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AN INVESTIGATION OF FINANCIAL RATIOS IN PREDICTING FIRMSFUTURE PERFORMANCE: AN APPLICATION OF PRs METHODOLOGY
A Dissertation
Presented to
the Faculty of the College of Business Administration
University of Houston
In Partial Fulfillment
of the Requirements o f the Degree
Doctor of Philosophy
by
Lijyun Angela Hwang
April 18, 1997
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UMI Number: 9817079
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AN INVESTIGATION OF FINANCIAL RATIOS IN PREDICTING FIRMS
FUTURE PERFORMANCE: AN APPLICATION OF PRs METHODOLOGY
APPROVED:
C.S7 Ames Cheng, Associate Pr|, then the ratio is likely to be a profitability-oriented ratio.
Gh hit (15)
The Retums-Target Prediction Model:
bhXhn (16)
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If a a; 0 and \a\ * \b\,then the ratio is likely to be a risk-oriented ratio.
I f a=*=0 and * \b\, then the ratio is likely to be a ratio with a mixture of both
profitability and risk.
Based on these relationships, the scheme of classifying financial ratios can be illustrated as
follows:
CLASSIFICATION OF FINANCIAL RATIOS BY COMPARING LOGISTIC
COEFFICIENTS OF EARNtNGS-TARGET PREDICTION MODEL
AND RETURNS-TARGET PREDICTION MODEL
a sare the coefficient estimates form the eamings-target prediction model. 6 s are
the coefficient estimates form the retums-target prediction model. The difference of"a 5 and bs is evaluated by taking the mean o f paired differences o f a and 6during each evaluation period.
a ~0 a *0
a ~ b Not useful Profitability
a &\b Risk Mixed
Table 5 reports the yearly coefficients obtained every three years from univariate
logistic regressions of the respective models. For example, the coefficients for year 1980
are obtained by pooling firm-year observations o f 1977-1979. Panels A and B report the
yearly coefficients for the eamings-target prediction model and the retums-target
prediction model during 1980-1986. Based on these yearly logistic regressions, an across-
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-and-hold exc ess returns are the dependent var iables I'mthe earnmgs-target prediction miHlel and the retums-target prediction model respect ively Independent variables are
those identified by principal component analysis Coefticieu ts labeled for year 1980 are obtained by pooling firm-year observations from 1977-1979.
Panel A: Earnings-Targct Prediction Model
Net profit margin %A in Net profitmargin
Debt-equityratio
%A in Debt-equity ratio
Inventory /totalassets
%A in Inventory/total assets
Quick ratio %A in Quickratio
1980 1.399 -0.030 -0.113 0.390 -1.586* -1.010b 0.403* 0.448"
1981 -2.703 -0.091 -0.062 0.855* -1.195b -1.572* 0.2 94 1 0.081
1982 -4.043* -0 .1571 -0.092 0.67 lb -0.264 -1.294* 0.130 -0.117
1983 -8.102* -0.250* -0.075 0.293 -0.401 -1.880* 0.107 0.185
1984 -5.095* -0.172* -0.169 0.082 -1.302b -1.191* 0,173 0.293
1985 -4.539* -0.141* -0.062 0.037 -1.182 -1.472* -0.013 0.332
1986 -4.048* -0.094 0.041 0.478* -1.578* -1.000b -0.061 -0.143
Meana -3.876k - A / i/ -0.076 0.401" -1.073* -1.345* 0.148 0.154
Mean Sii c rror 1.609 0.063 0.082 0.241 0.566 0.411 0.117 0.246
Wald Chi-square* 5.799 4.481 0.858 2.770 3.597 10.720 1.604 0.393
Panel B: Returns-" 'arget Prediction IVodel
1980 4.1 78 1, 0.007 -0.012 -0.151 -1.225b -1.152* -0.026 0.218
1981 1.776 0.046 -0.022 -0.080 -0.128 -0.618 0.134 -0.058
1982 -0.815 0.085 -0.1941 -0.103 0.873 -0.121 0.380* -0.246
1983 4.372* -0.046 -0.081 -0.216 0.107 -0.210 0.004 -0.053
1984 -0.199 -0.072 -0.045 -0.355 -0.457 -0.422 -0.049 0.435"
1985 1.885 -0.034 -0.024 -0.368 -1.688* -0.732 -0.203 0.450
1986 7.187* 0.125* -0.090 -0.112 -1.895* -0.062 -0.086 0.300
Mean 2.626" 0.016 -0.067 -0.198 -0.630 -0.474 0.022 0.149
Mean Std Error 1.583 0.060 0.082 0.255 0.562 0.401 0.115 0.243
Wald Chi-square 2.754 0.070 0.672 0.598 1.260 1.400 0.037 0.378
Panel C: Evaluation of Ratio Attribute
Mean dilTerencer 1.360 0.074 0.021 0.203 0.162 0.871 0.043 -0.023
Prob>|T| 0.302 0.039 0.516 0.098 0.539 0.006 0.619 0.707
a not equal to 0s ** ** * * *+*
Attribute Profitability Mix Not useful Mix Profitability Mix Not useful Nol useful
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TAB1.H5 (CONTINUED)UNIVARIATE ANALYSIS OF LlXJISTIC COIiM-lCU-lN IS AND FINANCIAL ATTRIBUTES FOR RATIOS IDENTIFIED BY PRINCIPAL COMPONENT ANALYSIS
Panel A: Earnings-Targct Prediction Model
Sales/total assets %A in sales /
total assets
%A in LT debt %A in total
assets
Cash dividend as
% of cash flows
Sales to fixed
assets
Sales to
inventory
Sales to
working capital
1980 -0.610* 1.1261 -0.145" -1.692* 1.956* -0.04Sb 0.008 -0.0131981 -0.250* 0.474 -0.140" -1.256* 1.453* -0.013 0.015 0.001
1982 0.173 0.891" -0.111 -0.936* 0.800" 0.051* 0.031* 0.013"
1983 0.196 0.173 -0.111 -2.450* 0.798b 0.036* 0.020* 0.006
1984 -0.069 1.119b -0.184* -2.181* 0.551 -0.006 0.017 -0.003
1985 -0.090 -0.065 -0.288* -1.943* 0.697* -0.055* 0.000 -0.014b
1986 -0.163 -0.161 -0.206b -0.829" 1.151* -0.046b 0.009 -0.017*
Mean -0.116 0.508 -o. i6r -1.612 i . o s r -0.011 0.014 -0.004
Mean Std Error 0.132 0.522 0.092 0.439 0.398 0.019 0.012 0.007
Chi-square 0.774 0.948 3.395 13.481 7.061 0.340 1.436 0.259
Panel B: Rctums-Target Prediction Model
1980 -0.542c 1.332b -0.072 0.248 -1.604* -0.025 0.001 -0.006
1981 -0.048 1.076b -0.074 -0.494 0.125 0.048' 0.010 -0.006
1982 0.388* 0.783 -0.041 -0.739* 0.218 0.082* 0.014 -0.013"
1983 0.469* 0.448 -0.119 -1.693' 0.724b&00o 0.035' 0.012"
1984 0.410* 0.366 -0.077 -1.343* 0.147 0.016 0.038' 0.012*
1985 0.245 0.276 -0.305* -1.795* 0.545 -0.031 0.043' 0.015b1986 0.200 0.427 -0.154 -0.581 0.686* -0.035 0.03 lb 0.004
Mean 0.160 0.673 -0.120 -0 .W / 0.120 0.015 0.025* 0.003
Mean Std Error 0.141 0.517 0.091 0.428 0.415 0.019 0.012 0.008
Wald Chi-square 1.300 1.691 1.730 4.564 0.084 0.573 4.133 0.118
Panel C: Evaluation of the Ratio Attr )UtCS
Mean difference -0.107 -0.100 0.049 0.628 0.480 -0,005 -0.010 0.000
Prob>|T| 0.195 0.560 0.028 0.012 0.022 0.627 0.236 0.971
a not equal to b * *** *+*
Attribute Not useful Not useful Mix Mix Mix Not useful Not useful Not useful
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T A U 1 ,1 - 5 ( C O N T I N I J I ' D )
UNIVARIATH ANALYSIS Ql; LOGISTIC COITTICTI-NTS AND FINANCIAL ATTRIBlITHS FOR RATIOS IDENTIFIED BY PRINCIPAL COMPONENT ANAI.YS1S
'' *c Denotes statistical significance at the 0.10.0 .05 . and 0.01 levels respectively, based on a two-tail t-test.
' Similar to Lev and Thiagarajan j 1993|, the yearly logistic regression is used to obtain an across-year mean, standard error to calculate Wald chi-square foreach financial ratio.
cThe statistical meanings of Wald chi-square is similar to that of t-value in regression analysis. It indicates the statistical significance of a coefficient.
r Mean difference is the mean of the differences between the absolute value of the coefficient for each variable obtained from the eamings-target prediction
model and the corresponding coefficient from the retums-target prediction model during the same time periods. As a result, 7 paired observations for each
financial ratio are included in the mean tests. As both of the parametric test (paired t lest) and the nonparamctric test (paired Wilcoxon singed rank test)
produce similar results, only the paired t test is reported as Prob>|T|.
KThis row summarizes across-year (mean) coefficients that are statistically significant in the earnings model as reported in Panel A. *. **, and *** denote the
significance level at 0.10. 0.05. and 0.01 respectively.
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year mean, standard error are used to calculate Wald chi-square for each financial ratio to
evaluate their statistical significance. This approach attempts to control for upward bias
due to cross-sectional correlation in a pooled analysis (Bernard [1987], Lev and
Thiagarajan [1993], and Cheng, Liu and Schaefer [1996]).
Panel C of Table 5 reports the classification o f the financial attributes of the 16
financial ratios based on the above framework. Net profit margin and inventory/total
assets are classified as profitability-oriented ratios. Percentage change (%A) in net profit
margin, %A in debt-equity ratio, %A in inventory/total assets, %A in long-term debt, %A
in total assets, and cash dividend as a percent o f cash flows are classified as ratios with a
mixture o f profitability and risk. Debt-equity ratio, quick ratio, %A in quick ratio,
sales/total assets, %A in sales/total assets, sales to fixed assets, sales to inventory and sales
to working capital are classified as non-useful ratios. None o f the ratios are classified as
pure risk-oriented ratios.
6.2.3 Prs Constructs
6.2 .3.1 An Initial Evaluation Based on Multivariate Logistic Regressions
The empirical models used to evaluate the constructs of Pr in the two multivariate
logistic regressions are expressed as follows:
The Eamings-Target Prediction model:
AEiti v ' / 1 - = 2 aioch,, ( 15 )
" h=\
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5 3
The Retums-Target Prediction model:
m
R~i = ^bkXh,t (16)>1=1
where,xh(/ = 1 ,2 m) is the set o f mfinancial ratios for firm iat timeI,and ahand bh
are the vectors o f the estimated coefficients for the financial ratios in the respective
models. The definition o f the dependent variables are the same in both the multivariate
models and the univariate models. Table 6 reports the yearly coefficients obtained every
three years from multivariate logistic regressions of the respective models. The estimation
of coefficients are similar to that of the univariate regressions except that only one
financial ratio is included in the univariate models but all 16 financial rations are included
in the multivariate models.
A coefficient estimated in a logistic model indicates the effect of a unit change in
an independent variable on the probability o f the occurrence o f the dependent variable.
Given a significant statistical test, a positive sign o f a parameter estimate suggests that the
probability o f one-year-ahead earnings changes (excess returns) increases with the value of
the financial ratio. A comparison o f the coefficients in the univariate analysis in Table 5
and multivariate analysis in Table 6 reveals consistent signs between the two analyses.
This implies the collinearity is not a problem for the multivariate analysis. However, the
significance level o f the coefficients is stronger in the univariate analysis than in the
multivariate analysis. This is expected because univariate analysis only accounts for the
effect of an individual independent variable. Ratios that are statist ically significant in the
eamings-target prediction model include: %A in debt-equity ratio, %A in inventory/total
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TABLE 6
MULTIVARIATE ANALYSIS OF THE LOGISTIC COEFFICIENTS FOR RATIOS IDENTIFIED BY PRINCIPAL COMPONENT ANALYSIS
Coefficients of logistic regressions arc estimated for every three .years. Signs of onc-ycar-ahcad earnings change without drift and signs of 12-month market-
adjusted buy-and-hold excess returns are the dependent variables for the eamings-target and the returns-target prediction model respectively. Independent
variables are those identified by principal component analysis. That is. coefficients labeled for year 1980 arc obtained by pooling firm-year observations from
1977-1979. The coefficients are then fitted to the accounting data of year 1980 to obtain the eamings-target Pr (E-Pr) and retums-target Pr (R-Pr).
Panel A: Eamings-Target Prediction ModelNet profit
margin
%A in Net
profit margin
Debt-equity
ratio
%A in Debt-
equity ratio
Inventory
/total assets
%A in Inventory /
total assets
Quick ratio %A in Quick
ratio
1980 3.143 0.019 0.049 1.859" -1.752b -0.607 0.255 0.642
1981 0.304 -0.016 0.036 2.164' -1.169 -1.366' 0.343 0.119
1982 0.475 -0.1411 -0.133 1.851" 0.205 -1.373" 0.114 -0.066
1983 -2.862 -0.1611, -0.161 1 .2 0 2 " -0.597 -1.560" 0.086 -0.054
1984 -4.653" -0.1511, -0.2921 1.075" -2.164" -0.999" 0.147 0.223
1985 -4.658b -0.086 -0.223b 1.162" -1.143 -1.390' -0 . 1 0 2 0.386
1986 -5.830" -0.073 -0.107 1.408" -2.216b -1.050* -0.135 0.146
Mean** -2 . 0 1 2 -0.087 -0.119 1.531' -1.262 - l . l 9 f 0 . 1 0 1 0.199
Mean Std Error 2.362 0.068 0.107 0.423 1.074 0.489 0.157 0.323
Wald Chi-Square 0.725 1.661 1.230 13.104 1.382 5.954 0.415 0.380
Mean Std. Estimate* -0.046 -0.050 -0.045 0.187 -0.070 -0,094 0.025 0.026
Panel B: Retums-Target Prediction Model
1980 5.829* -0.052 -0.039 0.530 -2.555* -1.528" -0 . 2 2 1 -0.172
1981 5.332b 0.006 0.077 0.492 -0.841 -0.978b -0.029 -0.3281982 -0.045 0.088 -0.096 0.248 0.861 -0.424 0.271 -0.640
1983 -1.675 -0 . 0 1 0 -0.098 0.298 1.300 0.071 0.016 -0.075
1984 3.007 -0.077 -0.009 0.297 1.287 0 . 0 0 2 -O.I18 0.476
1985 5.727" -0.038 -0.049 0.855" 0 . 0 2 0 -0.109 -0.356b 0.723
1986 9.345" 0.074 -0 . 0 1 1 0.85 lh -1.476 0.374 -0.3901 0 .6 6 8 "
Mean 3.931a -0 . 0 0 1 -0.032 0.510 -0 . 2 0 1 -0.370 -0.118 0.093
Mean Std Error 2.271 0.065 0,103 0.394 1.057 0.473 0.152 0.313
Wald Chi-Square 2.997 0 . 0 0 0 0.097 1.679 0.036 0.614 0.604 0.089
Mean Std. Estimate 0.081 -0 . 0 0 0 -0 . 0 1 2 0.065 -0 . 0 1 2 -0.027 -0.037 0.015
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TABLE 6 (CONTINUED)
MULTIVARIATE ANALYSIS OF THE LOGISTIC COEFFICIENTS FOR RATIOS IDENTIFIED BY PRINCIPAL COMPONENT ANALYSIS
Panel A. Earnings-Targct Prediction Model
Sales /
total assets
%A in sales /
total assets
%A in LT debt %A in total
assets
Cash dividend as
% of cash flows
Sales to fixed
assets
Sales to
inventory
Sales to working
capital
1980 -0 . 1 0 1 1.124" -0.2741 -2.296 1.292b -0,006 -0.024 -0.0071981 -0.074 1.057" -0.322 -1.759 0.737 0.009 -0 . 0 1 1 0.005
1982 -0.059 1,553c -0.2481 - 1. 1 0 2 " 0.555 0.06 lb 0.029 0 . 0 1 1
1983 -0.037 0.755 -0.025 -2.432 0.502 0.051" 0.014 0.005
1984 -0.047 l.793c -0.132 -1.703 0.358 0 . 0 2 2 -0 . 0 0 0 -0.007
1985 0.007 0.594 -0.400c -1.243h 0.292 -0.037 0.005 -0.028
1986 -0.008 0.446 -0.578c 0.086 1.190b -0.008 0.013 -0.044
Mean -0.046 1.046" -0.28? -1.493* 0,704 0.013 0.004 -0.009
Mean Std Error 0.047 0.615 0.128 0.652 0.456 0.028 0.019 0 . 0 1 0
Wald Chi-Square 1 . 2 0 0 2.894 4.906 5.245 2.382 0.217 0.038 0.819
Mean Std. Estimate -0.048 0.063 -0 . 1 0 1 -0 . 1 1 1 0.056 0 . 0 2 2 0 . 0 1 1 -0.044
Panel B: Retums-Target Prediction Model
1980 -0.068 1.693 -0.114 -0.262 -2.125b 0.036 -0.036* -0.016
1981 -0.023 1.071" -0.057 -0.891 -0 . 1 1 0 0.080 0.005 -0.009
1982 0.130 0.642 0.043 -0.680 0.209 0.064b 0.037* -0 . 0 1 0
1983 0.009 -0.184 -0.004 -1.546 0.715* 0.040 0.053 0.008
1984 0.031 -0.078 0.032 -1.833 -0.030 0.017 0.054 0.0041985 0.041 -0.056 -0.261 -2.289 -0.017 0.003 0,044b -0.004
1986 0.066 0.151 -0.247 -1.176 -0.045 0.017 0.014 -0 . 0 1 1
Mean 0 . 0 1 0 0.463 -0.087 -1.23? -0 . 2 0 0 0.037 0.024 -0.006
Mean Std Error 0 . 0 2 1 0.596 0.119 0.624 0.433 0.027 0 . 0 2 0 0 . 0 1 0
Wald Chi-Square 0.226 0.603 0.533 3.950 0.215 1.804 1.557 0.326
Mean Std. Estimate 0.026 0.027 -0.030 -0.094 -0 . 0 1 2 0.061 0.068 -0 . 0 2 0
' ' Denotes statistical significance at the 0.10, 0. 05, and 0 01 levels respectively, based on two-tail t-tesl
1Simil ar to Lev and 1'hiagarajan 11993 1, the yearly logis tic regress ion is us ed to obtain an across-year mean, standard error to calculate Wa ld Chi-Square for each
financial ratio
Standardized coeificients are reported here in order to compute the relative influence of independent variables in the models
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assets, %A in sales/total assets, %A in long-term debt, %A in total assets (see Panel A in
Table 6). In the retums-target prediction model, only two financial ratios are statistically
significant: net profit margin and %A in total assets (see Panel B in Table 6).
The signs of these ratios in both models are consistent except for the net profit
margin, which is operationalized as the ratio of earnings before extraordinary items to
sales. In the earnings model, the sign o f the net profit margin is negative which indicates
that an increase in the current earnings level will decrease the probability of an increase in
the future earnings change. This observation is consistent with the earnings reversal
behavior documented in previous studies (Freeman, Ohlson, and Penman [1982], Ou
[1990], Elgers and Pfeiffer [1996]). In the returns model, however, the net profit margin's
sign is positive which suggests that higher current earnings lead to higher probability of
future excess returns.
The other significant ratio in the retums-target prediction model is %A in total
assets, and it has a negative sign. These observations o f a positive coefficient for net
profit margin and a negative coeffcient for %A in total assets suggest that the probability
of future excess returns for a firm will increase if operating profits can grow without tying
up more investment in assets. These empirical results confirms the relationship between
returns and accounting information specified in the finance free cash flow concept. Firm
value equals the present value of discounted future free cash flow, and free cash flow is a
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positive function of net operating margin (profitability) and a negative function of growth
in operating assets as suggested in Ohlson and Feltham [1995] (p. 695).25
As reported in Panel A of Table 6, financial ratios that are significant in the
eamings-target prediction model are (%A in debt-equity ratio, %A in inventory/total
assets, %A in sales/total assets, %Ain long-term debt, %A in total assets. Based on Table
5, they are all classified as ratios with a mixture of profitability and risk except for %A in
sales/total assets, which is categorized as a non-useful ratio in the univariate logistic
analysis. Although these ratios are classified as ratios with a mixture of profitability and
risk, they are more profitability oriented because they are statistically significant in the
eamings-target prediction model but not significant in the retums-target prediction model.
6.2.3.2 A Further Look at Prs Constructs by Exam ining Trading
Profitabilities of the Earnings-Target Prediction Model and the Returns-Target
Prediction Model
The interpretation o f Prs constructs cannot be complete without looking into the
trading profitability for the two models. In HL, financial ratios that are significantly
associated with future earnings increases (excess returns) are used to form eamings-target
Pr (E-Pr) and retums-target P r (R-Pr), respectively. They found that the trading
' ' The free cash flow concept states that:Free cash flow,
= Operating earnings, + Operating assets,./ - Operating assets,
= Operating earnings, - (Operating assets, - Operating assets,./)
= Operating earnings, - (A in Operating assets,)
= [(Operating earnings, / Operating assets,./) - (A in Operating assets, / Operating assets,./)) * Operating assets,./= (Operating margin, - growth in operating assets,) * Operating assets,./
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profitability based on R-Pr dominates eamings-target Pr. In this study, principal
component analysis is used to obtain a set o f financial ratios that only depends on the
interrelationship among a large number o f financial ratios without considering their
association with the dependent variables to form Pr.
Trading profitability is measured by monthly rebalanced market-adjusted returns
gained from a hedge portfolio over various holding periods as in Greig [1992], Hedge
portfolios for the eamings-target prediction model and retums-target prediction model are
formed based on two schemes. The first scheme is to form a hedge portfolio that take a
long (short) position if Pr is greater (less) than 0.6 (0.4). The second scheme involves
trading strategy by dichotomizing the whole sample. That is, trading strategy is based on
taking a long position for Prs that is greater than 0.5 and taking a short position for Pr
less than and equal to 0.5. While Table 7 provides the small prints for the by-year
trading profitability to the long position, short position and hedge portfolio for various
holding periods of 3, 6, 9, 12, 18, 24, 36, 48, 60 and 72 months. Table 8 highlights the
mean returns for the average of the by-year returns reported in Table 7. To get a better
picture of the trading profitability trends, the trading profitability over various holding
periods are plo tted side-by-side. Finally, the trading profitability patterns for the various
trading strategies, on a common scale, are comprehensively presented in Figure 3.
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6
I Mill- 7
H Y - Y K A R T R A D I N G I 'R O I I I A H I I I T Y T O M il- : 11 I. IK .I -, P O R T F O L I O S O V I -R H O L D I N G P F R I O D S O T .3 . 6 , 9 . 1 2 . 1 8 . 2 4 , 3 6 . 4 8 . 6 0 A N D 7 2 M O N T H S
T h e m o n t h l y r e b a l a n c e d m a r k e t a d j u s t e d r e t u r n s t o t h e h e d g e p n r t o l i o s a r c c a l c u l a t e d b y t a k i n g l o n g p o s i t i o n f o r f i rm s w i t h P r > 0 .6 ( P r - 0 . 5 ) a n d s h o r t f o r f ir m s w i t h P r- 0 4
( P r - - 0 . 5 ) f o r t h e c a i n i n g s - t a r g c t m o d e l a n d t h e r c t o r n s - t a r g c t m o d e l . P o r t f o l io s a r e fo r m e d t h r e e m o n t h s a f t e r t h e D e c e m b e r y e a r e n d f o r w h i c h t h e a c c o u n t i n g i n f o r m a t i o n is
n s s m u c d t o b e p u b l i c l y a v a i l a b l e . T h e r e t u r n s a r e c a lc u l a t e d u s i n g e q u a t i o n s ( 1 0 ) . ( 1 1 ) . a n d ( 1 2 ) i n t h e t e x t . M e a n r e t u r n s a r e t h e ' a v e r a g e o f t h e b y - y e a r m e a n s .
lannel A: Kamings-'Parget Model with Pr 0 6 for long posilon (n -1017) and lr 0.4 (n 472) lor short position
No. of Observations Holding Period 3 Holding Period 6 Holding Period-9 Holding Period-12 Holding Periods-18
Year Ixmg Short t-ong Short 1ledge 1AMlg Short 1ledge long Short Hedge Ixtng Shon Hedge 1aitig Short Hedge
80 341 17 0.0457 -0.0086 0.0543 0.0146 -0.0876 0 1022 0.0207 -0.0744 0.0952 0.0371 -0.1527 0.1898 0 0218 -0.2638 0 285681 208 33 0 0100 -0.0229 0.0328 -0 0048 0.0071 -0.0119 0.0370 0.1177 -0.0807 0.0989 0.1783 -0.0794 0 1606 0.1739 -0.013382 56 127 0.0916 0.0389 0.0526 0.0808 0.0388 0.0420 0.0807 0.0551 0.0257 0 1063 0.0383 0.0680 00910 0.0124 0078683 50 107 0.0210 0 0121 0.0089 0.0094 -0.0089 -0.0006 -0.0797 -0.0332 -0.0465 -0.0597 -0.0143 0.0454 -0 0823 -0.0174 -0 064884 94 76 -0.0563 -0.0647 0.0083 -0.0281 -0 0532 0.0251 -0.0488 -0.0865 0.0377 -0.0215 -0.0766 0.0551 -0.0470 -0.1261 0.079083 161 42 -0.0113 0.0072 -0 0 184 -0.0123 -0.0419 0.0295 0.0132 -0.0229 0.0097 0.0283 0.0075 0 0208 0.0993 0.0246 0.123986 107 70 00199 -0.0308 0.0507 0.0534 0.0230 0.0765 0.0241 -0.0419 0.0659 0.1002 0.0717 0.0284 0 1008 0.1010 -0 0002
Mean Returns 0 0172 -0.0098 0.0270 0.0134 -0.0241 0.0375 00030 -0. 0123 0. 0153 0.0414 0.0075 0.0339 00492 -0.0207 00698
Pannel H: Famings-Targct Model with Pr 0.5 forlong posilon (n -1814) and P r 0.5 (n 1100) for short position
80 444 39 0.0479 0.0545 -0.0066 0.0047 -0.0294 0.0341 0.0076 -0.0015 0.0091 0.0275 0.0413 0.0689 0.0195 -0.0954 0.114881 362 105 -0.0002 -0.0215 0.0213 -0.0140 -0.0033 0.0108 0.0293 0.0595 -0.0302 0.0927 0.1490 -0.0563 0.1605 0.1754 -0.015082 130 298 0 0616 0.0416 0.0199 0.0630 0.0507 0.0123 0. 0784 0.0680 0.0104 0 1054 0.060S 0.0448 0.0904 0.0330 0.057483 170 247 0.0237 0.0037 0.0200 0 0081 -0.0115 0.0196 -0.0248 -0.0196 -0.0052 -0.0075 -0.0040 -0.0035 -0.0202 -00153 -0.0049
84 226 168 -0.0281 -0.0404 0.0122 0.0003 -0.0282 0.0286 -0.0065 -0.0429 0.0363 0.0214 0.0277 0.0491 0.0124 0.0676 0.080083 271 101 -0.0105 0.0220 -0.0325 0.0246 -0.0093 -0.0153 -0.0237 0.0121 -0.0116 0.0145 0.0230 0.0084 0.0534 0.0207 0.032786 211 142 0.0086 -0.0155 0 0241 00502 0.0037 0.0466 0.0259 0.0022 0.0238 0 1048 0.0924 0.0124 0.1102 0.0893 0.0209
Mean Returns 0.0147 00064 0.0084 0.0125 -0 .0039 0.0164 0 0123 0 007 7 0.0047 0.0513 0.0360 0.0153 0.0609 0.0200 0.0409
Pannel C: Retums-Targc t Model with 1Pr 0.6 for long positon (n 386) and Pr 0.4 (n; 487) forslion position
80 58 114 0.0522 0.0467 0.0055 -0.0177 0.0152 -0.0329 -0.0208 -0.0007 -0.0201 0.0220 0.0293 -0.0513 00830 0.0196 0.102581 21 74 0.0053 -0.0269 0.0322 0.0028 -0.0524 0.0551 0.1149 -0.0279 0.1428 0.2581 0.0658 0.1922 0.2382 0.1277 0.110582 100 41 0. 0967 0.0553 0.0414 0.0767 0.0631 0.0136 00673 0.1082 -0.0409 0.0568 0.1911 0.1343 0.0571 0.0560 0.001283 65 38 0.0355 -0.0020 0.0374 0.0139 -0.0049 0.0188 -0 0259 -0.0479 0. 0220 0.0073 0.0415 0.0342 0 0133 -0.0535 0066884 47 48 -00222 -0.0641 0.0418 -0.0169 -0.1061 0.0892 -0.0359 -0 1364 0.100S -0 0151 0.1278 0.1127 -0.0335 0.1806 0 147183 55 72 0.0190 -0.0154 0.0344 0.0207 -0.0643 0.0850 0.0204 -0.0787 0.0991 0.0763 -0.0563 0.1326 0.0848 -0 0784 0.163286 40 100 0.0100 0.0234 0.0334 0. 0383 0.0020 0.0363 0.0272 -0.0520 0.0792 0.0643 0.0381 00262 0.0772 0.0706 00066
Mean Returns 0 028) -0.0043 00323 0 0168 -0 0211 0.0379 0 0210 -00336 0.0546 0.0587 0.0141 0.0446 0 0506 -0.0055 0 0561
Pannel 1): Eamings-Target Model with Pr 0.5 for long positon (n 1381 ) and Pr 0 5 (n 15.73) lor short position
80 219 264 0.0483 0.0487 -0.0004 -0.0112 0 0131 -0 0243 -0 0089 0.0205 -0.0294 -0 0051 0.0452 -0 0502 0.0287 0.0435 -0 072281 154 313 0.0044 -0.0097 0.0141 0.0000 -0.0172 0.0172 0.0710 0.0194 0.0516 0.1398 0.0888 00510 0.1880 0.1524 (10356
82 281 147 00539 0.0357 0.0183 0 0515 00598 -0 0083 00585 0.0958 -0.0374 0 0541 0.1130 -0.0589 0 0498 0.0501 0.000383 233 184 0 0252 -0.0045 0.0297 0 0058 -0.0151 00208 -0 0141 -0 0310 0.0169 00047 -0.0180 0 02 26 -0.0032 0.0347 0 031584 177 217 -00227 -0.0419 0.0192 0 0031 -0.0239 0 027 0 -0 0030 -0.0374 0.0343 0 0213 -0.0164 0.0376 0.0135 0.0504 0.06.3983 175 197 0,0014 -0.0046 0 0061 0 0014 -0.0397 0 0411 0 0103 0.0476 0.0579 00563 0.0177 0.0740 0 1031 0 0060 0 109186 142 211 0 0116 -0 0098 00214 00372 00271 0.0101 0 0485 -0.0054 0.0539 0 0907 0.1054 00147 0 0X44 0 1128 -01)281
Mean Returns (10174 0 0020 0 0155 00125 0 0006 0 0120 0 0232 0 002) 0 0211 0 0517 0.0429 0 0088 0 0581 0 0382 0 0199
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IAHI I S
TRADING PROITIAI51I 11 Y I( ) ITU-: Ill- IKII l0 6 (Pr>() 5) and short for firms with
Pr0.6 for long position (n= 1017) and Pr0.5 ft
Months Long Short Hedge
.3 0.0147 0.0064 0.0084
6 0.0125 -0.0039 0.0164
9 0.0123 0.0077 0.0047
12 0.0513 0.0360 0.0153
15 0.0593 0.0374 0.0219
18 0.0609 0 . 0 2 0 0 0.0409
24 0.0929 0.0457 0.0472
.36 0.0950 0.0297 0.0653
48 0.0864 -0.0152 0.1016
54 0.0598 -0.0.388 00986
60 0.0817 -0.0317 0 11.34
72 0.0834 -00365 0.1198
0 2500
0.2000
0 1500
01000
0.0500
0.0000
-0 0500
-01000
-0 1500
-0.2000
L I
11AMlg I Short Hedge
0.1200
0 1000
0.0800
0.0600
0.0400
0.0200
00000
00 200
-II 0-10011ong Slum Iledge
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TABLE X(CONTINUED)
TRADING PROFITABILITY TO THE HEDGE PORTFOLIOS OVER HOLDING PERIODS OF 3.6 . 9. 12, 15, IX. 24. 36. 4X. 54.60 AND 72 MONTHS
Panel C: Rcturns-Targcl Model with Pr> ( ) . 6 for long position (iv=386) and Pr0.5 for long position (n -1381) and Pring I Short I ledge
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In contrast to HL [1992], this study finds that the trading profitability of Retums-Target
Pr (hereafter R-Pr) only dominates that o f Eamings-Target Pr (hereafter E-Pr) up to a 9-
months holding period (see Panels A & B in Table 8 and Figure 3). After that, the
trading profitability based on E-Pr continues to grow monotonically. On the other hand,
the trading profitability based on R-Pr remains constant and eventually declines (see
Panels C & D in Table 8 and Figure 3). Specifically, the excess returns observed from E-
Pr are monotonic increasing with the holding period (from 2% to 24%) and persistent
beyond 72 months. This suggests that E-Pr might only capture firms profitability
prospects and fails to incorporate risk factors. As a result, the trading profitability
generated by E-Pr is probably due to some omitted risk factors.
The R-Pr based trading profitability curve demonstrates a reverse V curve with a
peak at the holding period o f 9 months (5.6%),26 which signifies that the market slowly
adjusts to the fundamental value. In fact, the excess returns for R-Pr are not gre ate r than
zero when one considers the transactions cost, which ranges between 4.3% and 9.5%
(Holthausen and Larcker [1992]). The implication of the trading profitability observed
from R-Pr suggests that the market is efficient with respect to the use of accounting
information.
6Although the highest trading profitability of 9.3% is shown at 36-month, it is not significantly higher tlian tlwtof 9-month at the p-value of 0.21 (one-tail test).
eproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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6.2.3 .3 Benchmarking With Trading Profitability Patterns of Two Famou
Risk Proxies: Earnings-to-price Ratio and Book-to-Market Ratio
The conjecture that E-Pr proxies for some omitted risk factor is further evaluated
by comparing it with two benchmarks, namely trading strategies based on eamings-to-
price ratio (E/P) and book to market ratio (B/M) respectively. These two ratios are well
documented in studies o f market anomalies as proxies for omitted risk factors (Lev
[1978], Fama and French [1992], Bernard and Wahlen [1995] and others). E/P is the
earnings per share excluding extraordinary items (COMPUSTAT annual data item #58)
scaled by the price as o f December fiscal year-end. B/M is the book value of common
equity (COMPUSTAT annual data item #60) scaled by the market value of common
equity (product o f COMPUSTAT annual data items #25 and #199) as o f December fiscal
year-end. The monthly rebalanced market adjusted abnormal returns for each trading
strategy are equally-weighted pooled cross-sectional and time-series observation during
1980-1986. That is, once all observations have been assigned to a portfolio, the mean for
the portfolio is based on an equally-weighted average o f all observations in that
portfolio.27 Subsequently, cumulative abnormal returns for the long and short position are
calculated for various holding periods. As the E-Pr based trading strategy involves taking
long positions fo r 1017 firm-year observations with E-Pr>0 .6 and taking short positions
472 firm-year observations with E-Pr
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72
(B/M) based portfolios is determined by taking long positions for 1017 firm-year
observation with highest E/P (B/M) and taking short positions for 472 firm-year
observation with lowest E/P (B/M).
Imposing the same frequency of stocks in long and short position as in the
eamings-target prediction model, both E/P and B/M models demonstrate similar but
stronger trading profitability patterns than does E-P r (see Panel D in Table 9). Moreover,
stocks with long position have significantly higher E/P and B/M than those with short
position for the eamings-target model but not for the retums-target model. The result is
consistent with Ou and Penman [1989b] in which they find similar properties between E-
Pr and E/P and conclude that ...information in prices that leads (future) earnings is
contained in financial statements [p. I l l ] ,
6.2.3,4 Evaluation o f Firm Size Effects
In light of continuous trading profitability based on the Pr strategy, Greig [1992]
examines the firm size effect on the cross-sectional relation between Pr and subsequent
stock returns. He finds that the positive associations between Pr and subsequent stock
returns disappear after allowing for cross-sectional differences in CAPM beta and
implementing tighter controls of firm size than those in OP [1989a], The hypothesized
effect of E-Pr on trading profitability should be positive. When Greig regresses the E-Pr
and firm size, defined as the log of the market value o f equity, on the mean adjusted buy-
and-hold return for the twelve-months (Table 6, p. 432 in Greig [1992]), the significance
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R
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TABLE 9. COMPARISON OP TRENDS OF T R A D I N G PROFITABILITY TO THE HEDGE PORTFOLIOS BASED ON
EARNINGS-TA RGET Pr. EARNINGS-TO-PRICE RATIO (E/P) RATIO, AND BOOK-TO-MARKET (B/M) RATIO
The monthly rebalance d market adjusted returns associated with the trading strategies based on carnings-bascd Pr (E-Pr). carnings-pricc ratio, and
bo ok -to -m ark ct ra ti o ar c eq ua lly -w eig ht ed PO OL ED cr os s-s ec tio na l an d lim c- sc ric s ob se rva tio ns ov er the tim e pe rio d 1980 -198 6. Th e tr ad in g s tra teg y
by g oi ng lo ng for fir ms wi th E -P r >0 .6 an d sho rt for fir ms wit h E-P r- 0 4 re su lts in 1017 fir m s an d 472 fir ms res pec tiv ely . Th e tr ad in g str at egy for the
E/P (B/M) based portfolios is determine d by taking long for 1017 firm-vcar observations with highest E/P (B/M) and taking short for 472 firm-year_______________________________________________________ observat ions with lowest E /P (B/M ).
N u m b e r
P a n e l A .
M o n t h s
o f o b s e r v a t i o n s i s 1 0 1 7 f o r l o n g p o s i t i o n a n d 4 7 2 f o r s h o r t p o s i t io n .
T r a d i n g P r o f i ta b i l it y B a s e d o n P a m i n g s - t o - P r ic e R a t io ( P . /P )
L o n g S h o r t 1 l e d g e
.16
9
121 5
1 8
2 4
3 6
4 8
5 4
6 0
7 2
P a n e l B :
M o n t h s
0 0 1 9 5
0 . 0 1 5 2
0 . 0 2 7 9
0 . 0 7 8 9
0 . 0 9 0 5
0.10000 . 1 5 5 8
0 . 1 9 7 2
0 . 1 9 1 2
0 . 1 7 3 7
0 . 1 8 8 7
0 . 2 0 5 1
0 . 0 0 9 1
- 0 . 0 0 3 8
- 0 . 0 3 2 3
0 0 0 4 4
-0.0017- 0 . 0 1 2 8
- 0 . 0 0 6 8
- 0 . 0 3 5 4
- 0 . 0 4 9 3
- 0 0 7 4 5
- 0 . 0 4 0 3
- 0 . 0 5 3 0
0 . 0 1 0 4
0 0 1 9 0
0 . 0 6 0 2
0 . 0 7 4 5
0 . 0 9 2 3
0 . 1 1 2 9
0 . 1 6 2 6
0 2 3 2 6
0 . 2 4 0 5
0 . 2 4 8 2
0 . 2 2 9 0
0 . 2 5 8 1
0 . 3 0 0 0
0 . 2 5 0 0
02000
0 1 5 0 0
01000
0 . 0 5 0 0
0.0000
- 0 0 5 0 0
-0 1000 tUing Short -Hedge
T r a d i n g P r o f it a b i li ty B a s e d o n B o o k - l o - M a r k e l R a t i o ( B / M )
L o n g S h o r t I l e d g e
3
6
9
1215
1 8
2 4
3 6
4 8
5 4
6(17 2
0 . 0 2 1 6
0 . 0 1 7 4
0 . 0 2 6 5
0 . 0 8 5 5
0 . 0 9 5 1
0 . 0 9 3 1
0 . 1 5 4 3
0 . 1 8 3 5
0 . 1 7 7 4
0 . 1 5 5 4
( I 1 7 8 4
0 I 8 I < >
0 . 0 1 4 0
- 0 . 0 0 9 3
- 0.0120
- 0 . 0 0 4 7
- 0 . 0 0 1 8
- 0 . 0 2 6 9
- 0 . 0 2 6 1
- 0 . 0 5 1 3
- 0 . 0 7 9 2
- 0 . 1 0 8 0
- 0 0 9 2 8
- 0 1 0 4 2
0 . 0 0 7 7
0 . 0 2 6 7
0 . 0 3 8 5
0 . 0 9 0 2
0 . 0 9 6 9
0 . 120(1
0 . 1 8 0 4
0 . 2 3 4 8
0 2 5 6 7
0 2 6 3 4
0 . 2 7 1 1
0 2 8 5 7
0 3 0 0 0
0 . 2 5 0 0
02000
0 1 5 0 0
0.1000
0 0 5 0 0
00000
- 0 0 5 0 0
-01000
- 0 1 5 0 0
I
I "HI! I I S h o rt -Hedge
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TABLE 9 (CONTINUED): COM PARISON OF TRENDS OF TRADING PROFITABILITY TO THE HEDGE PORTFOLIOS BASED ON
Panel C Trading Profitability for Earnings-!ai'gel PTf!7
Months Long Short 1ledge0 2500
3 0.0181 -0 0 0 1 0 0 0214
6 0.0091 -0 009(i 0 0189 0 2 0 0 0
9 0.0116 -00092 0 0207 0150012 0.0491 0 01.18 0 0151
15 0.0612 0 0 ) 0 1 005110 . 1 0 0 0
18 0.0629 -0.0058 0.0687
24 0.1181 - 0 0 0 1 2 0.1193 0.0500
.16 0.1440 -0.0172 0 16120 0 0 0 0
48 0.1.114 -00511 0.182654 0.1007 -00715 0.1722 -0 050060 0 . 1 2 1 0 - 0 0621 0 1810
72 0.1.190 -00784 0 2174 I Ling I ledge
Panel D: Comparison of Trading Profitability to the Hedge Portfolios Based on Earnings-Targcl Pr (E-Pr), Earnings-to-Pricc Ratio (E/P), and Book-to-
Markcl Ratio (B/M)
0 3000 nB/M
E/ P0 2500-
E-Pr0 2000
0 1500-
01000-
0 0500
000006 1 5 24 363 9 12 1 8 5 44 8 6 0 7 2
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75
of E-Pr disappears and becomes negative. The control variable, firm size, is negative and
statistically significant. Moreover, when he forms a trading strategy merely based on size
quintiles, the results show that the size strategy outperfo rms OPs Pr measure in predicting
abnormal returns by going long in the smallest firms and short in the largest firms.
This study complements Greigs study [1992] by further examining whether E-Pr
or R-Pr proxies for size effect after controlling for the E/P and B/M effects. Table 10
reports the results o f regressing the market-adjusted buy-and-hold returns for the holding
periods o f 12, 24 and 36 month subsequent to the computa tion o f Pr. Similar to Greig, E-
Pr is not significant in explaining market-adjusted buy-and-hold returns in the presence of
firm size (measured as log o f market value) with or w ithout controlling for E/P, B/M (see
Panel A in Table 10). However, R-Pr remains significant despite the inclusion of firm size.
E/P and/or B/M (see Panel B in Table 10). One noticeable observation is that the
significance of firm size in both models disappears as the holding periods prolong. On the
other hand, the significance o f E/P and B/M remains robust.
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76
TABLE 10
COMPARISON OF CONDITIONAL COEFFICIENTS (T STATISTICS) OF EARNINGS-TARGET
PR (E-PR) AND RETURNS-TARGET PR (R-PR)
The sample comprises 2.914 December year-end industr ial firms from 1980-1986. AR,t is the market-
adjusted buy-and-hold return for the holding periods of 12 (24,36) months subsequent to thecomputation of E-P rlt (R-Prlt) for firm / at time t. E-P rIt (R-Pr,t) is the estimated probability o f an
earnings (returns) increase in year r. Size,t is the log of market value of equity as of December fiscal
year-end. E/Plt is earnings per share excluding extraordinary items (Compustat annual data item #58)
scaled by the price (Compustat annual data item #199) as o f December fiscal year-end. B/M,t is the
book value o f common equity' (Compustat annual data item #60) scaled by the market value o f common
equity' (product of Compustat annual data items #25 and #199) as of December fiscal vear-end.
Panel A: AR;t = Yo + Yi E-Pr;, + Yi E/P;, + 7 3 B/M ;t + Y4 Size;,
Ym Yi Y2 Y3 Y-v Adj-R2
Holding Period = 12 months
0.024
(0.692)
0.042
(0.857)-0.092
(-2.567)b0.0019
-0 . 0 2 2
(-0.611)
0.151
(0.889)
0.165
(3.08)c
0.027
(2.524)b
-0.008
(-2.089)b0.0073
Holding Period = 24 months
0.058
( 1 .0 2 2 )
0.046
(0.565)
-0.017
(-2.842)'
0.0023
-0.046
(-0.758)
0.058
(0.696)
0.398
(4.497)c
0.06
(3.406)'
-0.014
(-2.322)b
0.014
Holding Period = 36 months
0.054
( 0 622)
-0 . 0 2 1
(-0.169)-0.009
(-0.981)
-0.0004
-0.099
(-1.074)
-0.017
(-0.131)
0.53
(3.808)c
0.091
(3.402)'
-0.004
(-0.423)
0.0092
Panel B: ARIf = y0+ y xR-Pr;t + 7 2 E/P;, + 7 3 B/M;, + 7 4 Size;,
Y" Yi Y: Y3 Y4 Adj-R2
Holding Period = 12 months
-0.024
(-0.65)
0.152
(2.299)b
-0 . 0 1
(-2.784)'
0.0035
-0.072
(-1 743)-
0.151
(2.269)b
0.148
(2.793 )c
0.03
(2.882)'
-0.008
(-2.181)b
0.0088
Holding Period = 24 months
-0.013
(-2.215)
0.208
(1.889)
-0.018
(-3.014)'
0.0034
-0.113
(-1 642)
0 . 2
(1.820)
0.376
(4.293 )c
0.064
(3.71)'
-0.015
(-2.393 )b
0.015
Holding Period = 36 months
- 0 . 1 1 1
(-1.174)
0.331
(1.979)b
-0 . 0 1
(-1.15)
0 . 0 0 1
-0.263
(-2.498)b
0.324
(1.935)
0.511
(3.71 l)c
0.095
(3.576)'
-0.005
(-0.535)
0.0106
l c denotes statistical significance levels at 0.10. 0.05 . and 0.01 respectively.
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Chapter 7
CONCLUSIONS
Ou and Penman [1989a] form a trading strategy based on the predicted probability
of future earnings increase estimated by a set of financial ratios that can predict one-year-
ahead earnings change. In contrast , Holthausen and Larcker [1992] extract information
from financial ratios that can directly predict one-year-ahead excess returns to estimate the
probability o f future excess returns, which is then used to form a trading strategy. Both
trading strategies are able to generate substantial abnormal returns. However, the
persistence of abnormal returns resulted from using these P r methods has puzzled
researchers concerning the constructs o f Pr.
Based on a typical firm valuation model, returns can be expressed as a function of
the change o f earnings magnitude and a discount factor that reflects risk. If the change of
earnings magnitude captures mainly profitability, then, the construct of eamings-target Pr
(hereafter E-Pr) should be mainly related to profitability and retums-target Pr (hereafter
R-Pr) should be affected by both profitability and risk. Hence, comparing the relationships
between a common set o f financial ratios that compose Pr and the two prediction model
allows one to characterize the attributes o f the financial ratios and to evaluate the relative
importance of profitability and risk in predicting future unexpected earnings and future
excess returns.
77
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78
This study uses principal component analysis to identify a set of essentially
uncorrelated financial ratios that a ttempts to capture distinct aspects o f firm
characteristics. Because the set of financial ratios only depends on the interrelationship
among a large number o f financial ratios to form Pr without considering the association of
the ratios and the pred iction targets (i.e. the sign o f one-year ahead earnings change /
excess return), they can be applied in different methodologies. Using principal component
analysis, this study identifies a set of 16 essentially uncorrelated financial ratios from 59
financial ratios that were originally investigated by OP and HL. Based on a simple firm
valuation model, these ratios are subsequently classified into one of three categories:
profitability-oriented ratios, risk-oriented ratios and ratios with a mixture of risk and
profitability.
Because the targets that the financial ratios aim to predict are different for the
eamings-target prediction model and the retum s-target prediction model, investigating the
patterns of abnormal returns or trading profitability generated by eamings-target Pr (E-
Pr) and retums-target Pr (R-Pr) can provide insights regarding their respective economic
meanings. As expected, this study finds that the construct o f E-Pr different from that o f
R-Pr. Similar to eamings-to-price and book-to-market ratios, E-Pr proxies for some
omitted risk factors. Yet, R-P r supports the premise that operating profitability and
growth in operating assets are the two most important pieces of accounting information to
evaluate firm value and tha t the market is efficient in using accounting information. This
study complements Greigs study [1992] by further examines whether Pr is merely a
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manifestation o f the firm size effect. E-Pr is not significant in explaining market-adjusted
adjusted buy-and-hold returns in the presence of firm size (measured as log of market
value), eamings-to-price ratio, and book-to-market ratio. However, R-Pr remains
significant despite the inclusion o f firm size, eamings-to-price ratio, and book-to-market
ratio.
The understanding o f Pr s constru cts provides an explanation for the economic
meanings o f Pr and helps us to explain the market anomaly as reported in previous studies
Furthermore, it provides evidence as to the relative importance o f profitability or risk in
predicting future unexpected earnings and future excess returns.
Several limitations in this studyare: First, this study attempts to capture all relevant
aspects of firm characteristics from a relatively complete set of financial ratios, but there is
no guarantee that the set of ratios used in this study is complete . Principal component
analysis is a variable-sensitive statistical method; different financial patterns may be
generated as different financial ratios are fitted in the model. Second, the criteria for
selecting a financial ratio as a surrogate for each identified factor is somewhat subjective
The appropriateness of the ratios selected for proxying the factors and the potential
correlation among these ratios are also limitations to this study. Finally, this study is
limited to manufacturing firms with December 31 fiscal year-end. Therefore, the results
may not be generalized to other types o f firms and firms without a December 31 fiscal
year-end.
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