RATIONAL ASSET PRICING: BOOK-TO-MARKET EQUITY AS A PROXY FOR RISK IN UTILITY STOCKS. Brian J. Fratus

Transcription

1 RATIONAL ASSET PRICING: BOOK-TO-MARKET EQUITY AS A PROXY FOR RISK IN UTILITY STOCKS by Brian J. Fratus Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of MASTER OF ARTS in Economics APPROVED: '6a~id Meiselman, Chairman Russell Porter Na y Wentz}er April 1994 Falls Church, Virginia

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3 RATIONAL ASSET PRICING: BOOK-TO-MARKET EQUITY AS A PROXY FOR RISK IN UTILITY STOCKS by Brian J. Fratus Committee Chairman: David Meiselman Economics (ABSTRACT) Previous research has shown that the asset pricing model of Sharpe 1 Litner and Black fails to capture the relationship between market ~ and average return. This previous work showed that the relationship between ~ and average return was flat. Subsequently it was shown that a strong relationship between book-to-market equity and stock price returns existed. It has also been shown that book tomarket equity has strong roots in economic fundamentals. Utilities have historically used betas to justify rate increases 1 developing rate structures that meet the rate of return demands for investors given the risk profiles that the company betas suggest. Realizing that low betas argue against large rate increases 1 utilities have turned to other avenues to justify higher returns.

4 The suggested relationship of book-to-market equity and average stock returns would provide utilities with a new argument. This thesis will show that the search for a risk proxy in the rate of return relationship for the electric utility is not resolved. The relationship reported between book-to-market equity and stock price returns does not appear to be statistically significant in the electric utility sector and extreme caution is advised in using this empirical model to predict or explain stock price returns.

5 ACKNOWLEDGMENTS I thank Dr. David Meiselman, Dr. Russell Porter and Dr. Nancy Wentzler for their guidance and comments during the development and in the final review of this thesis. My sincerest appreciation is given to: Dr. James Jordan of the Finance department, in whose quantitative finance course I learned the background of the theory that inspired me to pursue the subject matter in this thesis and whose considerable time was spent assisting me through the data retrieval process. Christine Spriggs 1 my former secretary and friend who helped bring this study into its final form. Lastly, but with love, to my wife Carolyn who has endured this study and graduate program since the beginning and has given much appreciated support. iv

6 TABLE OF CONTENTS Page ACKNOWLEDGMENTS LIST OF ILLUSTRATIONS LIST OF TABLES iv vi vii I. INTRODUCTION 1 II. III. IV. BACKGROUND SCOPE OF STUDY METHODS OF ANALYSIS v. RESULTS 36 VI. VII. VIII. VITA CONCLUSIONS SOURCES CITED REFERENCES v

7 LIST OF ILLUSTRATIONS I. Possible Outcomes of Two Independent Asset Returns II. Variability of Returns Over Time III. The Efficient Frontier IV. The Capital Market Line 13 V. The Security Market Line 14 VI. CAPM Theory Versus Fama and French Beta Results 22 vi

8 LIST OF TABLES I. 90 Day Annual Average Treasury Bills II. Time Series Betas and t Ratios for Electric Util ies III. Cross Section Regression Results: Market Equity and Book-to-Market Equity Ratios for Electric Utilities vii

9 I. INTRODUCTION Two recent working papers produced at the University of Chicago's Center for Research Security Prices by Eugene Fama and Kenneth French suggest that the Sharpe, Litner and Black (SLB) capital asset pricing model fails to capture the relationship of market risk and average market returns in stock prices. Fama and French show that the data periods of the empirical work that supported the previous findings of the SLB model were an anomaly and that the relationship demonstrated by the SLB model in those tests fails to show similar results when tested over the last fifty years. Specifically the SLB model fails to demonstrate any significant relationship between market risk and average market returns over the period from This work has posed a serious challenge to the enduring idea that stocks more volatile than the market as a whole are the best performers. That is to say that the premise of risk related to return, and that the higher the risk or volatility in price then the higher the expected return, is being challenged by the empirical results yielded in the Fama and French tests. Exhibit I shows 1 risk and expected return

10 EXHIBIT I Possible Outcomes of Two Independent Assets Q) E 0 u +-' ::J 0 50% I I I I A /Less Risky (Variance smaller) -0 >- ;=:.n CJ) CJ) % // ""\. ~H [\) 0 10% 20% 30% 40% Expected Rate of Return

11 profiles for two individual stocks contrasting the 3 probabilities of each achieving the expected returns. This is not the first academic shot at the capital asset pricing model (CAPM) and its underlying concept of beta as a proxy for risk but it is now viewed as the most conclusive evidence against beta. 2 The SLB model is built around the concept that a proxy for risk, beta, is the primary explanatory variable in predicting stock price returns. The model suggests that risk beyond market risk or nondiversifiable risk is captured in the variable beta and the volatility of this variable relative to the market determines the riskiness and thus the required returns of investors. Exhibit II shows the path of variation between two independent stocks returns with different betas over time; C and D are correlated oppositely and B represents the market average return. This beta variable is represented for each individual asset on the security market line in the standard capital asset pricing model: 3

12 This one factor model where: 4 E(r) the expected return of the individual asset the risk free rate of return on a risk free asset = the beta coefficient and risk proxy for the asset the market return proxied by a market index portfolio The SLB model suggests the returns of an individual asset are driven by the risk or beta coefficients in the model. The betas are estimated for the individual assets by regressing the rf and Rm - rf factors on the returns of the individual firms. As mentioned earlier Fama and French found this relationship between beta and returns to be statistically weak. Fama and French in their paper "The Cross Section of Expected Stock Prices 11 showed that the variables of size (market equity) and book-to-market equity combined to capture the cross sectional variation in average stock returns. These two variables: the book value of the firm, which is the book equity less the deferred taxes value of the firm, as reported in the firms' annual financial statements and the size or market equity, the market value of the firm derived by multiplying the number of shares

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14 6 outstanding times the share trading price, are suggested to explain the relationship between returns and risk. The tests showed that the relationship between market beta and average market returns of stock prices was flat rather than the linear positive sloping notion held by investors and theoretically supported by CAPM, that increased volatility or risk was associated with increased returns. Fama and French suggest that the use of beta as a proxy for risk ls to explain the relationship of returns in their empirical tests. 4 In their first paper Fama and French demonstrated how leverage and earnings per share are absorbed within the variables of size and book-to-market equity. The results demonstrated that there existed a significant negative relationship between size and average returns, but controlling for size, there was no relationship between ~ and average return. The more significant relationship that was demonstrated in the cross-sectional variations was that between average returns and book-to-market equity. Fama and French find that there are indeed size and book-to-market factors in earnings that parallel those in stock returns. Admittedly they state the fundamentals of the analysis rests with accounting measures which are flawed. They sought the

15 7 best measures of returns, total book assets and book common equity. The results show the combined message that strong earnings and strong growth in earnings and assets are persistent properties of low book equity to market equity firms. They inferred that the market consistently rewards firms who have strong earnings with high stock prices, low expected returns on equity and low costs of capital. Conversely those firms with low earnings tend to have high book to-market ratios, low stock prices relative to book value, higher expected returns and higher costs of capital. Fama and French's conclusions were: 5 a) Beta does not explain the cross section of average stock returns, b) Market equity (ME) and book-to-market equity ratios (BE/ME) in combination absorbs the role of leverage and the earnings price ratio (E/P} at least during the period Although market size (market equity as defined above) has captured more attention in previous studies it is the market-to book equity ratios that Fama and French report to have the stronger statistical significance and explanatory

16 power in the cross section regression tests on average 8 returns of stock prices. If assets are priced rationally then the stock risks are multi-dimensional-one dimension of risk is proxied by size or market equity and another is proxied by book-to-market equity ratios. In their second paper "The Economic Fundamentals of Size and Book-to-Market Equity" Fama and French showed that ze and book-to-market equity have strong roots in economic fundamentals. They demonstrated that high book-to-market equity (low stock price relative to book value) is associated with sustained low earnings on book equity. 6 Why the Utility Sector Focus? Regulatory practice has traditionally been based on the premise of a correctly prescribed rate of return enabling a utility to sell s stock at book value. 7 These tests pose an interesting opportunity for the utility industry. Investors have demanded relatively low rates of return from this industry sector because the perceived sk was low compared to market risk. Fama and French have shown that there is no significant relationship between market ~ (risk) and average market returns. Exhibit III shows how the CAPM and its predecessor portfolio theory by Markowitz portray

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18 10 the risk-return relationship of assets along an optimum efficiency frontier, a curve trading off more risk for higher returns. 8 Utilities have been seeking opportunities to separate their regulated return prescription associated with the SLB model theory of low beta and low expected return. The suggested relationship of book-to-market equity and stock price performance would give the utility industry an argument against CAPM and enable it to seek ways to increase its market return by divorcing itself from the beta risk proxy. As with Fama and French's results, this thesis demonstrates a statistically insignificant relationship between average stock returns and beta; however, in testing the utility sector the results of this thesis show a stronger but statistically insignificant relationship between book-to-market equity and average stock returns whereas Fama and French report this former relationship to be statistically significant. However, as this thesis documents, the strength of this new model seems to lack empirical substance in tests of the electric utility sector. The results in this thesis are

19 11 also supported by a brief paper and journal article summarizing some recently completed empirical tests on the utility sector by two professors of finance, Frank Bacon and Joe Lavley, who used similar regression models as Fama and French to verify Fama and French's suggested relationship between stock returns and book-to-market equity Lavely and Bacon tested a five year period of with quarterly data from Value Line using two separate univariate equations containing beta and market size as independent variables and average returns as the dependent variable. They then combined these variables in a multivariate equation with the book-to-market equity ratio as a third independent variable and performed further seemingly unrelated regressions on the equation sets. Their results as previously stated demonstrated no statistically significant relationship between any of the independent variables and average stock returns.

20 II. BACKGROUND The traditional capital asset pricing model {CAPM} developed in the 1960's by economists William Sharpe and John Litner with subsequent forms by Fisher Black, now known as the SLB model, posed the theory that volatility of a firm's risk profile was proportional to its expected stock price return. This premise is shown graphically in Exhibits IV and V depicting the capital market line and the CAPM model security market line (SML). 11 Exhibit V shows the upward sloping "Security Market Line" (SML) the linear relationship between a firm's risk~ representing relative to market risk and the expected return. The vertical axis of expected returns shows that the SML intercept is at Rf. Rf is a risk free investment, which is usually associated with treasury bills, and the horizontal axis is a measure of a firm's risk or~ and the expected returns increase with an increase in beta. It is this traditionally accepted model that has been the basis for the rate of return structure for the utility industry. The Markowitz model of sk profiles and the efficient frontier developed in 1952, preceded the development and 12

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22 Expected Return on Investment EXHIBIT V The Capital Asset Pricing Model (CAPM) Rm Market Return Rr I~ Risk-free Return ~Treasury bills I Security Market Line ~ : ~ Market Portfolio I 1-1 ~ 1.0 B The Capital Asset Pricing Model shows the positive linear relationship between market risk and expected returns.

23 15 formed the foundation for the CAPM. The efficient frontier is mean-variance efficient for assets in the portfolio. The boundary of the efficient frontier is the optimum line for assets at various levels of risk. Each asset has its own risk profile and expected future returns and variance for those expected returns. The capital asset pricing model was developed as a simplified practical use of the Markowitz model of efficient portfolio theory. The CAPM is a logical extension of modern portfolio theory intuitively and mathematically. A simplified application correlates each asset's return with the returns of a weighted average index of all assets, such as the Standard and Poor's 500 or the Value Weighted Index of the Chicago Center for Research in Security Prices (VWCRSP) which is used as a proxy for the market in the Fama and French study and in this similar study as applied to the utility industry. This simplified process gives the same risk ranking as the Markowitz portfolio method of meanvariance efficiency. The CAPM uses a weighted average benchmark index for calculating correlation and uses this proxy as the market value-weighted portfolio of all possible investments. This market value weighted portfolio is the market portfolio. 12

24 16 The CAPM also introduces the risk free asset {Rf) as shown in Exhibit IV and proxied by 90 day treasury bills in Exhibit V's graphical depiction of CAPM. This theoretical risk free asset has zero variance and zero covariance-no risk. The risk free asset as shown in Exhibits IV and V lies on the y-axis providing a small positive return in exchange for the investors illiquidity. The risk free asset allows the creation of a new and more efficient frontier, the assets on this positive linear slope shown in Exhibit IV provides more return for the same risk-this is the capital market line, RfZ. This is the risk return trade off line for investors with optimally efficient assets or portfolios. Table I shows the annual average 90 day t-bill rates for , the period that this thesis tested. The rates in this table were used in the capital asset pricing model shown below, to derive the individual utility betas. The definition of risk in CAPM is the covariability of the asset s returns with the market returns. In other words 1 we can say that risk is the volatility of the security's returns relative to the volatility of the market portfolio 1 s returns. Risk that is firm specific or non-market risk can be diversified away. The risk that can be eliminated is called non-systematic risk, it is specific to the particular

25 17 TABLE I Annual Average Rate 90 Day Treasury Bills

26 18 asset. Investors require compensation for risks that cannot be diversified away. These systematic or market risks are factors in the expected returns and pricing of all assets. The CAPM designates systematic sk as beta, $. The beta of the market is defined as 1.0. Assets with betas less than 1.0 are said to have variances in their expected returns less than the market as a whole while assets with betas greater than 1.0 represent assets with variances in expected returns greater than the market as a whole. Beta =..;;;;;C..;;:o'""""v'-"a=r;;;;_;;;;:;.i=a=n;;...;;;c;...;;e;;;_""""'( R= 1rn.t-Rjl Variance m Where: Rm Rj = expected returns from the market portfolio expected returns from a given asset covariance Rm, Rj = [correlation j,m] (standard deviation of Rm) (standard deviation Rj) ] rn Market The CAPM formula for determining the expected returns for a given asset is:

27 19 Where; Rj return from the asset or portfolio Rf = return from the risk free security Rm return from the market ~j volatility of the asset or portfolio relative to that of the market m In Exhibit V the solid positive sloping line is the security market line-the plot of the risk and returns of assets that make up the market portfolio. This line is the trade off for systematic risk and return for each asset. Beta serves as a proxy for risk in the CAPM derived from the covariance matrices resulting from the above equation for beta. As stated above, the capital asset pricing model defines risk explicitly as the volatility of an asset's returns relative to the volatility of the market portfolio's returns. Utilities have historically had low betas which has kept the rate of return allowed relatively low compared with other market investment opportunities. Utilities periodically seek rate increases to boost their earnings which in turn raises the stock price albeit only for short periods, and their returns to investors. However, frequently they are denied increases and have been confronted with stagnant earnings growth and stock prices.

28 20 Their low market betas have resulted in low expected returns for investors. Recent events involving legislative actions and the increasing competition in electric generation coupled with consumer demand side management will cause structural changes in the rate setting and regulated return process but at present the industry is controlled by the decades old regulated return structure. Richard Roll demonstrated that the average returns of low-beta stocks are higher than CAPM predicts and that high beta stocks yielded returns that were lower than the model would suggest. It has led to the notion that there is some other variable that truly determines the expected returns demanded by investors. 13 If Roll is correct then the rate of return prescription for utilities tied to beta is likely to be in error and when empirically tested will show a weakly correlated, statistically insignificant relationship. The basic model equation of CAPM: E(r) =rt+,b[e(rm) - rt] Implies that the expected return E(r) equals the risk free return rt plus the firm's,8 coefficient for risk multiplied by the difference between the market portfolio's return Rm and the risk free return. The market portfolio or

29 21 index proxy is often one such as the Standard and Poor's 500 market average return index. Fama and French demonstrated that the relationship represented in this equation lacks statistical significance. See Figure VI showing the graphical contrast of the CAPM theory and the Fama and French empirical tests. 14 The pattern of results from the Fama and French cross-sectional tests of variation between market beta and average returns shows no correlation exists between the variable ~ and average returns for the period and the fifty year period of demonstrates a very weak relationship. In fact the relationship only demonstrates statistical significance for the 25 year period of , the years that are the major sample periods in the earlier studies of the SLB model. 15 This empirical result has led to the search for variables that better describe the relationship between risk and stock returns. Several previous studies have criticized the SLB model when empirically tested. One study by Rolf Banz focusing on the relationship between return and market value (1981), showed that market equity (price times shares outstanding) adds to the explanation of the cross-section of returns provided by market ~'s. He found that average returns on

30 Expected Return on Investment EXHIBIT VI CAPM Theory Compared to Fama and French Results 20% Linear relationship of the theory of CAPM ~ 10% Rf,, / / / / / _/ \ Pattern of results in Fama and French Empirical Tests ' \. ' \. ' l\j l\j a Increasing beta or relative volatility... JI"'

31 23 low market equity stocks are too high given the beta estimates and too low on large market equity stocks. 16 Indeed this size affect which is a negative relationship between market equity and average returns was confirmed in Fama and French's paper on the cross-section of stock returns. They demonstrated that the size effect was statistically stronger than the relationship between market beta and average returns. Subsequent to Banz's study Bhandari found that leverage helps explain returns in tests that contained size factors as well as ~. 17 This seemed to contradict the SLB model which should capture leverage within the market beta variable. In addition to these results Dennis Stattman at the University of Chicago independently found that average returns on U.S. stocks are positively correlated with their ratio of book value of common equity and their market equity. These results were supported in future tests by Barr Rosenberg, Kenneth Reid and Ronald Lanstein in their studies of market inefficiency. 18 Finally, Sanjoy Basu showed that earnings-price ratios (E/P) help explain the cross-section of average returns on U.S. stocks in tests that also include market equity (size) and market ~. 19 Fama and French demonstrated in the tests that the combination

32 24 of size and book to-market equity seems to absorb the roles of leverage and E/P in average stock returns. 20

33 III. SCOPE OF STUDY This thesis seeks to test the cross-sectional results of Fama and French in a specific industry, the electric ut ity industry, that has significant reliance on the previously accepted rate of return model CAPM. The utility industry sector would seem to be a good test for the replication of Fama and French's results. The CAPM has been used since the 1960's to determine an appropriate rate return for a utility stock. This industry is currently seeking alternative measures for its regulated return policy which is currently based on the SLB capital asset pricing model. This thesis will seek to show the measure of volatility in the returns that captures the relationship between average returns of utility stocks and their book tomarket equity ratios. As Fama and French implied the accounting measures are subject to skepticism but they found that the variables of total books assets (A) and book common equity {BE) were the best measures for testing their hypothesis. The inflation-adjusted measures of book assets and common equity are not generally available but this is 25

34 26 not a serious problem unless the inflation feet differs systematically across firms. 21 This thesis covers much of the same historical period as Fama and French but focuses specifically on the results of individual firms in the electric utility industry rather than the aggregate results of many firms in market size groupings. Fama and French 1 s study comprises all the firms in the New York stock exchange, the American stock exchange beginning in 1963 and NASDAQ as of The firms were ranked and sorted in ten groups by market size. The roles of market size and book-to-market equity were tested in aggregate and reported according to market size. The Fama and French tests suggested that the role of market size was significant but the combined role of book to-market equity was even stronger. This thesis tests the same variables in an individual firm context and within the single industry of electric utilities using a two stage time series measure of volatility.

35 IV. METHODS OF ANALYSIS Data was obtained for the monthly returns of all firms in the University of Chicago 1 s Graduate School of Business Center for Research in Security Prices (CRSP) data base. The period of evaluation was from , a twenty year period, whereas Fama and French tested the period as the primary focus of their study. The electric utility sector contained data on over one hundred firms, but when the data was merged with that of the industrial files of income statement and balance sheet data from the Compustat data base containing the annual financial statement results for the firms, a net 73 firms remained with apparently reliable data for all or nearly all of twenty year period Still, this sample size of firms and duration the stat testing period should be sufficient to capture ical relationship between the roles of the market equity and book-to-market equity variables, and average stock returns for utilities. The CRSP data of monthly returns for individual firms was annual averaged and regressed against the VWCRSP 27

36 28 market index less the risk free rate of return where the 90 day treasury bill rate was used as a proxy. The resulting beta represents a proxy for the firm's risk after apportioning the system or nondiversifiable risk. The CAPM model equation was used to derive the beta results for the second stage regression tests. The annual average 90 day t-bill rates for the period were used to develop the time series betas for the second stage model that tests the roles of size (market equity} and book-to-market equity. The regression equation for the time series betas is: where; Ri-rf + Bi(Rm- } + ui Ri Return on asset i; the stock returns of utility i rate of return on risk free security ai Bi intercept in the model* Beta coefficient for regression on asset i's returns ui = the residual error in the regression on asset i's returns * the CAPM model theory has been tested both with and without the intercept at the origin-the results are very similar.

37 29 Whereas Fama and French estimated betas for portfolios and then assigned the portfolio betas to each stock, the betas in this thesis were individually estimated for each utility. First and second order autocorrelation corrections by Cochran Orcutt methods produce trivial changes the betas. As with Fama and French's tests the simpler betas are used in the subsequent tests of market equity and bookto-market equity on average stock returns. The betas are shown in Table II for the individual firms in the thesis. The models were constructed realizing the accounting variables are known before the returns that they are supposed to explain. The second stage models were developed by lagging the independent market variables by a 6 month period, July of year t to June of year t+l, following the Compustat financial statement results for the period of year t-1, of common book equity, deferred taxes on the balance sheet, outstanding number of shares and year end share prices. Thus the market data used June end dates for shares outstanding and share prices to determine size or market equity, which is the number of outstanding shares times the share price at the June end date closing price. The bookto-market ratios are comprised of income statement and balance sheet data at the end of the year t-1.

38 30 TABLE II Time Series Betas and t ratios for Twenty Year Period ( ) by Utility Perm# Intercept VW Beta VW Std E t ratio * * denotes significant t ratios at the.05 level for 19 degrees of freedom.

39 ! 31 TABLE II Time Series Betas and t ratios for Twenty Year Period ( ) by Utility I I Perm# I Intercept I VW Beta I VW Std E I t ratio I '

40 I I TABLE II Time Series Betas and t ratios for Twenty Year Period ( ) by Utility Perm# I Intercept I VW Beta I VW Std E I t ratio I * * denotes significant t ratios at the.05 level for 19 degrees of freedom

41 33 The independent variables were constructed in the regression models in the same manner tested by Fama and French, that is the natural log of the market equity and book-to-market equity variables were used in conjunction with the beta estimates and regressed against the dependent variable of monthly average annual returns of firm (I) where firm (I) represents each individual firm the electric utility sector. Fama and French noted that preliminary tests show that natural logs are a good functional form for capturing the effects on average returns. 23 This lin-log format of the regression model below measures the absolute change in the expected returns for a given period and change in market equity and the book-to-market equity ratio. The model for the hypothesis to test; whether the roles of market equity (lnme} and book-to-market equity (lnbe/me) are statistically significant in a multivariate regression test on average stock price returns for the electric utility sector is shown below. Model: Rit Where; a = monthly average annual returns for utility {i) in year t intercept coefficient for utility (i)

42 34 (3 Beta coefficient from first pass time series regressions on average monthly returns for utility (i) Log of market equity for utility (i} in year t Log of ratio of common book equity to market equity for utility (i) in year (t) The model is a second stage time series regression measuring the volatility of the beta coefficients and the market equity and book to-market equity variables for individual utilities over the twenty year period. With the relatively few firms compared with the Fama and French study, the aggregate portfolio approach, i.e., splitting the firm into deciles by market size would not leave enough firms in each grouping to produce robust results. This second stage method is a practical approach for measuring the explanatory power of the variables in an individual firm context. The second stage regressions were tested for the statistical significance in accepting or rejecting the null hypothesis that there is a statistically significant relationship between expected returns and book-to market equity as well as market equity. The equations' variables

43 35 for market equity and book-to-market equity were individually tested for significant t-ratios at the.05 significance level for 17 degrees of freedom, having three independent variables in a twenty-year regression test. The resulting ordinary least squares regressions were compared for the statistical significance in support of the null hypothesis; that the roles of market equity and book-to-market equity were statistically insignificant, i.e., that the coefficients were not statistically different from zero.

44 V. RESULTS As in Fama and French's tests on the role of beta in explaining stock price returns the empirical evidence is lacking. The statistical significance of the beta regressions is very weak and even when tested in the univariate form the beta regression models fail to show any significant explanatory power. This empirical result led Fama and French to conclude that the previous positive results Fama and Macbeth obtained earlier, and that were consistent with the results that have been the basis of CAPM and Sharpe, Linter and Black's model structure, were produced in a period where the data had a bias in its historical context. The period tested in this thesis , yields the same result as in Fama and French's tests and their test. Again, in the Fama and French tests only the period produced results that support, although rather weakly according to Fama and French, the positive linear relationship between sk {beta) and stock price returns. 36

45 37 However, the focal point of this thesis and the departure point of agreement with Fama and French's testing concerns the role of market size and book-to-market equity in explaining the relationship between risk and average returns. Fama and French in testing the extremely large sample of over 2000 stocks find that when jointly tested that market size and book-to-market equity ratios have statistically significant explanatory power in the regressions formulated on market size portfolios. In individual two stage time series tests of firms in the utility sector, the scope of this thesis, there was no evidence that market size or book-to-market equity ratios are a good proxy for risk in the relationship with average stock price returns. In the sample of firms remaining after poor data sets were eliminated only seven firms in seventysix had significant t ratios at the.os level of significance for a two tail test. The book-to-market equity results, which Fama and French reported were even stronger than the market size variable in explaining the relationship of risk and market returns, showed only nine of the seventysix firms tested having a statistically significant result at the same.os level. These results are shown in Table III.

46 TABLE Ill Book-to-Market Equity as a Proxy for Risk in Utility Stocks Stage Two Regression Results VW BETA # PERM# Intercept Coeff. Ln ME Ln BE/ME Ln ME Ln BE/ME Ln ME Coeff. Coe ff. Std Err Std Err t ratio Ln BE/ME t ratio R Sqrd Adjusted R Sqrd F Stat O.Q O.Q O.Q * * w Q O.Q O.Q O.D * O.Q *denotes significantt ratios at the.05 level for 17 degrees of freedom and n=20 and k=4 for F

47 TABLE Ill Book-to-Market Equity as a Proxy for Risk in Utility Stocks Stage Two Regression Results VWBETA # PERM# Intercept Coeff. Ln ME Ln BE/ME Ln ME Ln BE/ME ln ME Coeff. Coeff. Std Err Std Err t ratio ln BE/ME t ratio R Sqrd Adjusted R Sqrd F Stat O.Q n* 3.017* * O.Q w l..d * * * * * * * * O.Q O.Q * denotes significant t ratios at the.05 level for 17 degrees of freedom and n= 20 and k= 4 for F

48 TABLE Ill Book-to-Market Equity as a Proxy for Risk in Utility Stocks Stage Two Regression Results VWBETA # PERM# Intercept Coeff. Ln ME Ln BE/ME Ln ME Ln BE/ME Ln ME Coeff. Coeff. Std Err Std Err t ratio Ln BE/ME t ratio R Sqrd Adjusted R Sqrd F Stat O.Q O.Q * * O.Q * * * O.Q O.Q p O.Q , D O.Q *denotes significantt ratios at the.05 level for 17 degrees of freedom and n=20 and k=4 for F

49 TABLE Ill Book-to-Market Equity as a Proxy for Risk in Utility Stocks Stage Two Regression Results VWBETA # PERM# Intercept Coeff. Ln ME ln BE/ME Ln ME Ln BE/ME Ln ME Coeff. Coeff. Std Err Std Err t ratio Ln BE/ME t ratio R Sqrd Adjusted R Sqrd F Stat n* * * * O.Q * t-f::>. ~ O.Q * * O.Q O.Q Q *denotes significantt ratios at the.05 level for 17 degrees of freedom and n=20 and k=4 for F

50 42 The R 2 multiple coefficients of determination, which measures goodness of fit for the fitted multiple regression line to the data set, were low. This is evidence of a weak relationship of the independent variables of market equity and book-to-market equity to average stock returns for the individual firms tested. Only two firms in the 76 firm sample demonstrated R 2 values greater than.5. This means in only two firms is more than 50% of the variation in stock returns explained by the combined effect of market equity and book-to-market equity ratio. The R 2 adjusted for the degrees of freedom in the multiple regression model does not provide much additional strength to the explanatory strength of the model. The joint null hypothesis of H 0 : B 2 =B 3 =0; where the coefficients for market equity (ME) and book-to-market equity (BE/ME) are zero was tested with the F statistic. The results of the F test for overall significance of the regression model were only 10 firms in the sample of 76 firms demonstrated joint explanatory power for the two variables lnme and ln(be/me) at a significant level where n=20 and k=4. Thus the results obtained for the two tests support the joint relationship of R 2 and the F statistic, that the F test as a measure of overall significance of the estimated regression is also a test of the significance of

51 R 2 A low F test result verifies a low R 2 result. The 43 adjusted R 2 results demonstrated only five firms with explanatory power higher than.3. These tests lead to the conclusion the null hypothesis should be accepted and the coefficients of market equity and book-to-market equity are statistically insignificant and equal to zero.

52 VI. CONCLUSIONS The empirical evidence of the tests conducted with the sample of firms in the electric utility industry in this thesis and in the independent research of Lavely and Bacon leads one to be skeptical of the strength of the roles of market size and book-to-market equity as a proxy for risk in explaining the average returns of stock prices. Although this does not aid the SLB model's faults and potential demise it signals that the role for risk proxies in determining stock returns may not be over. In fairness to the results obtained by Fama and French there may be some explanation for the failure of the tests in this thesis to produce similar results. The utility industry is unique in its financial and market return structure. Fama and French arrived at the book-to-market equity variable as a result of the tests on asset to book value ratios and asset to market equity ratios. The results having different signs but similar absolute values led Fama and French to conclude the relationship was the difference between the ratios of A/BE and A/ME or the BE/ME ratio

53 45 In the utility industry where the regulation objective is a book value equal to market value and the rates are adjusted accordingly the difference between the ratios is lost. The market place would normally create this difference and only by rare coincidence would it likely be zero, or in other words the ratio equal to one. Therefore although the Fama and French tests detect a role for BE/ME in all stocks the relationship in utility stocks may be exceptionally weak and leaves no better avenue for pricing the assets in this sector than the CAPM with the empirically weak beta tests. Electric utilities have placed a singular emphasis on rate increases to the exclusion of other means for improving earnings. The potential long-term impact of this policy may prove devastating. Virtually all rate requests stress the importance of increased rates in order to improve the market-to-book ratio (or reduce the BE/ME ratio-its inverse). The fact that utilities have not been traditionally price-takers has allowed them to artificially prop up the market-to-book ratio (MBR) with regulated rates. 25 But times are changing both in terms of price elasticity of demand and competitive pressure resulting from regulatory changes to the historical utility monopoly

54 structure. Today's electric customer has a variety of substitutes and alternatives where costs are quickly 46 declining. Consumer demand is not sufficiently inelastic to allow continued increases to adjust the MBR, thus as competition increase perhaps the statistical relationship found by Fama and French for all stocks in the role of BE/ME may become more pronounced in the utility sector. The price elasticity of demand for electricity rising rapidly and the demand curve has undergone a permanent shift as a result of demand side management techniques and substitutes as well as increased competition in generation. 26 There is increasing evidence that the long-term price elasticity of demand for electricity and other forms of energy is beginning to exceed unity. This effect has widespread significance for utility rate making since implies that total electric revenues can no longer be increased by raising price. Increased rates will only reduce total revenue. To maintain an MBR of 1 rates must be set on the cost basis of assets used to generate revenues. Competitive pressures are driving the accepted cost basis down and those with a net book basis higher than market equity are likely to have poorer earnings prospects. Since the MBR is a reflection of investor confidence in the future earnings capabilities of a company's assets the

55 47 expectation of lower MBR's for this industry seem apparent and inevitable for an industry that has not had any significant innovation in over fifty years.