-0.010-0.0560.0990.0150.046800375-79 & 79-83-0.058-0.1710.004-0.0960.0150.027810376-80 & 80-84-0.089-0.203-0.073-0.021-0.116-0.062820377-81 & 81-85-0.138-0.268-0.1740.024-0.087-0.122830378-82 & 82-86-0.121-0.137-0.170-0.215-0.0120.165840379-83 & 83-87-0.1140.040-0.191-0.235-0.074-0.072850380-84 & 84-88-0.081-0.096-0.0580.006-0.1680.039860381-85 & 85-89-0.0490.034-0.018-0.073-0.081-0.013Average-0.063-0.086-0.027-0.062-0.043-0.011the average correlation coefficients for the four-year growth distinguish between low- and high-growth companies, and’ forecasts of earnings growth, one mightthe median eight-year growth rate for quintile 3 — thus, the MedianExcess Eight-Year Growth Rates Q1Q2Q3Q4Q5Q1 - Q5 730310.6%-3.8%-0.8%0.0%-0.9%2.7%-6.6%74038.5%-3.3%0.3%0.0%1.3%1.8%-5.1%75037.1%-4.9%-2.8%0.0%0.0%3.6%-8.5%76038.0%-4.0%-1.7%0.0%1.0%2.9%-6.9%77037.1%-2.5%-1.0%0.0%1.6%1.9%-4.4%78035.0%-1.8%-0.4%0.0%1.5%4.2%-6.0%79034.4%-2.1%-3.4%0.0%-0.1%2.6%-4.7%80032.2%-1.1%-0.8%0.0%2.1%3.0%-4.1%81034.8%-2.9%0.0%0.0%0.9%0.5%-3.3%82035.7%-6.6%-4.2%0.0%-1.4%0.5%-7.2%Average6.3%-3.3%-1.5%0.0%0.7%2.4%-5.7%Note that for every portfolio formation period the excessear growth rate is negative for Q1 andthe difference between Q1 and Q5 is quite large. On average,the earnings growth rate for Q1 is 5.7% less per year,the excess growth rate increases monotonically from Q1 to Q5. That is, the excess growth rate for Q1 is less than that of Q2,earnings growth rates for Q1 and Q2 relative to Q4 and Q5 aresimply the result of Q1 and Q2 generating relatively low“forward” EXHIBIT 6Average Single-Year Excess EPS Changes for Forward Years T + 1 Through T + 8 (Industry-DiversifiedE/P Quintiles) Q3Excess EPS Change Q1Q2Q3Q4Q5Q1 - Q5 T + 110.2%-9.9%-3.6%0.0%3.7%8.6%-18.5%T + 28.6%-3.3%-1.2%0.0%1.2%3.7%-7.0%T + 38.8%-1.7%-0.6%0.0%0.5%1.9%-3.6%T + 49.5%-1.8%-1.4%0.0%0.7%1.1%-2.9%T + 59.2%-0.9%-1.3%0.0%-0.7%1.3%-2.2%T + 68.6%-1.0%0.4%0.0%0.1%1.0%-2.0%T + 77.2%0.2%-0.2%0.0%0.3%1.7%-1.5%T + 86.8%-0.3%-1.4%0.0%0.9%0.9%-1.2%We suspect that the very large differences in EPS growth inthe forward year T + 1 occur because iexample, if investors believe that a company has just reportedearnings, resulting in a high E/P ratio. If they are correct, and’s earnings decline, then the excess EPS change inyear T + 1 will likely be a large negative number. excess years, and perhaps as many as eight years, into the future, growth might account for the reported positive ’ FORECAST ERRORS“forecast,” as a forecasts incorporated in E/P ratios — that is, wegenerate low earnings growth, sample. The I/B/E/S historical data base includes data from EXHIBIT 7Average Forecast of Single-Year Excess EPS Change (Industry-Diversified E/P Quintiles) ForecastAverage Forecast of Excess EPS Change Q1Q2Q3Q4Q5Q1 - Q5 T + 114.3%-9.0%-3.3%0.0%5.2%16.0%-25.0%T + 213.2%-3.9%-1.3%0.0%2.3%5.6%-9.5%T + 312.8%-2.4%-0.7%0.0%1.5%3.9%-6.3%T + 412.7%-1.8%-0.8%0.0%1.1%2.8%-4.6%T + 511.9%-0.7%0.3%0.0%1.5%2.9%-3.6%T + 612.2%-1.6%0.1%0.0%0.6%2.6%-4.2%T + 712.2%-1.3%-0.2%0.0%0.5%1.9%-3.2%T + 811.6%-0.4%0.3%0.0%1.5%3.1%-3.5%For each company, forecasts of EPS change for Year T + 1 are based on the mean IBES forecast (as ofMarch 31 of that year) of EPS for the current fiscal year, compared to the actual earnings reported forthe forecast (as of 7603) is for the fiscal EPS ending 7612. The forecast of EPS change for T + 1 is based7712. The forecast of EPS change for Year T + 2 is based on the forecast of 7712 EPS compared to thedetermined in a similar manner. Companies with negative earnings are excluded from the calculations.change for Q1 companies for y’ forecast of excess EPS change for Q1for Q5 companies in year T + 1 is also large (8.6%, Exhibit 6). Q5 EPS changes was forecast to be a large negative number inyear T + 1. This difference difference remains negative as far out as the year T + 8. This isa pattern that is very similar to that of the actual differencebetween the Q1 and Q5 EPS changes reported in Exhibit 6.EPS changes) and Exhibit 6 (actual EPS changes) suggests’ forecasts of excess EPS changesbetween the mean of the analysts’ EPS forecasts (as of March31) and the company’s question, divided by the company’s previous fiscal year. That is,Forecast Error (T + X) = [Forecast (T + X) - MedianAverage Excess Forecast of EPS Change Q1Q2Q3Q4Q5Q1 - Q5 T + 14.4%1.2%1.0%0.0%-0.1%1.4%-0.2%T + 24.5%1.0%1.5%0.0%0.6%1.6%-0.6%T + 35.2%-0.3%-0.5%0.0%0.1%1.1%-1.4%T + 44.5%0.9%0.5%0.0%0.6%0.4%0.5%T + 54.8%-0.3%0.3%0.0%-0.6%1.1%-1.4%T + 64.8%-0.4%0.2%0.0%-0.6%2.3%-2.7%T + 74.7%0.4%1.0%0.0%0.6%2.1%-1.7%T + 85.7%0.9%1.0%0.0%0.1%0.6%0.3% forecasts were too high, and vice versa. The second column ofsuggests that, on average, analysts’ forecasts were high by 4%that analysts’ forecasts tend to be somewhat optimistic (see, for forecasts tend to be somewhat optimistic (see, for)More relevant to this article are the excess forecast errorsacross E/P quintiles. Notice that on average the excess forecasterrors are small, ranging from zero to plus or minus 2%, anddisplay no strong monotonic pattern across E/P quintiles.The last column in Exhibit 8 reports the difference in theaverage forecast errors for Q1 companies and Q5 companies.Notice that these differences tend to be negative, suggestingthat analysts overestimated the actual earnings of Q5companies by more than they did the Q1 companies. But,again, these differences are small and not statisticallysignificant.In our judgment, the differences in analysts’ forecast errorsbetween Q1 and Q5 companies are too small to explain thedifferences between the alphas associated with these two E/Pquintiles. Note that the differences (Q1-Q5) range betweenmonths except January (Exhibit 3).forecasts of the Q5 companies’ earnings, relative to those ofthis study. ’ estimates of earnings recorded by I/B/E/S areUnfortunately, these findings also imply that on averageARE OMITTED RISK FACTORS THE SOURCES OFinvestigate this possibility, we EXHIBIT 9BARRA PERFAN Analysis Q1Q5Q1 - Q5 Beta1.001.08-0.08Q1Q5Q1 - Q5 Earnings/Price0.60-0.741.34Variability in Markets-0.020.28-0.30Success-0.08-0.05-0.03Size-0.04-0150.11Trading Activity0.080.12-0.04Growth-0.280.49-0.77Book/Price0.36-0.14-0.50Earnings Variability0.020.42-0.40Financial Leverage0.050.21-0.16Foreign Income0.020.010.01Labor Intensity-0.08-0.04-0.04Yield0.24-0.400.64LoCap0.030.020.01Q1Q5Q1 - Q5 Beta Timing-0.1%0.4%-0.5%Return to E/P1.9%-2.4%4.3%Return to Size0.2%0.2%0.0%Return to Book/Price1.3%-0.6%1.9% Variability in Markets0.1%-0.8%0.9%Other Risk Factors-0.3%-0.7%0.4%All Industry Factors0.2%0.0%0.2%Specific Asset Selection0.0%-0.6%0.6%Total Alpha3.3%-4.5%7.8%1.00 for Q1 and 1.08 for Q5. Thus, the low E/P stocks tend to To illustrate the interpretation of these risk factorBy looking down the third column (Q1 - Q5), one canratio, with the Q1 portfolio having an E/P ratio 1.34 standardWith respect to growth, Q1 is below Q5; with respect to book/price and dividend yield, Q1 is0.50 and 0.64 standard deviations above Q5, respectively. Thevariability (variability in markets) and earnings variability; AsThe BARRA PERFAN system attempts to identify the“contributions to alpha,” andconsider the total alpha, which is 3.3% and -4.5% for Q1 and industry factors is only 0.2% and 0.0% for Q1 Clearly the most important factor in determining thedifference in alpha between Q1 Q1’s E/P exposure contributes -2.4% to Q5’s alpha, making thedifferential performance between Q1 the average size factor exposures are quite similar for Q1 andQ5, -0.04 and -0.15, respectively. As a result, the contributionto alpha associated with size is 0.2% for both Q1 and Q5.as “other risk factors” in factors contribute only -0.3% to Q1’s alpha and -0 7% to Q5’svariables to be highly correlated with E/P — certainly E/P andlikely that E/P and variability in markets are related — inthree sum to 7.1%, leaving only 0.7% out of a total difference explained.’s [1978] argument that E/P is a catchall proxy forwell as analysts’ forecast errors. We also use BARRA’sSubsequent earnings growth does not appear to account forAnalysts’ E/P quintiles. Thus, analysts’ forecast errors do not appear toFinally, BARRA’s “E/P effect” remains an enigma. See fuller, Huberts, and Levinson [1992]. It is pointing out rticle, that the authors of theoriginal Higgledy, Piggledy studies state only that earnings changes tendto be uncorrelated over time and do not necessarily imply that earnings The market value of an individual company’s commonstock was required to be equal to or greater than 0.0001 times the markettrillion, making the minimum market value screen equal to $220 million. In preparing this article we discovered, to our chagrin, aaffect in Table 1 of the 1992 article. While this programming e The term, “return,” refers to total return, i.e., price plus dividends received during the period divided by beginning of periodprice. All returns are initially measured over one-month periods. We also formed portfolios by capitalization-weighting each These estimates of alphas should not be confused with atrue CAPM equilibrium imated by regressing portfolio excessreturns agaiproxy for the market portfolio of all risky assets. Rather, because theyresult from regressing the excess returns for each quintile against theexcess return the entire sample, the alphas in Exhibit 2 should be thoughtadjusted differential performance of each E/P quintilealso regressed the E/P quintile excess returns against the value-weightedS&P 500 excess returns with qualitatively similar results. The betas for each quintile are close to 1.0, except for Q5,which has a beta of approximately 1.07, and all the beta coefficientsstatistically signifgreater level. Complete regression results are available from the authors. Given the number of monthly observations in allregressions, one can safely assume that a t-statistic with an absolute valueof 2.0 or more is statistically significant at the 5% level or less. For example, along the lines of Fama and MacBeth For example, along the lines of Fama and MacBeth we estimated the following monthly cross-sectional regressions: dependentvariable was the individual stock’s excess return; the indevariables were the stocks’ beta, the stocks’ E/P quintile ranking (from I to5), the stocks’ size quintile ranging (from 1 to 5), and last variable is a checkrankings.) The mean of the time series of monthly coefficients for each ofthe independent varicoefficients are significantly sign. These results suggest that both E/P and size help explain returns, butHowever, in this case the results are probably REFERENCESBall, R. “Anomalies in Relationships between Securities’ Yield-Surrogates.” Journal of Financial Economics, 15 (1978), pp . and Market Data: Some Evidence.” Journal of FinanceBasu, S. “The Relationship Between Earnings’ Yield. 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