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Predicting relative stock prices: an empirical study.

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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Dean W. DiGregorio, Southeastern Louisiana University
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)
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Title Annotation:MANUSCRIPTS
Author:DiGregorio, Dean W.
Publication:Academy of Accounting and Financial Studies Journal
Date:May 1, 2004
Words:8630
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