information risk

Electronic copy available at: http://ssrn.com/abstract=1439851

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Information Risk and Fair Values: An Examination of Equity Betas

Edward J. Riedl * Harvard Business School

George Serafeim

Harvard Business School Abstract: Using a sample of U.S. financial institutions, we exploit recent mandatory disclosures of financial instruments designated as fair value level 1, 2, and 3 to test whether greater information risk in financial instrument fair values leads to higher cost of capital. We derive an empirical model allowing asset-specific estimates of implied betas, and find evidence that firms with greater exposure to level 3 financial assets exhibit higher betas relative to those designated as level 1 or level 2. We further find that this difference in implied betas across fair value designations is more pronounced for firms with ex ante lower quality information environments: firms with lower analyst following, lower market capitalization, higher analyst forecast errors, or higher analyst forecast dispersion. Overall, the results are consistent with a higher cost of capital for more opaque financial assets, but also suggest that differences in firm’s information environments can mitigate information risk across the fair value designations. Key Terms: banks, risk, fair value, financial instruments, SFAS 157 JEL Classification: G12, G14, G21, M41

Acknowledgements: We thank the following individuals for useful discussions and comments: Mary Barth, Anne Beatty, John Core, Merle Erickson (editor), David Harris, Robert Merton, Jim Ohlson, Devin Shanthikumar, Kumar Shivakumar, Irem Tuna, Florin Vasvari, Sean Wang, and an anonymous reviewer. We also thank seminar participants from Boston University, the Financial Accounting Standards Research Initiative, the Financial Economics and Accounting 2009 Conference, the 2010 IMO Conference at Harvard Business School, the Journal of Accounting, Auditing and Finance 2009 Conference at New York University, the London Business School, New York University, Syracuse University, University of Connecticut, and the Research Accounting Conference at Yale University. * Corresponding Author Harvard Business School Morgan Hall 365 Boston, MA 02163 [email protected] 617.495.6368


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Abstract: Using a sample of U.S. financial institutions, we exploit recent mandatory disclosures of financial instruments designated as fair value level 1, 2, and 3 to test whether greater information risk in financial instrument fair values leads to higher cost of capital. We derive an empirical model allowing asset-specific estimates of implied betas, and find evidence that firms with greater exposure to level 3 financial assets exhibit higher betas relative to those designated as level 1 or level 2. We further find that this difference in implied betas across fair value designations is more pronounced for firms with ex ante lower quality information environments: firms with lower analyst following, lower market capitalization, higher analyst forecast errors, or higher analyst forecast dispersion. Overall, the results are consistent with a higher cost of capital for more opaque financial assets, but also suggest that differences in firm’s information environments can mitigate information risk across the fair value designations. Key Terms: banks, risk, fair value, financial instruments, SFAS 157


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1. Introduction

This paper examines whether information risk leads to higher cost of capital. We define

information risk as the ability of investors to ascertain the valuation parameters underlying a

particular asset. Financial reporting systems provide information that allows users to derive

these parameters. However, variation in the quality of this information can occur for two

reasons: first, measurement challenges inherent in the reporting elements; second, firm-level

implementation. Higher quality reporting enables better estimation of valuation parameters by

financial statement users (i.e., low information risk), while lower quality reporting leads to

noisier estimation of these parameters (i.e., high information risk).

To identify variation in information risk, we use as our setting fair value disclosures

reported by U.S. financial institutions under Statement of Financial Accounting Standards

(SFAS) 157, Fair Value Measurements. SFAS 157, effective 2008 (with early adoption allowed

for 2007), provides a framework for the measurement of reporting elements at fair value. In

particular, it distinguishes between three levels of inputs used to derive fair value estimates: level

1, reflecting observable inputs consisting of quoted prices in active markets for identical assets or

liabilities; level 2, reflecting observable inputs other than quoted prices; and level 3, reflecting

unobservable inputs. Regulatory motivation underlying the passage of SFAS 157 primarily

related to providing users with an understanding of the sources of information (i.e., inputs) used

to estimate reported fair values (FASB, Appendix C of SFAS 157). Accordingly, we proxy for

variation in information risk using the three fair value designations. Our sample focuses on

financial institutions, as SFAS 157 substantially affected their financial reporting due to their

broad exposure to financial instruments, many of which are reported at fair value.

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To empirically assess information risk, we rely on prior research that higher quality

disclosures lead to a lower beta and, thus a lower cost of capital (e.g., Lambert, Leuz, and

Verrecchia 2007). Specifically, we derive an empirical model of a firm’s equity beta. Since

equity beta is the weighted-average beta across a firm’s asset and liability structure, we estimate

asset-specific implied betas, focusing on financial assets reported at level 1, 2, and 3 fair values.

This provides the basis for two empirical predictions.

First, we predict that opacity is increasing across the level 1, 2, and 3 fair value

designations, leading to higher implied betas for level 3 financial assets. That is, we predict the

fair values based on unobservable inputs for their estimation will have inherently higher

information risk relative to those based on observable inputs. Second, we predict that variation

in the information environment will lead certain groups of firms to exhibit relatively larger

differences in opacity, and thus larger differences in implied betas, across the fair value

designations. That is, we expect that firms with ex ante higher quality information environments

better mitigate differences in information risk across the fair value designations. Accordingly,

we partition our sample firms into those with ex ante higher quality versus lower quality

information environments using four proxies. We argue that firms with higher quality

information environments have above median analyst following, above median market

capitalization, below median analyst forecast error, or below median analyst forecast dispersion.

We hypothesize that firms with lower quality information environments will exhibit larger

differences in information risk across the level 1, 2, and 3 fair value designations relative to firms

with higher quality information environments. That is, we predict that our proxies for higher

quality information environments will be positively correlated with the quality of firms’ general

and SFAS 157-specific disclosures.

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Empirical results are consistent with both predictions. We find that implied betas for

level 3 financial assets are significantly larger relative to those for either level 1 or 2 financial

assets, with implied betas increasing monotonically across the level 1, 2, and 3 categories. This

is consistent with a higher cost of capital for firms with a greater exposure to more opaque

financial assets, reflected in the level 3 designation. In addition, we find that firms with lower

quality information environments exhibit larger differences across the level 1, 2, and 3

designations relative to firms with higher quality information environments. We conclude that

while greater information risk is associated with level 3 financial assets, this risk is mitigated

through the firm’s information environment.

To provide a stronger empirical identification of the information risk measures, and to

mitigate the possibility that our results alternatively reflect systematic differences in fundamental

risk across the fair value designations, we follow finance theory and decompose our dependent

variable, equity beta, into its two mathematical components (Morck, Yeung, and Yu 2000;

Durnev, Morck, Yeung, and Zarowin 2003; Jin and Myers 2006). This allows the analysis to

isolate the component of beta capturing information risk: the correlation between the firm’s stock

return and the market return. All results are consistent using this alternative dependent variable.

In addition, results are consistent to alternative measurements of equity beta, to additionally

decomposing liabilities into the level 1, 2, and 3 designations, to controlling for unrecognized

assets and liabilities, to a preliminary analysis of pre- versus post-SFAS 157, and to extending

the sample period.

Our study contributes to three literatures. First, we contribute to the empirical literature

linking accounting disclosure to cost of capital (e.g., Botosan 1997; Leuz and Schrand 2009) by

providing an alternative approach to examine these associations. We also build upon prior

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research on estimation risk (Barry and Brown 1984; Clarkson and Thompson 1990) to provide a

direct test of Lambert, Leuz and Verrecchia (2007), documenting that information quality is

reflected in differential implied betas across firms’ asset structures, consistent with differential

effects on firms’ cost of capital. Second, we contribute to the literature on reporting for financial

institutions (e.g., Barth 1994; Beatty, Chamberlain, and Magliolo 1996) by showing that firms

with greater exposure to level 3 financial assets have higher opacity, and thus higher systematic

risk, leading to a higher cost of capital. Finally, we contribute to the literature on fair value

accounting, particularly relating to SFAS 157, by documenting that while information risk is

increasing across the level 1, 2, and 3 fair value designations (e.g., Song, Thomas, and Yi 2010),

it can be mitigated through higher quality information environments (e.g., Ryan 2008).

Section 2 reviews fair value reporting. Section 3 presents our hypothesis development,

and Section 4 our research design. Section 5 presents our sample selection, and Section 6 our

empirical results. Section 7 presents sensitivity analyses. Section 8 concludes.

2. Background

2.1 FAIR VALUE REPORTING FOR FINANCIAL SERVICES FIRMS

In 2007, U.S. standard setters adopted SFAS 157, Fair Value Measurement, to provide a

framework for the measurement of fair values.1 Thus, any financial reporting standard requiring

measurement at fair value would apply the provisions of SFAS 157. The standard defines fair

value as “the price that would be received to sell an asset or paid to transfer a liability in an

orderly transaction between market participants at the measurement date.” It further defines a

hierarchy of fair value measurements across three levels, reflecting the inputs used to derive the

1 The standard was effective for fiscal years beginning after November 15, 2007; early adoption was allowed for

the first calendar quarter of 2007.

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fair value estimation. Specifically, level 1 inputs are unadjusted quoted market prices in active

markets for identical assets and liabilities. With a few narrow exceptions, the standard requires

measurement using level 1 inputs when available. Level 2 are inputs other than quoted market

prices that are observable for the asset or liability, either directly or indirectly. These include

quoted prices for similar assets in active markets, quoted prices for identical or similar assets in

markets that are not active, as well as inputs other than quoted prices that are observable for the

asset (such as yield curves and exchange rates). While the inputs to these models are reliable,

the fair value estimation depends critically on the validity of the models used. Finally, level 3

inputs are unobservable, firm-supplied estimates, such as forecasts of home price depreciation

and credit loss severity on mortgage-related positions. These inputs generate mark-to-model

valuations that are largely undisciplined by market information. Firms are required to identify

assets reported at fair value under each of the level 1, 2, and 3 designations. In addition, SFAS

157 requires expanded disclosures for level 3 measures, owing to their higher subjectivity.

SFAS 157 substantially affected financial institutions, as many of the financial

instruments held by these firms must be reported at fair value. Of note, SFAS 115, Accounting

for Certain Investments in Debt and Equity Securities, provides guidance on the reporting of debt

and equity securities, classifying these investments into three categories. “Held-to-maturity” are

debt securities that the enterprise has the intent and ability to hold to maturity. “Trading

securities” are debt and equity securities bought and held principally for the purpose of selling in

the near term. “Available-for-sale securities” are debt and equity securities not classified as

either held-to-maturity or trading securities. Per SFAS 115, both “trading securities” and

“available-for-sale securities” must be reported at fair value on the balance sheet. In addition,

SFAS 133, Accounting for Derivative Instruments and Hedging Activities, requires that firms

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recognize all derivatives as either assets or liabilities in the statement of financial position and

measure those instruments at fair value. Finally, SFAS 159, The Fair Value Option for

Financial Assets and Financial Liabilities, expands the use of fair value measurement by

allowing firms to irrevocably measure, on an instrument by instrument basis, many financial

instruments at fair value, including interest in a variable interest entity that the firm is required to

consolidate, as well as deposit liabilities.

2.2 PRIOR LITERATURE

Prior research has examined the link between the quality of accounting disclosures and

cost of capital. Botosan (1997), one of the first papers to empirically test this link, uses a self-

constructed measure of voluntary disclosure based on annual reports, and finds that certain firms

(particularly those with low analyst following) exhibit lower cost of capital when their disclosure

increases. Thus, the paper provides an empirical test of theory, suggesting that greater disclosure

leads to reduced cost of capital by increasing market liquidity in the firms’ stock (e.g., Demsetz

1968; Diamond and Verrecchia 1991). Later theoretical work by Easley and O’Hara (2004)

affirms the notion that firms incur a higher cost of capital when their information environment is

of lower quality, as investors demand a higher return for stocks with greater private information.

Lambert, Leuz, and Verrecchia (2007) provides a framework for assessing how accounting

information affects firms’ cost of capital, demonstrating that higher quality disclosures allow

investors to better assess the covariances between the firm’s and other firms’ cash flows. Leuz

and Schrand (2009) provides empirical evidence that firms increase their disclosure levels due to

exogenous shocks that lead to higher cost of capital.

Due to the complex reporting and regulatory requirements for financial firms, prior

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research typically examines this industry in stand-alone contexts. A number of studies focus on

fair value reporting, owing to its substantial role in the reporting of these firms. Beatty,

Chamberlain, and Magliolo (1996) uses an event study methodology, documenting negative

stock market reactions for bank shares to events associated with the adoption of fair value

accounting under SFAS 115. However, Barth (1994) provides evidence that fair values of

investment securities are incrementally value relevant beyond historical costs. Barth, Beaver,

and Landsman (1996) provides similar evidence that fair value estimates of loans, securities, and

long-term debt under SFAS 107 provide incremental value relevance beyond historical costs,

while Eccher, Ramesh, and Thiagarajan (1996) and Nelson (1996) find this association only for

investment securities. More recent studies examine the effects of SFAS 157 on financial firms,

exploiting the level 1, 2 and 3 disclosures. Kolev (2008) and Goh, Ng, and Yong (2009)

document that level 3 fair values have lower value relevance compared to level 1 and 2 fair

values. In addition, Song, Thomas, and Yi (2010) finds that the value relevance of these fair

values is attenuated for firms with weaker corporate governance structures.

We build on these literatures in three ways. First, we propose an alternative empirical model to

assess information risk. Second, we complement prior findings on SFAS 157 by examining

whether information risk differs across the level 1, 2 and 3 designations. Finally, we examine

whether the firm’s information environment affects differences in information risk.

3. Hypothesis Development

We develop two hypotheses based on the theory of Lambert, Leuz, and Verrecchia

(2007), which demonstrates that a firm’s beta from the Capital Asset Pricing Model (CAPM) is a

function of its information quality. Specifically, higher quality information about a firm’s future

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cash flows lowers cost of capital through a reduction in the assessed covariances with other

firms’ future cash flows. Critically, the paper shows that these effects are not diversifiable in a

large economy, thereby making beta a function of information risk. We propose that variation in

this information risk manifests from two sources: first, differences in the reliability inherent in

the reporting elements themselves (i.e., across the level 1, 2, and 3 fair value designations);

second, differences in the ex ante information environment.

3.1 INFORMATION RISK DIFFERENCES ACROSS LEVEL 1, 2, AND 3 FAIR VALUES

We first hypothesize that investors face information risk that is increasing across

portfolios of assets designated as level 1, 2, and 3 fair values. This follows from the reporting

designations, which indicate progressively more subjective inputs used to derive the fair value

estimation. If this risk is not diversifiable, then investors will require a higher cost of capital for

firms with a greater exposure to level 3 assets. Prior research argues that information risk is not

diversifiable (Clarkson and Thompson 1990; Easley and O’Hara 2004). In our setting, the

uncertainty surrounding the future cash flows of financial assets (such as loans, investment

securities, and derivatives) can be highly correlated across financial institutions for several

reasons. Of primary importance, many financial institutions are exposed to similar types of

contracts (e.g., mortgage-backed securities), increasing the correlation in uncertainty across firms

within the banking sector. Thus, macro-economic shocks will similarly affect values across

these contracts: for example, declining housing prices or rising unemployment would similarly

affect the ability of individuals to repay mortgages. In addition, banks face counterparty risk,

since many of their assets are contracts with other financial institutions: examples include

derivatives or overnight repo agreements.

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Therefore, in an economy where information risk of financial assets is not diversifiable,

we expect a positive relation between the uncertainty surrounding the payoff distribution of a

portfolio and equity beta. In other words, we hypothesize that the implied beta of a portfolio of

assets is increasing in the information risk surrounding those assets. If the required fair value

designations capture this risk by reflecting the increasing subjectivity of inputs used to derive

them, then we expect that implied beta is increasing across asset portfolios designated as level 1,

2, and 3, consistent with the documented decreasing value relevance across the designations (e.g.

Song, Thomas, and Yi 2010). Thus, our first hypothesis (in alternative form) is:

H1: The association between a firm’s equity beta and its financial assets is increasing in the uncertainty about the parameters of the payoff distribution of those assets, as measured by the level 1, 2, and 3 fair value designations.

Three arguments provide tension against this hypothesis. First, if this risk is diversifiable

(that is, idiosyncratic to the individual firm), then the allocation of assets across different fair

value levels should have no relation to equity beta. This would be consistent with prior research

(Banz 1981; Reinganum and Smith 1983), which indicates that information risk should be

diversifiable in an economy. In general, if parameter uncertainty about expected future cash

flows is uncorrelated across a sample of low information assets, portfolio formation can increase

precision and eliminate any effects on systematic risk. Second and related, it may be that harder-

to-value assets have expected payoffs exhibiting lower correlation with the market return. If

assets receiving level 3 designations exhibit lower co-movement with the market index than

those receiving level 1 or 2 designations, this could lead to relatively lower implied betas for

level 3 assets, biasing against hypothesis 1. Third, SFAS 157 requires additional disclosures

(e.g., key assumptions and modeling techniques) for level 3 fair values, relative to level 1 and 2.

If effective, these disclosures could mitigate any incremental information risk.

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3.2 PARTITIONING ON THE EX ANTE INFORMATION ENVIRONMENT

The above discussion assumes fair value reporting fails to eliminate the information gap

across financial instruments with differing opacity. However, various forces interact to affect the

firm’s information environment, including that relating to SFAS 157 fair values. These include:

external factors, such as information intermediaries like analysts; firm-level internal factors, such

as its overall disclosure policy, auditor choice, and internal monitoring and governance systems;

and factors specific to the firm’s implementation of SFAS 157, such as disclosures on

management assumptions, access to market information for comparable values, and the

availability of in-house valuation experts. Thus, we suggest that firms with ex ante higher

quality information environments will mitigate any information gap across the level 1, 2, and 3

fair value designations. Restated, we assume that firms having higher quality information

environments likely also have higher quality disclosures, both generally and specific to SFAS

157. Accordingly, we use the overall information environment to proxy for the informativeness

of SFAS 157 related-disclosures. This leads to our second hypothesis (in alternative form):

H2: Firms with ex ante lower quality information environments exhibit larger differences in implied betas across the fair value level 1, 2, and 3 designations relative to firms with ex ante higher quality information environments.

If inherent characteristics of particular financial instruments, such as those designated as level 3

fair value, preclude the ability of the information environment to mitigate this information gap,

this will bias against finding relative differences across firm types.

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4. Research Design

4.1 INFORMATION RISK DIFFERENCES ACROSS LEVEL 1, 2 AND 3 FAIR VALUES 4.1.1. Derivation of Beta

Consider a firm, which is financed by both debt and equity in the absence of taxes. By

the balance sheet identity:

A = L + E (1)

where A is the firm’s total assets, L total liabilities, and E its equity. Decomposing assets

according to the fair value measurement bases yields the following relation:

A1 + A2 + A3 + OtherAssets = L + E (1a)

where A1 (A2) [A3] is assets measured at level 1 (level 2) [level 3] fair value, and OtherAssets is

remaining assets not measured at fair value.

Based on the relations in equation (1a), and scaling through by the firm’s total assets (A),

the weighted-average beta for the firm is calculated as:

βA1 A1/A + βA2 A2/A + βA3 A3/A + βOA OtherAssets/A = βL L/A + βE E/A (2)

Finally, solving for the equity beta leads to:

βE E/A = βA1 FVA1 + βA2 FVA2 + βA3 FVA3 + βOA OA – βL Leverage (2a)

where FVA1 (FVA2) [FVA3] are level 1 (level 2) [level 3] assets, OA is assets not measured at

fair value, and Leverage is total liabilities, all scaled by the firm’s total assets.

We then use equation (2a), the derivation of firm-specific beta with respect to the

decomposition of the firm’s assets, as the basis for the following regression (see Appendix A for

variable definitions):

Beta_adjit = 1 FVA1it + 2 FVA2it + 3 FVA3it + 4 OAit + 5 Leverageit + it (3)

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In this regression, the dependent variable is Beta_adj, firm i’s quarter t equity beta (Beta)

weighted by the equity ratio (equity divided by total assets). The independent variables include

the firm’s assets, decomposed into those reported at level 1 fair value (FVA1), level 2 fair value

(FVA2), level 3 fair value (FVA3), and all other (OA), all scaled by the firm’s total assets. Note

that our fair value measures are intended to capture market values, but use reported book values

as proxies. Thus, to maintain a consistent measurement base throughout the specification, we

also measure equity, debt, and other assets using book values. If the firm’s equity beta is simply

the composite of betas for the individual firm’s portfolio of assets, then the predicted signs for 1

through 4 in equation (3) are positive. Finally, we include the scaled level of debt financing

(Leverage). As demonstrated in equation (2a), the predicted sign for 5 is negative, and –5 is

the beta of firm debt. The empirical estimates of 1 through 5 are the implied betas that

investors face based on the distribution parameters of the market value of equity and the fair

value of the assets that management discloses. Our empirical test of hypothesis 1 is whether 3

> 2 > 1. Owing to the purported prominence of level 3 fair values, we particularly focus on

assessing the implied betas of level 3 financial assets relative to level 2 (i.e., 3 > 2) and level 1

(i.e., 3 > 1) financial assets. Note that equation (3) is estimated without an intercept in order

for the coefficients to directly reflect the implied betas on the portfolios of assets.2, 3

2 We could estimate equation (3) including an intercept and excluding other assets, in which case the coefficients

for assets at fair value capture the incremental beta relative to other assets. This estimation yields identical results to those presented. We focus on the presented specification to allow direct estimation of implied betas.

3 We do not estimate a change analysis, due to the challenge of identifying the components causing the level 1, 2, and 3 categories to change. That is, changes can occur due to movements of existing investments across categories (e.g., due to markets becoming less liquid), gains/losses on the underlying instruments, or due to new investment in particular categories. It is difficult to separate these changes within our sample data.

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Our empirical implementation of equation (3) requires an estimate of the firm’s equity

beta. To do so, we estimate a single-factor CAPM:4

RETiw = 0 + 1VW_RETiw + iw (4)

where RETiw is firm i’s common equity return, and VW_RETiw is the value-weighted stock

market return, both measured for week w. We estimate equation (4) using weekly data, as lower

frequency data reduces measurement error (e.g., Hou and Moskowitz 2005). We include all

available trading days for fiscal quarter t+1, corresponding to the quarter following fiscal quarter

t. This ensures that the relevant fair value disclosures for quarter t have become part of the

public information set, such as through the earnings press release or 10-Q filing. Thus, 1 is our

estimate of firm i’s equity beta (Beta) for each quarter t.

Our use of the single-factor CAPM is consistent with finance theory on asset pricing

(e.g., Sharpe 1964; Black 1972). Further, the single-factor CAPM ties to the model of Lambert,

Leuz, and Verrecchia (2007). We do not consider other CAPM derivations, such as the three-

factor model, as the theory underlying the other factors, particularly size and book-to-market,

remains unclear (Campbell, Hilscher, and Szilagyi 2008). Related, the three-factor model was

developed on non-financial firms (see Fama and French 1992, page 429), suggesting the role of

these other factors for our sample of financial firms remains unclear.

This research design makes several assumptions. First, we focus only on the

decomposition of assets into the fair value designations. However, liabilities can be similarly

decomposed into level 1, 2, and 3 fair values (and all other liabilities). This would appear

relevant, owing to linkages between assets and liabilities in financial institutions (e.g., reflecting

management of the interest spread). However, later descriptive evidence reveals that our sample

4 In untabulated results, we correct for non-synchronous trading (e.g., Dimson 1979) as our sample includes small market capitalization firms likely to have infrequent trading. Results applying this correction, which incorporates lagged returns into the CAPM model, are unchanged from those reported.

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firms’ economic exposures across the fair value designations are substantially greater for

financial assets relative to financial liabilities. Accordingly, the primary analyses focus on the

decomposition of assets into the fair value designations; results additionally decomposing

liabilities are unchanged (discussed in Section 7.2).

Second, we assume that capital structure is exogenously determined. Prior literature

suggests that in many industries, capital structure reflects characteristics such as asymmetric

information, the trade-off between taxes, and the costs of financial distress (Fama and French

2002), as well as market timing (Baker and Wurgler 2002). However, capital structure is subject

to significantly less variation within the banking sector that we examine, due to both the highly

leveraged structure of banks, as well as capital composition being dictated by regulatory

mandates. Descriptive evidence, presented in Table 2, is consistent with variation in leverage

ratios being quite small within our sample. Accordingly, we assume that endogenous variation

in capital structure is of secondary importance within the banking industry.

Third, our derivation ignores assets and liabilities not recognized in the accounting

system on the balance sheet by replacing market values with book values. Given the general

application of fair value accounting in the banking industry, differences between market and

book values are likely lower relative to other industry settings. Further, the use of book values

maintains consistency in the measurement of fair value measures and all other variables.

Nonetheless, results are robust to re-specifying model (3) in market value terms by substituting

market value of equity for book value of equity and including an additional variable of the

difference between market value and book value of equity (discussed in Section 7.3).5

5 Another consideration is the assumption of independence across the asset types. Empirically, the model allows

for correlations across the asset categories, similar to multivariate analysis: holding constant the average level of other assets, the coefficient (i.e., the implied asset beta) provides evidence of the association of a particular asset category with equity beta. Alternatively, if common macro factors drive observed values across the fair value

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To examine whether the quality of the information environment reduces the information

risk across financial instruments with different fair value designations, we partition our sample

firms using measures of the ex ante information environment to proxy for the informativeness of

the fair value disclosures. We use broader proxies of the firm’s information environment, versus

proxies specific to fair value disclosures, because the latter are unavailable, and we assume a

positive correlation between the quality of a firm’s overall information environment and that

specific to financial instrument fair values. We use four proxies to capture the ex ante quality of

the information environment: analyst coverage, market capitalization, analyst forecast error, and

analyst forecast dispersion (Lang and Lundholm 1993, 1996). Analyst coverage and market

capitalization (i.e., firm size) reflect measures of the informativeness of firm’s disclosures by

capturing the overall information environment. Forecast error and dispersion reflect measures of

the informativeness of firm’s disclosures by measuring analysts’ ability to translate information

into predictions of firm performance. As a fifth measure, we also apply principal component

analysis to the four factors to create a single measure of the information environment.

We measure analyst following using the number of analysts issuing quarterly earnings

forecasts for firm i for quarter t. We measure analyst forecast error by first obtaining the

absolute difference of actual earnings per share less the consensus analyst forecast for firm i for

quarter t. We measure analyst forecast dispersion by first obtaining the average standard

deviation of monthly forecasts for firm i across the three-month period of quarter t. To control

designations, this will lead to similar levels of perceived information risk across the designations, and accordingly bias against finding differences across them. Finally, a bank’s choice to hold certain assets (say, highly illiquid bonds) may affect its ability to hold other investments, as regulatory capital calculations may lead to certain portfolio weights. This should not give rise to any bias in the analyses, as it presents a constraint on the investment portfolio of the bank.

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for other factors leading to variation in these analyst forecast attributes, we then alternatively

regress analyst forecast error and forecast dispersion on forecast horizon, analyst coverage, an

indicator variable equal to 1 if the firm reports a loss, and the magnitude of actual reported

earnings per share, and use the residual from each regression. Finally, we measure market

capitalization at the end of quarter t.

Following predictions formulated in hypothesis 2, we expect that firms having higher

analyst following, lower analyst forecast errors, lower analyst forecast dispersion, and larger

market capitalization have ex ante higher quality information environments; by extension, we

assume these firms also have more informative fair value disclosures. Collectively, we designate

these firms as “HIGH_INF” firms. We suggest that the higher quality information environments

for these firms will mitigate informationally driven differences across the level 1, 2, and 3 fair

values designations. Alternatively, we expect that firms having lower analyst following, higher

forecast errors, higher forecast dispersion, and smaller market capitalization have ex ante lower

quality information environments; by extension, we assume these firms also have less

informative fair value disclosures. Collectively, we designate these firms as “LOW_INF” firms.

We suggest that the lower quality information environments for these firms will fail to mitigate

informationally driven differences across the level 1, 2 and 3 fair value designations.

Using the above four proxies, we implement equation (3) as follows:

Beta_adjit = HIGH_INF x (χ1H FVA1it + χ2H FVA2it + χ3H FVA3it + χ4H OAit + χ5H Leverageit)

+ LOW_INF x (χ1L x FVA1it + χ2L FVA2it + χ3L FVA3it + χ4L OAit + χ5L Leverageit)

+ ψit (5)

where HIGH_INF is an indicator variable equal to 1 for firms with above median analyst

following, below median forecast error, below median forecast dispersion, above median market

capitalization, or above median using the principal component, and 0 otherwise. LOW_INF is an

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indicator variable equal to 1 for firms with below median analyst following, above median

forecast error, above median forecast dispersion, below median market capitalization, or below

median using the principal component, and 0 otherwise. Thus, equation (5) is a fully-interacted

model of equation (3). Our primary test of hypothesis 2 compares coefficients across the firm

partitions; thus, it is a difference-in-difference design. Specifically, we predict that firms with

lower quality information environments exhibit relatively greater differences across the fair

value designations than firms with higher quality information environments. Empirically, we

examine relative differences across level 1 versus level 3 fair values as (χ3L – χ1L) > (χ3H – χ1H).

Similarly, we test relative differences across level 2 and level 3 as (χ3L – χ2L) > (χ3H – χ2H).

4.3 ISOLATING INFORMATION RISK AND THE DECOMPOSITION OF BETA One concern with our research design is the ability to isolate information risk, as opposed

to other forms of risk that may vary directly across the fair value designations. In particular,

fundamental risk―that is, the volatility of expected cash flows―(potentially) can vary directly

across the fair value designations we examine. We address this in two ways.

First and of primary importance, we note that equity beta from the single-factor model

may be decomposed into two mathematical components:

, (6)

where Beta is the firm’s equity beta from the single-factor model of equation (4) above; ρi,m is

the correlation of firm i’s stock return with that of the market; stdi is the standard deviation of the

firm i’s stock return; and stdm is the standard deviation of the stock return for the market.

Following this decomposition, and paralleling our derivation of Beta_adj, we use as alternative

dependent variables Correl_adj (which is ρi,m multiplied by firm i’s equity divided by total

19

assets) and Std_adj (which is stdi / stdm multiplied by firm i’s equity divided by total assets).

Consistent with implementation of equation (3), both are measured using weekly stock returns

over quarter t+1, using the value-weighted stock market return as the benchmark. This leads to

two alternative estimations of equation (3):

Correl_adjit = γ1 FVA1it + γ2 FVA2it + γ3 FVA3it + γ4 OAit + γ5 Leverageit + εit (3a)

Std_adjit = η1 FVA1it + η2 FVA2it + η3 FVA3it + η4 OAit + η5 Leverageit + θit (3b)

Critically, this decomposition allows empirical identification of the association between

information risk and the level 1, 2, and 3 fair value designations. In particular, finance theory on

stock price synchronicity proposes that ρi,m captures information risk by directly measuring the

co-movement between a firm’s stock return with the market (Morck, Yeung, and Yu 2000;

Durnev, Morck, Yeung, and Zarowin 2003; Jin and Myers 2006). Restated, stock returns of

more opaque firms exhibit higher correlation with the market return as insufficient firm-specific

information leads market participants to infer valuation parameters based on non-firm specific

(e.g., macro-economic) indicators. Accordingly, we predict that level 3 fair value instruments

will have a higher association with ρi,m relative to those designated as either level 1 or 2. That is,

if Correl _adj (i.e., ρi,m) captures information risk across the asset categories, then our

corroborating test of hypothesis 1 focuses on equation (3a): γ3 > γ2 and γ3 > γ1.6, 7 We similarly

use Correl_adj to assess hypothesis 2.

6 The measure of stdi / stdm can reflect either information risk or fundamental risk. In particular, firms with more

opaque financial assets may have more volatile stock returns owing to information risk, or firms with more liquid assets may have more volatile stock returns owing to the liquidity paradox (Myers and Rajan 1998). Therefore, the relation between Std_adj (i.e., stdi / stdm) and the fair value designations is an empirical question and we do not predict the signed effects; results for this dependent variable are presented for descriptive purposes only.

7 The volatility measures use actual volatility from historical returns. We alternatively use implied volatility to measure stdi / stdm, employing 60, 90 and 180 day implied volatilities that coincide with the measurement window of beta. Results are unchanged using these alternative measures.

20

Second, we note four aspects of our research design and setting that are consistent with

an information risk interpretation. First, our partition analyses identify subsamples of firms ex

ante expected to have differences in the quality of the information environment, but not ex ante

differences in fundamental risk. Second, regulatory motivation for SFAS 157, particularly

underlying the enhanced disclosures for level 3 fair values, reflected standard setter interest in

helping users understand the reliability of fair value estimates and related inputs, which is

consistent with an information risk notion. The standard setters do not refer to fundamental risk

as a motivation for SFAS 157, or for the need for disclosures that vary in proportion to the level

of expected outcomes. Third, the correlation between the information risk component of equity

beta (Correl) and a typical measure of firm-level “fundamental” risk (the standard deviation of

daily stock returns) is low for our sample firms at –0.07%, suggesting Correl captures an

element distinct from a fundamental risk notion. Finally, hand-collection of the financial

instruments comprising the level 1, 2, and 3 categories for a sub-sample of firms suggests that

fundamental risk is not necessarily increasing across these categories. For example, while level

1 financial assets include U.S. treasuries, they also include common stock; while level 3 assets

include derivatives, they also include bonds.8

5. Sample Selection and Descriptive Statistics

Table 1 Panel A presents the sample selection. We identify all firms defined as financial

institutions (SIC between 6020–6726), as fair value standards relate most directly to financial

instruments, which constitute the primary operating structure of these firms. Among financial

institutions, we focus on commercial banks (SIC 6020), savings institutions federally chartered

8 Concurrent research similarly provides descriptive evidence that level 1 assets include disproportionately more investment securities (which tend to be more liquid), while level 3 assets include more loans (which tend to be less liquid) (Song, Thomas, and Yi 2010).

21

(6035), and security brokers and dealers (6211), as these firms are most likely to have substantial

exposure to financial instruments measured across the fair value levels we examine. We then

include firms with fair value data available either through Compustat or hand-collection, as well

as market data from CRSP. This leads to our final sample of 467 firms. Panel B reveals that this

sample is comprised of 367 commercial banks, 70 savings institutions, and 30 security brokers.

Panels C and D present data regarding the time series. Our sample period begins with the first

fiscal quarter 2007, which was the earliest allowable reporting period for adoption of SFAS 157,

and thus the earliest time period to obtain the fair value categorizations.9 To focus the analyses

on the effect of SFAS 157, versus an examination of the financial crisis, our sample period ends

at second quarter 2008 due to the substantial increase in market volatility coinciding with the

third quarter of 2008.10 The final sample includes 952 firm-quarters spanning 2Q 2007 through

2Q 2008. Finally, Panel D presents the distribution by institution type and fiscal quarter.

Table 2 presents descriptive statistics for the variables used in the regressions. Of note,

financial assets recognized at fair value (FVA) are 17.40% of firms’ total assets on average

across our sample firm-quarters, with considerable variation across the sample.11 Of these, level

1 financial assets represent 2.29% of total assets (FVA1), level 2 represent 14.23% (FVA2), and

level 3 represent 0.87% (FVA3).12 Consistent with our focus on the financial assets measured at

fair value, liabilities reported at fair value have substantially lower economic significance, with

level 1 liabilities representing 0.61% of total assets (FVL1), level 2 liabilities 1.46% (FVL2), and

9 Fair values reported under SFAS 157 in 2007 were provided under an early-adoption option; data for 2007 was

hand-collected from firms’ quarterly reports. Results excluding these firms are unchanged (see Section 7.6). 10 Results are robust to extending the sample period through 3Q 2009 (see Section 7.5). 11 Results across all analyses are unchanged to excluding maximum and minimum observations. 12 Untabulated descriptive statistics reveal a shift towards more illiquid financial assets over our sample period.

Among early adopters, mean level 1 financial assets decreases from 11% of total assets at 1Q 2007 to 6% at 2Q 2008; in contrast, mean level 2 (level 3) assets increases from 23.5% to 29.0% (2.4% to 3.7%).

22

level 3 liabilities 0.07% (FVL3). Also, as expected for this industry, Leverage is high with a

mean of 89.45%.13 Finally, the sample firms have mean total assets of $50.667 billion (median

of $1.529 billion), and are economically significant, with 2Q 2008 total assets of $16 trillion.

6. Empirical Results

6.1 INFORMATION RISK DIFFERENCES ACROSS LEVEL 1, 2, AND 3 FAIR VALUES

Table 3 presents results from our primary regression examining the effect of information

risk, proxied using financial instrument fair value designations, on implied asset betas. Across

all regressions, we include fixed effects for quarter, as well as time-varying effects for sector

(commercial bank, savings institution, or security broker) and stock exchange (NYSE, AMEX).

Column (1) presents a base regression, wherein the dependent variable is Beta_adj. Other assets

not reported at fair value under SFAS 157 (OA) have an implied asset beta of 1.032, while assets

reported at fair value (FVA) have an implied asset beta of 1.019.14 Column (2) then presents

results decomposing financial assets reported at fair value into level 1 (FVA1), level 2 (FVA2),

and level 3 (FVA3). The results reveal a monotonic increase in the implied asset betas across

these designations: FVA1 = 0.769, FVA2 = 0.933, and FVA3 = 1.600. Consistent with hypothesis

1, F-tests reveal that the coefficient for FVA3 is significantly larger than that for either FVA1 (p-

value = 0.007) or FVA2 (p-value = 0.014). To the extent opacity is increasing across the fair

13 Note that several firms have extremely low leverage relative to the broad sample (see the minimum Leverage in

Table 2); these are broker-dealers (SIC = 6211), which do not have deposits, and thus have low leverage. 14 Because our hypotheses focus on the relative differences in coefficients across the level 1, 2, and 3 fair value

designations, and not on the absolute coefficients, we do not discuss the significance levels of individual coefficients in these analyses. However, we note that most coefficients are highly significant; this is not surprising, given the derivation and empirical estimation of equation (3).

23

value designations, this is consistent with more opaque financial assets leading to greater

information risk, and thus a higher cost of capital.15

Columns (3) and (4) then present results decomposing the dependent variable, Beta_adj,

into its two mathematical components: Correl_adj and Std_adj. Because Correl_adj captures

information risk (e.g., Morck, Yeung, and Yu 2000; Jin and Myers 2006), which is the focus of

our study, we discuss results for this component only; results for Std_adj are presented for

informational purposes. Column (3) reveals a similar monotonic increase across the fair value

designations when the dependent variable is Correl_adj: FVA1 = 0.385, FVA2 = 0.419, and

FVA3 = 0.517. F-tests reveal the FVA3 coefficient remains significantly larger than FVA1 (p-

value = 0.048) and marginally more positive than FVA2 (p-value = 0.096). If this component

isolates information risk, this provides corroborating evidence that more opaque financial assets,

reflected in the level 3 designation, lead to greater information risk, consistent with hypothesis 1.


We then examine sample partitions across firm characteristics expected to capture the

firm’s ex ante information environment. Table 4 provides univariate comparisons across four

partitions: analyst following, forecast error, forecast dispersion, and market capitalization (all as

previously defined). Across all panels, columns (1) and (2) present firms expected to have ex

ante higher quality information environments; columns (3) and (4) present firms expected to

have ex ante lower quality information environments. Panel A presents firms with high analyst

15 While not the primary focus of our study, column (3) of Table 3 reveals that the coefficient on OA (0.417) is

greater than that for FVA1 (0.385), suggesting higher information risk for other assets relative to level 1 fair value assets. This, and similar associations in our other analyses, likely reflect the uncertainty and declines in value regarding bank loan portfolios. Specifically, the variable other assets is primarily comprised of loans held-to-maturity for our sample firms, comprising approximately 68% of total assets on average. Such loans exhibited substantial declines in value (and increased uncertainty) during our sample period. However, our primary focus remains in comparisons across the level 1, 2, and 3 fair value designations.

24

following (HIGHFOLL, N = 368) versus low analyst following (LOWFOLL, N = 288); Panel B

presents firms with low forecast error (LOW_ERR, N = 329) versus high forecast error

(HIGH_ERR, N = 327); Panel C presents firms with low forecast dispersion (LOW_DISP, N =

265) versus high forecast dispersion (HIGH_DISP, N = 262); and Panel D presents firms with

large market capitalization (LARGE, N = 496) versus small market capitalization (SMALL, N =

456). As discussed previously, we expect that firms with high analyst following, low forecast

error, low forecast dispersion, or large market capitalizations will have ex ante higher quality

information environments.

Table 4 reveals that exposure to level 2 and 3 financial assets varies across the partitions.

Firms with higher analyst following (Panel A) or larger market capitalization (Panel D) have

significantly greater exposure to portfolios of level 2 and 3 financial assets than firms with lower

analyst following or smaller market capitalization. There is no difference in level 1, 2, or 3

portfolios across firms with high versus low forecast error (Panel B). However, firms with lower

forecast dispersion have significantly lower exposure to level 2 and 3 financial assets than firms

with higher forecast dispersion (Panel C). Critically, these comparisons suggest that the four

partitions do not reflect a systematic selection of exposure to fair value portfolios, mitigating the

risk of misattributing differences in implied betas to the ex ante information environment, when

it reflects differences in the asset portfolios.

Table 5 presents results across these four sample partitions as well as the combined

factor; within each panel, we estimate a fully-interacted model (i.e., seemingly unrelated

regression) to allow statistical comparisons of coefficients. Panel A presents results using

analyst following. Column (1) presents results for firms with high analyst following; while there

is a monotonic increase in coefficients (FVA1 = 1.241, FVA2 = 1.250, and FVA3 = 1.344), F-

25

tests immediately below fail to provide evidence of significant differences. This is consistent

with our priors that firms ex ante expected to have higher quality information environments, such

as those having high analyst following, will be less likely to exhibit differential information risk

across the fair value designations. Column (2) presents results for firms with low analyst

following, again revealing a monotonic increase across the coefficients (FVA1 = 0.361, FVA2 =

0.399, and FVA3 = 3.695); the coefficient for FVA3 is significantly greater than either FVA1 (p-

value = 0.002) or FVA2 (p-value = 0.003). This is consistent with our priors that firms ex ante

expected to have lower quality information environments, such as those with low analyst

following, exhibit differential information risk across the fair value designations. Finally, F-tests

at the bottom of the panel present comparisons of coefficients across the high and low analyst

following subsamples (i.e., a difference-in-difference design). The coefficient for FVA3 is

relatively more positive than either FVA1 (p-value = 0.002) or FVA2 (p-value = 0.002) for low

analyst following firms as compared to high analyst following firms. This supports hypothesis 2.

In columns (3) and (4), we present results using as the dependent variable Correl_adj, the

component of beta expected to isolate information risk. In column (3) for firms with high

analyst following, there is no increase in coefficients across the fair value designations (FVA1 =

0.477, FVA2 = 0.480, and FVA3 = 0.475), with F-tests immediately below indicating

insignificant differences. In column (4) for firms with low analyst following, while there is a

monotonic increase in the coefficients (FVA1 = 0.285, FVA2 = 0.309, and FVA3 = 0.821), the F-

tests again are insignificant. However, again consistent with hypothesis 2, F-tests at the bottom

of the panel reveal that, compared to high analyst following firms, low analyst following firms

exhibit relatively more positive coefficients for FVA3 than either FVA1 (p-value = 0.056) or

FVA2 (p-value = 0.062).

26

Panels B, C, D, and E present results for partitions using forecast error, forecast

dispersion, market capitalization, and the combined factor, respectively.16 Results are consistent

with those presented above, though significance levels vary. That is, firms ex ante expected to

have lower quality information environments exhibit relatively larger differences in implied asset

betas across the fair value designations than firms expected to have higher quality information

environments. We focus the discussion on columns (3) and (4), where the dependent variable is

Correl_adj. In Panel B, compared to firms with low forecast errors (LOW_ERR), firms with

high forecast errors (HIGH_ERR) exhibit relatively more positive coefficients for FVA3 than

either FVA1 (p-value < 0.001) or FVA2 (p-value = 0.001). In Panel C, compared to firms with

low forecast dispersion (LOW_DISP), firms with high forecast dispersion (HIGH_DISP) exhibit

a marginally more positive coefficient for FVA3 than FVA1 (p-value = 0.100), but not FVA2 (p-

value = 0.431). In Panel D, compared to firms with large capitalization (LARGE), firms with

low capitalization (SMALL) exhibit a marginally more positive coefficient for FVA3 than FVA1

(p-value = 0.099) but not FVA2 (p-value = 0.159). Finally, in Panel E, compared to firms with

higher quality information environments (HIGH_INF), firms with lower quality information

environments (LOW_INF) exhibit a significantly more positive coefficient for FVA3 than FVA1

(p-value = 0.005) or FVA2 (p-value = 0.016).

Overall, the results suggest that ex ante higher quality information environments mitigate

differences across the level 1, 2, and 3 fair value designations relative to lower quality

information environments. To the extent that the quality of the information environment is

positively correlated with disclosures specific to SFAS 157, this is consistent with better

disclosures under SFAS 157 mitigating information risk across the fair value designations.

16 The first principal component of the four measures captures 42% of the total variation and has an eigenvalue of 1.72. Firm size, followed by analyst following, forecast error and dispersion have the largest influence on the principal component (the eigenvectors are respectively 0.63, 0.58, 0.38, and 0.34).

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7. Sensitivity Analyses

7.1 ALTERNATIVE MEASUREMENTS OF BETA

Our primary analyses employ two key dependent variables: first, the firm’s leverage-

adjusted equity beta (Beta_adj); second, the leverage-adjusted correlation coefficient

(Correl_adj). Both variables are calculated from estimations of the single-factor CAPM model

using weekly stock returns over the quarter t+1 and the value-weighted stock market return (i.e.,

Equation (4)). However, there are multiple approaches to empirically estimate these variables.

Accordingly, we assess the robustness of our results by varying the measurement window, the

frequency of returns data, and the benchmark return.

First, we vary the measurement window to estimate the CAPM model. The primary

analyses use returns measured over quarter t+1 to ensure that the relevant fiscal quarter t 10-Q

and related fair value designations are within the public information set. We consider two

alternative measurement windows, both using weekly stock returns. First, we use the 6-month

window of quarter t and t+1; this captures both the official release of the quarterly financials, as

well as anticipated information (sourced from the firm or externally, such as by analysts).

Second, we use the 15-month window of quarter t-3 through t+1. Panel A of Table 6 presents

the results under the headings “6 MONTH” and “15 MONTH,” respectively. The coefficients

consistently increase across the level 1, 2, and 3 designations, with F-tests providing some

support that FVA3 is significantly more positive than for FVA1 or FVA2.

Next, we vary the frequency of returns data used to estimate the CAPM model. Our

primary analyses use weekly stock returns, which reduces volatility in the estimation process

(e.g., Hou and Moskowitz 2005). We use two alternative frequency measures: daily stock

28

returns over the 3-month window of quarter t+1; and monthly returns over the 15-month window

of quarter t-3 through quarter t+1.17 Results are presented in Panel B under the headings

“DAILY” and “MONTHLY,” respectively; again, the coefficients consistently increase across the

level 1, 2 and 3 designations. However, F-tests reveal FVA3 is significantly more positive than

FVA1 and FVA2 only using monthly returns; differences are insignificant using daily returns.

Finally, we vary the benchmark return. Our primary analyses use the value-weighted

stock market return, consistent with finance theory underlying beta. We use two alternative

benchmarks: the equal-weighted stock market return; and the S&P 500 return. Results,

presented in Panel C under the headings “EQUAL” and “SP500,” respectively, reveal that the

coefficient for FVA3 is significantly more positive than that for FVA1 or FVA2. Overall, the

results appear generally robust to alternative measurements of the dependent variables.

7.2 DECOMPOSING LIABILITIES AT FAIR VALUE

As discussed, our primary analyses focus on financial assets, due to the larger economic

magnitude reported at fair value relative to liabilities (see Table 2). However, assets of financial

services firms are often tied to their liabilities, as banks manage the “spread” in interest earned

on assets versus that paid on liabilities. Accordingly, we incorporate the decomposition of

liabilities designated at level 1, 2, and 3 fair values by re-estimating equation (3) as:

Beta_adjit = τ1 FVA1it + τ2 FVA2it + τ3 FVA3it + τ4 OAit

+ τ5 FVL1it + τ6 FVL2it + τ7 FVL3it + τ8 OLit + it (7)

where FVL1 (FVL2) [FVL3] are liabilities reported at level 1 (2) [3], and OL is all other

liabilities; all variables remain scaled by total assets. Consistent with hypothesis 1, we expect

17 We use the 3-month window of quarter t+1 for the daily stock return estimation to correspond to our primary

analyses. We extend this to 15 months for the monthly stock return estimation to ensure sufficient observations.

29

that increasingly opaque liability fair values, particularly captured in the level 3 designation, will

lead to higher information risk, and thus higher implied liability betas; that is, we expect the

coefficients to be increasingly negative across liabilities designated as level 1, 2, and 3.18

Table 7 Panel A presents the results. In column (1), where the dependent variable is

Beta_adj, the coefficients remain monotonically increasing across the asset designations of

FVA1, FVA2, and FVA3. In addition, there is a significantly monotonic decrease in coefficients

across liabilities designated as level 1 (FVL1 coefficient = –0.511), level 2 (FVL2 = –0.936) and

level 3 (FVL3 = –4.367). In column (2), where the dependent variable is Correl_adj, the

coefficient for FVL3 is again significantly more negative than that for FVL1 or FVL2. Overall,

the results suggest that information risk, reflected in implied beta, is increasing for more opaque

fair values for financial liabilities as well as financial assets.

7.3 CONTROLLING FOR UNRECOGNIZED ASSETS AND LIABILITIES

Our empirical estimation of equity beta and the fair value decomposition of assets uses

book value of equity to proxy for market value of equity. We now examine the robustness to

directly incorporating market value of equity by re-estimating equation (3) as:

Beta_MVEit = σ1 A1/MVAit + σ2 A2/MVAit + σ3 A3/MVAit + σ4 OtherAssets/MVAit

+ σ5 L/MVAit + σ6 UnrecogAL/MVAit + υit (8)

Relative to our primary equation (3), there are three changes. First, Beta_MVE remains firm i’s

quarter t equity beta, but is now weighted by the market value of equity scaled by the market

value of equity plus book value of liabilities. Second, we add the variable UnrecogAL, defined

18 Note that the predicted coefficients for liabilities are increasingly negative across the level 1, 2, and 3

designations, while the predicted coefficients for financial assets are increasingly positive. This follows from our derivation of equation (1): liabilities are subtracted from assets to arrive at equity, leading to the negative-signed coefficients. However, a more negative coefficient for a liability is consistent with an increasing implied liability beta, and thus consistent with higher information risk and a higher cost of capital.

30

as market value of equity less book value of equity, to control for any unrecognized (i.e., off-

balance sheet) assets and liabilities to the extent the equity market prices such components into

their expectations of the firm’s future cash flows. Third, we now scale all variables by market

value of equity plus book value of liabilities (i.e., MVA), versus our previous deflator of total

assets. Table 7 Panel B presents the results, revealing that implied asset betas on level 3

financial assets remain more positive relative to those for either level 1 or 2 assets.

7.4 DOES ADOPTION OF SFAS 157 REDUCE INFORMATION RISK?19

The regulatory motivation behind SFAS 157 was to enhance disclosures to assist users in

understanding the reliability of the reported fair values. This suggests that disclosures provided

upon adoption of SFAS 157 should reduce information risk, relative to before the standard.

However, direct examination of the impact of SFAS 157 requires estimates of the pre-SFAS 157

assets across the three fair value categories, as these are not disclosed prior to the standard’s

adoption. To provide a preliminary analysis, we perform the following. First, we identify the

proportion of total assets designated as level 1, 2, and 3 fair value (with the remaining assets

assumed at historical cost) for Q1 2008 for each non-early adopter firm i. Second, we apply

these proportions to firm i’s quarterly total assets for Q1 through Q4 2007 to derive pre-SFAS

157 observations; that is, we use Q1 2008 to proxy for the unobservable proportions across the

fair value categories prior to SFAS 157 adoption.20 Finally, we compare implied asset betas for

the pre-SFAS 157 observations to those for the post-SFAS 157 observations, again using

19 We thank the editor for suggesting this analysis. 20 We use Q1 2008 as this is the closest temporal quarter to 2007, so it more likely approximates 2007 fair value

proportions relative to later 2008 quarters.

31

seemingly unrelated regression. Results, presented in Table 8 Panel A, reveal directionally

consistent but insignificant relative differences across pre- versus post-SFAS 157 observations.

However, our second hypothesis suggests higher quality information environments

mitigate differences across the fair value designations. Accordingly, we partition the sample

following Panel A of Table 5, our primary measure of the ex ante information environment: low

quality (defined as firms with below median analyst following), and high quality (defined as

firms with above median analyst following). As expected, Panel B reveals no differences across

the pre- and post-SFAS 157 observations for firms expected to have lower quality information

environments, i.e., the low following firms. However, Panel C reveals differences across the fair

value designations are reduced following adoption of SFAS 157 for firms expected to have

higher quality information environments, i.e., the high following firms.21 Similar results obtain

using the partitions of analyst forecast error, forecast dispersion, and market capitalization.

7.5 EXTENDING THE SAMPLE PERIOD

The primary research question and analyses focus on assessing differential information

risk across the fair value designations under SFAS 157, versus assessing the effect of the

financial crisis per se. In addition, volatility in the stock market increases substantially with Q3

2008.22 Accordingly, we end the sample period for the primary analyses at Q2 2008. However,

to assess the robustness of our findings, we expand the time series to include five additional

fiscal quarters spanning Q3 2008 through Q3 2009.

21 Note, we do not tabulate results for the dependent variable Std_adj in Table 8 for parsimony. 22 For example, relative to January–August 2008, the VIX measure of volatility increased threefold for September–

December 2008. This likely reflects uncertainty, particularly regarding financial institutions, coinciding with (among other events) the Lehman Brothers bankruptcy of September 15.

32

First, we replicate Table 3 using the expanded sample period. Results, reported in Panel

A of Table 9, are unchanged from those previously reported, except that significance is reduced

(particularly using Correl_adj as the dependent variable). Next, we replicate the analyst

following partition of Table 5. Results, reported in Panel B of Table 9, are again unchanged

from those previously reported. Untabulated results, replicating the other partitions of Table 5,

are again unchanged from those previously reported.

Finally, we examine the robustness to expanding the sample to include only the 2009

fiscal quarters; that is, excluding Q3 and Q4 2008. We exclude the latter two quarters for two

reasons. First, these exhibit substantially higher volatility across all of our dependent variable

measures relative to any other sample quarters. Second, while estimated betas exhibit positive

correlations across time, this association does not hold for these two quarters. Untabulated

results are unchanged from those reported above, except that significance levels increase

substantially when excluding Q3 and Q4 2008.

7.6 SUBSAMPLE ANALYSES

We also assess the robustness of the results to subsample analyses. In particular, we

restrict the sample to commercial banks, which comprise the majority of the sample firms (see

Table 1). These banks likely having differing characteristics from other financial institutions,

such as investment banks. Second, we eliminate firms electing early-adoption of SFAS 157, to

mitigate issues associated with potential self-selection. Descriptively, the early adopter firms (N

= 25 firms) are the largest in the sample, with average total assets (market capitalization) of $344

billion ($33 billion), compared to $28 billion ($2.3 billion) for the non-early adopters. Results

for both analyses are unchanged from those reported.

33

8. Conclusion

This paper examines whether information risk in reported fair values affects firms’ cost

of capital. We use as our setting financial institutions over the period 2Q 2007 through 2Q 2008.

This coincides with the earliest availability of SFAS 157 disclosures, which require any financial

instruments reported at fair value to be designated at level 1, 2, or 3, indicating progressively

more subjective inputs. The research design decomposes the statement of financial position to

map the firm’s observed equity beta into implied asset betas of individual asset classifications,

particularly financial assets for the level 1, 2, and 3 fair value categories.

Empirical results are consistent with two predictions. First, we find that firms with

greater exposure to more opaque financial assets, reflected in the level 3 fair value designation,

exhibit a higher cost of capital, reflected in relatively higher implied asset betas. Second, we

partition our sample using proxies of the ex ante information environment, predicting that

differences in information risk across the level 1, 2, and 3 fair values will be mitigated for firms

with higher quality information environments. That is, we expect that firms with higher quality

information environments will also have better disclosures under SFAS 157. We designate firms

with high analyst following, low forecast errors, low forecast dispersion, or large market

capitalization as having ex ante higher quality information environments; firms with low analyst

following, high analyst forecast errors, high analyst forecast dispersion, or small market

capitalization we designate as having ex ante lower quality information environments. We then

compare differences in coefficients for the level 1, 2, and 3 designations across these two groups

of firms. Consistent with expectations, we find relatively higher information risk for level 3

versus level 1 and 2 fair values for firms with ex ante lower quality information environments.

34

To provide a stronger empirical identification of information risk, and to rule out an

alternative explanation of fundamental risk varying directly across the fair value designations,

we decompose our dependent variable, beta, into its two mathematical components: the

correlation between a firm’s stock returns and those of the market; and the standard deviation of

a firm’s stock returns divided by the standard deviation of the market’s returns. Finance theory

argues that the first component―the correlation―captures the information risk attribute that we

wish to investigate. Results are consistent focusing on this component of beta, as well as across

numerous sensitivity analyses.

Overall, we conclude that greater exposure to more opaque financial instruments,

reflected in the level 3 fair value designation, leads to higher information risk, and thus a higher

cost of capital, consistent with previous findings of lower value relevance for level 3 fair values

(e.g., Song, Thomas, and Yi 2010). In addition, we document that higher quality information

environments, likely reflective of more informative fair value disclosures under SFAS 157, can

mitigate differences in information risk across the fair value designations, consistent with

suggestions in Ryan (2008). While we may be unable to fully rule out alternative explanations

(such as fundamental risk varying directly across the fair value designations), the motivation

underlying passage of SFAS 157, the decomposition of equity beta into components, the sub-

sample partition analyses, the pre- and post-SFAS 157 research design, and descriptive data all

appear consistent with the information risk interpretation.

35

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38

APPENDIX A Variable Definitions

Category Definition

Dependent Variables

Betait The coefficient from a regression of firm i’s weekly stock returns for quarter t+1 regressed on the weekly value-weighted stock market returns for quarter t+1.

Beta_adjit Beta multiplied by the ratio of equity to total assets for firm i at quarter t.

Correlit The first mathematical component of beta: the correlation between firm i’s weekly stock returns for quarter t+1 and those for the value-weighted stock market for quarter t+1.

Correl_adjit Correl multiplied by the ratio of equity to total assets for firm i at quarter t.

Stdit The second mathematical component of beta: the standard deviation of firm i’s weekly stock returns for quarter t+1 divided by the standard deviation of weekly stock returns for the value-weighted market for quarter t+1.

Std_adjit Std multiplied by the ratio of equity to total assets for firm i at quarter t.

Experimental Variables

FVAit Assets listed at fair value divided by total assets for firm i at the end of quarter t.

FVA1it (FVA2it) [FVA3it]

Assets listed as level 1 (level 2) [level 3] fair value divided by total assets for firm i at the end of quarter t.

Control Variables

OAit Assets not listed at fair value divided by total assets for firm i at the end of quarter t.

Leverageit The ratio of total liabilities to total assets for firm i at the end of quarter t.

FOLLit The number of analysts following firm i during quarter t.

Mcapit The market value of equity for firm i at the end of quarter t.

ERRit (DISPit) The forecast error (forecast dispersion) for firm i at the end of quarter t, measured as the absolute value of actual earnings less the consensus earnings forecast (the standard deviation of each analyst’s latest earnings forecast for quarter t). We obtain the residual from a regression of this forecast error (forecast dispersion) upon forecast horizon, analyst coverage, an indicator variable equal to 1 for reporting a loss and zero otherwise, and the magnitude of actual reported earnings per share.

Variables for Sensitivity Analyses

OLit Liabilities not listed at fair value divided by total assets for firm i at the end of quarter t.

FVLit Liabilities listed at fair value divided by total assets for firm i at the end of quarter t.

FVL1it (FVL2it) [FVL3it]

Liabilities listed as level 1 (level 2) [level 3] fair value divided by total assets for firm i at the end of quarter t.

UnrecogALit Unrecognized assets and liabilities for firm i at the end of quarter t, measured as the difference between market and book value of equity over the sum of market value of equity and book value of liabilities.

39

TABLE 1 Sample Selection and Frequency Statistics

Panel A: Firm Selection

All financial institutions with SIC between 6020-6726 962

Less: institutions not classified as Commercial Banks (SIC 6020), Saving Institutions Federal Chartered (6035), or Security Brokers and Dealers (6211)

219

Remaining firms with SIC codes of 6020, 6035, or 6211 743

Less: Institutions lacking fair value information per Compustat or missing stock returns 276

Final number of firms 467

Panel B: Frequency of Firms by Institution Type

Commercial Banks (SIC 6020) 367

Saving Institutions Federal Chartered (SIC 6035) 70

Security Broker and Dealers (SIC 6211) 30

Panel C: Frequency of Observations by Fiscal Quarter

Fiscal Year Fiscal Quarter Observations 2007 2 21 2007 3 22 2007 4 25 2008 1 454 2008 2 430

Total observations 952 Panel D: Frequency of Observations by Institution Type and Fiscal Quarter

Institution Type Fiscal Year Fiscal Quarter Observations Commercial Banks 2007 2 14 Commercial Banks 2007 3 14 Commercial Banks 2007 4 17 Commercial Banks 2008 1 356 Commercial Banks 2008 2 345 Saving Institutions Federal Chartered 2007 2 2 Saving Institutions Federal Chartered 2007 3 2 Saving Institutions Federal Chartered 2007 4 2 Saving Institutions Federal Chartered 2008 1 68 Saving Institutions Federal Chartered 2008 2 63 Security Broker and Dealers 2007 2 5 Security Broker and Dealers 2007 3 6 Security Broker and Dealers 2007 4 6 Security Broker and Dealers 2008 1 30 Security Broker and Dealers 2008 2 22 Total observations 952

This table presents the firm selection in Panel A, frequency of firms by institution type in Panel B,

frequency of observations by fiscal quarter in Panel C, and frequency of observations by institution type and fiscal quarter in Panel D.

40

TABLE 2 Descriptive Statistics

Variable Mean Std Dev Max Q3 Median Q1 Min

Dependent Variables Beta 0.897 0.860 11.993 1.346 0.815 0.359 –2.000

Beta_adj 0.097 0.153 1.826 0.122 0.069 0.032 –0.152

Correl 0.404 0.278 0.969 0.623 0.450 0.226 –0.722

Correl_adj 0.043 0.054 0.532 0.056 0.038 0.018 –0.095

Std 2.293 1.449 21.779 2.791 1.989 1.447 0.308

Std_adj 0.238 0.266 3.075 0.259 0.177 0.120 –0.006

Experimental Variables FVA 17.40 % 13.40 % 90.14 % 22.32 % 14.80 % 8.65 % 0.01 %

FVA1 2.29 % 6.08 % 77.74 % 1.21 % 0.13 % 0.00 % 0.00 %

FVA2 14.23 % 11.47 % 76.88 % 19.38 % 12.72 % 5.92 % 0.00 %

FVA3 0.87 % 2.82 % 40.47 % 0.47 % 0.00 % 0.00 % 0.00 %

Control Variables OA 82.60 % 13.40 % 99.99 % 91.36 % 85.20 % 77.68 % 9.86 %

Leverage 89.45 % 9.03 % 100.00 % 92.65 % 91.07 % 89.41 % 10.35 %

Descriptive Variables Sales 868 3,912 32,526 92 32 14 2

Total Assets 50,667 222,738 1,775,670 4,661 1,529 721 43

ROA 0.07% 0.66% 3.92% 0.24% 0.16% 0.07% -10.93%

Variables for Sensitivity Analyses FVL 2.15 % 8.24 % 78.72 % 0.11 % 0.00 % 0.00 % 0.00 %

FVL1 0.61 % 3.93 % 69.69 % 0.00 % 0.00 % 0.00 % 0.00 %

FVL2 1.46 % 6.08 % 53.38 % 0.05 % 0.00 % 0.00 % 0.00 %

FVL3 0.07 % 0.34 % 3.23 % 0.00 % 0.00 % 0.00 % 0.00 %

This table provides descriptive statistics for the variables used in the regression analyses. Sales is quarterly sales in $ millions. Total Assets is ending total assets in $ millions. ROA is net income divided by ending total assets. All other variables are defined in Appendix A. Across all variables, N = 952 firm-quarter observations.

41

TABLE 3 Information Risk Differences Across Level 1, 2, and 3 Fair Values

Dependent Variable:

Beta_adj Beta_adj Correl_adj Std_adj

Variable Predicted Sign (1) (2) (3) (4) OA + 1.032 *** 0.970 *** 0.417 *** 2.159 *** FVA + 1.019 *** FVA1 + 0.769 *** 0.385 *** 1.905 *** FVA2 + 0.933 *** 0.419 *** 1.994 *** FVA3 + 1.600 *** 0.517 *** 2.868 *** Leverage – –1.053 *** –0.982 *** –0.416 *** –2.170 ***

Fixed effects for:

Quarter Included Included Included Included

Exchange x Quarter Included Included Included Included

Sector x Quarter Included Included Included Included

Tests of hypothesis 1 (one-sided p-values for F-tests comparing coefficients):

FVA1 ≤ FVA2 ≤ FVA3 0.004 0.078 0.033 FVA1 < FVA2 0.038 0.094 0.305 FVA1 < FVA3 0.007 0.048 0.016 FVA2 < FVA3 0.014 0.096 0.029

This table presents results from regressions examining the effect of fair value disclosures upon scaled beta and its mathematical

components. The fair value disclosures are the decomposition of sample firms’ financial assets into those designated as level 1, 2 and 3. Across all regressions, N = 952 firm-quarters. We present coefficient estimates, followed by ***, **, * indicating significance at the less than 1%, 5%, and 10% levels using one-sided tests, respectively. Standard errors are robust to heteroscedasticity and clustered at the firm level. Below the regressions, we present p-values from F-tests of coefficients testing hypothesis 1.

Column (1) presents a base regression, wherein the dependent variable is Beta_adj, the leverage-adjusted equity beta. Column (2) provides a similar regression with the same dependent variable, with financial assets at fair value (FVA) decomposed into those designated at level 1 (FVA1), level 2 (FVA2), and level 3 (FVA3). Columns (3) and (4) replace the dependent variable Beta_adj with its two mathematical components: Correl_adj and Std_adj, respectively. All variables are defined in Appendix A.

42

TABLE 4 Univariate Comparisons Across Partitions on the Ex Ante Information Environment

Ex Ante Higher Quality

Information Environment

Ex Ante Lower Quality

Information Enviroment

Differences Mean Median Mean Median Mean Median (1) (2) (3) (4) (5) (6)

Panel A. Analyst Following

Variable HIGHFOLL (N = 368) LOWFOLL (N = 288) (p-value) Beta_adj 1.228 1.193 0.743 0.647 < 0.001 < 0.001 Correl_adj 0.534 0.580 0.346 0.359 < 0.001 < 0.001 Std_Dev_adj 2.401 2.205 2.204 1.963 0.024 0.023 FVA1 2.61 % 0.21 % 2.05 % 0.10 % 0.246 0.199 FVA2 15.37 % 13.10 % 12.23 % 10.80 % 0.001 0.001 FVA3 1.31 % 0.18 % 0.49 % 0.00 % < 0.001 < 0.001 Panel B. Forecast Error

Variable LOW_ERR (N = 329) HIGH_ERR (N = 327) (p-value)

Beta_adj 1.033 1.013 0.997 0.941 0.544 0.663 Correl_adj 0.481 0.526 0.422 0.469 0.005 0.023 Std_Dev_adj 2.201 1.991 2.428 2.224 0.009 0.007 FVA1 2.23 % 0.11 % 2.50 % 0.18 % 0.580 0.681 FVA2 13.94 % 12.19 % 14.05 % 12.50 % 0.904 0.907 FVA3 0.82 % 0.00 % 1.09 % 0.01 % 0.187 0.467 Panel C. Forecast Dispersion

Variable LOW_DISP (N = 265) HIGH_DISP (N =262) (p-value)

Beta_adj 1.110 1.054 1.145 1.098 0.578 0.468 Correl_adj 0.504 0.543 0.488 0.535 0.455 0.467 Std_Dev_adj 2.289 2.067 2.450 2.256 0.095 0.060 FVA1 1.72 % 0.13 % 3.39 % 0.23 % 0.004 0.007 FVA2 13.27 % 11.89 % 15.60 % 13.27 % 0.021 0.030 FVA3 0.74 % 0.00 % 1.52 % 0.13 % 0.001 0.003 Panel D. Market Capitalization

Variable LARGE (N = 496) SMALL (N = 456) (p-value) Beta_adj 1.200 1.106 0.568 0.477 < 0.001 < 0.001 Correl_adj 0.521 0.563 0.276 0.291 < 0.001 < 0.001 Std_Dev_adj 2.337 2.118 2.244 1.879 0.327 0.109 FVA1 2.74 % 0.20 % 1.80 % 0.02 % 0.016 0.010 FVA2 16.32 % 13.65 % 11.97 % 10.57 % < 0.001 < 0.001 FVA3 1.29 % 0.07 % 0.42 % 0.00 % < 0.001 < 0.001 This table presents univariate comparisons of the primary dependent and independent variables across partitions of the firm’s ex ante information environment. Columns (1) and (2) present means and medians, respectively, for the subsamples of firms expected to have ex ante higher quality information

43

environments. Columns (3) and (4) present means and medians, respectively, for the subsamples of firms expected to have ex ante lower quality information environments. Columns (5) and (6) present tests of differences in means and medians across the partitions, respectively.

In Panel A, the partitioning variable is analyst following, defined as the number of analysts issuing earnings forecasts for firm i during quarter t. HIGHFOLL (LOWFOLL) includes firms with analyst following greater than or equal to (less than) the sample median.

In Panel B, the partitioning variable is forecast error, defined in two steps. First, we use the absolute value of actual earnings per share less the consensus analyst forecasted earnings per share for firm i for quarter t. Second, we obtain the residual from a regression of this forecast error upon forecast horizon, analyst coverage, an indicator variable equal to one for reporting a loss and zero otherwise, and the magnitude of actual reported earnings per share. LOW_ERR (HIGH_ERR) includes firms with consensus forecast error below (above) the sample median.

In Panel C, the partitioning variable is forecast dispersion, similarly defined in two steps. First, we use the average standard deviation of monthly forecasts for firm i across the three-month period of quarter t. Second, we obtain the residual from a regression of this forecast dispersion upon forecast horizon, analyst coverage, an indicator variable equal to one for reporting a loss and zero otherwise, and the magnitude of actual reported earnings per share. LOW_DISP (HIGH_DISP) includes firms with forecast dispersion below (above) the sample median.

In Panel D, the partitioning variable is market capitalization, defined as market capitalization of firm i’s common shares at the end of quarter t. LARGE (SMALL) includes firms with market capitalization above (below) the sample median.

Across all four panels, medians are defined within each fiscal quarter. N varies across the panels due to data availability. All other variables are defined in Appendix A.

44

TABLE 5 Partitioning on the Ex Ante Information Environment

Dependent Variable: Beta_adj Correl_adj Std_adj

(1) (2) (3) (4) (5) (6)

Panel A. Analyst Following (HIGHFOLL N = 368; LOWFOLL N = 288)

HIGHFOLL LOWFOLL HIGHFOLL LOWFOLL HIGHFOLL LOWFOLL OA 1.223 *** 0.418 ** 0.474 *** 0.296 *** 2.413 *** 1.937 *** FVA1 1.241 *** 0.361 ** 0.477 *** 0.285 *** 2.336 *** 1.967 *** FVA2 1.250 *** 0.399 *** 0.480 *** 0.309 *** 2.363 *** 1.800 *** FVA3 1.344 *** 3.695 *** 0.475 *** 0.821 *** 2.454 *** 5.174 *** Leverage –1.245 *** –0.397 ** –0.470 *** –0.290 *** –2.447 *** –1.946 ***

One-sided p-values for F-tests comparing fair values within subsamples:

FVA1 < FVA2 0.434 0.198 0.459 0.243 0.481 0.237 FVA1 < FVA3 0.330 0.002 0.444 0.109 0.431 0.003 FVA2 < FVA3 0.288 0.003 0.426 0.149 0.439 0.003

Tests of hypothesis 2 (p-values for F-tests comparing fair values across subsamples):

(FVA2 – FVA1)HIGHFOLL < (FVA2 – FVA1)LOWFOLL 0.430 0.373 0.174 (FVA3 – FVA1)HIGHFOLL < (FVA3 – FVA1)LOWFOLL 0.002 0.056 0.006 (FVA3 – FVA2)HIGHFOLL < (FVA3 – FVA2)LOWFOLL 0.002 0.062 0.006

Panel B. Forecast Error (LOW_ERR N = 329; HIGH_ERR N = 327) LOW_ERR HIGH_ERR LOW_ERR HIGH_ERR LOW_ERR HIGH_ERR OA 1.468 *** 0.850 *** 0.590 *** 0.338 *** 2.299 *** 2.435 *** FVA1 1.525 *** 0.672 *** 0.650 *** 0.264 *** 2.079 *** 2.455 *** FVA2 1.459 *** 0.815 *** 0.586 *** 0.349 *** 2.262 *** 2.248 *** FVA3 1.947 *** 2.229 *** 0.465 *** 0.762 *** 3.438 *** 2.784 *** Leverage –1.522 *** –0.847 *** –0.598 *** –0.332 *** –2.349 *** –2.453 ***


FVA1 = FVA2 0.339 0.279 0.034 0.104 0.166 0.157 FVA1 = FVA3 0.086 0.029 0.073 0.001 0.045 0.388 FVA2 = FVA3 0.068 0.036 0.146 0.001 0.068 0.322


(FVA2 – FVA1)LOW ERR < (FVA2 – FVA1)HIGH ERR 0.133 0.001 0.025 (FVA3 – FVA1)LOW ERR < (FVA3 – FVA1)HIGH ERR 0.059 < 0.001 0.170 (FVA3 – FVA2)LOW ERR < (FVA3 – FVA2)HIGH ERR 0.101 0.001 0.275

45


(1) (2) (3) (4) (5) (6)

Panel C. Forecast Dispersion (LOW_DISP N = 265; HIGH_DISP N = 262) LOW_DISP HIGH_DISP LOW_DISP HIGH_DISP LOW_DISP HIGH_DISP OA 1.207 *** 0.910 *** 0.452 *** 0.414 *** 2.495 *** 2.234 *** FVA1 1.412 *** 0.818 *** 0.558 *** 0.374 *** 2.331 *** 2.233 *** FVA2 1.289 *** 0.837 *** 0.480 *** 0.408 *** 2.494 *** 2.073 *** FVA3 1.201 2.328 *** 0.569 *** 0.534 *** 1.949 ** 3.872 *** Leverage –1.240 *** –0.893 *** –0.451 *** –0.404 *** –2.549 *** –2.236 ***




(FVA2 – FVA1)LOW DISP < (FVA2 – FVA1)HIGH DISP 0.331 0.129 0.431 (FVA3 – FVA1)LOW DISP < (FVA3 – FVA1)HIGH DISP 0.041 0.100 0.052 (FVA3 – FVA2)LOW DISP < (FVA3 – FVA2)HIGH DISP 0.028 0.431 0.028

Panel D. Market Capitalization (LARGE N = 496; SMALL N = 456) LARGE SMALL LARGE SMALL LARGE SMALL OA 1.028 *** 0.890 *** 0.415 *** 0.427 *** 2.336 *** 1.852 *** FVA1 0.932 *** 0.514 *** 0.396 *** 0.340 *** 2.234 *** 1.546 *** FVA2 0.983 *** 0.806 *** 0.412 *** 0.408 *** 2.249 *** 1.583 *** FVA3 1.601 *** 1.760 ** 0.479 *** 0.671 *** 3.028 *** 2.455 *** Leverage –1.024 *** –0.905 *** –0.403 *** –0.432 *** –2.382 *** –1.818 ***




(FVA2 – FVA1)LARGE < (FVA2 – FVA1)SMALL 0.068 0.188 0.464 (FVA3 – FVA1)LARGE < (FVA3 – FVA1)SMALL 0.259 0.099 0.451 (FVA3 – FVA2)LARGE < (FVA3 – FVA2)SMALL 0.353 0.159 0.461

46


(1) (2) (3) (4) (5) (6)

Panel E. Partition Using Principal Component Analysis (HIGH_INF N = 263; LOW_INF N = 262)

HIGH_INF LOW_INF HIGH_INF LOW_INF HIGH_INF LOW_INF OA 1.409 *** 0.910 *** 0.536 *** 0.376 *** 2.576 *** 2.318 *** FVA1 1.306 *** 0.847 *** 0.505 *** 0.365 *** 2.538 *** 2.222 *** FVA2 1.407 *** 0.897 *** 0.536 *** 0.406 *** 2.543 *** 2.085 *** FVA3 1.274 ** 2.188 ** 0.402 ** 0.619 *** 2.640 *** 3.444 *** Leverage –1.441 *** –0.906 ** –0.538 *** –0.367 *** –2.616 *** –2.338 ***


FVA1 < FVA2 0.201 0.089 0.590 0.081 0.489 0.585 FVA1 < FVA3 0.944 0.078 0.610 0.034 0.445 0.112 FVA2 < FVA3 0.800 0.300 0.530 0.052 0.4490 0.095


(FVA2 – FVA1)HIGH INF < (FVA2 – FVA1)LOW INF 0.332 0.498 0.331 (FVA3 – FVA1)HIGH INF < (FVA3 – FVA1)LOW INF 0.074 0.005 0.166 (FVA3 – FVA2)HIGH INF < (FVA3 – FVA2)LOW INF 0.080 0.016 0.189

This table presents results from multivariate regressions examining the effect of fair value disclosures upon scaled beta and its mathematical components, estimated for sample partitions expected to capture ex ante differences in the firm’s information environment. Regressions are estimated by fully interacting the regression model based on the indicated partitioning variable. All variables are defined in Appendix A. N varies across the panels due to data availability.

We present coefficient estimates, followed by ***, **, * indicating significance at the less than 1%, 5%, and 10% levels using one-sided tests, respectively. Standard errors are robust to heteroscedasticity and clustered at the firm level. All regressions include untabulated fixed effects for quarter, as well as time-varying effects for sector (commercial bank, savings institution, or security broker) and stock exchange (NYSE, AMEX). Below the regressions, we present p-values from F-tests of coefficients testing hypothesis 2. Across all panels, Columns (1) and (2) use as the dependent variable Beta_adj, the leveraged-adjusted equity beta. We then alternatively use as the dependent variable the two mathematical components of beta: Correl_adj in Columns (3) and (4); and Std_adj in Columns (5) and (6). Columns (1), (3), and (5) present parameter estimation for the subsamples of firms expected to have ex ante higher quality information environments. Columns (2), (4), and (6) present parameter estimation for the subsamples of firms expected to have ex ante lower quality information environments.

In Panel A, the partitioning variable is analyst following, defined as the number of analysts issuing earnings forecasts for firm i during quarter t. HIGHFOLL (LOWFOLL) includes firms with analyst following greater than or equal to (less than) the sample median.

In Panel B, the partitioning variable is forecast error, defined in two steps. First, we use the absolute value of actual earnings per share less the consensus analyst forecasted earnings per share for firm i for quarter t. Second, we obtain the residual from a regression of this forecast

47

error upon forecast horizon, analyst coverage, an indicator variable equal to one for reporting a loss and zero otherwise, and the magnitude of actual reported earnings per share. LOW_ERR (HIGH_ERR) includes firms with consensus forecast error below (above) the sample median.

In Panel C, the partitioning variable is forecast dispersion, similarly defined in two steps. First, we use the average standard deviation of monthly forecasts for firm i across the three-month period of quarter t. Second, we obtain the residual from a regression of this forecast dispersion upon forecast horizon, analyst coverage, an indicator variable equal to one for reporting a loss and zero otherwise, and the magnitude of actual reported earnings per share. LOW_DISP (HIGH_DISP) includes firms with forecast dispersion below (above) the sample median.

In Panel D, the partitioning variable is market capitalization, defined as market capitalization of firm i’s common shares at the end of quarter t. LARGE (SMALL) includes firms with market capitalization above (below) the sample median.

In Panel E, the partitioning variable is the principal component derived from four inputs: analyst following, analyst forecast error, analyst forecast dispersion, and market capitalization. Analyst following, analyst forecast error, analyst forecast dispersion, and market capitalization are as defined above. HIGH_INF (LOW_INF) firms are those with above (below) median values of the highest eigenvalue factor derived from the principal component analysis.

Across all panels, medians are defined within each fiscal quarter.

48

TABLE 6 Sensitivity Analyses: Alternative Measurements of Beta

Panel A. Varying the Measurement Window of Returns

Dependent Variable: 6 MONTH 15 MONTH

Beta_adj Correl_adj Beta_adj Correl_adj

OA + 0.924 *** 0.401 *** 0.867 *** 0.390 *** FVA1 + 0.719 *** 0.350 *** 0.780 *** 0.320 *** FVA2 + 0.890 *** 0.401 *** 0.899 *** 0.391 *** FVA3 + 1.492 *** 0.444 *** 1.406 *** 0.426 *** Leverage – –0.941 *** –0.406 *** –0.899 *** –0.372 ***

Tests of hypothesis 1 (p-values for F-tests comparing coefficients): FVA1 ≤ FVA2 ≤ FVA3 0.019 0.110 0.037 0.120 FVA1 < FVA2 0.048 0.030 0.076 0.040 FVA1 < FVA3 0.027 0.170 0.045 0.180 FVA2 < FVA3 0.072 0.280 0.081 0.270

Panel B. Varying the Frequency of Returns

Dependent Variable: DAILY MONTHLY


OA + 1.532 *** 0.336 *** 0.798 *** 0.291 *** FVA1 + 1.184 *** 0.264 *** 0.541 *** 0.219 *** FVA2 + 1.456 *** 0.317 *** 0.760 *** 0.288 *** FVA3 + 1.531 ** 0.372 *** 1.241 *** 0.361 *** Leverage – –1.544 *** –0.344 *** –0.810 *** –0.292 ***


Panel C. Varying the Benchmark Return

Dependent Variable: EQUAL SP500


OA + 1.040 *** 0.425 *** 0.880 *** 0.392 *** FVA1 + 0.884 *** 0.399 *** 0.685 *** 0.356 *** FVA2 + 0.993 *** 0.425 *** 0.847 *** 0.394 *** FVA3 + 1.735 ** 0.533 *** 1.473 *** 0.484 *** Leverage – –1.059 *** –0.423 *** –0.883 *** –0.389 ***


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This table presents sensitivity analyses assessing the robustness of results to alternative measurements of the dependent variables, Beta_adj and Correl_adj. In our primary analyses, both variables are derived from estimation of the single-factor CAPM model using weekly stock returns measured over the quarter t+1 and a benchmark of the value-weighted stock market return. All regressions in the panels above include untabulated fixed effects for quarter, as well as time-varying effects for sector (commercial bank, savings institution, or security broker) and stock exchange (NYSE, AMEX).

In Panel A, we vary the measurement window to estimate the CAPM model, and thus derive both Beta_adj and Correl_adj. Under the heading “6 MONTH,” we use the 6-month window including the contemporaneous quarter t as well as quarter t+1. Under the heading “15 MONTH,” we use the 15-month window spanning quarter t-3 through quarter t+1. Both windows use weekly stock returns.

In Panel B, we vary the frequency of data to estimate the CAPM model. Under the heading “DAILY,” we use daily stock returns over the 3-month window of quarter t+1. Under the heading “MONTHLY,” we use monthly stock returns over the 15-month window spanning quarter t-3 through quarter t+1.

In Panel C, we vary the benchmark used to determine the market return in estimating the CAPM model. Under the heading “EQUAL,” we use weekly stock returns over quarter t+1 and the equal-weighted stock market return. Under the heading “SP500,” we use weekly stock returns over quarter t+1 and the S&P 500 index.

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TABLE 7 Sensitivity Analyses: Incorporating Additional Variables


Variable Predicted Sign (1) (2) (3)

Panel A. Including the Decomposition of Liabilities

OA + 0.976 *** 0.406 *** 2.209 *** FVA1 + 0.612 *** 0.381 *** 1.684 *** FVA2 + 0.944 *** 0.417 *** 2.019 *** FVA3 + 1.655 *** 0.519 *** 2.939 *** OL – –0.987 *** –0.405 *** –2.218 *** FVL1 – –0.511 ** –0.408 *** –1.497 *** FVL2 – –0.936 *** –0.411 *** –2.087 *** FVL3 – –4.367 *** –1.493 *** –3.852 *

One-sided p-values for F-tests comparing coefficients:

FVA1 ≤ FVA2 ≤ FVA3 0.001 0.068 0.028 FVA1 < FVA2 0.003 0.117 0.037 FVA1 < FVA3 0.001 0.046 0.001 FVA2 < FVA3 0.007 0.063 0.020

FVL1 ≤ FVL2 ≤ FVL3 0.001 0.007 0.026 FVL1 < FVL2 0.002 0.698 0.069 FVL1 < FVL3 0.001 0.009 0.058 FVL2 < FVL3 0.001 0.010 0.110

Dependent Variable: Beta_MVE Correl_MVE Std_MVE

Variable Predicted Sign (1) (2) (3)

Panel B. Including Unrecognized Assets and Liabilities

OtherAssets/MVA + 0.923 *** 0.422 *** 2.037 *** A1/MVA + 0.687 *** 0.371 *** 1.762 *** A2/MVA + 0.876 *** 0.419 *** 1.882 *** A3/MVA + 1.483 *** 0.525 *** 2.629 *** L/MVA – –0.936 *** –0.420 *** –2.055 *** UnrecogAL/MVA + 0.928 *** 0.522 *** 1.755 ***

One-sided p-values for F-tests comparing coefficients:

A1 ≤ A2 ≤ A3 0.030 0.080 0.110 A1 < A2 0.022 0.060 0.230 A1 < A3 0.023 0.070 0.065 A2 < A3 0.065 0.150 0.110

This table presents results from sensitivity analyses examining the effect of fair value disclosures

upon scaled beta and its mathematical components to the incorporation of additional variables. Across all regressions, N = 952 firm-quarters. All regressions include untabulated fixed effects for quarter, as well as time-varying effects for sector (commercial bank, savings institution, or security broker) and stock exchange (NYSE, AMEX). We present coefficient estimates, followed by ***, **, * indicating

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significance at the less than 1%, 5%, and 10% levels using one-sided tests, respectively. Standard errors are robust to heteroscedasticity and clustered at the firm level. Below the regressions, we present p-values from F-tests of coefficients across the indicated fair value designations.

In Panel A, we re-estimate the primary analyses of Table 3 to include the decomposition of firms’ financial liabilities into those designated at level 1 (FVL1), 2 (FVL2), and 3 (FVL3) fair value. For Column (1), the dependent variable is Beta_adj, the leverage-adjusted equity beta. Columns (2) and (3) replace the dependent variable Beta_adj with its two mathematical components of Correl_adj and Std_adj, respectively. All variables are defined in Appendix A.

In Panel B, we re-estimate the primary analyses of Table 3 to replace book values with market values through three changes. First, we redefine the dependent variable to be beta weighted by the market value of equity scaled by the market value of equity plus book value of liabilities (Beta_MVE). Second, we scaled all variables by market value of equity plus book value of liabilities (MVA), versus total assets in our primary analyses. Thus, the previous variable FVA1 is now A1/MVA, FVA2 is now A2/MVA, etc. Third, we include an additional variable, UnrecogAL/MVA, which is the market value of equity less the book value of equity, to control for off-balance sheet assets and liabilities. For Column (1), the dependent variable is Beta_MVE. Columns (2) and (3) replace the dependent variable with its two mathematical components of Correl_MVE and Std_MVE, respectively.

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TABLE 8 Sensitivity Analyses: Pre-SFAS 157 versus Post-SFAS 157

Dependent Variable: Beta_adj Correl_adj (1) (2) (3) (4)

Panel A. Pooled Sample (PRE_157 N = 1,522; POST_157 N = 859)

PRE_157 POST_157 PRE_157 POST_157 OA 0.897 *** 0.903 *** 0.339 *** 0.412 *** FVA1 0.584 ** 0.632 *** 0.256 *** 0.361 *** FVA2 0.843 *** 0.846 *** 0.334 *** 0.411 *** FVA3 1.841 *** 1.644 *** 0.561 *** 0.535 *** Leverage –0.938 *** –0.904 *** –0.351 *** –0.409 ***

One-sided p-values for F-tests comparing fair values within subsamples: FVA1 < FVA2 0.032 0.038 0.094 0.094 FVA1 < FVA3 0.001 0.007 0.031 0.048 FVA2 < FVA3 0.013 0.014 0.042 0.096

Tests of hypothesis 2 (p-values for F-tests comparing fair values across subsamples): (FVA2 – FVA1)POST 157 < (FVA2 – FVA1)PRE 157 0.350 0.210 (FVA3 – FVA1)POST 157 < (FVA3 – FVA1)PRE 157 0.290 0.190 (FVA3 – FVA2)POST 157 < (FVA3 – FVA2)PRE 157 0.350 0.250

Panel B. Low Analyst Following Sample (PRE_157 N = 431 ; POST_157 N =293 )

PRE_157 POST_157 PRE_157 POST_157 OA 0.830 *** 0.373 ** 0.374 *** 0.305 *** FVA1 0.950 *** 0.083 0.379 *** 0.241 *** FVA2 0.883 *** 0.267 * 0.413 *** 0.295 *** FVA3 2.499 *** 2.476 *** 0.645 *** 0.596 ** Leverage –0.904 *** –0.331 ** –0.409 *** –0.291 ***



Panel C. High Analyst Following Sample (PRE_157 N =543 ; POST_157 N =293 )

PRE_157 POST_157 PRE_157 POST_157 OA 1.149 *** 1.082 *** 0.377 *** 0.408 *** FVA1 0.998 *** 1.052 *** 0.342 *** 0.553 *** FVA2 1.128 *** 1.098 *** 0.369 *** 0.424 *** FVA3 3.064 *** 1.479 ** 0.765 *** 0.517 *** Leverage –1.201 *** –1.081 *** –0.378 *** –0.399 ***



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This table presents results from sensitivity analyses examining the effect of fair value disclosures

upon scaled beta and its mathematical components. Specifically, we compare observations from two groups: those following adoption of SFAS 157 (“POST_157”); and those prior to adoption of SFAS 157 (“PRE_157”). For the latter group, to proxy for the proportion of assets across the fair value designations prior to SFAS 157 adoption, we use the firm-level proportions disclosed for Q1 2008. We present coefficient estimates, followed by ***, **, * indicating significance at the less than 1%, 5%, and 10% levels using one-sided tests, respectively. Standard errors are robust to heteroscedasticity and clustered at the firm level. Below the regressions, we present p-values from F-tests of coefficients testing hypothesis 2. All regressions include untabulated fixed effects for quarter, as well as time-varying effects for sector (commercial bank, savings institution, or security broker) and stock exchange (NYSE, AMEX).

Panel A presents results using the pooled sample. Panel B presents results for the subsample of firms expected to have ex ante lower quality information environments: low analyst following firms, defined as firms with analyst following below the median. Panel C presents results for the subsample of firms expected to have ex ante higher quality information environments: high analyst following firms, defined as firms with analyst following equal to or greater than the median.

Columns (1) and (2) use as the dependent variable Beta_adj, the implied leveraged-adjusted equity beta. Columns (3) and (4) use as the dependent variable Correl_adj. All variables are defined in Appendix A.

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TABLE 9 Sensitivity Analyses: Expanded Sample of Q1 2007 to Q3 2009

Panel A. Replication of Table 3 (N = 2,994)

Variable Predicted Sign Dependent Variable: Beta_adj Correl_adj Std_adj OA + 0.747 *** 0.352 *** 2.270 *** FVA1 + 0.454 ** 0.314 *** 1.971 *** FVA2 + 0.674 *** 0.364 *** 1.988 *** FVA3 + 1.426 *** 0.385 ** 4.513 *** Leverage – –0.755 *** –0.371 *** –2.151 ***

Tests of hypothesis 1 (one-sided p-values for F-tests comparing coefficients):

FVA1 < FVA2 0.055 0.100 0.450 FVA1 < FVA3 0.031 0.080 0.001 FVA2 < FVA3 0.080 0.420 0.001

Panel B. Replication of Table 5, Panel A: Partition by Analyst Following (HIGHFOLL N = 790 ; LOWFOLL N = 631)

Dependent Variable: Beta_adj Correl_adj Std_Dev_adj

(1) (2) (3) (4) (5) (6) HIGHFOLL LOWFOLL HIGHFOLL LOWFOLL HIGHFOLL LOWFOLL OA 1.162 *** 0.963 *** 0.537 *** 0.460 *** 2.125 *** 1.995 *** FVA1 0.991 *** 0.826 ** 0.505 *** 0.432 *** 1.848 *** 1.885 *** FVA2 1.211 *** 0.846 *** 0.568 *** 0.460 *** 2.036*** 1.678 *** FVA3 1.080 * 4.363 *** 0.288 0.590 *** 2.827 *** 7.431 ** Leverage –1.134 *** –0.964 *** –0.533 *** –0.465 *** –2.070 *** –1.910 ***

p-values for F-tests comparing fair values within subsamples:



(FVA2 – FVA1)HIGHFOLL < (FVA2 – FVA1)LOWFOLL 0.053 0.160 0.020 (FVA3 – FVA1)HIGHFOLL < (FVA3 – FVA1)LOWFOLL 0.072 0.049 0.060 (FVA3 – FVA2)HIGHFOLL < (FVA3 – FVA2)LOWFOLL 0.058 0.039 0.051

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This table presents results from sensitivity analyses examining the effect of fair value disclosures upon scaled beta and its mathematical components using an extended sample period. Specifically, we extend the sample period from Q1 2007 to Q2 2008 to include five additional quarters spanning Q3 2008 to Q3 2009. These latter quarters are excluded from the primary sample due to substantial volatility in the equity market coinciding with the additional quarters, particularly Q3 and Q4 2008. We present coefficient estimates, followed by ***, **, * indicating significance at the less than 1%, 5%, and 10% levels using one-sided tests, respectively. Standard errors are robust to heteroscedasticity and clustered at the firm level. All regressions include (untabulated) fixed effects for quarter, as well as time-varying effects for sector (commercial bank, savings institution, or security broker) and stock exchange (NYSE, AMEX).

Panel A replicates the analysis corresponding to Table 3. Below the regression, we present p-values from F-tests of coefficients testing hypothesis 1.

Panel B replicates the analysis corresponding to Table 5, Panel A, which partitions the firms into ex ante higher quality information environment firms (defined as above median analyst following) and ex ante lower quality information environment firms (defined as below median analyst following). Below the regression, we present p-values from F-tests of coefficients testing hypothesis 2. Columns (1) and (2) use as the dependent variable Beta_adj. We then alternatively use as the dependent variable the two mathematical components of beta: Correl_adj in Columns (3) and (4); and Std_adj in Columns (5) and (6).

All variables are defined in Appendix A.

information risk

Documents

fair value level

higher analyst

financial institutions

financial economics

fair value designations

higher betas relative

lower analyst

firms information environments