Predicting relative stock prices: an empirical study.
DiGregorio, Dean W.
ABSTRACT
This study investigates the ability of two valuation methods, the
income approach and the comparable sales approach, to predict the
year-ahead, rank-ordered prices of publicly traded stocks. The sample
firms are stratified by industry. Actual values and rank measurements
are used in general models. Cross-sectional and pooled data is analyzed using nonparametric and parametric statistical methods.
Overall, the results support the use of both valuation approaches.
Several of the variables used in the valuation models were able to
explain a substantial amount of the variation in ranked year-ahead
prices. However, it was noted that results could vary by SIC code and
that care must be taken when valuing stocks in different industries.
Also, as expected it was generally easier to predict the rank of
year-ahead prices than to predict actual prices.
INTRODUCTION
This study investigates the ability of two valuation methods, the
income approach and the comparable sales approach to predict the
year-ahead, rank-ordered prices of publicly traded stocks. In general,
researchers strive to identify valuation models which have high
explanatory power and model coefficients which are stable across
populations, and over time. They also prefer to use parametric
statistical methods in order to obtain greater power. Unfortunately, the
models used in most prior valuation studies had low explanatory power
and coefficients which were unstable over time.
This study investigates valuation from a relative versus an
absolute perspective. The decision to predict relative price ranks
instead of actual values is motivated by two ideas. First, when analysts
advise clients to either buy, sell, or hold a stock, the recommendation
is based on the stock's expected performance relative to other
stocks. Expected performance is in effect ranked as better, worse, or
the same compared to other stocks. Second, if only limited success has
been obtained when attempting to predict actual prices, then why not use
a more general measure? If the underlying valuation process is somewhat
understood, it should be easier to compare two stocks and predict which
stock should have a higher price, rather than predict the actual price
of each stock. This situation is analogous to betting on a sporting
event. If there is a valid understanding of the strengths and weaknesses
of each team, it should be easier to predict the winner of the event,
rather than predict the actual score.
METHODOLOGY
This study investigates the valuation of publicly traded stocks
from a relative versus an absolute perspective. It evaluates the
association of year-ahead rank-ordered stock prices with variables used
in two basic valuation models. The industries included in the study are
based on a random sample of four-digit SIC codes. It is assumed that
stratifying firms based on four-digit SIC codes will control for
differences between industries. The number of companies within each
four-digit SIC code varies considerably. Annual sample sizes range from
as few as five firms to as many as 59. The data from each SIC code was
analyzed both annually, and pooled across the sample period (1981-1994).
The annual results were difficult to interpret. Results varied widely
between and within SIC codes. The pooled results by SIC code are easier
to interpret and are reported in the tables.
Spearman's rank correlation coefficient ([r.sub.s]), a
nonparametric measure of association, is computed using the SPSS exact
test module for small-sample nonparametric tests. Values for
Spearman's [r.sub.s] can range between -1 and +1. Spearman's
rank correlation coefficient has an asymptotic relative efficiency of
.912 compared to the Pearson correlation coefficient when data meets the
assumptions necessary for the Pearson correlation coefficient to be
valid (Daniel, 1990). Nonparametric methods are useful when rank-order
is of interest and when data sets are sparse or do not meet the
assumptions necessary to rely on parametric methods. The Pearson
correlation coefficient, a parametric measure of association, is also
computed for comparative purposes.
Spearman's rank correlation coefficient ([r.sub.s]) is used to
measure the degree of association between pairs of rankings and is equal
to the Pearson correlation coefficient computed using ranks instead of
actual values. Thus, the value of the Spearman rank correlation
coefficient can be squared and is equal to the coefficient of
determination ([R.sup.2]) computed for a simple linear regression when
the actual values of both the independent and dependent variables have
been replaced by their ranks.
This valuation study uses independent variable specifications
suggested by both theory and practice. It also measures the association
between independent variables measured in [year.sub.(t)] and price ranks
in [year.sub.(t+1)]. As such, the models can be considered predictive
models. Thus, statistically significant values for Spearman's
[r.sub.s] can be squared and interpreted as the strength of the
model's predictive ability.
Supplemental analysis is also performed for all hypotheses. It is
intended to help summarize the results, determine whether the
alternative variable specifications provide the same or additional
information, and to evaluate whether the quality of the information
changes over time.
LITERATURE REVIEW
Both academic and professional literature was reviewed in order to
identify the valuation approaches and independent variables used in this
study. As noted in Foster (1986), many early studies used
cross-sectional multiple regression methods to investigate the
relationship between firm or equity valuation and independent variables
such as expected earnings. The results generally indicated that some
coefficients were significant but none were stable over time. This
indicated an inability to use the results for predictive purposes.
Possible explanations for the results could include measurement error,
the existence of omitted variables, misspecified relationships, and/or
market inefficiencies.
After the seminal stock price research efforts of the late
1960's and early 1970's, researchers generally switched their
focus to predicting stock returns. However, in the 1990's there was
renewed interest in price valuation models. Ohlson (1995) and Feltham
and Ohlson (1995) developed a model in which firm value is equal to book
value plus the net present value of excess earnings on book value, when
clean surplus accounting is used. A basic version of this model was
described in Appeals and Review Memorandum (A.R.M.) 34 in 1920.
Bernard (1995) noted that models using the book value of equity and
abnormal earnings predictions based on Value Line forecasts explained
security prices substantially better than a valuation model using
expected dividends. A series of articles by Fama and French challenged
the validity of the capital asset pricing model (CAPM) and renewed
interest in valuation models. Fama and French (1992) note that beta
alone does not explain the cross-section of stock returns and that firm
size, as measured by market capitalization, and the (book value/market
value of equity) ratio are related to returns. Fama and French (1993,
1994, 1995, and 1996) discuss, test and defend their model. They
concluded that their model could explain most of the anomalies noted in
regard to the CAPM model. Daniel and Titman (1997) disagreed with the
Fama and French conclusion and argued that the differences in returns
were due to firm characteristics. Penman (1996) found that both the
price/earnings ratios (P/E) and price/book value of equity ratios (P/B)
were positively correlated with the premium of market price over book
value and future abnormal earnings.
The professional literature identifies a host of methods and
variables potentially relevant to the valuation process. Many of the
following variables are included in this study. Tax related valuations,
prepared for closely held or infrequently traded businesses, must
consider the factors noted in Revenue Ruling 59-60 (1959) and other
promulgations issued by the Internal Revenue Service (IRS). The general
factors include: 1) the nature of the business and history of the
enterprise; 2) the general economic outlook, and the condition and
outlook of the specific industry; 3) the book value of the stock and the
financial condition of the business; 4) the earnings capacity of the
company; 5) the dividend paying capacity; 6) whether or not the
enterprise has goodwill or other intangible value; 7) prior sales of the
stock and the size of the block of stock to be valued; and 8) the market
price of stocks of corporations engaged in the same or similar line of
business, having their stocks actively traded in a free and open market,
either on an exchange or over the counter. The Internal Revenue Service
also noted that the facts and circumstances of the each case must be
considered when estimating fair market value and that the weight of the
factors is determined by the nature of the business.
Although Revenue Ruling 59-60 applies to closely held or
infrequently traded stocks, the factors indicated are expected to be
useful in explaining differences between the prices of publicly traded
stocks. As such, this study stratifies the sample firms by industry and
includes variables related to equity, size, financial condition,
earnings, dividends, cash flows, returns, growth, and other
profitability measures.
Support for the factors noted in Revenue Ruling 59-60 appears
throughout the professional literature. The professional literature
tends to focus on either business valuation (Copeland et al. 1994;
Cornell 1993; Ehrhardt 1994; Fishman et al. 1994; Trugman 1993) or the
selection of common stocks for investment purposes (Bernhard 1980;
Damodaran 1994; Frailey 1997; Graham 1973; O'Neil 1995). Both
business appraisers and investors consider many of the factors discussed
in Revenue Ruling 59-60 and use variations of the income approach and
comparable sales approach.
INCOME APPROACH
The income approach is based on the underlying theory that the
price of an investment should not exceed the "value of the
income" received from the investment. This approach can be applied
to the firm as a whole, or to the separate debt and equity components.
The income approach is most appropriate when the underlying assets are
being used to their highest and best use, and when buying or selling
decisions are being made for business versus personal reasons. Two
popular applications of the income approach include capitalizing
earnings and discounting expected cash flows. The basic capitalized earnings model is: Price = "Normal" earnings of the
investment/Capitalization rate. The basic discounted expected cash flows
model is: Price = Expected net future cash flows of the
investment/Discount rate.
In order to operationalize the numerator of the capitalized
earnings model, the normal earnings of the investment must be specified
and measured. This study uses actual current amounts consistent with a
random walk assumption and evaluates the performance of three different
earnings specifications on a per share basis. Supplemental analysis is
also performed to determine whether the predictive ability of the models
can be improved by including growth rate measures.
In order to operationalize the numerator of the discounted expected
cash flows model it is necessary to specify which cash flows will be
valued. This study evaluates the performance of six different cash flow
specifications on a per share basis (three to the company, three to the
shareholder) and uses actual current amounts consistent with a random
walk assumption. Supplemental analysis is also performed to determine
whether the predictive ability of the models can be improved by
incorporating growth rate measures.
It is expected that the rank of year-ahead price per share will be
directly associated with the rank of current-year income and cash flow
per share measures, for firms within the same four-digit SIC code.
Hypothesis 1 (stated in the alternative) is:
H1: There is a direct relationship between [(Income; Cash
flows).sub.(t)] and [Price.sub.(t+1)]
The null hypothesis of no association will be rejected if:
[r.sub.s] (computed) > positive [r.sub.s] (critical value). Income
per share specifications for [year.sub.(t)] include 1) operating income after depreciation (OIAD); 2) earnings before interest and taxes (EBIT);
and 3) net income (NI).
Cash flows per share specifications for year(t) include cash flows
to the company and to the stockholder. Cash flows per share to the
company are specified as: 1) net cash flows from operations (CFO for
years 1981-1987; CFON for years 1988-1994); 2) net cash flows from
operations - net cash flows for investing activities (CFOLI for years
1981-1987; CFONLI for years 1988-1994); and 3) net cash flows (NCF).
Cash flows per share to the stockholder for year(t) are specified
as: 1) dividends per share (DPS); 2) dividend payout ratio (DPR), which
is defined as (dividends per share)/(net income per share); and 3) free
cash flows to equity per share (FCFE) which is defined as (net cash
flows + dividends on common stock - proceeds from sale of common stock +
purchases of common stock)/(common shares used to compute earnings per
share).
[Price.sub.(t+1)] is specified as the year-ahead December 31
closing price, as adjusted for stock splits and dividends relative to
the December 31 closing price [year.sub.(t)] as per the annual COMPUSTAT
tapes.
Supplemental analysis is also performed to determine if the
alternative specifications for income, cash flows to the company, and
cash flows to the shareholder provide the same or additional
information, and whether the quality of the information changes over
time.
To operationalize the denominator of the capitalized earnings model
and the discounted expected cash flows model, it is necessary to
determine the appropriate capitalization rate and discount rate,
respectively. The Internal Revenue Service noted in Revenue Ruling 59-60
that the appropriate capitalization rate depends on the nature of the
business, the risk involved, and the stability of earnings. Two methods
are widely used to estimate capitalization and discount rates, the
build-up approach and the capital asset pricing model (CAPM). The
build-up approach adds the riskfree rate of return, a general risk
premium for the difference in risk between stocks and bonds, and a
specific risk premium based on the firm's business or industry. The
CAPM adds the risk-free rate of return, and a risk premium for market
risk which can not be avoided through diversification (beta times the
expected difference in returns between the stock market and the risk
free rate). This study investigates factors used in the build-up
approach.
If actual current income or cash flow measures are used in the
numerator of the income approach models (a random walk assumption) then
all perceived risk should be reflected in the denominator of the model.
It is expected that firms with different levels of risk will have
different capitalization or discount rates, and that the rates will
approximate year-ahead total returns. This study intended to use annual
cross-sectional analysis to control for changes in the risk-free rate of
return and the general risk premium. It was reasoned that if the
risk-free rate of return and general risk premiums could be controlled,
then differences in capitalization or discount rates should be due to
industry or firm specific factors. Firms within the same industry should
have similar risk factors. Thus, differences in capitalization or
discount rates between firms within the same industry should be
primarily due to measurable differences between the firm's
industry-relevant risk factors. Growth, profitability, size and
financial condition have been suggested as proxies for industry and firm
specific risk. Supplemental analysis evaluates the association of
selected growth (5), profitability (7), size (3), and financial
condition (4) variable specifications with year-ahead total returns, and
the ability of those variables to improve the explanatory power of the
variables used in the income approach models.
COMPARABLE SALES APPROACH
The comparable sales approach is also known as the market approach
or the relative sales value approach. It is based on the underlying
theory that perfect substitutes should have the same price and that
similar assets should sell for similar prices. This approach can be
applied to the firm as a whole, or to the separate debt and equity
components. The comparable sales approach is most appropriate when
substitutes exist and direct comparisons can be made between the
products. Stocks can be viewed as products and can be compared based
upon their measured level of value relevant variables.
The basic comparable sales model is: Price = (price multiple or
ratio) x (independent variable amount). This model can be viewed as:
price per share = (unit price) x (quantity per share). The price
multiple is simply the unit price of the value relevant variable being
acquired (such as price per dollar of income, cash flows, sales, assets,
etc.), and quantity is the firm's per share level of the variable
in which the rate is denominated. The price multiple or ratio is
interpreted in the same manner as a regression coefficient.
To implement this model, one must first identify "comparable
firms." Firms may be considered comparable when they are similar
along factors mentioned in the valuation literature. These factors
include the nature and condition of the business and industry, growth
prospects, economic conditions, operating risks, financial leverage and
the stability of earnings. Similar firms should have similar price
multiples. If firms have different price multiples, then there must be
some differences between the firms which are considered relevant. For
example, there could be differences in the perceived quality of the
income, cash flows, sales, etc. per share. A simple analogy is that
while similar quantities of the same grade of wheat should have the same
unit price, different grades of wheat should have different unit prices.
This study attempts to ensure comparability among sample firms by
stratifying the firms by four-digit SIC code.
Second, the researcher must identify which variables are associated
with value and determine how to measure them. Variables used in practice
and suggested by theory include the income and cash flow measures
previously discussed in the income approach section, and size related
variables. Size related variables can either ignore the effect of debt,
such as sales or total assets, or consider it, such as the book value of
stockholders equity. This study uses actual current values consistent
with a random walk assumption and then ranks them.
It is expected that the rank of year-ahead price will be directly
associated with the rank of current-year income, cash flow, and size
specifications, for firms within the same four digit SIC code.
Hypothesis 1 evaluates the association between the income and cash flow
variable specifications and year-ahead price. Hypothesis 2 evaluates the
association between the size variable specifications and year-ahead
price. It is also expected that some of the size variable specifications
are more appropriate for predicting the value of the firm as a whole
versus the price of the equity component. As such, this study also
investigates whether the association between year-ahead price and the
size variable specifications is improved when total debt is included in
the model. Additional analysis evaluates whether the association between
the year-ahead price and the income, cash flow, and size variable
specifications is improved when growth measures are included in the
model.
It is expected that the rank of year-ahead price will be directly
associated with the rank of current-year size per share measures, for
firms within the same four digit SIC code. Hypothesis 2 (stated in the
alternative) is:
H1: There is a direct relationship between [(Income; Cash
flows).sub.(t)] and [Price.sub.(t+1)]
The null hypothesis of no association will be rejected if:
[r.sub.s] (computed) > positive [r.sub.s] (critical value). Size
specifications which ignore debt are measured on a per share basis at
the end of year(t) and include: 1) net sales (SPS); 2) adjusted book
value of total assets (TAPS); and 3) and adjusted book value of tangible
assets (TGAPS). Size specifications which consider debt are measured at
the end of [year.sub.(t)] and include: 1) book value of common
stockholder's equity per share (CSEPS); and 5) net tangible assets
per share (NTGA) which is defined as (adjusted book value of tangible
assets total debt) per share. [Price.sub.(t+1)] is specified as the
year-ahead December 31 closing price, as adjusted for stock splits and
dividends relative to the December 31 closing price [year.sub.(t)].
SAMPLE SELECTION
The data for this study was obtained from the annual COMPUSTAT
tapes and covered the period 1981-1994. Firms were stratified by
four-digit SIC code and 30 of the 148 qualifying fourdigit SIC codes
were ultimately selected on a random basis for testing. To insure adequate power for the nonparametric tests, SIC codes with fewer than
five active firms in each year of the study were eliminated from
consideration in the sample. It initially appeared that 185 SIC codes
were eligible for selection. Subsequently, 33 additional SIC codes were
eliminated due to insufficient minimum annual sample size and four
Depository institutions SIC codes (6000-6099) were eliminated due to
their data format. The SIC codes selected and their maximum pooled
sample size over the period 1981-1994 are presented in Table 1.
RESULTS: HYPOTHESIS 1
It was expected that there would be a direct relationship between
the rank of year-ahead price ([year.sub.(t+1)]) and the rank of
current-year income and cash flows variable specifications
([year.sub.(t)]). The results for Hypothesis 1 are reported in Table 2.
The table provides the range of values of Spearman's rank
correlation coefficient for each variable tested and the number of SIC
Codes for which the value was significant. The supporting tables for
each SIC Code are available, but have not been presented.
The association between the ranked current-year income per share
specifications (OIAD, EBIT, NI) and ranked year-ahead price was positive
and significant for each pooled SIC code in the sample. Spearman's
rank correlation coefficients ranged from a low of .434 to a high of
.813 (Table 2). The level and range was similar for all three income
specifications. Spearman's rank correlation coefficient is equal to
the Pearson correlation coefficient computed using ranks instead of
actual values. As a result, the value of the Spearman's rank
correlation coefficient can be squared and is equal to the coefficient
of determination ([R.sup.2]) computed for a simple linear regression
when actual values of both the independent and dependent variables have
been replaced by their ranks. As such, it can be stated that the ranked
current-year income specifications could explain between approximately
19%-66% of the variation in ranked year-ahead stock prices. The results
indicate that while the income specifications are relevant to the
valuation process, results do vary by industry and that there is room
for improvement in the model.
The association between the ranked current-year cash flows to the
company specifications and ranked year-ahead price was mixed. The
association between ranked current-year net cash flows from operations
(CFO for years 1981-1987; CFON for years 1988-1994) and ranked
year-ahead price was positive and significant for all but a few pooled
SIC codes in the sample. Spearman's rank correlation coefficients
ranged from a low of -.029 to a high of .845 (Table 2).
The association between ranked current-year net cash flows from
operations - net cash flows for investing activities (CFOLI for years
1981-1987; CFONLI for years 1988-1994) and ranked year-ahead price was
not significant for any SIC codes during 1981-1987, but was positive and
significant for 27 SIC codes during 1988-1994 (Table 2). The statement
of cash flows was not a required part of the financial statements for
years ending before July 15, 1988 and thus there is a difference between
the cash flow variable specifications before and after 1988. This did
not appear to be a serious problem regarding cash flows from operations
but could be a problem regarding the cash flows from investing
activities.
The association between ranked current-year net cash flows (NCF)
and ranked year-ahead price was only significant for five SIC codes.
Spearman's rank correlation coefficients ranged from a low of -.039
to a high of .275 (Table 2).
The association between ranked current-year cash flows to the
shareholder and ranked yearahead price was generally positive and
significant as expected. Spearman's rank correlation coefficients
ranged from a low of -.439 to a high of .780 (Table 2). In general,
association was higher for dividends per share (DPS) and free cash flows
to equity per share (FCFE) than it was for the dividend payout ratio
(DPR).
For comparative purposes, the values of the Pearson correlation
coefficient were also computed for all income and cash flow variables.
When each SIC code was pooled over the 19811994 period, the Pearson
values generally had a wider range but were consistent with the results
of the nonparametric tests.
HYPOTHESIS 1: SUPPLEMENTAL ANALYSIS
Supplemental analysis was performed to determine if the alternative
specifications for income, cash flows to company, and cash flows to the
shareholder provided the same or additional information, and whether the
quality of the information changed over time. The entire sample was
separately pooled and ranked for the periods 1981-1994, 1988-1994, and
1981-1987. Variable specifications reported under the full model were
entered into the regression and backward elimination was performed. The
requirement for entry was a probability of F of .05. The requirement for
removal was a probability of F of .10. Each variable was noted as either
included in, or excluded from, the final model.
The results for the ranked current-year income specifications
(OIAD, EBIT, NI) indicate that all three variables provide similar
information, that little is gained by using more than one variable for
prediction purposes, and that there is little change in the predictive
ability of the models over time. The adjusted [R.sup.2] for the
1981-1994 pooled full model is .494 and the values for all pooled
periods lie within a range of .031. The adjusted [R.sup.2] for the
separate models over the pooled periods fell within the range of .414 to
.498.
The results for the ranked current-year cash flow to company
specifications indicate that the ranked current-year cash flow from
operations variables (CFO, CFON) explain over 90% of the variation
explained by the full models. The adjusted [R.sup.2] for the full model
is .477 for 1988-1994, and .379 for 1981-1987. It is difficult to
determine whether the explanatory power of cash flow from operations
increased because the data items used changed in 1988. Ranked
current-year net cash flows (NCF) explained almost none of the variation
in any of the periods.
The results for the ranked current-year cash flows to shareholder
specifications indicate that ranked current-year dividends per share
(DPS) was more useful than either the ranked current-year dividend
payout ratio (DPR) or ranked current-year free cash flows to equity
(FCFE). The adjusted [R.sup.2] for the full model is .409 for 1981-1994
and within .013 for the other reported pooled periods. The adjusted
[R.sup.2] for the DPS separate models over all pooled periods fell
within the range of .349 to .400. The adjusted [R.sup.2] for the DPR and
FCFE separate models over all pooled periods fell within the range of
.081 to .133 and .159 to .208, respectively.
The above results were also tested using actual values instead of
ranks. The adjusted [R.sup.2] for regressions using ranks was generally
at least 33% higher in all cases than the adjusted [R.sup.2] for
regressions using the actual values.
It was also expected that year-ahead total returns could proxy for
the capitalization rate or discount rate used in the income approach
models. It was also expected that growth, profitability, size and
financial condition could proxy for industry and firm specific risk and
could be used to predict year-ahead total returns. As such, ranked
year-ahead total returns were regressed on ranked current-year growth
(5), profitability (7), size (3), and financial condition (4) variable
specifications. The results were disappointing. For comparative
purposes, ranked year-ahead total returns were also regressed on ranked
current-year dividends per share. It was found that the ranked
current-year dividends per share captured most of the information
contained in the ranked current-year growth, profitability, size and
financial condition variable specifications. Ranked current-year
dividends per share were then used as a surrogate for the capitalization
rate or discount rate in the income approach models.
It was found that including ranked current-year dividends per share
a surrogate for the capitalization or discount rate in regressions with
the ranked current-year income and cash flow to company variable
specifications did little to improve their ability to predict ranked
year-ahead price. The adjusted [R.sup.2] of the models increased by less
than .05, or by approximately less than 10%. Tables for the above
results are available, but have not been presented.
RESULTS: HYPOTHESIS 2
It was expected that there would be a direct relationship between
the rank of year-ahead price ([year.sub.(t+1)]) and the rank of
current-year size per share variable specifications ([year.sub.(t)]).
Results for Hypothesis 2 are reported in Table 3. The table provides the
range of values of Spearman's rank correlation coefficient for each
variable tested and the number of SIC Codes for which the value was
significant. The supporting tables for each SIC Code are available, but
have not been presented.
The association between the ranked current-year size per share
specifications that ignored debt levels [net sales (SPS), adjusted book
value of total assets (TAPS), adjusted book value of tangible assets
(TGAPS)] and ranked year-ahead price was positive and significant for at
least 28 of the 30 pooled SIC codes. Spearman's rank correlation
coefficients ranged from a low of -.087 to a high of .813 (Table 3). The
level and range was similar for all three variables. For comparative
purposes, the values of the Pearson correlation coefficient were also
computed. When each SIC code was pooled over the 1981-1994 period, the
Pearson values generally had a wider range but were consistent with the
results of the nonparametric tests.
The association between the ranked current-year size per share
specifications that considered debt levels had more variation. The
Spearman's rank correlation coefficients for the ranked currentyear
book value of common stockholder's equity per share (CSEPS) and
ranked year-ahead price ranged from a low of -.120 to a high of .895 and
were significant for 29 of the 30 SIC codes (Table 3). The
Spearman's rank correlation coefficients for ranked current-year
net tangible assets per share (NTGA) and ranked year-ahead price ranged
from a low of -.228 to a high of .728 and were significant for 25 of the
30 SIC codes (Table 3). For comparative purposes, the values of the
Pearson correlation coefficient were also computed. When each SIC code
was pooled over the 1981-1994 period, the Pearson values generally had a
wider range but were consistent with the results of the nonparametric
tests.
HYPOTHESIS 2: SUPPLEMENTAL ANALYSIS
Supplemental analysis was performed to determine if the alternative
specifications for size provided the same or additional information, and
whether the quality of the information changed over time. The entire
sample was separately pooled and ranked for the periods 1981-1994,
19881994, and 1981-1987 using the same procedures discussed for the
supplemental analysis of Hypothesis 1.
The results for the ranked current-year size specifications that
ignored debt levels (SPS, TAPS, TGAPS) indicate that all three variables
provide similar information, that little is gained by using more than
one variable for prediction purposes, and that there is little change in
the predictive ability of the models over time. The adjusted [R.sup.2]
for the 1981-1994 pooled model is .384 and all pooled periods lie within
a range of .044. The adjusted [R.sup.2] for the separate models over the
pooled periods fell within the range of .297 to .379. The above models
were also tested using actual values instead of ranks. The adjusted
[R.sup.2] for regressions using ranks was generally at least 50% higher
than the adjusted [R.sup.2] for regressions using the actual values.
Tables for the above results are available, but have not been presented.
The current-year size specifications that considered debt levels
[book value of common stockholder's equity per share (CSEPS), net
tangible assets per share NTGA)] were also further tested. As the
variables were highly correlated, a pooled model was not analyzed.
However, results for the separate models indicate that CSEPS is more
useful for predicting year-ahead price and is more stable over time than
NTGA. The adjusted [R.sup.2] for the CSEPS separate models over the
pooled periods were very stable and fell within the range of .455 to
.477. The adjusted [R.sup.2] for the NTGA separate models over the
pooled periods fell within the range of .238 to .350. The above models
were also tested using actual values instead of ranks. The adjusted
[R.sup.2] for regressions using ranks for CSEPS was generally slightly
higher than the adjusted [R.sup.2] for regressions using the actual
values. In contrast, the adjusted [R.sup.2] for regressions using ranks
for NTGA was generally substantially higher than the adjusted [R.sup.2]
for regressions using the actual values. Tables for the above results
are available, but have not been presented.
Value multiples based on size measures that ignore debt can be
viewed as gross value multiples for the firm as a whole. Gross firm
value should equal the market value of the equity plus the market value
of the debt. To the extent that total debt per share divided by the size
variable per share is the same between firms, the firms should have the
same price multiples. To the extent that firms have different debt/size
ratios, they should have different price multiples.
It was expected that including ranked current-year total debt along
with the ranked current-year size specifications would improve the
predictive ability of the regression of ranked year-ahead price. The
entire sample was separately pooled and ranked for the periods
1981-1994, 1988-1994, and 1981-1987. All of the regressions were
significant. When individually tested with ranked current-year total
debt, each of the ranked current-year size variables that ignored debt
were significant and had coefficients with the expected sign. Although
ranked current-year total debt per share (TLPS) was often significant in
the regressions, it did little to improve the power of ranked
current-year sales per share (SPS) or ranked current-year adjusted book
value of tangible assets per share (TGAPS), to predict the rank of
year-ahead stock prices. The adjusted [R.sup.2] increased by less than
.04 in any period. Including ranked current-year total debt per share
(TLPS) along with the ranked current-year adjusted book value of total
assets per share (TAPS) initially appeared to increase the adjusted
[R.sup.2] of the model. However, this result must be interpreted with
caution as the two variables were highly correlated.
The above regressions were also run using actual values instead of
ranks. The adjusted [R.sup.2] for regressions using ranks was generally
at least 50% higher than the adjusted [R.sup.2] for regressions using
the actual values for all but the combined (TAPS) and (TLPS) model,
where the difference was negligible. The supporting tables are
available, but have not been presented.
SUPPLEMENTAL ANALYSIS: GROWTH RATES
Researchers have noted that firms within the same industry can have
different price multiples based on the same value relevant variable.
This could be due to perceived differences in the quality of the
variable being measured. The difference between firm growth rates is
frequently proposed as an explanation for the difference in quality
between variable measures. For example, many would argue that two firms
with the same level of current earnings, but different earnings growth
rates, should have different Price/Earnings ratios. This issue is
closely related to whether the actual or an expected variable
measurement is multiplied by the price ratio, and what assumptions are
made about expected value, such as random walk, naive trend, or time
series.
As this study used actual firm-level measures, supplemental
analysis was performed to determine: 1) whether including growth
measures for income, cash flow, and size variable specifications would
materially increase the predictive ability of the comparable sales
models; and 2) whether the quality of the information changed over time.
The growth measures evaluated included the change in level from the
prior year ([year.sub.(t)] - [year.sub.(t-1)]), the one year growth rate
([year.sub.(t)]/ [year.sub.(t-1)]), and the change in one year growth
rate [([year.sub.(t)]/ [year.sub.(t-1)])/([year.sub.(t-1)]/
[year.sub.(t-2)]] .The entire sample was separately pooled and ranked
for the periods 1981-1994, 1988-1994, and 1981-1987 using the same
procedures discussed for the supplemental analysis of Hypothesis 1.
All of the models were significant. The adjusted [R.sup.2] of each
regression was used to evaluate the usefulness of each model. For
comparative purposes, the adjusted [R.sup.2] of each simple linear
regression for the underlying ranked current-year income, cash flow and
size variables was also noted. The results indicated that including
ranked growth variables in the regressions did very little to increase
the explanatory power of the models above that provided by the
underlying ranked current-year income, cash flow or size measures. None
of the adjusted [R.sup.2] values increased by more than .03. The
supporting tables are available, but have not been presented. This
finding provides additional support for the decision to use actual
current values (random walk assumption) when measuring the income, cash
flow and size variable specifications.
SUPPLEMENTAL ANALYSIS: PRICE AT CURRENT-YEAR END
For comparative purposes, the market value of common
stockholder's equity per share at December 31 of the current-year
(PC12: [Price.sub.(t)] at closing) was also used to predict year-ahead
price. It was found to have the highest and most stable level of
association with year-ahead price ([Price.sub.(t+1)]) compared to any
other single variable in the study. Spearman's rank correlation
coefficients ranged from a low of .786 to a high of .949 and were
significant for all 30 SIC Codes tested.
The above results were also tested using actual values instead of
ranks. The adjusted [R.sup.2] for regressions using ranks for the
current-year market value of common stockholder's equity per share
(PC12) was generally slightly higher than the adjusted [R.sup.2] for
regressions using the actual values.
In addition, a regression including the ranked current-year income,
cash flow, and size variables was run and found to have no additional
explanatory power over that provided by a model using only the ranked
current-year market value of common stockholder's equity per share
(PC12). When PC12 was not included in the model, total explanatory power
was reduced by more than .26, or by approximately 32% for the 1981-1994
period. When actual values were used in the regressions instead of
ranks, the results were consistent with the above conclusions.
CONCLUSIONS
This study investigates the ability of two valuation methods, the
income approach and the comparable sales approach, to predict the
year-ahead, rank-ordered prices of publicly traded stocks. The income
approach was investigated with Hypothesis 1 and with supplemental
analysis. The comparable sales approach was investigated with Hypotheses
1 and 2 and with supplemental analysis.
It was expected that ranked current-year income and cash flow
variable specifications would be directly associated with ranked
year-ahead price (H1). The ranked current-year income variables were
found to be significant and directly associated with ranked year-ahead
price. All three income specifications provided consistent results and
there was little practical difference in explanatory power between them.
However, although the ranked current-year income variables were
significant, they explained less than 50% of the variation in ranked
year-ahead price. In addition, the cash flow variables were found to be
less useful than the income variables.
It was expected that ranked current-year size variable
specifications would be directly associated with ranked year-ahead price
(H2). Size variable specifications either ignored or considered the
effect of debt. The ranked current-year size variables that ignored debt
(SPS, TAPS, TGAPS) were found to be significant and directly associated
with ranked year-ahead price. All three variable specifications provided
consistent results and there was little practical difference in
explanatory power between them. However, although the ranked
current-year size variables were significant, they explained less than
40% of the variation in ranked year-ahead price. Supplemental analysis
indicated that including ranked current-year total debt in the
regressions generally did very little to improve the explanatory power
of the variables, and it also created problems with multicollinearity in
the model.
Additional analysis indicated that including selected ranked growth
variables along with the underlying ranked current-year income, cash
flow and size measures that ignore debt, in the regressions of
year-ahead price did very little to increase the explanatory power of
the models. This finding provides support for using current-year values
(a random walk assumption) in the valuation models.
The ranked current-year size variables that considered debt (CSEPS,
NTGA) were found to be significant and directly associated with ranked
year-ahead price. Although both variable specifications provided
consistent results, book value of common stockholder's equity per
share (CSEPS) generally had higher explanatory power. However, although
the ranked current-year size variables that considered debt were
significant, they explained less than 50% of the variation in ranked
year-ahead price.
For comparative purposes, ranked current-year market value of
common stockholder's equity per share (PC12: i.e. [Price.sub.(t)])
was also used to predict the year-ahead, rank-ordered stock prices and
was found to have the highest and most stable level of association
compared to any other variable used in the study. The adjusted [R.sup.2]
for the 1981-1994 pooled sample was .846 and all pooled periods fell
within a range of .032. In addition, a regression including the ranked
current-year income, cash flow, and size variables was run and found to
have almost no additional explanatory power over that provided by a
model using only the ranked current-year market value of common
stockholder's equity per share (PC12). When PC12 was not included
in the model, total explanatory power was reduced by more than .26, or
by approximately 32% for the 1981-1994 period. Unfortunately, knowing
that ranked current-year price is a very good predictor of ranked
year-ahead ranked price doesn't help explain how the initial
rankings were established.
The conclusions drawn from this study were also tested using actual
values instead of ranks. As expected, it was generally easier to predict
the rank of year-ahead prices than it was to predict the actual
year-ahead prices. The adjusted [R.sup.2] for regressions using ranks
was generally (with two exceptions) at least 33% higher than the
adjusted [R.sup.2] for regressions using the actual values. However,
there was little practical difference between using ranks and actual
values for the current-year market value of common stockholder's
equity per share (PC12) and the book value of common stockholder's
equity per share (CSEPS). The difference in adjusted [R.sup.2] between a
regression using the ranks compared to a regression using actual values
was less than .03 for PC12 and slightly more for CSEPS for the 1981-1994
period.
Overall, the results support the use of the income approach and the
comparable sales approach to predict ranked year-ahead stock prices.
Both methods were able to explain a substantial amount of the variation
in ranked year-ahead prices and the explanatory power was reasonably
consistent over the 1981-1994 period. However, each method has room for
improvement. In addition, the analysis by SIC code indicated that
results varied by SIC code and that care must be taken when valuing
stocks in different industries.
LIMITATIONS
As with all research efforts, this study is subject to certain
limitations. Due to data availability, only those firms reported on
COMPUSTAT have been included in the sampling population and sampling
period. These firms may not be representative of the entire population
of firms and care should be taken in generalizing the results to firms
not reported in COMPUSTAT. Also, the generalizability of the results to
other time periods may be limited to the extent to which conditions
during the time period covered by COMPUSTAT are different from other
time periods.
In general, nonparametric statistical methods are not as powerful
as parametric methods under conditions where the assumptions necessary
to rely on parametric methods are met. However, nonparametric methods
should be used when stratified sample sizes are small, and data does not
meet the assumptions necessary for parametric methods. Also, in order to
allow adequate statistical power, four-digit SIC codes with fewer than
five firms were excluded from the study.
Firms were stratified by four-digit SIC code and a large random
sample of four-digit SIC codes was selected. Each four-digit SIC code
was analyzed both separately and pooled along with all of the other SIC
codes selected, over various time periods. Drawing samples based on SIC
code implicitly assumes that SIC codes can control for industry
differences. This assumption may not be valid to the extent that firms
are also involved in other lines of business. Also, to the extent that
industries do differ, the results obtained by examining one industry may
not be generalizable to other industries.
This study assumes that the market is efficient. To the extent that
inefficiencies exist, differences which exist between the model
predictions and actual prices ranks may be inappropriately identified as
model related errors. To the extent the market is efficient, differences
between predicted price rank and actual price rank could be due to a
number of reasons including model misspecification, measurement error,
and differences across the sample firms and/or differences over time.
Many alternative variable specifications exist for each of the
models examined. This study recognized that fact and examined a large
number of alternatives. However, it did not examine all possible
variable choices and as such, there is no assurance that other variables
might not have performed better than the ones examined.
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Table 1: Sample Description, 1981-1994
SIC Code Industry description Maximum pooled
sample size
1311 Crude petroleum and natural gas 595
1381 Drilling oil and gas wells 130
1531 Operative builders 301
2040 Grain and mill products 71
2761 Manifold business forms 98
2800 Chemicals and allied products 104
2834 Pharmaceutical preparations 447
2844 Perfume, cosmetic, toilet preparations 102
2860 Industrial organic chemicals 126
2911 Petroleum refining 455
3140 Footwear, except rubber 95
3420 Cutlery, hand tools, general hardware 112
3490 Misc. fabricated metal products 167
3510 Engines and turbines 101
3540 Metalworking machinery 102
3559 Special industry machinery 108
3570 Computer and office equipment 84
3661 Telephone and telegraph apparatus 133
3674 Semiconductor, related devices 250
3711 Motor vehicles and car bodies 109
3724 Aircraft engine, engine parts 70
4011 Railroads, line-haul operating 118
4911 Electric services 825
4923 Natural gas transmission and distribution 228
4924 Natural gas distribution 522
4941 Water supply 112
5051 Metals service centers-wholesale 71
5063 Electrical apparatus and equip.-wholesale 71
5140 Groceries and related products-wholesale 88
5912 Drug and proprietary stores 115
Table 2: Association Between Ranked Year-ahead Price and Ranked
Current-year Income and Cash Flow Variables Using Spearman's
Rank Correlation Coefficient ([r.sub.s]) Significance based on
one-tail test at .05 level
High Low Number of SIC
Codes Positive
and
Significant
Income:
OIAD .813 .485 30
EBIT .793 .434 30
NI .788 .493 30
Cato company:
CFO .818 .312 30
CFON .845 -.029 27
CFOLI .097 -.779 0
CFONLI .777 .113 27
NCF .275 -.039 5
Cash flows to
shareholders:
DPS .780 .225 30
DPR .544 -.439 20
FCFE .578 .092 25
Description of Variables Used in Table 2:
Year-ahead price:
[Price.sub.(t+1)] = December 31 closing price, as adjusted for
stock splits and dividends relative to [Price.sub.(t)]
Income specifications for [year.sub.(t)]:
OIAD = Operating income after depreciation per share
EBIT = Earnings before interest and taxes per share
NI = Net income per share
Cash flows to company specifications for [year.sub.(t)]:
CFO = Net cash flow from operations per share (1981-1987)
CFON = Net cash flow from operations per share (1988-1994)
CFOLI = Net cash flows from operations--net cash flows for
investing activities per share (1981-1987)
CFONLI = Net cash flows from operations--net cash flows
for investing activities per share (1988-1994)
NCF = Net cash flows per share
Cash flows to shareholder specifications for [year.sub.(t)]:
DPS = Dividends per share
DPR = Dividend payout ratio: (dividends per share)/(net income
per share)
FCFE = Free cash flows to equity per share: (net cash flows +
dividends on common stock--proceeds from sale of common
stock + purchases of common stock)
Table 3: Association Between Ranked Year-ahead Price and
Ranked Current-year Size Specifications using Spearman's
rank correlation coefficient values ([r.sub.s]) Significance
based on one-tail test at .05 level
High Low Number of SIC Codes
Positive and Significant
Size (ignores debt):
SPS .780 -.087 28
TAPS .799 .280 30
TGAPS .813 -.019 29
Size (considers debt):
CSEPS .895 -.120 29
NTGA .728 -.228 25
Descriptions used in Table 3:
Year-ahead price:
[Price.sub.(t+1)]: The December 31 closing price, as adjusted for
stock splits and dividends relative to [Price.sub.(t)]
Size specifications for year(t) that ignore debt:
SPS = Net sales per share
TAPS = The adjusted book value of total assets per share
TGAPS = The adjusted book value of tangible assets per share
Size specifications for year(t) that consider debt:
CSEPS = Book value of common stockholder's equity per share
NTGA = Net tangible assets per share: (adjusted book value
of tangible assets--total debt)