A Comparison of Market-based and Accounting-based Descriptions of Business Risk

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1 A Comparison of Market-based and Accounting-based Descriptions of Business Risk Frank Ecker Duke University Jennifer Francis Duke University Per Olsson* Duke University Katherine Schipper Duke University We compare market-based descriptions of business risk, derived from firms information and trading environments, with accounting-based descriptions of business risk, derived from firms operating environments. In broad samples, we find that market and accounting representations have similar explanatory power with respect to cross-sectional variation in three ex ante indicators of investors resource allocation decisions (the implied cost of equity, debt ratings and implied volatility) and that neither the market descriptors nor the accounting descriptors subsume each other. We also find that the accounting descriptors provide greater explanatory power for the cost of equity than do market descriptors in low information environments and in trading environments characterized by market friction. February 2009 Work in progress. Please do not quote. Comments welcome. * Corresponding author: Fuqua School of Business, Duke University, Durham, NC This research was supported by the Fuqua School of Business, Duke University.

2 A Comparison of Market-based and Accounting-based Descriptions of Business Risk I. INTRODUCTION We compare a market-based description of the firm s business risk with an accounting-based description, in terms of the ability of the two risk representations to explain cross-sectional variation in three ex ante indicators of investors resource allocation decisions. The market-based description, specifically the Fama-French characteristics (e.g., Fama and French, 1992), is derived from the firm s information and trading environments (with accounting data being one source of information to these environments). The accounting-based description is derived from the firm s operating environment, and contains accounting representations of the characteristics in the three factor model (CAPM beta, size as captured by market capitalization, and growth, distress and other factors as captured by the book-to-market equity ratio). Specifically, we use accounting beta to represent market beta; log of total assets to represent size; and financial leverage, asset growth, loss intensity and return-on-assets to represent the book.-tomarket equity ratio. As benchmarks to calibrate the market- and accounting-based descriptions of risk we use three ex ante summary indicators of investors resource allocation decisions: implied cost of equity estimates from Value Line forecasts of prices and dividends, bond ratings (an ex ante indicator of default risk and therefore of the cost of debt), and implied volatility (an ex ante indicator of total return variability). Of these three benchmarks, the first two are direct indicators of the costs of equity and debt capital, respectively, and therefore are ex ante risk measures. The third is an indirect indicator, which captures a forecast of total returns risk. Our analysis is motivated by two strands of research in accounting and financial economics that are concerned with empirically tractable representations of required returns (that is, with ex ante risk measures). Accounting researchers have investigated the relation between accounting and market measures of risk, often taking the latter as fundamental and asking which, if any, accounting measures are associated with market risk measures. For example, Beaver, Kettler and Scholes (1970) investigate the extent to 1

3 which several accounting risk measures are impounded by the CAPM beta, and whether the accounting measures can be used to predict CAPM betas. Their paper is related to ours if the CAPM beta is used as the proxy for the cost of equity; however, they are not concerned with a comparison of market-based risk measures and accounting-based risk measures. 1 In a different context, Hodder, Hopkins and Wahlen (2006) analyze several income measures to determine which is more closely aligned with market risk measures such as market-model beta, the standard deviation of realized returns, and an interest-rate beta. Taking a different tack, Baginski and Wahlen (2003) use the difference between a residual-income based measure of intrinsic value and observed market prices (that is, a price differential) to infer the portion of a firm s cost of equity that is excess to the risk-free rate, and test whether two measures of risk in residual income explain the cross-sectional variation in price differentials. Like previous accounting research, we are concerned with accounting-based representations of risk. Unlike previous research, we directly compare an accounting-based representation of business risk that derives from the firm s operating environment with a market-based representation that derives from the firm s information and trading environments, and which includes accounting information as one information source. The market-based representation is distinguished from the accounting basedrepresentation because the market mechanism aggregates information from many sources (of which financial reporting is one) and filters that information through the perceptions of market participants. The accounting-based representation directly measures firm characteristics and risks in the operating environment, subject to accounting rules that introduce imperfections. We discuss the implications of this distinction in detail in section II. Our investigation has three parts. First, we investigate whether the market-based representation dominates the accounting-based representation in a broad sample. For a sample of Value Line firms during , we find that the market-based and accounting-based descriptions of business risk have similar explanatory power for the implied cost of equity (adjusted R 2 s of 16-17%), that the accounting-based model has more explanatory power for bond ratings (60% versus 53%), and less explanatory power for implied 1 We note (in section 2) that circa 1970 there was no viable alternative market-based risk measure to the CAPM beta. 2

4 volatility (49% versus 52%). For all three ex ante indicators of investors resource allocation decisions, combining the accounting-based and market-based descriptions increases the explanatory power by between six and 10 percentage points, indicating substantial explanatory power in one risk representation that is not subsumed by the other. Second, for the Value Line sample, we investigate the extent to which the accounting representations of the three distinct constructs represented by the three market characteristics in the Fama- French model provide an empirical characterization of business risk that is comparable to the characterization provided by the three market-based representations, with particular focus on the book-tomarket equity ratio. As discussed in more detail later, the book-to-market equity ratio has been identified with financial leverage, growth, distress (in the sense of poor performance), and profitability. 2 Our findings show that accounting representations of these constructs eliminate the explanatory power of the book-tomarket ratio for all three ex ante risk measures. Beta and market value of equity, however, retain their explanatory power. 3 Further analyses examine the ability of accounting-based risk measures that are orthogonalized with respect to their corresponding market-based risk measures, and vice versa, to explain cross-sectional variation in the implied cost of equity capital. These tests show that two market-based risk measures (beta and market value of equity) and three accounting-based measures (asset growth, loss intensity, and profitability) consistently retain explanatory power. Our third analysis performs conditional tests in settings where we expect the market-based representation to outperform the accounting-based representation, or vice versa. In particular, the marketbased description derives from the firm s information and trading environments, while the accountingbased description derives from the operating environment. Given these fundamental differences, we investigate whether the two models perform differently in low versus high information environments and high versus low trading friction environments. We predict and find that the market-based description 2 For example, Daniel and Titman (2006) dispute Fama and French s (1995) analysis of the book-to-market ratio as an indicator of distress, and perform their own analysis of this ratio as an indicator of valuation-relevant information that is not contained in past accounting-based performance measures. 3 In-process extensions of the analyses of the book-to-market ratio reported in this paper provide similar analyses of the market value of equity. 3

5 performs relatively (to the accounting-based description) poorly in terms of explaining the cost of equity capital in low information/high trading friction environments, and that it performs substantially better than the accounting-based description in high information/low trading friction environments. Analogous tests for bond ratings indicate that the accounting-based description of risk has higher explanatory power for bond ratings than does the market-based description, regardless of the information and trading environments; analogous tests for implied volatility yield inferences similar to those for the cost of equity. We draw two conclusions from our results. First, the weight of the evidence indicates that an accounting-based representation of the risk characteristics included in the market-based three-factor model is comparable, in terms of explanatory power, to the three-factor model itself in a broad sample of Value Line firms. Combined with Fama and French s (1997) discussion of the imprecision of cost of equity estimates obtained from direct application of the three-factor model, this conclusion suggests that including accounting-based risk factors might sharpen the results. Results of our conditional tests suggest that the accounting-based description is superior to the market-based description in low information environments, in high trading friction settings, and for bond ratings generally. Second, we believe that our results shed light on the question of the expected-return-relevant constructs captured by the book-to-market equity ratio. Specifically, we believe that the ratio captures a combination of distress (measured by accounting loss incidence), profitability (measured by ROA), growth (measured by asset growth), and (for bond ratings) financial leverage (measured by the debt-to-assets ratio). The rest of this paper proceeds as follows. Section II develops our research question and places it in the accounting and finance literatures. Section III describes our sample and variables for our main (unconditional) tests and section IV presents the results of these unconditional tests. Section V reports the conditional tests. Sensitivity tests are described in section VI, and section VII concludes. II. PREVIOUS RESEARCH AND DEVELOPMENT OF OUR RESEARCH QUESTION In this section we first discuss previous accounting research that investigates accounting-based risk representations, specifically, Beaver et al. (1970), hereafter BKS, and place our analysis in the context of 4

6 that previous work. We then discuss research in financial economics that investigates constructs associated with the risk factors in the three-factor model and link this research to our research question. We also discuss some key distinctions between accounting-based and market-based representations of business risk. Research on accounting-based risk representations. BKS proposed that the accounting system generates information on several relationships that are considered by many to be measures of risk, and asked what is the relationship between accounting determined and market determined measures of risk? (page 654). Perhaps because the premier (and, for some, the only) market-based risk measure identified at the time was the CAPM beta, BKS motivated their paper largely in terms of the practical utility of accounting risk measures for assessing or predicting the CAPM beta, or for estimating risk in settings in which CAPM betas are not available (for example, initial public offerings). Thus, they took the CAPM beta as the benchmark against which they calibrated seven accounting risk measures: dividend payout, growth in assets, leverage, liquidity as captured by the current ratio, total assets, earnings variability and covariability (with economy-wide earnings). BKS s earnings measures are mixtures of accounting and market data, based on income divided by market value of equity (that is, price-earnings, or P/E, ratios). Our study builds on and extends BKS in several ways that are linked to the development of a more complete representation of risk and required returns than was available to BKS and to the development and use of alternative (to beta) ex ante indicators of investors resource allocation decisions. In particular, the circa 1970 representation of risk, in the sense of required return, was the CAPM beta (or the one-to-one mapping of the CAPM beta with a cost of equity estimate derived from it), so BKS had no viable alternative to beta, a market risk descriptor, in terms of a benchmark cost of equity variable. 4 As a practical matter, BKS could not compare the explanatory power of accounting-based and market-based risk descriptions of the cost of equity, since the accepted measure of equity risk at the time, CAPM beta, is itself the market descriptor. Nor does the CAPM itself allow for factors other than a security s covariation with the market return to affect expected returns. Subsequent research, in particular, the Fama and French three- 4 While both bond ratings and (realized) returns volatility were available as risk indicators, BKS were explicitly concerned with the cost of equity (not the cost of debt) and the notion of implied volatility as an ex ante indicator was developed later, in the context of option pricing. 5

7 factor model shows that, empirically, market capitalizations (a proxy for size) and the book-to-market equity ratio (described as a proxy for growth, distress and other characteristics) as well as beta are related to expected returns. Further, research has developed several measures of the cost of equity that are distinct from the CAPM beta, including implied cost of equity estimates (such as those derived from analysts earnings forecasts or price targets) and measures derived from the Fama-French three-factor model. Based on these developments, we revisit and extend BKS by identifying three ex ante indicators of risk (implied cost of equity estimate, bond ratings, and implied volatility) that reflect investors resource allocation decisions. We use these benchmarks to calibrate the three-factor market-based representation of risk and a purely-accounting-based representation of risk that includes accounting representations of the risk constructs included in the three factor model, one of which is a pure-accounting beta. Thus, the overlap between our analysis and BKS s lies in the relation between the CAPM beta and the accounting beta. With respect to the latter, BKS report that: (i) their measure of accounting beta (actually, P/E ratio covariance with a market P/E ratio) is largely uncorrelated between the two subperiods they study, suggesting measurement error; (ii) at the individual security level, their accounting beta is correlated with the CAPM beta between.23 and.44 (depending on the time period and whether the correlation is a rank or a productmoment correlation); and (iii) their accounting beta is not a useful predictor of future CAPM beta. More recently, Hodder et al. (2006) assess how the variability in three income measures that differ in their inclusion of fair value changes explains four market-based measures of risk: market-model beta, short-term and long-term interest rate beta and stock return volatility. The income measures are net income, comprehensive income and a pro forma measure of full-fair-value income that incorporates unrealized fair value changes on most financial instruments as they arise. As was the case with BKS, their analysis takes the market risk measures as the benchmark. However, unlike BKS, Hodder et al. create alternative indicators of the same construct earnings variability that differ with respect to measurement, and also extend their analysis to pose the question of whether their income volatility measures capture risk factors that are priced. With regard to the latter analysis, Hodder et al. assess the explanatory power of their three income volatility measures for cross-sectional variation in cost of equity estimates derived using the 6

8 Ohlson and Juettner-Nauroth (2005) model. They find that variability in net income and full-fair-value income is more highly associated with the cost of equity than is variability in comprehensive income. Taking a residual-income valuation perspective, Baginski and Wahlen (2003) propose and test that the discount for risk (in excess of the risk-free rate) can be captured by the price differential, equal to the difference between observed share prices and residual income intrinsic values based on a risk-free discount rate. They relate the price differential their measure of equity risk to volatility in abnormal return on equity (AROE) and an AROE beta, as well as CAPM beta; in some tests they control for both market capitalization and the book-to-market equity ratio. They are not concerned with comparing the ability of a market-based risk representation and an accounting-based risk representation to explain variation in their measure of equity risk. Their primary interest is in whether the residual income-based measures explain variation in the price differential on their own and incremental to the market-based descriptors. To summarize, previous accounting research has investigated the degree to which accounting risk measures, and in particular measures of income variability, are correlated with market risk measures and with measures of the cost of equity. Our research question investigates the practical value of an accounting-based risk representation of the constructs intended to be captured by a well-accepted marketbased risk representation (the three factor model). As discussed later in this section, we view our investigation as an inquiry into the distinction between a risk representation that arises from the firm s operating environment versus one that arises from its information and trading environments, recognizing that one information source for the latter is the former. Our reliance on the three factor model as the market-based representation allows us to use accounting-based representations to probe, separately, each of the constructs in the three factor model. Finally, because our approach allows us to directly compare market-based and accounting-based representations of risk, we can apply this approach both unconditionally (to determine the average effect of the two representations, for a broad sample) and conditionally (to determine if one representation 7

9 outperforms the other in specific settings). 5 The settings we examine are low information intensity environments (i.e., environments characterized by little news arrival) and high trading friction environments (i.e., environments characterized by low trading volume, low percentage shares traded, and high PIN scores), and their high information intensity and low trading friction counterparts. We predict that in the low information intensity/high trading friction environments, accounting-based representation of risk will perform relatively better than market-based representations. We predict the opposite in high information intensity/low trading friction environments. Research in financial economics on the constructs captured by the three factor model. Research on the Fama-French three factor model is voluminous and we will not attempt to summarize it here. Our intent is to focus on the constructs that are intended to be captured by the model, and the links between those constructs and accounting measures. We consider each of these in turn. Beta. There is general agreement in the literature about what beta stands for, presumably because it is a theory-based measure of risk (e.g., Sharpe; 1964, Lintner, 1965). We posit that the accounting measure which corresponds to beta is the covariability of a firm s earnings (specifically, its return-onequity) with industry earnings, often referred to as the accounting beta (e.g., Brealey, Myers, and Allen, 2005). Market value of equity. Most researchers seem to subscribe to the idea that market capitalization captures firm size. However, Berk (1995), while not disagreeing with the size interpretation, shows that the negative relation between market capitalization and discount rates follows by valuation model necessity, not necessarily from some innate characteristic(s) of small or large firms. He argues that because discount rates are denominators in valuation models, a negative relation between market value of equity (the outcome of the market s valuation) and discount rates follows mechanically, unless the variation in discount rates is totally offset by variation in the valuation model numerator (e.g., cash flows). As an implication, any risk factor that affects discount rates will likely be related to market capitalization. 5 BKS also performed a conditional analysis of actual and hypothetical associations between CAPM beta and earnings variability measures based on allocated and nonallocated interperiod taxes. They find that the nonallocated numbers exhibit a higher association, despite the fact that the allocated numbers were reported in the annual report. 8

10 We posit that total assets is the accounting size measure that corresponds to market value of equity. However, we also note that total assets is a measure of scale or the amount of productive capacity that is available without regard to the efficiency and effectiveness of management in operating that capacity (assets that are too large represent overcapacity, not value). In contrast, market capitalization explicitly considers both scale and the management of assets. Thus, although we expect and find that market value of equity and total assets are highly correlated, we believe that they also contain distinct risk elements. Book-to-market equity ratio. The third characteristic, the book-to-market (BM) ratio, is subject to substantially more debate about what it represents, especially, what systematic risk-related (and therefore cost of capital relevant) dimensions it captures. Fama and French (1993) argue that variation in BM represents variation in relative distress risk. Confirming evidence is presented in Fama and French (1995), who document that BM proxies for persistently poor (good) earnings. The literature continues to investigate risk-based explanations for the BM effect in expected returns. For example, Daniel and Titman (2006) dispute the distress interpretation, Petkova (2006) links the BM effect to macroeconomic risk notions, and Fama and French (2006) argue that BM is related to expected return through basic valuation model algebra. The last argument is not dissimilar to Berk s argument concerning market capitalization. Accounting research has linked BM to several accounting measures with intuitive risk interpretations. As Penman (1996) points out, several researchers refer to low BM firms as growth firms, a notion that goes back at least to Preinreich (1932). Similarly, other authors link BM to financial leverage (Graham, Dodd and Cottle, 1962; Fama and French, 1992). Penman (1996) shows a strong empirical relation between BM and accounting profitability, measured by ROE. Based on these arguments and empirical findings, we use separate accounting risk measures to capture intended each of these dimensions of the book-to-market equity ratio. Specifically, we include growth in assets, accounting leverage (measured as the ratio of the firm s total debt to total assets), loss intensity (measured as the percentage of losses in the last seven years), and return on assets (ROA). We do not use ROE because we include accounting leverage. We note that loss intensity, in particular, is a strong indicator of poor performance (the firm must be earning less than its cost of capital) and one that is uniquely linked to the firm s operating 9

11 environment. Because of the incomplete agreement in the finance literature about the construct that is captured by the book-to-market ratio, we include one accounting measure for two market-based risk factors (beta and market capitalization) and four accounting measures for the book-to-market ratio. As noted earlier, part of our investigation seeks to shed light on the debate about the characteristic(s) that are subsumed in the book-to-market equity ratio. Qualitative comparison of the three-factor market-based risk representation with an accountingbased risk representation. The characteristics contained in the widely-used three-factor model have their origins in theory (beta) and in empirical induction (market capitalization and the book-to-market equity ratio). The original capital asset pricing model (CAPM, Sharpe 1964, Lintner 1965) is a model of capital market equilibrium, specifying the sensitivity of a firm s returns to market returns (beta) as the only measure for risk. Given this derivation, beta has therefore naturally been measured using stock returns. Following the development of the CAPM, empirical research in financial economics explored other variables that have predictive power over expected returns. For example, Banz (1981) empirically associated returns with market capitalization; several price ratios (cash flow to price, earnings to price, dividends to price) were also shown to support trading strategies that produced consistently positive returns. After analyzing this stream of research, Fama and French (1992, 1996) showed empirically that a model with three market-based variables beta, market capitalization and the book-to-market equity ratio subsumes the expected return effects of the other price ratios, and they argue that these three variables provide a parsimonious, yet powerful, description of expected returns. Since then, the Fama and French model has been widely used in empirical research. Although they are all derived from the firm s trading and information environment, beta and the other two variables differ in ways that have implications for our analysis. Specifically, beta is derived as a risk measure from a theory of market equilibrium, whereas market capitalization and the book-to-market equity ratio are included in the three-factor model on empirical, not theoretical, grounds, lacking formal theoretical support as risk measures. Put differently, beta is formally analytically linked to expected returns, while market capitalization and the book-to-market equity ratio are firm-specific characteristics 10

12 that are empirically linked to realized returns; they lack a model analogous to the CAPM that demonstrates why they should not be diversifiable in large samples. Although theory identifies beta as a risk measure, market capitalization and the book-to-market equity ratio have neither a formal nor an immediate intuitive interpretation as risk factors. Given the empirical success of the Fama and French model, however, researchers have identified risk notions that are empirically associated with these characteristics. That is, they have taken market capitalization and the book-to-market-equity ratio as given and have searched empirically for measures that capture intuitive risk notions. For example, Fama and French (1995) show that high (low) book-to-market firms have poor (good) earnings performance, and argue that the book-to-market equity ratio therefore can be thought of as a relative distress factor; other research ascribes a different interpretation. Because two of the three characteristics in the Fama and French three-factor model are included on empirical grounds, we regard it as an empirical question whether accounting-based representations of these characteristics might perform as well as, and perhaps under certain conditions better than, the widely-used market-based representations. Our basis for posing these questions is the distinction between measures that arise in trading/information environments and measures that arise in operating environments. Marketbased risk measures, because they are measured in the trading environment, capture market participants perceptions of a firm and its risk characteristics, conditional on the available information. Accounting, in contrast, directly measures firm characteristics and risk in the operating environment, subject to the requirements of authoritative accounting guidance. Financial statement analysis texts specify accounting measures whose construction captures detailed aspects of firm risk; for example, does the firm have frequent losses? What is its profitability over time? We view the role of the market s trading mechanism as aggregating and filtering the available information, including accounting information. An efficient market mechanism discards cost-of-capital irrelevant information, including that in accounting measures. In reality, of course, the market s aggregation and filtering varies across information environments and trading environments, and can be noisy if information is sparse and/or trading frictions are high. We view one role of financial reporting as 11

13 the provision of information about business risk, and the related role of one branch of fundamental financial statement analysis as the development of appropriate summary indicators of risk. While we recognize the myriad and well-documented imperfections and inconsistencies that plague financial reporting, we also point to accounting measures as direct, unfiltered-by-perceptions measures that are developed with the explicit purpose of capturing decision-relevant information about (among other things) business risk. We argue that it is, therefore, an empirical question whether the information aggregation and filtering properties of the trading environment provide more benefits, in terms of producing a market-based representation of risk, than the disadvantage of the noise it introduces compared to a direct, but constrained by accounting guidance, measurement of risk in the operating environment. That is, it is an empirical question whether a market-based description of business risk is more or less useful than an accountingbased description of business risk for investors resource allocation decisions. III. VARIABLE DEFINITIONS AND SAMPLE DESCRIPTION III.A Market-based and accounting-based descriptors of business risk We use the Fama and French three factor model as the market-based description of risk because of its widespread acceptance in the literature. Fama and French (1992, 1993) show that three factors a firm s equity beta, its ratio of book value of common equity to market capitalization, and its size as measured by its market capitalization explain a substantial portion of the variation in expected returns (or cost of equity capital). 6 We measure the firm-specific market beta (Beta) as the slope coefficient from a standard CAPM regression estimated over 60 months (a minimum of 24 months is required): Mkt jm, Fm, α j β j m ε jm, R R = + RMRF +, (1) where R j,m is the return to security j in month m, R F,m is the monthly risk-free rate, and RMRF m is the monthly excess market return. We measure the book-to-market ratio (BM) at fiscal year-end as the ratio 6 Fama and French (1996) show that the three factors largely subsume certain other market-based returns regularities, such as the long-term returns reversal and several so-called value-glamour ratios. 12

14 between the book value of common equity and the market capitalization. Similarly, market capitalization (MktCap) is measured at fiscal year end. In our tests, we follow Fama and French (1992) and use the natural logarithm of BM and MktCap. The accounting-based measures that correspond to the constructs in the three factor model are the accounting beta, total assets, the debt-to-assets ratio, growth in assets, loss intensity, and return on assets. The accounting beta (AcctBeta) has been identified by, among others, BKS as an accounting counterpart to the returns-based beta. 7 We estimate AcctBeta as the firm-specific slope coefficient (over seven years) in the following equation: ( ) Acct j, T F, T α j β j T F, T ε j, T ROE R = + IndROE R +, (2) where ROE j,t is firm j s return on common equity in year T, measured as earnings before extraordinary items in year T, divided by the average, over years T-1 and T, of the book value of common equity; R F,T is the annual risk-free rate; IndROE T is the year T industry average ROE, based on the Fama and French (1997) industry classification. Our main accounting measure of firm size is the natural logarithm of total assets, AssetSize, measured at fiscal year end. 8 The book-to-market ratio (BM) has been shown to proxy for more than one characteristic of business risk, and thus requires more than one accounting-based descriptor. The first BM component is financial leverage (e.g., Graham, Dodd, and Cottle 1962, Fama and French 1992); our accounting-based measure of leverage is total interest-bearing debt over total assets (DebtAssets). The second BM component is growth (e.g., Preinreich, 1932; Fama and French, 1995; Mohanram 2005). Our accountingbased descriptor of growth is the annualized growth in total assets (AssetGrowth) over the last seven years (a minimum of three years required). The third component is relative distress risk (e.g., Fama and French, 1995; Lemmon and Griffin, 2002), for which our accounting-based is LossIntensity, the percentage of reported losses over the past seven years (or a minimum of three years). Finally, building on the residual 7 Beaver et al. calculate their accounting beta using earnings-to-price ratios (page 666). We use return on equity. The difference is standardizing by book value of equity, an accounting number, versus market value of equity, a market-based number. 8 As an alternative size measure, we use sales revenues (not tabulated). This measure is 90.3% correlated with total assets, and test results are virtually identical for either accounting measure of firm size. 13

15 income formula derived in Preinreich (1938), Edwards and Bell (1961) and Peasnell (1982), Penman (1996) shows that there is an empirical association between the book-to-market ratio and accounting profitability. We use return on assets, ROA, rather than return on equity as the accounting profitability variable because ROE is mechanically associated with financial leverage, also included as a BM component. We define ROA as operating income over average total assets. III.B. Summary indicators of investors resource allocation decisions We use three ex ante indicators of investors resource allocation decisions: the implied cost of equity, bond ratings, and implied volatility. Our main measure for the cost of equity, CofE, is derived from Value Line (VL) analysts four-year-ahead price targets (TP), dividend forecasts (DIV), and dividend growth rates (g). Because they are based on forecasts, not realizations, our CofE measures reflect implied cost of equity estimates. Assuming that interim dividends are reinvested at the firm cost of equity, Brav, Lehavy and Michaely (2005) arrive at the following expression for the ex ante expected return: 4 + = + (3) (1 CofE) TP P 4 4 (1 + CofE) (1 + g) DIV CofE g P where P = stock price nine days prior to the date of the VL report. For each firm in our sample, the value of CofE that satisfies the equality is our estimate of the firm s implied cost of equity. This CofE measure has been used by Brav et al. (2005) and Francis et al. (2004), and is qualitatively the same as the VL-based measure used by Botosan and Plumlee (2002, 2008). Botosan and Plumlee (2005) compare the construct validity of four proxies for the cost of equity (the VL CofE estimate, a Gordon growth model estimate, a residual income estimate, and a PEG ratio based estimate), and conclude that the VL CofE estimate (as well as a PEG estimate) is a reliable cost of capital proxy, and that it outperforms other approaches. While we believe the literature indicates that the VL CofE measure is preferred, we recognize that there is no consensus on the best measure of the cost of equity. Consequently, we report the results of 14

16 additional tests with cost of equity proxies based on analyst earnings forecasts and based on realized returns, in section VI. Our ex ante measure of credit risk, a component of the cost of debt, is bond ratings, specifically, Standard & Poor s domestic long term issuer credit ratings. We transform the ratings from AAA (for the least risky firms) to D (for the most risky firms) into an ordinal scale numerical rating as described below: 9 AAA 1 BB+ 11 AA+ 2 BB 12 AA 3 BB- 13 AA- 4 B+ 14 A+ 5 B 15 A 6 B- 16 A- 7 CCC+ 17 BBB+ 8 CCC 18 BBB 9 CCC- 19 BBB- 10 D 20 Our ex ante measure of volatility is a standardized implied volatility measure based on data from the OptionMetrics Standardized Options dataset. Specifically, we measure the average standardized implied volatility of call options with the shortest maturity available (30 days) over the last month of a fiscal year. The standardized options are hypothetical at-the-money options with specified durations, with the calculations based on observed values of traded options (see OptionMetrics, 2006 for a detailed description of this variable). III.C. Sample description Our main sample covers the 11 year period, We begin the sample period in 1995 because of the availability of data on two variables (information intensity and PIN scores) that we use in our conditional tests, described in section V. 10 The alignment of market and accounting variables with cost of equity variables is based on the fiscal years from which we obtain the financial information that produces the accounting-based risk 9 Some view the break at BBB (the lowest investment grade rating) as an indicator of credit risk. We do not adopt this two-way split of our sample. 10 In ongoing work, we are extending our analyses by repeating all tests that do not require these variables for the period

17 variables. For the Value Line CofE, which is available by quarters, we use the last quarter of the fiscal year. The set of firms included in each sample year is constrained by Value Line coverage (for the cost of equity estimate) and by the existence of sufficient data to calculate the business risk variables. The latter require a minimum of three years of data. Our sample thus contains large firms and relatively stable firms (because Value Line tends to cover such firms). Table 1, panel A, compares our Value Line sample to the overall market. The sample contains between 1,002 and 1,137 firms per year, for a total of 11,953 firmyears. The % Mkt Cap column shows that our sample accounts for between 45% (in 2003) and 52% (in 1995) of the total market capitalization of Compustat firms, with an over-time average of 48%. Thus, while the sample is constrained by the cost of equity variable, it still represents about half of the U.S. market capitalization. These proportions are similar to results reported in Brav et al. (2005) and Francis et al. (2004), who also use Value Line-based samples. Panel B details the distribution of the VL-based cost of estimate, the market-based risk descriptors, and the accounting-based risk descriptors. Our sample s mean (median) value of 15.42% (13.94%) for the cost of equity is similar to results in Brav et al. (2005), who report 15.0% (14.2%) for the portion of their sample period ( ) that overlaps with ours. The distribution of market betas (mean is 0.87 and median is 0.78) is below the market average of one, consistent with the relative stability of Value-Linefollowed firms; however, there is a fairly wide cross-sectional dispersion (standard deviation of ). The average ROA of 5.68% exceeds the Compustat average, which was 2.48% over our sample period, although there is substantial variation in profitability within our sample (the standard deviation of ROA is ). A comparison of the means and standard deviations for the other market- and accounting-based risk descriptors generally indicates sufficient variation in our sample to make effects statistically detectable. The mean of LossIntensity requires interpretation. Recall that LossIntensity is a firm-specific measure of firm j s loss incidence over the past seven years; for example, the 75 th percentile value of the pooled sample implies one loss out of seven years (0.1429) and the 90 th percentile value of the pooled distribution implies three losses out of seven years (0.4286). These statistics do not, however, imply that 16

18 there are few or no losses in the sample; 41% of the firm-year observations report that one year or more losses occurred over the prior seven years (this statistic is not reported in the table). The bottom portion of panel B contains descriptive statistics for debt ratings and implied volatility for the set of firm-year observations over with data on these variables. For the DebtRating variable, the sample consists of 9,090 firm-year observations, of which 6,708 overlap with the VL sample; for the ImplVolatility variable, the sample consists of 11,445 observations, of which 7,557 overlap with the VL sample. The average (median) debt rating is (9.000), which corresponds to BBB, i.e., investment grade. The average (median) implied volatility is (0.4499), similar to the (0.430) reported in Rogers, Skinner and Van Buskirk (2008). Both variables show substantial dispersion relative to their means. Table 2 reports correlations among the variables (Pearson above the diagonal and Spearman below) for the VL cost of equity sample; correlations for the debt rating and implied volatility samples are not tabulated. Of particular interest are the correlations between market-based descriptors and accountingbased descriptors meant to capture the same underlying construct. Not surprisingly, the Pearson (Spearman) correlation between the size measures, market capitalization and total assets, is high, (0.8563). In contrast, the correlation between the market beta and the accounting beta is modest, (0.0951). The correlations between the book-to-market ratio and its corresponding accounting-based descriptors are strong for ROA, ( ), and more modest for the other variables: (0.1636) for the debt-to-asset ratio, ( ) for AssetGrowth, and (0.1518) for LossIntensity. Overall, we conclude from these correlations that the size measures are highly overlapping, while the other dimensions have overlap between market- and accounting-based descriptors, but in no case is one subsumed by the other The Pearson and Spearman correlations between Beta and LossIntensity and between Beta and AssetGrowth are between 20% and 31%. This is natural from a CAPM perspective (where beta is the risk variable), as firms with higher loss incidence and firms in the growth stage of their business life cycle intuitively are riskier. It is interesting to contrast this fact to recent asset pricing literature, which heavily favors book-to-market as a growth and financial distress variable. However, the cost of equity effect of book-to-market is greater than that of beta (e.g., Fama and French, 1992), arguably making book-to-market links more important. 17

19 The table also reports univariate correlations between each descriptor and CofE, some of which are substantial: MktCap ( Pearson and Spearman), BM ( and ), LossIntensity ( and ), and ROA ( and ). The other associations with CofE are more modest. Overall, it appears that the univariate correlations between cost of equity and market-based variables are of similar strength as the correlations between cost of equity and accounting-based variables. We also calculated correlations for the portions of the debt rating sample and the implied volatility sample that overlap with the VL cost of equity sample (results not tabulated). Pearson (Spearman) correlations with the cost of equity are (0.2582) for DebtRating and (0.4315) for ImplVolatility. DebtRating and ImplVolatility are (0.5045) correlated with each other. We conclude from these correlations that while CofE, DebtRating and ImplVolatility are positively correlated (as expected), they are sufficiently distinct to warrant separate tests IV. RESULTS OF UNCONDITIONAL TESTS In this section we report the results of our main tests. Sections A, B and C contain results for analyses using the cost of equity debt market, bond ratings, and implied volatility from options market as the summary indicators of investor resource allocation decisions. In all cases, we compare the ability of market-based and accounting-based descriptions of business risk to capture cross-sectional variation in these benchmark indicators. IV.A Cost of Equity Panel A of Table 3 contains the results of univariate regressions of cost of equity on each of the market-based and accounting-based descriptors: CofE = α + α Descriptor + ε (5) k k k k it, 0 1 it, it, where Beta, MktCap,BM, k. AcctBeta, AssetSize, DebtAssets, AssetGrowth, LossIntensity, ROA 18

20 The regressions are estimated by fiscal year (T), and the reported coefficients are the average of the annual coefficients. The reported t-statistics are based on the time-series standard error of the annual coefficients. We use this method for all tests to control for cross-sectional dependence (Fama and Macbeth, 1973). The first three columns of Panel A use the raw values of the individual variables. The R 2 s confirm the descriptive correlation evidence from Table 2 that among the accounting-based descriptors, LossIntensity and ROA dominate, whereas MktCap and BM dominate among the set of market-based variables. All variables, however, exhibit statistically significant associations with CofE, with no t-statistic below The next three columns repeat the same test using the decile ranks of the descriptors instead of their raw values, so that each coefficient corresponds to the cost of equity increment of moving from one decile to the next, an indicator of the economic significance of the associations. The cost of equity difference between the top and bottom decile is nine times the estimated coefficient (i.e., nine steps from the first to the tenth decile). Generally, the economic significance follows the statistical strength of the associations. Among the market-based variables, MktCap has the biggest effect, -85 basis points (bp) per decile, or a 7.7 percentage point (pp) difference between the top and bottom decile. The BM coefficient is 71 bp per decile (6.4 pp difference between top and bottom decile). The Beta coefficient is 29 bp per decile (3.8 pp difference between top and bottom decile). All three market-based variables are significant at conventional levels. Among the accounting variables, ROA has the economically largest effect with a coefficient of -87 bp per decile (7.8 pp difference between top and bottom decile). AssetSize has a coefficient of -55 bp per decile (4.9 pp difference between top and bottom decile). Because LossIntensity cannot be ranked into deciles (roughly 60% of all firm-years have a value of zero), we transform LossIntensity into an indicator variable equal to zero if the firm has had no losses during the past seven years, and one if the firm has had one or more losses. The coefficient on LossIntensity is 445 bp, i.e., a difference between pure profit firms and firms with past loss(es) of 4.45 pp. The accounting beta, AcctBeta, has a coefficient of 28 bp (2.5 pp difference between top and bottom decile). Both AssetGrowth and the debt-to-asset ratio are at best marginally significant and have coefficients of only bp. 19

21 Panel B of Table 3 contains the results of multivariate regressions, where we regress cost of equity on the raw values of the market-based descriptors, the accounting-based descriptors, and the combination of the two, respectively: CofE = λ + λ Beta + λ MktCap + λ BM + ς (6) Mkt j, T 0 1 j, T 2 j, T 3 j, T j, T CofE = δ + δ AcctBeta + δ AssetSize + δ DebtAssets jt, 0 1 jt, 2 jt, 3 jt, + δ AssetGrowth + δ LossIntensity + δ ROA + ς Acct 4 j, T 5 j, T 6 j, T j, T (7) CofE = φ + φbeta + φ MktCap + φ BM jt, 0 1 jt, 2 jt, 3 jt, + φ AcctBeta + φ AssetSize + φ DebtAssets 4 jt, 5 jt, 6 jt, + φ AssetGrowth + φ LossIntensity + φ ROA + ς Combined 7 jt, 8 jt, 9 jt, jt,. (8) The two leftmost columns of panel B contain the estimates from the market-based variable regression (equation 6). Beta, MktCap, and BM all have significant coefficients of the expected sign. The adjusted R 2 is 16.65%. The middle two columns of Panel B contain the estimates from the accountingbased variable regression (equation 7). The explanatory power (R 2 =15.98%) is similar to that of the market variable regression. Looking at the individual variables, we see that ROA and loss intensity have the highest significance, with t-statistics of and 8.44 respectively. AssetGrowth and AssetSize are also strongly significant, whereas the accounting beta and the debt-to-assets ratio have at best marginal significance. All coefficients are in the expected direction. In the two rightmost columns we report the results from the combined regression (equation 8), with all market-based and accounting-based variables included. Since we have attempted to capture the same constructs with the set of market-based variables and the set of accounting-based variables, this regression allows us to examine the extent to which the market-based measures (or the accounting-based measures) lose importance in the presence of the other. The adjusted R 2 of 22.18% indicates that while the market and accounting descriptors clearly overlap, there is information in the accounting variables that is not contained in the market variables and vice versa the incremental R 2 is 5.53% and 6.21% respectively. Of the market descriptors, BM loses all importance, with a coefficient close to zero and a t-statistic of -0.11, whereas Beta and MktCap remain strong. Of the accounting descriptors, ROA, LossIntensity and AssetGrowth remain 20

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