A Study Relation Between Market Beta And

A study on Relation Between Market Beta and Accounting Beta: Highly Leveraged Firm Case

Changwan Kim1)

Abstract

This paper investigates the co-movements of two measures, market beta and accounting beta, of systematic risk of a firm's return. Unlike previous studies on the issue, this study traces the changes in the betas along a firm's history and compare them at individual firm level for highly leveraged companies. The estimation results suggest that the two betas do not move together in general. We believe that the leverage effects and financial distress from debt seriously affect equity holders' interests and induce an increase in risk measured in market betas, whereas accounting betas do not immediately reflect the changes in debt-quity ratios.

1 Introduction Assessing risk of an asset is one of the most important issues in business. When financial analysts evaluate capital investment projects or securities, they need to come up with some estimate of the required rate of return in order to discount the future returns. The required rate of return should reflect the individual riskiness of specific projects or securities. Thus, risk measure plays a key role in constructing the appropriate discount rate. Financial economists have devoted tremendous efforts in developing theoretical and empirical models for estimating appropriate risk measures. One branch of empirical studies have searched for the appropriate empirical counterparts to future returns. Because, obviously, we are not able to observe them in real life. Main research question in this field is to compare the risk measures estimated from two different empirical counterparts of a firm's future returns: stock returns and accounting returns. Set aside the

1) Kim is from Korea Information Strategy Development Institute.

academic interests, this issue also has some meanings in practical financial researches. When one evaluates a firm's security, he usually refers to the stock market returns and estimates the market beta of security. However, sometimes stock market returns are not available for various reasons, for example, the firm in question is a non-public firm or a regulated firm so that stock price may not deliver useful information. Then he may have no choice other than seek accounting statements and estimate an accounting beta. Important matter in this case is that one must be aware of the informational difference in market beta and accounting beta. This study investigates the co-movements of two risk measures of the firms that underwent highly leveraged public recapitalizations. We believe this is an interesting case to reveal the informational differences in stock market data and accounting statements. Financial distress or leverage effect from overwhelming debt may seriously affect shareholders' interests, which maybe reflected in stock return. Also, unlike the existing literature, we estimate the possible changes in risk measures and compare the two risk measures at individual firm level. Tracing a firm's data delivers more information than cross sectional studies because individual firm level research may smooth out the noises stemming out from the differences in business environments each individual firm faces. The organization of the rest of this study is as follows: Section 2 briefly introduces CAPM model, reviews previous studies, and presents our motivations. Section 3 describes our data sampling procedure, estimation model and estimation strategy and reports the estimation results. Section 4 concludes with some remarks.

2 Literature Review and Motivation CAPM (Capital Asset Pricing Model), originally proposed by Nobel Prize winner William Sharpe, relates ex ante expected return on a security to ex ante expected return on a market portfolio with the relation,

(1)

where , , and are return on security , risk free return, market

return and a measure of sensitivity of return on security to the market return

respectively. In words, a security's risk can be decomposed into two parts: market risk and individual firm specific risk. Firm specific risk may be vanished away for an investor with a well-diversified portfolio. Therefore, only the market risk matters and a security's sensitivity to the unavoidable market risk is counted and priced. Traditionally, the beta has been used as a generic term for the systematic sensitivity of some measure of a security return to the broad-based index of that same return. This beta plays a pivotal role in calculating the discount rate in asset pricing model.2) Although the theory relates an expected returns to an expected market returns, empirical studies use historic return data for actual estimation under the assumption that past records are the best estimators for future returns. In the actual estimation of beta, stock return data are used in order to calculate the market beta. Also, an accounting beta is an accounting analogue to the market beta under the implicit assumption that accounting returns are generated by a statistical process structurally similar to the one that generates the stock market returns. Textbook on corporate finance relates asset beta as the weighted sum of debt beta and equity beta.3) Naturally, this has led to many studies extending the knowledge on the two betas both in theoretical and empirical aspects. The central issues in the empirical works are: first finding appropriate measures of accounting returns for equation (1), secondly comparing the two betas in order to seek the possible informational differences. This paper focuses on the extension of second issue.

2) There are many empirical studies testing the empirical validity of CAPM. Also APT (Arbitrage Pricing Theory) is developed with a quite different view on asset pricing. We do not review those literatures because we do not think this study is about to justify or reject the CAPM itself. 3) More precisely, textbook relationship is as follows.

. In this expression, A, D, and E

stand for the values of asset, debt, and equity evaluated at market prices, not book values.

Many studies examine the co-movements of two betas and report mixed results depending on choices of sample period and accounting measures. Beaver, Kettler, and Scholes (1970) examine the correlation coefficients of the two betas in various subperiods and find that correlation coefficients are positive and highly significant. After their work, many researchers provide more information on this issue by changing the sample periods and definition of accounting measures. Gonedes' (1973) study is an example of sensitivity test on the equational form. He finds a significant relationship between market and accounting betas only when the accounting based estimates are derived from the first-difference or scaled first-differences of the return series in a case study of 99 firms during 1946 - 1968 period. In the similar vein, Elgers and Murray (1982) investigate the choice of market index in calculating account betas and suggest that accounting betas are sensitive to the choice of index. Also the sensitivity of correlation to the length of sample period is examined by Beaver and Manegold (1975). Their study reveals that a longer estimation interval tends to produce a stronger correlation between accounting and market betas. Karels and Sackley (1993) find that cross-sectional correlations are sensitive to the length of the estimation interval for the betas in a case study of banking industry. Lee, Newbold and Finnerty (1986) compare the forecasts of security beta based respectively on accounting and market information. They conclude that each of forecast contains useful information for the prediction of systematic risk. In sum, previous studies examine the sensitivity of correlation between the two betas with various sample periods and definitions of accounting measures. However, it is not impossible to find some common factors in their approaches. First, previous studies employ OLS estimation method to obtain market and accounting betas and compared them at industry-level. That is : 1) pairs of risk measures, market beta and accounting beta, are estimated from firms within an industry, then two series of betas are constructed by stacking up the individual betas, finally the comovements of the two beta series are examined, 2) stability and uniqueness of a firm's beta is assumed in their empirical methodologies. No researchers, however, have examined the comovements of two betas at individual firm level. Consequently, all the previous approaches are based on an implicit assumption that the betas are stable over time. Accounting data record how a firm has performed in past periods. A firm's

stock price contains various information, including financial statements and expectations, which could be wrong ex post, on the firm's future performance. It is possible, at least in theory, that a firm with good current accounting records can show a poor stock return performance if the firm in question faces a gloomy future. For this reason, we believe that accounting beta and market beta deliver different information on firm risks. In other words, financial statements deliver backward-looking information, whereas information contained in stock price have forward-looking property. Also, it is well known that a firm's beta changes over time to the changes in expectation on future cash flows. Many studies provide evidences on the unstability of beta.4)

To highlight those two points, we try to find the firms who experienced the shocks which are supposed to affect seriously market return and have relatively small effects on accounting performance. This study selects firms that underwent highly leveraged public recapitalization and traces the changes in the betas a firm's history. It is generally believed that dramatic increases in debt-equity ratios induce financial risks because of the higher possibility of default in highly leveraged firms.5) Thus, the equity beta would change due to this financial distress, whereas we do not expect a dramatic change in accounting beta unless the firm in question change its business portfolio.6) In other words, an accounting beta reflect business risk and a market beta reflect financial risk in addition. This study uses time-varying coefficients method to calculate the beta series for each firm and perform correlation coefficient and cointegration test to compare the two series at individual firm level.

3 Estimation This section describes the sample selection procedure, estimation model and estimation results in our study.

4) There are many papers contribute to this issue following Harvey (1991), and Ferson and Harvey (1993). 5) See Kaplan and Stein (1993) for the evidence on increases in defaults rates in LBO debt. 6) Kaplan (1989) reports the improvement in cash flow following an LBO. However, this does not necessarily means a change in business risk.

Company Name CRSP Perm. Completion DateFMC 60708 05/29/86

Kroger 16678 12/05/88Owens 24811 11/06/86

Shoney's 70376 08/04/88Swank 44345 03/01/88

Table 1: Company Names and Recapitalization Completion Dates

3.1 Sample Selection Kaplan and Stein (1990) reports an increase in the systematic risk of equity, market beta in our study, of the twelve firms which undergo highly leveraged public recapitalization between 1985 and 1988.7)8) We choose the twelve firms in their study and trace the required data for 1960?997 period on annual base. Restricting our sample to these firms, we expect significant changes in market betas while relatively small changes in accounting betas during the sample period. For twelve firms, we exclude Multimedia Corporation since it is not listed in any of the major stock exchanges. Among the eleven remaining firms, only five firms have complete data set in their tenures while the other firms have many missing variables in accounting statements. Table 1 lists the names of those five companies, CRSP permanent firm numbers, and their recapitalization completion dates. One may question the generality of our work, because of rather small number of firms in our study. It is true that many firms, who underwent MBO or LBO, experienced debt-equity ratio changes in 1980's. However, most of those firms

7) After the recapitalization, sample firms' debt-equity ratios go over 80%. 8) It is not theoretically explained why firms go public recapitalizations. However, financial analysts believe that the firms with stable cash flow and small growth opportunity are the main target of LBO, MBO or recapitalization. The process of MBO usually goes like this. A firm's insider group, CEO or top management team, raise fund from junk-bond market or big investors. Then this management group buy out the firm's shares through stock market. After gained the control of the firm, fund-contributors take the seats in Board of Directors and reap the cash inside the firm.

privatized and unlisted from stock market after the buyouts, which prohibit us from obtaining stock price information. There is no doubt that number of sample is small in our study may bother us extending the empirical results to general conclusion on this issue. However, there are very small number of firms satisfying our research purpose, we have a small playground. All of the accounting return variables are extracted from COMPUSTAT data base, whereas individual firm's annual stock returns and the value-weighted market returns are calculated from the CRSP data base. Risk free returns are from CRSP bond market data base.

3.2 Estimation Models Usual market models are employed in estimating market and accounting betas in our study, following the previous studies in this field. Since our study focuses on the movements of betas at individual firm, we modify the market model to allow the betas change over time for each firm.

Market Beta Annual stock returns over the sample period are used in deriving empirical estimates of the market beta from the familiar market model:

(2)

where

= rate of return on security i in period t

= rate of return on market portfolio (value weighted index in the CRSP)

= market beta for security i in period t

= risk-free return rate in period t

= error term for i in period t

Accounting Beta Annual observations over the same period are used in estimating the accounting beta using the regression equation:

(3)

where = accounting return for firm i in period t

= market index(weighted average) for accounting returns drawn from

COMPUSTAT

= accounting beta for firm i in period t

= risk-free return rate in period t

= error term for i in period t

To measure the accounting return, we use the following typical earnings return variables. Note that the numbers in brackets are COMPUSTAT annual data numbers.

․ Earnings : Income available to common equity divided by market value of common equity at the beginning of period : [20 /(24 + 25) ]

․ Fund Flow : Income available to common equity plus depreciation divided by market value of common equity at the beginning of period : [(20 + 14) / (24

+ 25) ]

․ Operating Income : Operating earnings after depreciation divided by total assets: [(13 - 14) / 6 ]

3.3 Estimation Methods Empirical estimation is performed in two steps: the first step is to calculate the betas (market and accounting) at the individual firm levels, and the second step is to compare the betas for each firm. We employed time-varying coefficient method for the first step, and calculate correlation coefficient and perform cointegration test in the second step. For the sensitivity check we redo the same

test over various values of and and choices of accounting measures

defined in section 3.2.

Obtaining the beta series

The first step imposes the following simple statistical structure on market model in order to apply Kalman's time varying coefficients. (We drop the subscript i for simplicity) In this structure, a time varying coefficient at time t is the sum of previous value at t - 1 and an error term.

(4)

(5)

(6)

Rewritten in more compact and general way, measurement equation and transition equation9) are :

(7)

(8)

where and

. It is further assumed on the error terms,

∼

(9)

×

(10)

where and are constants. We assume a common variance in the transition

equation for simplicity. In the actual estimation step, we need to impose a structure on the initial state variables. It is assumed that the initial variables follow a normal distribution, ∼ , where is a 2 by 2 diagonal matrix with 0.001 as

a common argument. Expectation of equals zero means that a firm's return is

9) See Hamilton (1995) and other textbook for general description of Kalman's filtering.

not related to the unexpected risk (a risk that can not be avoided through

market portfolio), and expectation of equals one implies that a firm's return

is perfectly related to the market return or market conditions. Then our coefficients evolve following the usual Kalman's filtering formula,

(10)

(11)

(12)

(13)

In order to check the sensitivity of coeffcients to the parameters and , we

calculate the state variables over various values of and .

Co-movement Test In the second stage, we calculate correlation coefficients and perform cointegration test between the two beta series to test the hypothesis that market beta and accounting beta move together, that is the two betas contain the similar information about the firm's return. Following Engle and Granger(1987), the cointegration tests are performed by two step regressions. The first regression is :

(14)

where, and are accounting beta series and market beta series for a firm

respectively, and is a residual term. The equation form is inspired by the

basic text relationship between asset beta and market beta,

where D and E stand for the market values of debt and equity. In words, asset beta is a weighted average of the debt beta and the market beta. After obtaining the residual term, a Dickey-Fuller test is performed on the residual term, .

Sensitivity TestSince our estimation method requires some initial prior on the variances of error

Com. Name

Sensitivity of correlation to initial values, and

Sensitivity of correlation to choice of accounting measures

FMC unstable correlation coefficients unstable correlation coefficientsKroger unstable correlation coefficients unstable correlation coefficientsOwens stable correlation coefficients unstable correlation coefficientsSwank stable correlation coefficients insignificant correlation

coefficientsShoney's stable correlation coefficients insignificant correlation

coefficients

terms, represented by and , it is possible that our estimation results vary

on the size of those initial values. If the estimates are sensitive to the choices of initial variables, we may say that the estimation results are unstable. We need to perform sensitivity check on the estimation. For sensitivity test, we vary the parameter and which are the initial variances for the error terms in the

measurement equation and the transition equation respectively. For the same purpose, we check the responses of correlation to the choice of accounting measures in the accounting beta estimation.

3.4 Estimation Results

Table 2 : Summary on Estimation Results : Sensitivity Test

Table 2 summarizes the main estimation results in this study. First column in the tables lists up the company names, second column reports the responses of correlation coefficients between market and accounting betas to the variation in initial values, and . The last column reports the stability and level of

correlation coefficients to the choice of accounting measures. Appendix provides the detailed tables on estimation results.Except for Swank and Shoney's, the correlation coefficients between market betas and accounting betas show a wide range of values as we change the initial values of variances, and . FMC corporation case shows that the sign of the

correlation coefficients change from negative values to positive values as we

increase at the higher level of . When Earnings variables are considered in

the estimation, the coefficient varies from 0.18 to 0.34. Also, the sizes of correlation coefficients are not big enough to ensure a significant relationship between two betas. The biggest value is only 0.34. In Kroger corporation case, we observe the similar patterns. The coefficients generally have negative values in the cross section of low and high regardless of choice of accounting

return variable. However, the signs of the coefficients turn to positive values as we increase and decrease . The most dramatic changes in the size of

coefficients occur when Operating Income is employed as the return variable. The coefficients varies from 0.12 to 0.16, which are not believed to be a significant level. Owens Corning case shows a little different kinds of unstability in correlation coefficients. The size of the coefficients are relatively high and stable over the whole range of initial variances when Earnings and Fund Flow variables are used in accounting beta equation. The values stay around 0.8 level as we change the initial variances. However, this stability collapses when Operating Income is put in the accounting beta equation. The sign changes as we move from low and high zone to high and low region. Also,

the level of correlation coefficients are poorly low: smallest value is 0.47 and biggest is only 0.24. We obtain the similar results when the unit root test is employed. For the above three firms, we may confidently conclude that the relation between the two betas are unstable and sensitive to the choice of initial variables and accounting measures. For Swank and Shoney's, we have a fairly stable relationship over the whole range of initial variances. In Swank Corporation case, the size of correlation coefficients do not show significant variation across the level of and .

However, the size of correlation coefficients vary as we change the measures of accounting return. The value drops from 0.68 to 0.30 as we switch the accounting measure Operating Income to Earnings. Shoney's estimation results follow the similar patterns. The correlation coefficients are stable to the value of initial variance within each accounting measures, however, the level of coefficients are sensitive to the choice of accounting measures. Our results are robust regardless of whether we use the correlation coefficient method or the unit root test.

For our sample firms, we do not find the hard evidences supporting the co-movement between two betas. Either correlations are sensitive to the initial priors or to the choice of accounting measures. Therefore, we can conclude that market beta and accounting beta do not always yield the same measure of riskiness of capital although in past years the two betas have been treated as similar measures. One more implication of this result is that the market beta, which is estimated from stock return series, may reflect the variations in risk from debt-equity ratio changes, whereas the accounting beta, which is estimated from accounting returns, do not or at least not immediately measure the changes in financial risk. Although this study does not intend to attack the Modiglian-Miller theorem, our finding can serve as a small reference to the empirical meanings of the theorem.

4 Concluding Remarks Many financial economists have examined the co-movements of two measures, market beta and accounting beta, of a firm's systematic risk in order to seek the appropriate empirical counterpart. The existing literature in this field generally have focused on cross sectional similarities and sought informational differences of the two measures. Unlike the previous studies, this paper investigates the co-movements of the two betas along a firm's history by applying time-varying coefficient method. Time series data of highly leveraged firms are analyzed for emphasizing the effects of financial distress and leverage effects on stock return. We believe that individual firm level data have more information because each firm is unique in real world and using individual firm level data has advantages in controlling . Our estimation results suggest that market beta and accounting beta do not show co-movement when analyzed at the individual firm level. For all of our sample firms, the two measures show very weak and fragile correlation. Some apparent similarities disappear when we modify the estimation model specification or change the definition of accounting returns. Estimation results suggest that the leverage effects and financial distress from high debt-equity ratio cause the difference in movements of two risk measures. We hope that the results of this

study may extend the understandings in debt pricing and evaluation of a firm when appropriate stock return data are not available. Although this study provides some implications on this issue, it has room to be improved in several ways. First, the estimation results in this study are based on a rather small number of firms that experienced significant debt-equity ratio changes. This study applies the debt-equity structure model to relate the stock return and accounting statements. We do not believe that this leverage effects are the only source which causes the information differences in stock return and financial data. Thus, more serious and general theoretical models on connecting stock price and financial data are in need. Secondly, more challenging question would be to identify when the two risk measures show similarity and dissimilarity. We still do not have theory and hard evidences on this issue. However, our on-going work, which are not reported in this paper, on equity-only firms cases suggests that a firm with stable cash flow and financial structure show a relatively high correlation between the two measures. We think that this finding could serve as a starting point toward the second question.

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.25 0.18 0.13 0.094 0.066 0.043 0.024 0.0081 -0.0057 -0.0180.02 0.3 0.25 0.21 0.18 0.15 0.13 0.11 0.094 0.079 0.0660.03 0.31 0.28 0.25 0.22 0.2 0.18 0.16 0.15 0.13 0.120.04 0.32 0.29 0.27 0.25 0.23 0.21 0.19 0.18 0.17 0.150.05 0.33 0.3 0.28 0.26 0.25 0.23 0.22 0.2 0.19 0.180.06 0.33 0.31 0.29 0.28 0.26 0.25 0.23 0.22 0.21 0.20.07 0.33 0.32 0.3 0.29 0.27 0.26 0.25 0.24 0.22 0.210.08 0.33 0.32 0.31 0.29 0.28 0.27 0.26 0.25 0.24 0.230.09 0.33 0.32 0.31 0.3 0.29 0.28 0.27 0.26 0.25 0.240.1 0.34 0.32 0.31 0.3 0.29 0.28 0.27 0.26 0.25 0.25

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -1.8 -1.9 -2 -2.1 -2.1 -2.2 -2.2 -2.2 -2.2 -2.30.02 -1.8 -1.8 -1.9 -1.9 -2 -2 -2.1 -2.1 -2.1 -2.20.03 -1.8 -1.8 -1.8 -1.9 -1.9 -2 -2 -2 -2.1 -2.10.04 -1.8 -1.8 -1.8 -1.9 -1.9 -1.9 -2 -2 -2 -20.05 -1.8 -1.8 -1.8 -1.9 -1.9 -1.9 -1.9 -2 -2 -20.06 -1.8 -1.8 -1.8 -1.9 -1.9 -1.9 -1.9 -2 -2 -20.07 -1.8 -1.8 -1.8 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -20.08 -1.8 -1.8 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -20.09 -1.8 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -20.1 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -2 -2

Appendix Tables in the appendix report the correlation coefficients between accounting and market betas and the Dickey-Fuller t values of unit root test in equation (14). Note that six tables are reported for each firm because we employed three different accounting measures for calculating accounting beta and performed two different tests in order to compare the betas.

Table 1 : Correlation coefficients w/ Earnings : FMC Corp

Note: , are initial variances for measurement and transition equations.

Note: Earnings variable is used in the estimation of accounting betas.

Table 2 : Dickey-Fuller t-value w/ Earnings : FMC Corp



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.037 -0.02 -0.053 -0.074 -0.089 -0.099 -0.11 -0.11 -0.12 -0.120.02 0.079 0.028 -0.005 -0.029 -0.047 -0.061 -0.072 -0.081 -0.089 -0.0950.03 0.1 0.056 0.026 0.002 -0.016 -0.03 -0.043 -0.053 -0.062 -0.0690.04 0.12 0.076 0.047 0.025 0.0077 -0.0069 -0.019 -0.03 -0.039 -0.0470.05 0.13 0.09 0.064 0.043 0.026 0.012 -0.000 -0.011 -0.02 -0.0280.06 0.14 0.1 0.077 0.057 0.041 0.028 0.016 0.0053 -0.0038 -0.0120.07 0.14 0.11 0.088 0.07 0.054 0.041 0.029 0.019 0.01 0.00210.08 0.15 0.12 0.098 0.08 0.065 0.053 0.041 0.031 0.023 0.0150.09 0.16 0.13 0.11 0.09 0.075 0.063 0.052 0.042 0.034 0.0260.1 0.16 0.13 0.11 0.098 0.084 0.072 0.062 0.052 0.044 0.036

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -1.9 -1.9 -2 -2.1 -2.1 -2.2 -2.3 -2.3 -2.4 -2.40.02 -1.7 -1.7 -1.8 -1.8 -1.9 -1.9 -1.9 -2 -2 -2.10.03 -1.7 -1.6 -1.7 -1.7 -1.7 -1.8 -1.8 -1.8 -1.9 -1.90.04 -1.6 -1.6 -1.6 -1.6 -1.7 -1.7 -1.7 -1.7 -1.8 -1.80.05 -1.6 -1.6 -1.6 -1.6 -1.6 -1.6 -1.6 -1.7 -1.7 -1.70.06 -1.6 -1.5 -1.5 -1.6 -1.6 -1.6 -1.6 -1.6 -1.6 -1.70.07 -1.5 -1.5 -1.5 -1.5 -1.5 -1.6 -1.6 -1.6 -1.6 -1.60.08 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.6 -1.6 -1.60.09 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.60.1 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5

Table 3 : Correlation Coefficients w/ Operating Income : FMC Corp


Note: Operating Income variable is used in the estimation of accounting betas.

Table 4 : Dickey-Fuller t-value w/ Operating Income : FMC Corp



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.084 0.025 -.016 -.046 -.070 -.090 -.11 -.12 -.13 -.140.02 0.12 0.083 0.051 0.025 0.0029 -.016 0.032 -.047 -.059 -.0700.03 0.13 0.11 0.082 0.061 0.041 0.025 0.0095 -.0040 -.016 -.0270.04 0.13 0.12 0.099 0.081 0.065 0.05 0.037 0.024 0.013 0.00230.05 0.14 0.12 0.11 0.095 0.081 0.068 0.055 0.044 0.034 0.0240.06 0.14 0.13 0.12 0.1 0.092 0.08 0.069 0.059 0.049 0.040.07 0.14 0.13 0.12 0.11 0.099 0.089 0.079 0.07 0.061 0.0530.08 0.13 0.13 0.12 0.11 0.1 0.096 0.087 0.079 0.07 0.0630.09 0.13 0.13 0.12 0.12 0.11 0.1 0.093 0.085 0.078 0.0710.1 0.13 0.13 0.13 0.12 0.11 0.1 0.098 0.091 0.084 0.077

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -2.8 -3.1 -3.2 -3.3 -3.3 -3.4 -3.4 -3.4 -3.4 -3.40.02 -2.6 -2.9 -3 -3.1 -3.2 -3.2 -3.3 -3.3 -3.3 -3.40.03 -2.5 -2.7 -2.9 -3 -3.1 -3.1 -3.2 -3.2 -3.3 -3.30.04 -2.4 -2.7 -2.8 -2.9 -3 -3 -3.1 -3.1 -3.2 -3.20.05 -2.4 -2.6 -2.7 -2.8 -2.9 -3 -3 -3.1 -3.1 -3.20.06 -2.3 -2.6 -2.7 -2.8 -2.9 -2.9 -3 -3 -3.1 -3.10.07 -2.3 -2.5 -2.7 -2.8 -2.8 -2.9 -3 -3 -3.1 -3.10.08 -2.3 -2.5 -2.6 -2.7 -2.8 -2.9 -2.9 -3 -3 -3.10.09 -2.3 -2.5 -2.6 -2.7 -2.8 -2.8 -2.9 -2.9 -3 -30.1 -2.3 -2.4 -2.6 -2.7 -2.7 -2.8 -2.9 -2.9 -3 -3

Table 5 : Correlation coeffi챠ents w/ Fund Flow : FMC Corp


Note: Fund Flow variable is used in the estimation of accounting betas.

Table 6 : Dickey-Fuller t-value w/ Fund Flow : FMC Corp



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.25 0.18 0.13 0.094 0.066 0.043 0.024 0.0081 -0.0057 -0.0180.02 0.3 0.25 0.21 0.18 0.15 0.13 0.11 0.094 0.079 0.0660.03 0.31 0.28 0.25 0.22 0.2 0.18 0.16 0.15 0.13 0.120.04 0.32 0.29 0.27 0.25 0.23 0.21 0.19 0.18 0.17 0.150.05 0.33 0.3 0.28 0.26 0.25 0.23 0.22 0.2 0.19 0.180.06 0.33 0.31 0.29 0.28 0.26 0.25 0.23 0.22 0.21 0.20.07 0.33 0.32 0.3 0.29 0.27 0.26 0.25 0.24 0.22 0.210.08 0.33 0.32 0.31 0.29 0.28 0.27 0.26 0.25 0.24 0.230.09 0.33 0.32 0.31 0.3 0.29 0.28 0.27 0.26 0.25 0.240.1 0.34 0.32 0.31 0.3 0.29 0.28 0.27 0.26 0.25 0.25

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -1.8 -1.9 -2 -2.1 -2.1 -2.2 -2.2 -2.2 -2.2 -2.30.02 -1.8 -1.8 -1.9 -1.9 -2 -2 -2.1 -2.1 -2.1 -2.20.03 -1.8 -1.8 -1.8 -1.9 -1.9 -2 -2 -2 -2.1 -2.10.04 -1.8 -1.8 -1.8 -1.9 -1.9 -1.9 -2 -2 -2 -20.05 -1.8 -1.8 -1.8 -1.9 -1.9 -1.9 -1.9 -2 -2 -20.06 -1.8 -1.8 -1.8 -1.9 -1.9 -1.9 -1.9 -2 -2 -20.07 -1.8 -1.8 -1.8 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -20.08 -1.8 -1.8 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -20.09 -1.8 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -20.1 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -2 -2

Table 7 : Correlation coefficients w/ Earnings : Kroger



Table 8 : Dickey-Fuller t-value w/ Earnings : Kroger



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.037 -0.02 -0.053 -0.074 -0.089 -0.099 -0.11 -0.11 -..12 -..120.02 0.079 0.028 -0.005 -0.029 -0.047 -0.061 -0.072 -0.081 -0.089 -0.0950.03 0.1 0.056 0.026 0.0025 -0.016 -0.03 -0.043 -0.053 -0.062 -0.0690.04 0.12 0.076 0.047 0.025 0.0077 -0.0069 -0.019 -0.03 -0.039 -0.0470.05 0.13 0.09 0.064 0.043 0.026 0.012 -0.00023 -0.011 -0.02 -0.0280.06 0.14 0.1 0.077 0.057 0.041 0.028 0.016 0.0053 -0.0038 -0.0120.07 0.14 0.11 0.088 0.07 0.054 0.041 0.029 0.019 0.01 0.00210.08 0.15 0.12 0.098 0.08 0.065 0.053 0.041 0.031 0.023 0.0150.09 0.16 0.13 0.11 0.09 0.075 0.063 0.052 0.042 0.034 0.0260.1 0.16 0.13 0.11 0.098 0.084 0.072 0.062 0.052 0.044 0.036

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -1.9 -1.9 -2 -2.1 -2.1 -2.2 -2.3 -2.3 -2.4 -2.40.02 -1.7 -1.7 -1.8 -1.8 -1.9 -1.9 -1.9 -2 -2 -2.10.03 -1.7 -1.6 -1.7 -1.7 -1.7 -1.8 -1.8 -1.8 -1.9 -1.90.04 -1.6 -1.6 -1.6 -1.6 -1.7 -1.7 -1.7 -1.7 -1.8 -1.80.05 -1.6 -1.6 -1.6 -1.6 -1.6 -1.6 -1.6 -1.7 -1.7 -1.70.06 -1.6 -1.5 -1.5 -1.6 -1.6 -1.6 -1.6 -1.6 -1.6 -1.70.07 -1.5 -1.5 -1.5 -1.5 -1.5 -1.6 -1.6 -1.6 -1.6 -1.60.08 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.6 -1.6 -1.60.09 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.60.1 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5

Table 9 : Correlation coefficients w/ Operating Income : Kroger



Table 10 : Dickey-Fuller t-value w/ Operating Income : Kroger



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.084 0.025 0.016 -0.046 -0.07 -0.09 -0.11 -0.12 -0.13 -..140.02 0.12 0.083 0.051 0.025 0.0029 -0.016 -0.032 -0.47 -0.059 -0.070.03 0.13 0.11 0.082 0.061 0.041 0.025 0.0095 -0.004 -0.016 -0.0270.04 0.13 0.12 0.099 0.081 0.065 0.05 0.037 0.024 0.013 0.00230.05 0.14 0.12 0.11 0.095 0.081 0.068 0.055 0.044 0.034 0.0240.06 0.14 0.13 0.12 0.1 0.092 0.08 0.069 0.059 0.049 0.040.07 0.14 0.13 0.12 0.11 0.099 0.089 0.079 0.07 0.061 0.0530.08 0.13 0.13 0.12 0.11 0.1 0.096 0.087 0.079 0.07 0.0630.09 0.13 0.13 0.12 0.12 0.11 0.1 0.093 0.085 0.078 0.0710.1 0.13 0.13 0.13 0.12 0.11 0.1 0.098 0.091 0.084 0.077

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -2.8 -3.1 -3.2 -3.3 -3.3 -3.4 -3.4 -3.4 -3.4 -3.40.02 -2.6 -2.9 -3 -3.1 -3.2 -3.2 -3.3 -3.3 -3.3 -3.40.03 -2.5 -2.7 -2.9 -3 -3.1 -3.1 -3.2 -3.2 -3.3 -3.30.04 -2.4 -2.7 -2.8 -2.9 -3 -3 -3.1 -3.1 -3.2 -3.20.05 -2.4 -2.6 -2.7 -2.8 -2.9 -3 -3 -3.1 -3.1 -3.20.06 -2.3 -2.6 -2.7 -2.8 -2.9 -2.9 -3 -3 -3.1 -3.10.07 -2.3 -2.5 -2.7 -2.8 -2.8 -2.9 -3 -3 -3.1 -3.10.08 -2.3 -2.5 -2.6 -2.7 -2.8 -2.9 -2.9 -3 -3 -3.10.09 -2.3 -2.5 -2.6 -2.7 -2.8 -2.8 -2.9 -2.9 -3 -30.1 -2.3 -2.4 -2.6 -2.7 -2.7 -2.8 -2.9 -2.9 -3 -3

Table 11 : Correlation coefficients w/ Fund Flow : Kroger



Table 12 : Dickey-Fuller t-value w/ Fund Flow Kroger



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.82 0.81 0.81 0.81 0.81 0.81 0.8 0.8 0.8 0.80.02 0.82 0.82 0.81 0.81 0.81 0.81 0.81 0.8 0.8 0.80.03 0.82 0.82 0.81 0.81 0.81 0.81 0.81 0.8 0.8 0.80.04 0.82 0.82 0.81 0.81 0.81 0.81 0.8 0.8 0.8 0.80.05 0.82 0.82 0.81 0.81 0.81 0.8 0.8 0.8 0.8 0.80.06 0.82 0.81 0.81 0.81 0.81 0.8 0.8 0.8 0.8 0.80.07 0.82 0.81 0.81 0.81 0.8 0.8 0.8 0.8 0.8 0.790.08 0.81 0.81 0.81 0.81 0.8 0.8 0.8 0.8 0.79 0.790.09 0.81 0.81 0.81 0.8 0.8 0.8 0.8 0.79 0.79 0.790.1 0.81 0.81 0.8 0.8 0.8 0.8 0.79 0.79 0.79 0.79

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -2 -1.9 -1.9 -2 -2 -2.1 -2.2 -2.2 -2.3 -2.40.02 -2.1 -2 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -2 -20.03 -2.2 -2 -2 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -1.90.04 -2.2 -2.1 -2 -1.9 -1.9 -1.9 -1.9 -1.8 -1.8 -1.80.05 -2.2 -2.1 -2 -1.9 -1.9 -1.9 -1.8 -1.8 -1.8 -1.80.06 -2.2 -2.1 -2 -2 -1.9 -1.9 -1.8 -1.8 -1.8 -1.80.07 -2.2 -2.1 -2 -2 -1.9 -1.9 -1.8 -1.8 -1.8 -1.80.08 -2.2 -2.1 -2 -2 -1.9 -1.9 -1.8 -1.8 -1.8 -1.80.09 -2.2 -2.1 -2 -2 -1.9 -1.9 -1.8 -1.8 -1.8 -1.80.1 -2.2 -2.1 -2 -2 -1.9 -1.9 -1.8 -1.8 -1.8 -1.8

Table 13 : Correlation coefficients w/ Earnings : Owens



Table 14 : Dickey-Fuller t-value w/ Earnings : Owens



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -.062 0.054 0.11 0.14 0.17 0.19 0.2 0.22 0.23 0.240.02 -.14 0.024 0.11 0.16 0.2 0.23 0.25 0.27 0.28 0.30.03 -.21 -.022 0.085 0.15 0.2 0.24 0.27 0.29 0.31 0.320.04 -.27 -.070 0.053 0.13 0.19 0.23 0.27 0.29 0.32 0.330.05 -.32 -.12 0.018 0.11 0.18 0.22 0.26 0.29 0.32 0.340.06 -.36 -.16 -.018 0.083 0.16 0.21 0.25 0.29 0.31 0.340.07 -.39 -.20 -.055 0.054 0.13 0.19 0.24 0.28 0.31 0.330.08 -.43 -.24 -.090 0.024 0.11 0.17 0.23 0.27 0.3 0.330.09 -.45 -.28 -.12 -.0062 0.085 0.15 0.21 0.25 0.29 0.320.1 -.47 -.31 -.16 -.036 0.059 0.13 0.19 0.24 0.28 0.31

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.02 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.03 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.04 -2.9 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.05 -3 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.06 -3 -2.9 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.07 -3.1 -2.9 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.08 -3.2 -2.9 -2.8 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.09 -3.2 -3 -2.8 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7 -2.70.1 -3.3 -3 -2.9 -2.8 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7

Table 15 : Correlation coefficients w/ Operating Income : Owens



Table 16 : Dickey-Fuller t-value w/ Operating Income : Owens



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.88 0.87 0.87 0.86 0.86 0.85 0.85 0.85 0.84 0.840.02 0.88 0.88 0.87 0.87 0.87 0.87 0.86 0.86 0.86 0.860.03 0.88 0.88 0.88 0.87 0.87 0.87 0.87 0.87 0.87 0.860.04 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.87 0.87 0.870.05 0.88 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.87 0.870.06 0.89 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.87 0.870.07 0.89 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.87 0.870.08 0.89 0.88 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.870.09 0.89 0.88 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.870.1 0.89 0.88 0.88 0.88 0.88 0.88 0.87 0.87 0.87 0.87

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.40.02 -4.3 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.40.03 -4.2 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.40.04 -4.2 -4.3 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.40.05 -4.1 -4.3 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.40.06 -4.1 -4.3 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.40.07 -4.1 -4.2 -4.3 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.40.08 -4 -4.2 -4.3 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.40.09 -4 -4.2 -4.3 -4.4 -4.4 -4.4 -4.4 -4.5 -4.5 -4.50.1 -4 -4.2 -4.3 -4.4 -4.4 -4.4 -4.4 -4.5 -4.5 -4.5

Table 17 : Correlation coefficients w/ Fund Flow : Owens



Table 18 : Dickey-Fuller t-value w/ Fund Flow: Owens



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.89 0.89 0.89 0.89 0.88 0.88 0.87 0.87 0.86 0.860.02 0.88 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.88 0.880.03 0.87 0.88 0.89 0.89 0.89 0.89 0.89 0.89 0.89 0.890.04 0.86 0.88 0.88 0.89 0.89 0.89 0.89 0.89 0.89 0.890.05 0.85 0.87 0.88 0.88 0.89 0.89 0.89 0.89 0.89 0.890.06 0.85 0.87 0.87 0.88 0.88 0.89 0.89 0.89 0.89 0.890.07 0.84 0.86 0.87 0.88 0.88 0.88 0.89 0.89 0.89 0.890.08 0.84 0.86 0.87 0.87 0.88 0.88 0.88 0.89 0.89 0.890.09 0.84 0.85 0.86 0.87 0.88 0.88 0.88 0.88 0.89 0.890.1 0.83 0.85 0.86 0.87 0.87 0.88 0.88 0.88 0.88 0.89

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -3.9 -4 -4 -3.9 -3.8 -3.8 -3.7 -3.7 -3.6 -3.60.02 -3.6 -3.9 -4 -4 -4 -4 -4 -3.9 -3.9 -3.90.03 -3.5 -3.8 -3.9 -4 -4.1 -4.1 -4.1 -4.1 -4.1 -40.04 -3.3 -3.7 -3.9 -4 -4 -4.1 -4.1 -4.1 -4.1 -4.10.05 -3.3 -3.6 -3.8 -3.9 -4 -4.1 -4.1 -4.1 -4.2 -4.20.06 -3.2 -3.5 -3.7 -3.9 -4 -4 -4.1 -4.1 -4.2 -4.20.07 -3.2 -3.4 -3.6 -3.8 -3.9 -4 -4.1 -4.1 -4.2 -4.20.08 -3.1 -3.4 -3.6 -3.8 -3.9 -4 -4 -4.1 -4.2 -4.20.09 -3.1 -3.4 -3.6 -3.7 -3.8 -3.9 -4 -4.1 -4.1 -4.20.1 -3.1 -3.3 -3.5 -3.7 -3.8 -3.9 -4 -4.1 -4.1 -4.2

Table 19 : Correlation coefficients w/ Earnings : Shoney's



Table 20 : Dickey-Fuller t-value w/ Earnings : Shoney's



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.51 0.5 0.49 0.48 0.46 0.45 0.44 0.43 0.43 0.420.02 0.49 0.5 0.49 0.48 0.48 0.47 0.46 0.46 0.45 0.440.03 0.48 0.48 0.48 0.48 0.47 0.47 0.47 0.46 0.46 0.450.04 0.46 0.47 0.47 0.47 0.47 0.46 0.46 0.46 0.45 0.450.05 0.45 0.46 0.46 0.46 0.46 0.45 0.45 0.45 0.45 0.440.06 0.44 0.44 0.45 0.45 0.45 0.45 0.44 0.44 0.44 0.440.07 0.43 0.43 0.43 0.44 0.44 0.44 0.43 0.43 0.43 0.430.08 0.41 0.42 0.42 0.42 0.42 0.43 0.42 0.42 0.42 0.420.09 0.4 0.41 0.41 0.41 0.41 0.42 0.42 0.41 0.41 0.410.1 0.39 0.4 0.4 0.4 0.41 0.41 0.41 0.41 0.41 0.4

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -2.2 -2.2 -2.3 -2.3 -2.4 -2.4 -2.4 -2.4 -2.4 -2.50.02 -2.1 -2.1 -2.2 -2.2 -2.3 -2.3 -2.3 -2.3 -2.3 -2.40.03 -2 -2.1 -2.1 -2.2 -2.2 -2.2 -2.2 -2.3 -2.3 -2.30.04 -2 -2 -2.1 -2.1 -2.1 -2.2 -2.2 -2.2 -2.2 -2.20.05 -2 -2 -2 -2.1 -2.1 -2.1 -2.1 -2.2 -2.2 -2.20.06 -2 -2 -2 -2 -2.1 -2.1 -2.1 -2.1 -2.1 -2.20.07 -1.9 -2 -2 -2 -2 -2 -2.1 -2.1 -2.1 -2.10.08 -1.9 -1.9 -2 -2 -2 -2 -2 -2.1 -2.1 -2.10.09 -1.9 -1.9 -1.9 -2 -2 -2 -2 -2 -2.1 -2.10.1 -1.9 -1.9 -1.9 -1.9 -1.9 -2 -2 -2 -2 -2

Table 21 : Correlation coefficients w/ Operating Income : Shoney's



Table 22 : Dickey-Fuller t-value w/ Operating Income : Shoney's



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.9 0.9 0.9 0.89 0.89 0.88 0.88 0.87 0.87 0.860.02 0.9 0.9 0.9 0.9 0.9 0.9 0.89 0.89 0.89 0.890.03 0.89 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.890.04 0.89 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.90.05 0.89 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.90.06 0.88 0.89 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.90.07 0.88 0.89 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.90.08 0.88 0.89 0.89 0.9 0.9 0.9 0.9 0.9 0.9 0.90.09 0.88 0.89 0.89 0.9 0.9 0.9 0.9 0.9 0.9 0.90.1 0.88 0.89 0.89 0.9 0.9 0.9 0.9 0.9 0.9 0.9

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -3.4 -3.3 -3.2 -3.1 -3.1 -3 -3 -3 -3 -2.90.02 -3.3 -3.4 -3.4 -3.3 -3.3 -3.2 -3.2 -3.2 -3.1 -3.10.03 -3.3 -3.4 -3.4 -3.4 -3.4 -3.3 -3.3 -3.3 -3.2 -3.20.04 -3.2 -3.4 -3.4 -3.4 -3.4 -3.4 -3.4 -3.3 -3.3 -3.30.05 -3.2 -3.3 -3.4 -3.4 -3.4 -3.4 -3.4 -3.4 -3.4 -3.40.06 -3.1 -3.3 -3.4 -3.4 -3.4 -3.4 -3.4 -3.4 -3.4 -3.40.07 -3.1 -3.3 -3.3 -3.4 -3.4 -3.4 -3.4 -3.4 -3.4 -3.40.08 -3.1 -3.2 -3.3 -3.4 -3.4 -3.4 -3.4 -3.4 -3.4 -3.40.09 -3 -3.2 -3.3 -3.4 -3.4 -3.4 -3.4 -3.5 -3.5 -3.50.1 -3 -3.2 -3.3 -3.4 -3.4 -3.4 -3.4 -3.5 -3.5 -3.5

Table 23 : Correlation coefficients w/ Fund Flow : Shoney's



Table 24 : Dickey-Fuller t-value w/ Fund Flow : Shoney's



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.37 0.35 0.34 0.34 0.33 0.33 0.33 0.32 0.32 0.320.02 0.37 0.35 0.34 0.33 0.32 0.32 0.31 0.31 0.31 0.30.03 0.35 0.34 0.33 0.32 0.32 0.31 0.3 0.3 0.3 0.290.04 0.34 0.33 0.32 0.31 0.31 0.3 0.3 0.29 0.29 0.280.05 0.32 0.32 0.31 0.31 0.3 0.29 0.29 0.29 0.28 0.280.06 0.31 0.31 0.3 0.3 0.29 0.29 0.28 0.28 0.28 0.270.07 0.3 0.3 0.29 0.29 0.28 0.28 0.28 0.27 0.27 0.270.08 0.29 0.29 0.28 0.28 0.28 0.27 0.27 0.27 0.26 0.260.09 0.27 0.28 0.27 0.27 0.27 0.27 0.26 0.26 0.26 0.250.1 0.26 0.27 0.27 0.26 0.26 0.26 0.26 0.25 0.25 0.25

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -.99 -.84 -.83 -.87 -.94 -1.0 -1.1 -1.2 -1.2 -1.30.02 -1.2 -.95 -.85 -.81 -.79 -.79 -.81 -.83 -.86 -.890.03 -1.2 -1.1 -.93 -.86 -.81 -.79 -.77 -.77 -.77 -.780.04 -1.3 -1.1 -1.0 -.92 -.86 -.82 -.79 -.77 -.76 -.760.05 -1.3 -1.2 -1.1 -.97 -.91 -.86 -.82 -.80 -.78 -.760.06 -1.4 -1.2 -1.1 -1.0 -.95 -.90 -.86 -.83 -.80 -.780.07 -1.4 -1.2 -1.1 -1.0 -.98 -.93 -.89 -.85 -.83 -.800.08 -1.4 -1.3 -1.2 -1.1 -1.0 -.96 -.92 -.88 -.85 -.830.09 -1.4 -1.3 -1.2 -1.1 -1.0 -.99 -.94 -.91 -.87 -.850.1 -1.4 -1.3 -1.2 -1.1 -1.1 -1.0 -.96 -.93 -.89 -.87

Table 25 : Correlation coefficients w/ Earnings : Swank



Table 26 : Dickey-Fuller t-value w/ Earnings : Swank


＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.67 0.67 0.67 0.66 0.66 0.65 0.65 0.64 0.64 0.630.02 0.67 0.68 0.68 0.67 0.67 0.67 0.67 0.67 0.66 0.660.03 0.67 0.68 0.68 0.68 0.68 0.68 0.67 0.67 0.67 0.670.04 0.66 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.67 0.670.05 0.66 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.670.06 0.65 0.67 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.680.07 0.63 0.67 0.68 0.68 0.68 0.68 0.68 0.68 0.68 0.670.08 0.62 0.67 0.67 0.68 0.68 0.68 0.68 0.68 0.67 0.670.09 0.61 0.66 0.67 0.68 0.68 0.68 0.67 0.67 0.67 0.670.1 0.59 0.65 0.67 0.67 0.67 0.67 0.67 0.67 0.67 0.67

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -3.5 -3.1 -3 -3 -2.9 -2.9 -2.9 -2.9 -2.8 -2.80.02 -3.9 -3.4 -3.1 -3 -3 -2.9 -2.9 -2.9 -2.8 -2.80.03 -4.3 -3.6 -3.3 -3.1 -3 -2.9 -2.9 -2.9 -2.8 -2.80.04 -4.6 -3.8 -3.4 -3.2 -3 -3 -2.9 -2.9 -2.8 -2.80.05 -4.9 -3.9 -3.5 -3.2 -3.1 -3 -2.9 -2.9 -2.8 -2.80.06 -5 -4.1 -3.6 -3.3 -3.1 -3 -2.9 -2.9 -2.8 -2.80.07 -5.1 -4.2 -3.7 -3.4 -3.2 -3.1 -3 -2.9 -2.8 -2.80.08 -5.1 -4.3 -3.8 -3.5 -3.2 -3.1 -3 -2.9 -2.8 -2.80.09 -5.1 -4.4 -3.9 -3.5 -3.3 -3.1 -3 -2.9 -2.9 -2.80.1 -5.1 -4.5 -4 -3.6 -3.4 -3.2 -3.1 -3 -2.9 -2.8

Table 27 : Correlation coefficients w/ Operating Income : Swank



Table 28 : Dickey-Fuller t-value w/ Operating Income : Swank



＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 0.43 0.41 0.39 0.38 0.36 0.35 0.34 0.33 0.32 0.310.02 0.47 0.45 0.44 0.43 0.42 0.41 0.4 0.39 0.39 0.380.03 0.49 0.48 0.46 0.45 0.45 0.44 0.43 0.43 0.42 0.410.04 0.51 0.49 0.48 0.47 0.46 0.46 0.45 0.45 0.44 0.430.05 0.53 0.51 0.5 0.49 0.48 0.47 0.46 0.46 0.45 0.450.06 0.54 0.52 0.5 0.5 0.49 0.48 0.47 0.47 0.46 0.460.07 0.54 0.52 0.51 0.5 0.49 0.49 0.48 0.48 0.47 0.470.08 0.55 0.53 0.52 0.51 0.5 0.49 0.49 0.48 0.48 0.470.09 0.55 0.53 0.52 0.51 0.5 0.5 0.49 0.49 0.48 0.480.1 0.55 0.54 0.52 0.51 0.51 0.5 0.49 0.49 0.48 0.48

＼ 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.01 -0.2 0 -0.9 -0.8 -0.7 -0.7 -0.7 -0.6 -0.6 -0.60.02 0 -0.9 -0.8 -0.7 -0.6 -0.6 -0.5 -0.5 -0.5 -0.40.03 -0.8 -0.7 -0.6 -0.6 -0.5 -0.4 -0.4 -0.3 -0.3 -0.30.04 -0.6 -0.6 -0.5 -0.4 -0.4 -0.3 -0.3 -0.2 -0.2 -0.10.05 -0.4 -0.4 -0.4 -0.3 -0.3 -0.2 -0.2 -0.1 -0.1 00.06 -0.2 -0.3 -0.2 -0.2 -0.1 -0.1 -0.1 0 0 -0.90.07 -0.1 -0.1 -0.1 -0.1 -0.1 0 0 -0.9 -0.9 -0.90.08 0 0 0 0 0 -0.9 -0.9 -0.9 -0.8 -0.80.09 -0.8 -0.9 -0.9 -0.9 -0.9 -0.9 -0.8 -0.8 -0.8 -0.70.1 -0.7 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.7 -0.7 -0.7

Table 29 : Correlation coeffients w/ Fund Flow : Swank



Table 30 : Dickey-Fuller t-value w/ Fund Flow : Swank



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Ismail, B. E., and Kim, M. K., "On the Association of Cash Flow Variables with Market Risk", The Accounting Review, Jan. 1989, 54, 125-136. Kaplan, S. N., and Stein, J. C., "How Risky is the Debt in Highly Leveraged Transactions?", Journal of Financial Economics, Sep. 1990, 27, 215-245. Kaplan, S. N., and Stein, J. C., "The Evolution of Buyout Pricing and Financial Structure in the 1980s", Quarterly Journal of Economics, 1993, 108, 313-357. Karels, G. V., and Sackley, W. H., "The Relationship Between Market and Accounting Betas for Commercial Banks", Review of Financial economics, Spring 1993, 2, 59-72. Lee, C. F., Newbold, P., and Finnerty, J. E., "On Accounting-Based, Market-Based and Composite-Based Beta Prediction: Methods and Implications", Financial Review, Feb. 1986, 21, 51-68. Lutkephol, H., Introduction to Multiple Time Series Analysis, New York: Springer-Verlag, 1991.

A Study Relation Between Market Beta And

Documents

fund flow

fund flow

operating

operating

unit root

stable cash

perform cointegration

stock return