Open AccessArticle

Pension Risk and the Sustainable Cost of Capital

Paul John Marcel Klumpes

Faculty of Social Sciences and Humanities, Aalborg University Business School, Aalborg University, 9220 Aalborg, Denmark

J. Risk Financial Manag. 2024, 17(12), 536; https://doi.org/10.3390/jrfm17120536

Submission received: 26 September 2024 / Revised: 7 November 2024 / Accepted: 11 November 2024 / Published: 25 November 2024

(This article belongs to the Special Issue Featured Papers in Corporate Finance and Governance)

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Abstract

Prior research empirically finds that the systematic equity risk for US firms as measured by beta reflects the risk of their defined benefit pension plans, despite opaque and complicated pension accounting rules. This paper re-examines this question in the context of subsequent clarification of these rules, and the growing importance of non-defined benefit pension funds. This issue is examined by comparing standard equity-based models with a broader pre-existing shareholder model of the reporting entity to re-examine the relationship between firm equity risk and pension plan risk. The empirical tests are conducted on a sample of S&P 500 firms during the first three years of the introduction of the revised pension accounting rules (2006–2008), based on panel data regression relating firm risk to pension risk and controlling for other variables. In contrast to the prior findings of JMB, the estimated cost of capital is additionally sensitive to the following: (a) alternative explicit versus implicit definitions of pension liability; (b) the nature and scope of long-term deferred compensation arrangements; and (c) the scope and nature of investment-related risks through investment in sponsoring company stock that are associated with these pension arrangements.

Keywords:

pension plans; cost of capital; equity risk

JEL Classification:

J23; M41s

1. Introduction

Jin et al. (2006, hereinafter, JMB) find that pension risk is priced despite arcane financial reporting for pensions. They assume that pension risk is entirely reflected in the systematic risk of pension plan sponsoring firms (as measured by beta from the capital asset pricing model (CAPM)), although they acknowledge examining the broader relation of pension risk to ‘idiosyncratic risk, or total risk may be of interest’ (p. 2). This paper extends JMB’s research in several ways besides integrating the extended pension arrangements into the firm. First, it re-estimates the cost of capital, by using more detailed pension asset allocation decomposition than that reported in JMB, as well as data on longevity risk and credit risk, using data drawn from annually published industry sources. It also further decomposes the pension liability beta to reflect the underlying demographics of the maturity profile of the scheme liabilities. These can be important since simulation studies show that pension assets and liabilities are extremely sensitive to even minor variations in these assumptions (Selling and Stickney 1986; Winkelvoss 1993). Furthermore, the definition of operating assets is more explicit than JMB, and consistent with that of the prior empirical results reported in the relevant financial analysis literature.1

Moreover, understanding the financial dimensions and long-term sustainability of relations between firms and their employees is increasingly recognized by public policy makers and standard setters.2 Human capital is the measure of the economic value that an employee provides, through their knowledge, skills, and abilities.3 However an important implication of reporting the full financial dimensions of these relations under a sustainability reporting framework is their implications for the economic scope of the consolidation, and the sensitivity of the cost of capital estimates to alternative definitions of the scope of the reporting entity (Callahan et al. 2012). However, despite the material impact of corporate failure on implicit contractual promises made to employees (Tinker and Ghicas 1992), the broader dilution impact of divestitures and investments in implicit contracts on outsider investor interests has received little attention (Zambon and Zan 2000). Moreover, the broader valuation dilution impact of divestitures and investments in implicit contracts on employee wealth on outsider investor interests has received little attention. Landsman and Penman (2007) demonstrate that, under the existing entity theory of accounting, by corporations whereby employer own stock investments, employee stock options, pension funds, and other post-retirement investments are not recognized. By contrast, under an alternative proprietorship theory perspective, passive individual investors collectively control management by holding them accountable for profit, where debt and equity are sharply antagonistic, so that the ‘business does not stand in the same relation to its proprietors or its capitalists as to its ‘other liabilities’ (Sprague 1907, p. 57).4

However, such divestitures as part of equity consideration are currently not fully accounted for (Forker 2000). Indeed, recently the Urgent Issues Task Force (2010, guidance 38) proposed that the outside equity diluting effects of all divestitures in company stock should be fully accounted for and that all employee-related benefits with significant levels of own stock investments should be deducted in calculating shareholder equity. Nevertheless, current US GAAP and IFRS continue to apply the entity theory perspective; so that such transactions are ignored.

This paper defines a ‘sustainable’ cost of capital as existing where relevant entities have sufficient finance when needed to make it possible to maintain long-term, demographically sensitive, and implicit contractual relations with their employees, at their current quality and intensity. This is to be contrasted with a standard procedure which accounts for neither the long-term nature of the relationship nor the equity diluting effect of employee ownership of company own stock. The purpose of this paper is to take a proprietary theory to estimate the diluting impact of significant and material investments and divestitures of company own stock by employee pension and post-retirement and stock ownership trusts in the equity of US firms, and to consider their implications for estimating a long-term sustainable cost of capital for such entities. Forker (2000) argues that a distinguishing feature of the alternative pre-existing equity model of the reporting entity (hereinafter ‘PEEM’) is that the interests of pre-existing shareholders are identified with that of the business entity.5

Existing evidence suggests that the PEEM is more informative than the EM to investors evaluating employee stock options. Landsman et al. (2006) show that employee stock options measured under the PEEM are more value relevant to investors than under existing US GAAP, which implicitly assumes the EM. However, their study is restricted to only examining short-term equity-based compensation and therefore does not consider the valuation implications of longer-term employee compensation arrangements. Currently, US GAAP and IFRS treat these elements separately by expensing the former, but not the latter. Arguably, this has led to an overstatement of profits and incentives for management to manipulate earnings (Picconi 2006).

This inconsistent treatment of equity-based employee compensation does not adhere to the principles of clean surplus accounting and instead proposes the pre-existing equity model (Forker 2000). Forker (2000) identifies PEEM as being superior to EM in providing useful information when accounting for employee benefits. This also has important implications for analyzing the impact of firm-specific risks related to long-term employment compensation arrangements and the sponsoring firms’ cost of capital. Although finance theory suggests that only non-diversifiable risks are awarded and firms’ idiosyncratic risks do not affect investors’ expected returns or firms’ cost of capital, there is growing evidence concerning the impact of idiosyncratic risk in explaining cross-sectional expected returns (e.g., Malkiel and Xu 2002; Brockman et al. 2009). Practitioner-oriented textbooks (e.g., Brealey et al. 2006; Pratt et al. 2014) also argue that investors’ concerns about lack of diversification, insider stock ownership, liquidity, financial distress, and management incentives cause stock markets to price firm-specific risk. However, these textbooks fail to mention the relationship between pension risk and firm risk in estimating the cost of capital.

However, the existing literature provides little guidance as to how such factors can affect a firms’ cost of capital. This paper explores the effect of firm-specific risks, in particular, pension-related risks, on firms’ cost of capital from a PEEM perspective. This is important where employees hold material investment in companies’ own stocks, whether explicitly in the form of stock options, or implicitly through the delegated ownership of company stock through participation in company sponsored 401K, investment trusts, health care plans, or defined benefit plans due to lack of diversification or liquidity.6 Research shows that this kind of idiosyncratic risk has impact on firms’ cost of capital. For example, Himmelberg et al. (2002) find a positive association between the concentration of inside ownership and the cost of capital, even in countries with relatively high degrees of investor protection such as the UK and the US.7

During the financial crisis of 2007–2009, the combination of declining stock prices and lower interest rates has attracted substantial attention on the nature and magnitude of firms’ exposure to pension fund commitments to their employees, and in particular, the declining significance of defined benefit pension funds relative to non-defined pension and post-retirement benefits.8 At the same time, financial markets experience difficulties in valuing even just the defined benefit pension promises made by firms. Coronado and Sharpe (2003) and Coronado et al. (2008) find that stock prices of S&P 500 companies providing defined benefit pension plans were generally misvalued over their sample periods, while others (Picconi 2006; Hann et al. 2007; Franzoni and Marin 2006) suggest that opaque accounting has caused firms to be undervalued relative to overfunded pension plans.

In contrast, the analysis also disentangles the proportion of ‘enterprise value’ belonging to the firm’s’ sub-group of external, diversified stockholders from its separate sub-group of mostly undiversified, employee stockholders. On the one hand, equity interests of outside investors may be severely diluted by employees who hold company stocks; on the other hand, employees are undiversified investors and expose themselves to firm-specific risk through participation in 401K plans. For the purposes of presentation, this paper delineates any post-retirement benefit arrangement other than defined benefits plans (DB), including 401K plans, defined contribution plans, health care plans, stock option plans, and saving plans, which involve significant or material investment in company own stock by employee participants in these schemes, who thereby become undiversified investors, the combined impact of which is labeled ‘NDB’-related plans for simplicity. NDB plans are thus a significant source of pension-related sources of idiosyncratic risk of the sponsoring firm and can be very significant for firms that curtail their DB plans, as disclosed in the pension footnotes.

While JMB identify the value and risk errors of not consolidating the DB plans, the analysis in this paper develops this insight further by integrating NDB plans, as forms of idiosyncratic risk which affect the equity claims of existing shareholders.9 This paper characterizes these NDB and DB arrangements as either as segregated insurance contracts or as fully consolidated sources of retirement income risk capital. These alternative treatments have important debt—equity mix implications since these exposures can either be fully merged with the firm as an insurance subsidiary or consolidated into the firm as an equity ‘company own stock’ investment activity by undiversified NDB plans, thus effectively diluting the interests of outside equity holders.

In contrast to the entire population of US firms as the basis for the analysis undertaken by Jin et al. (2006), this paper also contributes by estimating the cost of capital for a sample of large US S&P 500 firms under various scenarios where material changes in pension related Generally Accepted Accounting Principles (GAAP) can occur. The estimated cost of capital is found to be sensitive to the following: (a) alternative pension GAAP; (b) whether a firm’s pension exposure is classified primarily as a debt or equity instrument; and (c) the scope and nature of the pension plans being consolidated with the firm. Consolidating the defined benefit pension fund into the broader set of deferred compensation arrangements between employees and the firm significantly and materially alters the debt and equity composition of the firm. This results in a significantly higher cost of capital estimates than those reported by JMB. In contrast to JMB, the relationship between a firm’s systematic risk and pension risk is not statistically significant. Identifying the relationship between firm and pension risk that is associated with a broader set of deferred compensation arrangements, such as underfunded health care plans and company own stock investments of 401K and defined contribution plans, increases the strength of association with firm risk, particularly for the sub-set of firms which terminated their defined benefit arrangements.10 Finally, the cross-section of returns is explained incrementally by the degree of idiosyncratic risk exposure, especially for firms with significant levels of pension under-funding.

The remainder of this paper is as follows: Section 2 outlines the prior literature and the proposed model; Section 3 describes the sample and data; Section 4 reports the baseline empirical results; Section 5 reports robustness tests; Section 6 concludes.

2. Review of Literature and Proposed Model

Forker (2000) argues that choosing a model of the reporting entity (MRE) for the purpose of measuring profit is important for both conceptual and practical reasons, particularly in the context of accounting for equity-based consideration (EBC), and identifies three main MREs:

In Paton’s (1922) ‘All-Equities’ model (AEM), the balance sheet equation is assets = equities. The boundary of the residual entity includes all financial instruments and there is no distinction, for the purpose of measuring income, between equity and liability financing. Interest, dividends, and wealth transfers between ‘equities’ are accounted for as appropriations of income and the method of financing EBC has no impact on income. This model is considered to be outdated as it ignores the effect of financing.
The equity model (EM)is based on the assets less liabilities = equity equation, where equity is defined to include all equity instruments including EBC financed by the issue of new shares. This is the standard model of equity which currently underlies GAAP in many countries and internationally under international financial reporting standards.
The pre-existing equity model (PEEM) is also based on the assets less liability equals equity relationship, but the residual entity is more narrowly defined to include only the rights of the pre-existing equity. In the PEEM, the full cost of equity-based consideration payable to employees is recognized as an expense irrespective of whether it is funded by cash or equity or a mixture of the two. Thus, compared to existing GAAP practices in accordance with EM, periodic income and return on capital employed is lower in the PEEM and reflects the change in the wealth of pre-existing shareholders in the firm.

A major motivation for this analysis is doubts expressed by the relevant prior literature (e.g., Forker 2000) over the validity of the EM as a valid basis for recognizing long-term implicit equity-based employee compensation components, which is the maintained assumption underlying prior research. This study, therefore, reexamines the JMB analysis of the relationship of pension value and risk to firm systematic risk that is premised on the EM, with the PEEM.

This in turn has implications for identifying the appropriate measure of pension obligations that should be recognized by employer sponsors (i.e., accumulated benefit obligation (ABO), or the projected benefit obligation (PBO) under these alternative models of the reporting entity, which are briefly outlined below.

(i) Accumulated benefit obligation (ABO). The pension liability is estimated without incorporating any assumptions about the future growth of the obligations defined in terms of accrued benefit obligations. It was formerly required under US GAAP SFAS 87 (FASB 1985, 2003), before the introduction of SFAS 158 (FASB 2006). It is also consistent with an all-equities model (hereinafter AEM), since changes are netted as a surplus or deficit and no distinction is made between debt and equity components of pension arrangements. It was previously required to be recognized in financial statements, but only if underfunded (Jin et al. 2006, p. 10). In other words, firms were not required to report the full ABO prior to 2006. In measuring pension risk, JMB uses the Form 5500 pension asset categorization to identify pension asset risk and acknowledge that they are only able to use the average risk level for each broader asset class. We consider the allocation of pension assets at a more detailed level than reported under the Form 5500 data. The detailed pension asset allocation data is expected to lead to higher accuracy in estimating pension asset beta.11

(ii) Projected benefit obligation (PBO). This pension liability incorporates allowances for salary growth, as set out under new pension accounting rules SFAS 158, effective for reporting periods ending on or after 15 December 2006, which is the basis of this study. Barth (1991) shows evidence that capital markets place greater weight on the projected benefit obligation, which incorporates future salary growth assumptions. This measure of the pension obligation is consistent with the EM, since all intra-equity transfers are netted as a surplus or deficit, but price changes on liabilities are recognized on the comprehensive income statement.

This paper specifically focuses on the distinctions between alternative MRE and their implications to help financial analysts and regulators to better understand the relationship between a sponsoring firm’s capital structure and that of its sponsored DB and NDB plans, under alternative AEM, EM, and PEEM models of the corporate reporting entity which has material exposure to such employee benefit obligations. A comparison of the characteristics of different models of the reporting entity and their implications for the appropriate treatment of equity-based employee consideration is provided in Table 1.12

We define NOA as the value of net operating assets, NFL as the net financial liabilities, PA_DB as the value of pension asset for a DB plan, PA_NDB as the value of pension asset for a NDB plan, PL_DB as the value of pension liability for the DB plan, PL_DB as the pension liability value of the DB plan, and PL_NDB as the liability value of NDB plans. Although NDB plans in theory cover any form of post-retirement benefit arrangement, due to the lack of availability of publicly available data, PL_NDB is defined to cover 401k plans, post-retirement unfunded health care benefits subject to the disclosure requirements of SFAS 106, and other forms of publicly disclosed DC plan.

Taking account of employees’ interest in company stock as equity investments to be eliminated upon consolidation, we also discriminate between E_CE as the value of common equity (outsider shareholders) and, E_EE as the value of employee equity (employee shareholders). Note OPT pension plan-related options, including PBGC and employer’s call option, on net pension fund worth.

Similar to JMB, we consider cases without taxes. The economic balance sheet can be written as:

NOA + PA_DB + PA_NDB + OPT = NFL + PL_DB + PL_NDB + E_CE + E_EE

(1)

Denoting NPL_DB = PL_DB − PA_DB = NPA_DB,

NPL_NDB = PL_NDB − PA_NDB = NPA_NDB, and

E = E_CE + E_EE.

Thus, under the consolidated approach, E, equity of the firm is segregated into two components: common equity of the firm, E_CE, and equity of employer securities, E_EE, the equity invested by the firm’s sponsoring pension plans (both DB and NDB pension plan assets).

Systematic risk or beta of operating asset, B_NOA when both the pension value and pension risk are correctly considered, is

\begin{matrix} β_{N O A} = \frac{E}{N O A} β_{E} + \frac{N F L}{N O A} β_{N F L} - (\frac{P A_{D B}}{N O A} β_{P A_{D B}} - \frac{P L_{D B}}{N O A} β_{P L_{D B}}) \\ - (\frac{P A_{N D B}}{N O A} β_{P A_{N D B}} - \frac{P L_{N D B}}{N O A} β_{P L_{N D B}}) - \frac{O P T}{N O A} β_{O P T} \end{matrix}

(2)

Error case 1: The calculation of operating asset risk ignores both DB and NDB pension plans, including their values and risks. The estimated operating asset beta becomes

\hat{β_{N O A}} = \frac{E}{N O A} β_{E} + \frac{N F L}{N O A} β_{N F L} - \frac{O P T}{N O A} β_{O P T}

(3)

The resulting estimation specification error, defined as

{\hat{ε}}_{N O A} = {\hat{β}}_{N O A} - β_{N O A}

, is

{\hat{ε}}_{N O A} = \frac{P A_{D B}}{\hat{N O A}} (β_{P A_{D B}} - β_{P L_{D B}}) + \frac{P A_{N D B}}{\hat{N O A}} (β_{P A_{N D B}} - β_{P L_{N D B}}) - \frac{N P A_{D B}}{\hat{N O A}} (β_{N O A} - β_{P L_{D B}}) - \frac{N P A_{N D B}}{\hat{N O A}} (β_{N O A} - β_{P L_{N D B}})

(4)

where

\hat{NOA} {= NOA + NPA}_{DB} {+ NPA}_{NDB}

Proof.

See Appendix A. □

Without considering the NDB plan, this expression of difference between “true” and estimated systematic risks of operating assets is the same as that in JMB. For both DB and NDB plans, it is usually true that:

β_{P A} \geq β_{P L} and β_{N O A} \geq β_{P L}

Therefore, if both DB and NDB pension surpluses are not large, then

{\hat{ε}}_{N O A} > 0

β_{N O A} < {\hat{β}}_{N O A}

i.e., the specification error on the estimation of the operating asset beta generally leads to an upward bias. If both DB and NDB pension funds are in balance, NPA = 0, or if NPA_DB = 0, then

N P A_{N D B} < P A_{D B} \frac{(β_{P A_{D B}} - β_{P L_{D B}})}{(β_{N O A} - β_{P L_{N D B}})} + P A_{N D B} \frac{(β_{P A_{N D B}} - β_{P L_{N D B}})}{(β_{N O A} - β_{P L_{N D B}})}

or, if NPA_NDB = 0, and

N P A_{D B} < P A_{D B} \frac{(β_{P A_{D B}} - β_{P L_{D B}})}{(β_{N O A} - β_{P L_{D B}})} + P A_{N D B} \frac{(β_{P A_{N D B}} - β_{P L_{N D B}})}{(β_{N O A} - β_{P L_{D B}})}

, then

β_{N O A} < {\hat{β}}_{N O A}

holds.

Error case 2: The calculation of operating asset risk includes both pension values, but inappropriately assumes the associated risks for both pension plans. If, for example, both DB and NDB pension asset and pension liability risks are assumed to be the same and equal to the risk of the debt of the firm,

{\hat{\hat{β}}}_{P A} = {\hat{\hat{β}}}_{P L} = β_{N F L}

, then the estimated operating asset beta becomes

{\hat{\hat{β}}}_{N O A} = \frac{E}{N O A} β_{E} + \frac{N F L - N P A_{D B} - N P A_{N D B}}{N O A} β_{N F L} - \frac{O P T}{N O A} β_{O P T}

(5)

The specification error in the estimated beta is given by

{\hat{\hat{ε}}}_{N O A} = \frac{P L_{D B}}{N O A} (β_{N F L} - β_{P L_{D B}}) + \frac{P A_{D B}}{N O A} (β_{P A_{D B}} - β_{N F L}) + \frac{P L_{N D B}}{N O A} (β_{N F L} - β_{P L_{N D B}}) + \frac{P A_{N D B}}{N O A} (β_{P A_{N D B}} - β_{N F L})

(6)

Proof of Equation (6).

If both the value and the risk of the pension plans, including DB and NDB plans, are ignored, then the estimated operating asset is

\hat{NOA} {= E + NFL - OPT = NOA + NPA}_{DB} {+ NPA}_{NDB}

The estimated operating asset beta becomes

{\hat{β}}_{N O A} = \frac{E}{\hat{N O A}} β_{E} + \frac{N F L}{\hat{N O A}} β_{N F L} - \frac{O P T}{\hat{N O A}} β_{O P T}

Define

\hat{NOA} {= NOA + NPA}_{DB} {+ NPA}_{NDB}

Note that

\hat{NOA} {= NOA + NPA}_{DB} {+ NPA}_{NDB}

The weighted average betas of NPA and

\hat{NOA}

are given by:

β_{N P A} = \frac{P A}{N P A} β_{P A} - \frac{P L}{N P A} β_{P L}

and

\begin{array}{l} {\hat{β}}_{N O A} & = \frac{N O A}{N O A + N P A_{D B} + N P A_{N D B}} β_{N O A} + \frac{N P A_{D B}}{N O A + N P A_{D B} + N P A_{N D B}} β_{N P A_{D B}} \\ + \frac{N P A_{N D B}}{N O A + N P A_{D B} + N P A_{N D B}} β_{N P A_{N D B}} \\ = β_{N O A} + \frac{N P A_{D B}}{N O A + N P A_{D B} + N P A_{N D B}} (β_{N P A_{D B}} - β_{N P A_{N D B}}) + \frac{N P A_{N D B}}{N O A + N P A_{D B} + N P A_{N D B}} (β_{N P A_{N D B}} - β_{N O A}) \\ = β_{N O A} + \frac{N P A_{D B}}{N O A + N P A_{D B} + N P A_{N D B}} (\frac{P A_{D B}}{N P A_{D B}} β_{P A_{D B}} - \frac{P L_{D B}}{N P A_{N D B}} β_{P L_{D B}} - β_{N O A}) \\ + \frac{N P A_{N D B}}{N O A + N P A_{D B} + N P A_{N D B}} (\frac{P A_{N D B}}{N P A_{N D B}} β_{P A_{N D B}} - \frac{P L_{D B}}{N P A_{N D B}} β_{P L_{N D B}} - β_{N O A}) \\ = β_{N O A} + \frac{P A_{D B}}{N O A + N P A_{D B} + N P A_{N D B}} (β_{P A_{D B}} - β_{P L_{D B}}) - \frac{N P A_{D B}}{N O A + N P A_{D B} + N P A_{N D B}} (β_{N O A} - β_{P L_{D B}}) \\ + \frac{P A_{N D B}}{N O A + N P A_{D B} + N P A_{N D B}} (β_{P A_{D C}} - β_{P L_{N D B}}) - \frac{N P A_{N D B}}{N O A + N P A_{D B} + N P A_{N D B}} (β_{N O A} - β_{P L_{N D B}}) \end{array}

{\hat{ε}}_{O A} = \frac{P A_{D B}}{\hat{N O A}} (β_{P A_{D B}} - β_{P L_{D B}}) + \frac{P A_{N D B}}{\hat{N O A}} (β_{P A_{N D B}} - β_{P L_{N D B}}) - \frac{N P A_{D B}}{\hat{N O A}} (β_{N O A} - β_{P L_{D B}}) - \frac{N P A_{N D B}}{\hat{N O A}} (β_{N O A} - β_{P L_{N D B}})

□

As JMB point out that usually the risk level of pension liabilities and firm debt are similar with normal leverage ratios, i.e.,

β_{P L} \approx β_{N F L}

, but the portion of pension assets that are invested in equities has significantly higher beta risk than the firm debt, i.e.,

β_{P A} > β_{N F L}

. Therefore, it generally holds that

{\hat{\hat{β}}}_{N O A} > β_{N O A}

. Again, operating asset beta is biased upward when both pension fund risks are assumed to be the same as firm’s liability risk.

In terms of the implicit contracting theory, JMB’s model is adjusted as follows. Note that

NOA + PA_DB + PA_NDB − (PL_DB + PL_NDB) + OPT = NFL + E,

NOA + PA_DB + (PA_NDB − E_EE) − (PL_DB + PL_NDB) + OPT = NFL + E_CE,

and both DB and NDB net pension plan risks are separately ‘consolidated’ into the firms’ accounts, where E = E_CE + E_EE. Note that

β_{E + N F L} = \frac{E}{E + N F L} β_{E} + \frac{N F L}{E + N F L} β_{N F L}

β_{E C E + N F L} = \frac{E_{C E}}{E_{C E} + N F L} β_{E C E} + \frac{N F L}{E_{C E} + N F L} β_{N F L}

Therefore,

β_{E + N F L}

can be rewritten as

β_{E + N F L} = β_{D B 1} + β_{N D B} + \frac{N O A}{E + N F L} β_{N O A} + \frac{O P T}{E + N F L} β_{O P T}

(7)

where

β_{D B} = (\frac{P A_{D B}}{E + N F L} β_{P A_{D B}} - \frac{P L_{D B}}{E + N F L} β_{P L_{D B}})

β_{N D B} = (\frac{P A_{N D B}}{E + N F L} β_{P A_{N D B}} - \frac{P L_{N D B}}{E + N F L} β_{P L_{N D B}})

Similarly,

β_{E_{C E} + N F L}

can be rewritten as

β_{E_{C E} + N F L} = β_{D B} + β_{D C E} + \frac{N O A}{E_{C E} + N F L} β_{N O A} + \frac{O P T}{E_{C E} + N F L} β_{O P T}

(8)

where

β_{D C E} = (\frac{P A_{N D B E}}{E_{C E} + N F L} β_{P A_{D C E}} - \frac{P L_{D B}}{E_{C E} + N F L} β_{P L_{N D B}})

β_{N D B} = (\frac{P A_{N D B}}{E + N F L} β_{P A_{N D B}} - \frac{P L_{N D B}}{E + N F L} β_{P L_{N D B}})

PA_NDBE = PA_NDB − E_EE, and

β_{P A_{D C E}}

is the systematic risk of PA_NDBE.

By considering a merged case of pension risk, we can assign a single coefficient b in the regression, assuming that the degree of sensitivity of firm risk to DB pension plan and NDB pension plan is the same. On the other hand, in the separate risk view, one can differentiate sources of pension risk between DB and NDB.

One can use the relationships in Equations (7) and (8) to test whether the beta risk of pension is incorporated in the risk of the firm’s capital structure as below:

β_{E + N F L} = a_{1} + b_{1} β_{p e n s i o n 1} + ε

(9)

β_{E_{C E} + N F L} = a_{2} + b_{2} β_{p e n s i o n 2} + ε^{'}

(10)

where

β_{p e n s i o n 1} = β_{D B 1} + β_{N D B}

and

β_{p e n s i o n 2} = β_{D B 2} + β_{D C E}

In these regressions, b represents the sensitivity of firm risk to firm pension risks and intercept a represents the part of the expected firm risk that cannot be captured by the pension risks. A number of instrumental variables are used to pick up the effect of the intercept and are expected to be positive.

3. Sample and Data

The sample is based on the S&P 500 firms that (1) are in continuous existence in the index for the study period from 1 January 2006 to 31 December 2008; (2) have all available stock price in CRSP and financial information on Compustat; and (3) have complete DB and NDB plan asset allocation information reported in the relevant Money Market Directory publication and finally provided sufficient data to complete analysis of their pension risk and value in the period from the date the relevant balance sheet recognition requirements of SFAS 158 for pension assets and liabilities became fully effective, i.e., for reporting periods ending after 15 December 2008. Financial firms are also excluded. This resulted in a final sample of 150 firms. These comprise sample firms based on the majority of SIC code categories, including mining and construction (12), transportation and utilities (32), manufacturing (87), trade (11), and other services (8).13

3.1. Sample and Data Collection Procedures

Data for this study were collected from a variety of sources. Stock price and return data were captured from the merged CRSP and Compustat file. Compustat was also used to capture the main DB pension variables: ABO, PBO, and market value of pension assets. The Money Market Directory was the source of data for detailed asset allocation. The Ratings Direct service of Standard & Poor provided the credit rating history.

3.2. Data Description

Table 2 reports the descriptive statistics for the sample firms. It reports selected company balance sheet information separately by type of pension liability used. To be included in the final sample, Compustat has complete financial and pension data related to the sample of S&P 500 firms for the entire study period with fiscal years ending from 2006 to 2008. The descriptive statistics show that the book value of equity is sensitive to the measurement of pension liability used.

The total pension plan liabilities and asset values are much higher than under the implicit approach (iii) due to the additional recognition of the net worth of unfunded post-retirement NDB plans, although the consolidation reduces this value through the equity elimination of investment in company sponsoring stock. The pension assets and liabilities also incorporate estimates of future cash flows, risk capital, and credit insurance margins which insurance firms would expect to incur. This in turn also increases the amount of equity in the ‘combined’ firm.14

The insurance hypothesis, advanced by Bodie (1990), assumes that shareholders of the sponsoring firm share the ownership of future pension deficit (surplus) with the employees in a form of a put (call) option.15 Shareholders, therefore, have the option to default on the portion of pension liabilities that are not covered by the pension fund’s collateral (i.e., plan assets) (Bodie 1990).16 A curtailment transaction can thus be viewed as the firm’s exercise of a ‘default’ option on this shared ownership. This ‘default’ option is exercisable when the action is optimal for the sponsoring firm. It is possible that pension curtailments will constitute part of a broader corporate restructuring program. Consequently, it is predicted that pension curtailments with subsequent corporate restructuring are associated with the likelihood of default on pension obligations. Marcus (1985) applies option-pricing theory in estimating the value of firms’ put option to default on their portion of pension liabilities. The put option values derived in Marcus (1985) allow for the calculation of fair value-based measures of pension obligations in which the sponsoring firm’s termination decision is determined endogenously under various operating conditions. Following Marcus (1985), the estimate of the put option value is derived as a proxy measure for firms’ propensity to exercise the default option (PUT). Marcus defines the rate of firm contributions into the pension fund net of payments to retirees;, this is calculated as the difference between the periodic pension employer contributions less the periodic pension benefits divided by end of period ABO. Marcus also defines a ‘net growth rate in accrued benefits attributable to demographic factors’. This is defined as the periodic difference between accrued pension cost and the pension benefits deflated by end of period ABO.

Table 3 reports relevant data on the composition of the pension plans sponsored by these companies. It shows the impact of pensions as a percentage of firm value. The amount of DB and, NDB plan net worth as a proportion of total corporate market capitalization is shown. The total percentage of DB and NDB plan investments in the corporate sponsor’s own stock is also shown. It averages nearly 5% in 2006, but this reduces to 3% in 2008. The decrease is due to the declining economic significance of plans relative to stock options over this period. Relative to stockholders’ equity, both DB and NDB plan pension funds are on average very significant. It should be noted that this descriptive statistical information is not available from JMB as neither the sample selection procedure nor the composition of the data sets is described. Consequently, it is not possible to establish whether the descriptive statistics are comparable to those of JMB.

Table 3 also shows the assumed beta of each asset category identified by the Money Market Directory (MMD). The MMD lists at a detailed level, the asset composition of pension schemes on a ‘functional’ basis. For example, MMD decomposes investments across various debt instruments, from government bonds, corporate bonds, high-yield bonds, convertible bonds, indexed linked bonds, and international bonds. Similarly pension equities are decomposed into various risk classes, including small, medium, or large stock, and/or growth versus value stocks, as well as international, indexed, and emerging market equities.

The asset allocation for the relevant DB plan and NDB plan is shown separately in the table. Note that NDB plans, on average, have invested 35% of a sponsoring company’s stocks relative to 2% invested by DB plans. This has important implications for risk transformation and changes in capital structure for sponsoring companies.

JMB suggests that the cost of capital should be ‘corrected’ to allow for both the value and risk of pension plans. However, they do not consider NDB plans, which have a significant investment in the sponsoring company’s own stock. Since NDB plans own a significant proportion of company own stock, they can be ‘eliminated upon consolidation’ in recognizing the equity or ‘book value’ of the sponsoring company, i.e., by eliminating these common investments made by ‘undiversified’ investors. Because of the materiality and increasing economic significance of such investments by NDBs, they also complicate the relationship of pension risk to firm risk as if it were just a form of systematic risk, as represented by JMB.

4. Empirical Results

This section re-examines the empirical results previously reported in JMB concerning the formal relationship between firm risk and pension risk, using Fama McBeth regressions. The results are confined to non-distressed firms since firms in financial distress are likely to behave differently from non-distressed firms due to PBGC.

Following the procedure used in JMB, three measures are used to identify financially distressed firms: book to market, return on investment, and leverage. These capture measures of overall risk, operating risk and financial risk. Then, in each year of the sample, all firms are ranked by each measure of financial distress, and the deciles of firms with the most severe measure as distressed and the rest are treated as non-distressed. Regressions are run on firms that are not in distress in the previous year. The following panel data regression is fitted, where Equation (11) is the adjusted specification for case (iv), i.e., where the SOE plan is merged with the firm, but as a separate financial services entity.

β_{E + N F L} = a + b β_{p e n s i o n 1} + c o n t r o l var i a b l e + ε

(11)

In terms of the PEEM, where the presently off-balance sheet SOE plans and the DB plans are ‘fully consolidated’; i.e., either merged with the firm as an additional or consolidated as an equity investment, the JMB model is adjusted as follows:

NOA + PA_DB + PA_SOE − (PL_DB + PL_SOE) + OPT = NFL + E,

NOA + PA_DB + (PA_SOE − E_EE) − (PL_DB + PL_SOE) + OPT = NFL + E_CE,

and both DB and SOE net pension plan risks are separately ‘consolidated’ into the firms’ accounts consistent with case (iv). Note that

β_{E + N F L} = \frac{E}{E + N F L} β_{E} + \frac{N F L}{E + N F L} β_{N F L}

β_{E C E + N F L} = \frac{E_{C E}}{E_{C E} + N F L} β_{E} + \frac{N F L}{E_{C E} + N F L} β_{N F L}

Therefore,

β_{E + N F L}

can be rewritten as

β_{E + N F L} = β_{D B 1} + β_{S O E} + \frac{N O A}{E + N F L} β_{N O A} + \frac{O P T}{E + N F L} β_{O P T}

(12)

where

β_{D B} = (\frac{P A_{D B}}{E + N F L} β_{P A_{D B}} - \frac{P L_{D B}}{E + N F L} β_{P L_{D B}})

β_{S O E} = (\frac{P A_{S O E}}{E + N F L} β_{P A_{S O E}} - \frac{P L_{S O E}}{E + N F L} β_{P L_{S O E}}) .

Similarly,

β_{E C E + N F L}

can be rewritten as

β_{E C E + N F L} = β_{D B 2} + β_{D C E} + \frac{N O A}{E_{C E} + N F L} β_{N O A} + \frac{O P T}{E_{C E} + N F L} β_{O P T}

(13)

where

β_{D B 2} = (\frac{P A_{D B}}{E_{C E} + N F L} β_{P A_{D B}} - \frac{P L_{D B}}{E_{C E} + N F L} β_{P L_{D B}})

β_{D C E} = (\frac{P A_{S O E}}{E_{C E} + N F L} β_{P A_{D C E}} - \frac{P L_{S O E}}{E_{C E} + N F L} β_{S O E})

PA_SOEE = PA_SOE − E_EE, and PA_DCE is the systematic risk of PA_SOEE.

We can use the relationships in Equations (12) and (13) to test whether the beta risk of pension is incorporated in the risk of the firm’s capital structure as below:

β_{E + N F L} = a + b β_{p e n s i o n 1} + ε

(14)

β_{E C E + N F L} = a + b β_{p e n s i o n 2} + ε

(15)

where

β_{p e n s i o n 1} = β_{D B 1} + β_{S O E}

, and

β_{p e n s i o n 2} = β_{D B 2} + β_{D C E}

In these regressions, b and c represent the sensitivity of firm risk to firm pension risks, and intercept a represents the part of the expected firm risk that cannot be captured by the pension risks. A number of instrumental variables are to pick up the effect of the intercept and expect b and c to be positive.

4.1. Pension Risk and Cost of Capital

Table 4 shows the beta estimates, relating to each of the three alternative treatments of measuring DB pension liability contracts outlined above.17: (i) where the reported defined benefit pension obligation is measured as the accrued benefit obligation (ABO), based on the AEM of the reporting entity; (ii) where the reported defined benefit pension obligation is measured as the projected benefit obligation (PBO) based on the PEEM of the reporting entity, and additionally includes other elements of the deferred compensation package, e.g., unfunded health care obligations, defined contribution plans, 401K plans, as well as implicit calls and puts on the PBGC.18

Table 4 shows that the beta estimates for firm operating asset beta slightly increase from cases (i) to (iii) as more risk is taken on by the pension liability risk measure. The operating asset beta errors related to risk (error 2) are significantly higher than when value and risk (error 1).

Table 5 reports the cost of capital estimates based on the betas reported in Table 4 and the CAPM. The cost of capital is increasing as the definition of pension liability is broadened from ABO to PBO. In this case, the overestimates related to risk (error 2) are again significantly greater than the errors related to valuation overestimates (error 1). The results also show significant variation across the cases.19 Panel B shows the corresponding cost of capital estimates based on assumptions consistent with those used by JMB. These estimates are also significantly higher than the cost of capital estimates estimated using JMB’s assumptions (panel C), and moreover, increase as the level of pension obligation increases from ABO to PBO.

Following the procedure outlined in JMB, we run Fama and MacBeth (1973) methodology OLS time series tests to compute robust standard errors for the coefficient estimates, by first running cross-sectional regressions for each year separately, while controlling for fixed effects at the industry levels using the two-digit Standard Industrial Classification (SIC) code, and report the time-series averages of the coefficient estimates and use the time series standard errors of the average slopes to draw inferences., The regression coefficients for each of the three measures of risk and their t-statistics are initially reported for the ‘simplistic’ cases (i) and (ii) in Table 6.

Contrary to the results reported in JMB, this study finds large variation in the pension asset betas. The standard deviations increase as we move from the ABO towards the PBO. Furthermore, in none of the cases, this study finds a significant association between firm risk and pension risk, contrary to the results obtained by JMB. This is due to an error in variables problem, different specifications of data, or to a different time period.

4.2. Tests by Incorporating Various Control Variables for Operating Asset Risk

This paper follows JMB by running multiple regressions which incorporate various control variables as proxies for differences in the no-pension operating asset risks across the firms.

The list of control variables and the procedures used to describe them are also initially based on those described in Jin et al. (2006, p. 15) and are reproduced again in Table 7.

The results of the Fama and MacBeth (1973) multiple regressions with control variables are listed in Table 8.

Table 8, Panel A shows that neither old US GAAP (ABO) or new US GAAP (PBO) (i.e., cases (i) and (ii), respectively) demonstrate any relationship between firm risk and pension risk. However, there are limitations associated with estimating standard pension risk to firm risk comparisons in the latter cases, since the consolidation or merger of the pension plans with the sponsoring firm also change the nature of overall firm risk. This issue is examined further in Section 5 below.

5. Robustness Checks and Filtered Tests

This section reports various robustness checks on the regression results that were reported in Section 4, following the procedures described in JMB for financial distressed firms and filtered tests, and then delineates sub-samples of DB pension terminating from non-terminating firms.

5.1. Financially Distressed Firms

Following Jin et al. (2006, p. 17), this study first re-runs the regression analysis specified in Table 8. JMB posit that distressed firms are likely to have a distinctly different pattern than non-distressed firms. Table 9 reports the results.

The overall results for financially distressed firms are not consistent with those reported by JMB and show that the relation between pension risk and firm risk are even more significant for those firms relative to the simple regression results reported in Table 6 for non-distressed firms. These results may be attributed to differences associated with the more restricted sample selection procedures used in this study, since up to two-thirds of the JMB sample did not include firms with significant pension exposure, whereas over 90% of the sample of firms in this study did so.20

5.2. Exclude Firms with Significant Company Stock in the Pension Plan

Following the procedure suggested by JMB (Table 10), the baseline regressions are also rerun by excluding pension investment in company own stock. However, the outcome of this procedure is more significant since we also include company stock owned by SOE plans, which is both material and has a bearing on overall equity ownership between outside equity holders and non-diversified employee holders.

The results reported in Table 10 are nevertheless largely consistent with those reported in our Table 8 but with a slight but significant increase in explanatory power of the overall regressions. Thus, eliminating the company stock ownership significantly enhances the relation of firm risk to pension risk, but only at the conditioning of the external stockholders from the inside employee stockholders.

5.3. Filter Tests

Following JMB, filter tests are conducted to examine whether our results are robust to restricting the sample to only those firms with at a minimum threshold of pension exposure. These tests (not reported) replicated the analysis in JMB by restricting the threshold to the proportion of DB pension assets relative to firm debt and equity. Those results further corroborate earlier findings reported in Table 8 that, contrary to those obtained by JMB, there is no significant relation between pension risk and firm risk.

5.4. DB Pension Plan Termination Decisions

One of the more intriguing aspects of the baseline results reported in Table 4 is the equivocal nature of the relation of firm overall risk, pension risk, and their components to pension plan termination decisions. This section examines this issue by decomposing the sample between continuing (i.e., surviving DB plan sponsors) and terminating DB pension plan sponsors.21

Approximately one-third of the sample firms terminated their DB pension plans during the three-year period of 2006–2008, when the schemes were subject to significant changes in both regulation and GAAP–based reporting and funding requirement. The remaining two-thirds of the sample firms (283 pooled firm observations) continued to operate the schemes over the three fiscal reporting years subsequent to that ending 2008. To address this issue, baseline results reported in Table 6 and Table 7 delineate between DB-continuing and DB-terminating pension plan sponsors.

Table 11 reports the results of a regression of firm systematic risk and pension risk, again separately for continuing (Panel A) and terminating (Panel B) firms.22 Moreover, these results hold after controlling for significant relationships between firm systematic risk and other factors posited by JMB, including cash position, financial leverage, and research and development.

5.5. Analysis of Surviving Firms

This study was conducted during the period of 2006–2008, when both US GAAPs had clarified the previously confusing treatment of pension assets and liabilities that had partially motivated the JMB study, and when there was a sharp decline in DB pensions and a corresponding rise in DC plans in the United States (Wolff 2015). To investigate the impact of subsequent regulatory developments, further analysis of the surviving firms was conducted in the latest 2024 fiscal year reporting period. The analysis suggests that two-thirds (105) of the original 150 sample firms survived and whose shares are actively traded listed in either the NYSE or Nasdaq stock exchanges. Moreover, while both the market value of equity and total financial debt of these firms has increased by 150%, their DB-sponsored pension plan assets and liabilities have only increased by 15% and 17%, respectively. In most cases, DB plans are also now financially immaterial in comparison to their entire business operations, in contrast to the situation formerly applicable to the JMB study in 1993–1998. Moreover, a third (36) of these firms have subsequently terminated or frozen their DB plans. Consequently, it is concluded that the proposal of this paper to apply the PEEM model of the MRE and incorporating NDB plans into the cost of capital estimates is both a valid and material issue and more likely reflects current market conditions.

6. Conclusions

Although the importance of human capital to corporations has been recognized by public policy makers and regulators as important elements of their long-term sustainable value, the cost of capital implications of employee commitments has received scant attention. This study contributes to this issue by examining how alternative treatments of equity-based employee compensation and models of the reporting entity can impact the sensitivity of cost of capital, that is premised on prior research (Forker 2000) which questions the standard entity perspective of the MRE that does not recognize the potentially material impact of employee investments in company own stock and other sources of corporate exposure to defined benefit pensions and unfunded health care benefits which are incorporated into the PEEM.

This study re-examines the cost of capital implications of prior research conducted by JMB in examining the relation between firm risk and pension risk, by considering the impact of applying alternative EM and PEEM reporting entity perspective that incorporates both explicit and implicit long-term contracts between a firm and its employees by quantifying and then analyzing the impact of stock divestitures and investments in company own stock by employee pension, post-retirement, and equity stock investments. The PEEM insights into the MRE requires a re-examination of prior empirical analysis. This paper also incorporates detailed adjustments related to asset allocation that allow for more detailed estimates of both pension asset risk and pension liability risk. The empirical analysis of cost of capital estimates is also sensitive to broader PBO estimates of pension liability risk implied by PEEM and subsequently endorsed by US GAAP (SFAS 158), relative to the more narrowly defined ABO measure that estimates the minimum liability that firms must bear in an event of default, which is implied by EM and former US GAAP (SFAS 87).

The empirical results concerning the association of pension risk to firm risk are much more equivocal than those reported by JMB and are also sensitive to variations in pension asset and liability values and risk under various cases. In addressing the full theoretical implications of PEEM, this paper further considers the impact of mergers or consolidation of NDB plans and by extending the concept of firm risk and pension risk to incorporate various elements of idiosyncratic risk. These subtle changes as a result of apparently minor variations have a significant impact on the magnitude, relative weighting, and risk implications of any inference about the relation of firm risk to pension risk. The baseline empirical results are robust to alternative specifications of these risks and corroborative tests are also consistent with those of the broader literature which find a positive association between idiosyncratic risk and stock returns in the presence of high degrees of agency costs in the form of insider ownership.

The empirical results should be treated with caution where it has applied the one-period standard CAPM, and consequently, issues concerning duration and multi-period impact of value changes in financial and/-or business risk on various operating, financial, and pension components of the firm have not been addressed.23 This paper has also not considered the broader impact on idiosyncratic risk of other firm strategies related to derivative usage or other sources of transferable capital. These remain issues for further research. Furthermore, in seeking to replicate the environmental conditions applicable to the original JMB study, this study has not decomposed the various types of NDB and their incremental and relative importance in affecting the overall cost of capital estimates that evolved over the subsequent two decades since the research was originally undertaken. Additionally, there are strategic managerial issues related to the shifting of risk from the firm to employees in times of economic uncertainty which may mitigate the impact of pension funds on a firm’s cost of capital (Cumming et al. 2024). Furthermore, there are issues concerning the cross-sectional variation between firm risk, pension plan asset allocation, and the credit rating and funding policy of pension plans (Rauh 2009). These and other issues are left as issues for future research.

Subject to these caveats, this paper finds that the extent of overestimation because of omitting pension value and risk is less than what prior researchers imply. This paper also finds that there are systematic variations in the association of pension risk and firm value for firms with implicit contracts and those with explicit contracts. Sources of idiosyncratic risk appear to explain the relation of pension risk to firm risk, especially for firms that terminate their defined benefit pensions. Finally, our findings suggest that altering the mix and magnitude of value and risk components of pension assets and liabilities can affect the cost of capital and pension risk. Our analysis also bears upon standard models used to explain the cross-section of stock returns, since unfunded pension exposure appears to be important for many firms.

The paper also has identified a number of practical implications for financial analyst professionals and regulators. In particular, it has identified the importance of NDB arrangement in both conditioning and supplementing well-known standard cost of capital applications that are not identified in the professional literature (e.g., Pratt et al. 2014). The primary contributions of the paper are the following:

(1): It is important to control alternative measurement bases for defined benefit pension liabilities that incorporate salary growth assumptions that firms now recognize on their balance sheets, i.e., beyond the previously reported spinoff termination value (ABO). Specifically, current GAAP requires firms to report the broader PBO, which includes wage growth assumptions. Both the ABO and PBO make restrictive assumptions about the explicit and short-term nature of DB employment contracts. A broader EBO or long-term funding measure of pension liabilities is conceptually more consistent with a long-term asset pricing or returns model. However, the estimated cost of capital increases as the DB pension liability measure broadens from an ABO to a PBO estimate of the pension liability.24
(2): Any analyst estimating a firm’s WACC should adjust explicitly for various sources of firm risk management strategy (e.g., O’Brien 2006), and such procedures should be sufficiently robust to more clearly delineate the categories of ‘net operating assets’ from ‘net financial liabilities.
(3): Cost of capital estimates should also be sufficiently precise in modeling details of a firm’s pension asset allocation to enable more reliable and robust inferences to be drawn concerning the predicted relationship between pension risk and firm risk, allowing for both DB and NDB plans.
(4): It is important to adjust WACC estimates for the purposes of ‘fundamental value’ analysis by separating the impact of ‘implicit contracts’ with employees, arising from the recognition of (i) salary growth assumptions (PBO vs. ABO) and the (ii) avoid ‘double counting’ problems by separating the interests of both diversified external investors and non-diversified employee stock investors that participate in pension plans with significant investments in parent company stock.
(5): The adjustment procedures suggested in (1) to (4) above are particularly relevant to those examining the explanatory power of Fama and French (1992) three-factor plus momentum models, and especially in examining the cross-section of returns of significantly underfunded firms.

This paper proposes a simple set of procedures for estimating the cost of capital that incorporates both systematic and non-systematic sources of pension risk. By considering the debt and equity implications, our analysis suggests that standard procedures underestimate these risks. Further research can address these issues even more comprehensively by examining broader inter-relationships between various retained and transferred risk sources which are often off-balance sheet contingent claims.

Funding

This research received no external funding.

Acknowledgments

The author would like to thank Pengguo Wang for his contribution to the paper in developing the modelling analysis, and the referees for their valuable comments.

Data Availability Statement

Data is available upon request.

Conflicts of Interest

The author declares no conflicts of interest.

Appendix A

Proof of Equation (4).

If the values of both DB and NDB plans are included, then the estimated operating asset is

\hat{N O A} = NOA = E + NFL - {NPA}_{DB} - {NPA}_{NDB} - OPT

The estimated operating asset beta becomes

\hat{β_{N O A}} = \frac{E}{N O A} β_{E} + \frac{N F L - N P A_{D B} - N P A_{N D B}}{N O A} β_{N F L} - \frac{O P T}{N O A} β_{O P T}

Define

\hat{ε_{N O A}} = \hat{β_{N O A}} - β_{N O A}

\begin{array}{l} \hat{ε_{N O A}} = \frac{E}{N O A} β_{E} + \frac{N F L - N P A_{D B} - N P A_{N D B}}{N O A} β_{N F L} - \frac{O P T}{N O A} β_{O P T} \\ - (\frac{E}{N O A} β_{E} - \frac{N F L}{N O A} β_{N F L}) - (\frac{P A_{D B}}{N O A} β_{P A_{D B}} - \frac{P L_{D B}}{N O A} β_{P L_{D B}}) - (\frac{P A_{N D B}}{N O A} β_{P A_{N D B}} - \frac{P L_{N D B}}{N O A} β_{P L_{N D B}}) - \frac{O P T}{N O A} β_{O P T}) \\ = \frac{(P A_{D B} - P L_{D B}) - (P A_{N D B} - P L_{N D B})}{N O A} β_{N F L} + (\frac{P A_{D B}}{N O A} β_{P A_{D B}} - \frac{P L_{D B}}{N O A} β_{P L_{D B}}) + (\frac{P A_{N D B}}{N O A} β_{P A_{N D B}} - \frac{P L_{N D B}}{N O A} β_{P L_{N D B}}) \\ = \frac{P L_{D B}}{N O A} (β_{N F L} - β_{P L_{D B}}) + \frac{P A_{D B}}{N O A} (β_{P A_{D B}} - β_{N F L}) + \frac{P L_{N D B}}{N O A} (β_{N F L} - β_{N D B}) + \frac{P A_{N D B}}{N O A} (β_{P A_{N D B}} - β_{N F L}) \end{array}

□

Notes

1	Dhaliwal (1986) argues that financial leverage and fundamental risk should be separately incorporated into cost of capital estimates. Chen et al. (2008) finds that fundamental risk affects the cost of capital estimates. This paper, therefore, calculates net financial liabilities and net operating assets using the definition in the standard financial analysis literature.
2	The United Nations, International Labour Organizsation, and the Principles for Responsible Investment haves also recognizsed the increasing prominence of labor and social issues for corporate responsibility reporting, through the establishment of a new “TaskForce for Social Related Financial Disclosures”, which has yet to formally issue international guidance on this issue.
3	SEC amendment to 101(c) of Regulation S-K, US listed companies require “a description of a registrant’s human capital resources, including any human capital measures or objectives that the registrant focuses on in managing the business” (Securities and Exchange Commission 2020). The SASB’s Human Capital Management Research Project (SASB 2020) states that “Human capital is a critical element of the SASB standards. As a thematic issue, it is the second most prevalent issue across the SASB standards, second only to climate risk”.
4	Previts (1974) subsequently identified Sprague a having an important impact on subsequent professional and academic thinking on the relation of liabilities and proprietorship equity.
5	This study follows Forker (2000) with the PEEM and EM models because it relates more clearly to alternative accounting treatments of equity-based employee compensation and for analyzsing its implications for the estimating the impact of alternative pension accounting treatments of the reporting entity, including the all-equity model.
6	A 401K plan permits employees to elect to have a portion of their compensation contributed to a qualified retirement plan (EBRI 2009). Investors in 401K plans issued by Lucent Technologies sued based on the Employee Retirement Income Security Act (ERISA) of 1974, which states that plan sponsors have a fiduciary responsibility to provide prudent and diversified investing options. However, it does not impose any upper restrictions on the amount of company stock that a 401K plan can invest in.
7	Himmelberg et al. (2002) derive a model whereby cost of capital, capital structure, and ownership concentration are endogenous variables.
8	The Employee Benefits Research Institute (EBRI 2011a) reports that participation in defined contribution plans (which promise a specified contribution to an employee’s account) is growing faster than participation in traditional defined benefit pension plans (which promise a specified benefit at retirement). The percent of private-sector active-worker participants in a defined benefit plan where the defined benefit plan was the only plan that declined from 62 percent in 1975 to 7 percent in 2009, while the percent of private-sector active-worker participants in a defined contribution plan where the defined contribution plan was the only plan increased from 16 percent in 1975 to 67 percent in 2009. EBRI (2011b) also identifies significant increases in the average 401(K) plan accounts to 2009, except for 2008, with the bulk of assets invested in stocks, of which a significant (but declining) proportion is invested in the sponsoring company’s own stock (EBRI 2011a).
9	Non-defined benefit plans (NDB) can vary widely and may range from post-retirement health care benefits (subject to US GAAP SFAS 106), to section 401K pension plans and other forms of retirement income savings, such as endowment funds, and employee stock options. For the purposes of this research, and simplicity of expositions, these different types of entity are consolidated these into a single term “NDB” although in practice, they widely significantly in contractual form.
10	It is recognizsed that the full range of deferred compensation arrangements are necessarily off-balance sheet in nature and asymmetric; hence the analysis reported is confined to direct company exposure to underfunded defined benefit plans and health care obligations, company own stock investments of 401K, and defined contribution plans.
11	This is one of the caveats acknowledged by JMB. Not being able to assign specific beta risk to each asset under a specific asset class may lead to some measurement error in their analysis.
12	This table is like Forker (2000) Table 5, but additionally includes the implications for the appropriate measure of the pension obligation.
13	This decomposition of the sample reflects the SIC itself, in which manufacturing sector firms (2000–4999) dominate. Sample manufacturing firms are further decomposed into industry sub-sectors: food and apparel (18), paper and publishing (39), chemical and petrol (66), rubber-glass and metal (24), equipment and machines (84); other (36).
14	Our measures of the ABO, PBO, and EBO are highly positively correlated, consistent with the simulation results of Selling and Stickney (1986) and are not reported here.
15	Bodie (1990) views pension funds as an insurance subsidiary. The pension promises are viewed as participating annuities that offer a guaranteed minimum nominal benefit determined by the plan’s benefit formula. This guaranteed benefit is permanently enriched from time to time, at the discretion of management, depending on the financial condition of the plan sponsor, the increase in the living cost of retirees, and the performance of the fund’s assets. Evidence in support of this ‘guaranteed minimum’ contention is the fact that many UK plans have given ad hoc benefit increases to plan participants in the past.
16	The optionality element inherent in pension commitments is introduced by Sharpe (1976), who focuses on the impact of the introduction of government pensions insurance in ERISA on the nature of an employer sponsors’ pension obligations. However, he does not model an equivalent implicit contingent claim by employees on the pension fund surplus, which is the focus of the insurance view of pension contract.
17	Because the empirical analysis is focused on the post-disclosure period from 2006 to 2008 only, the study does not amend the CAPM estimates to reflect longer-run changes in risk factor loadings or learning-based approaches to estimate CAPM (e.g., Adrian and Franzoni 2009), although it is recognized that this may also bear on the validity of the model and findings. See the limitations discussion in the conclusion.
18	In the ‘combination case’, the highest quartile of firms with ‘growth’ are treated as (iii), the next quartile of firms with the highest estimated put options are treated as (iv); and firms with minimal pension exposure are treated as (i). The remainder are treated as (ii).
19	Further analysis of cost of capital estimates by industry 2-SIC code breakdown (not reported) shows that significant inter-industry variation in cost of capital estimates. The lowest sector is utilities, while the highest if retail. These results are consistent with the finding that incorporating risk and value of pension risk in utilities has little impact on their already structured balance sheets, whereas it has a more significant impact on more leveraged retail firms.
20	Curme and Kahn (1990) predict and find that, for a sample of US firms, the incidence of pension arrangements is significantly lower on average for distressed firms. These findings are consistent with the explanation that the failure to delineate relatively large S&P 500 firms that are more likely to have significant pension exposure may lead to the findings reported in JMB of a non-significant relation between pension risk and firm risk for their (much larger) sample of distressed US firms.
21	Decomposing results by whether firms terminate or continue DB pension plans is important because Bulow and Scholes (1983) argue that there is a separating equilibrium by which firms either have continuing or terminating contracts with their employees.
22	The definitions of control variables used in this paper are consistent with those employed by JMB to clarify the incremental explanatory power of alternative proxies and measurement bases of pension risk.
23	Stapleton and Subrahmanyam (1984) overview a taxonomy of alternative multi-period CAPM models that could be applied to overcome this issue. However, Fama (1977) demonstrated that the application of CAPM to multiperiod valuation is theoretically valid. Application texts such as Pratt et al. (2014) outline the procedure for calculating discount rates based on changing business and-or financial risk over time.
24	We suspect this is a major reason why financial analysts prefer not to use the PBO for cost of capital estimation purposes.

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Table 1. Comparison of models of the reporting entity (MRE).

Characteristic	All-Equities Model (AEM)	Equity Model (EM)	Pre-Existing Equity Model (PEEM)
Boundary of the model of the reporting entity (MRE)	All funding instruments	Equity instruments, including rights to contingently issuable shares	Existing equity shareholders
Income measurement and capital structure	No distinction between debt and equity	Debt and equity separately classified	All funding instruments, except existing equity classified as liabilities
Accounting for wealth transfers within the boundary of the MRE	All transfers are netted with zero impact on income	Intra-equity transfers are netted, but price changes on liabilities are recognized in the income statement	All wealth transfers are recognized in the income statement
Clean surplus accounting	No	Yes, for liability instruments. No for equity instruments	Yes
Accounting for employee stock options, share of DB and DC, and 401K equity investments in own firm	Yes, for DB only (assume ‘surplus’ = ABO − MV of pension assets); no unexpected variations affect income	Yes, for DB (assume ‘surplus’ = ABO − MV pension assets); no for DC or 401K employee ownership of company own stock	Yes, for DB (assume ‘surplus’ = PBO − MV pension assets); yes, for DC or 401K employee ownership of company own stock as liabilities

Table 2. Descriptive statistics: selected company balance sheet information. (Standard deviations statistics in brackets).

Variable	No	Mean	Std Dev	25%	Median	75%
DB PA	450	3967	7912	484	1517	3584
PFL1	450	3925	7051	508	1627	3834
PFL2	450	4290	7582	582	1758	4116
NDBPA	450	2225	3264	420	1115	2500
NDBPL	450	1730	2831	270	715	1713
MVE	450	22,336	32,726	5174	11,326	24,945
BVE1	450	8655	13,211	1997	4620	9806
BVE2	450	8432	13,228	1933	4460	9571
NFL	450	3797	8095	328	2056	5513
Put	450	957	2653	0	51	497
Call	450	1004	2932	0	99	629
Employee eEquity	450	441	771	0	139	470

Pension assets, pension liability, and market cap information are obtained from Compustat. Figures are in millions of dollars. The sample is 150 S&P 500 firms. Data are pooled for 2006–2008. Pension asset DB is the market value of pension assets in the defined benefit fund. PFL is the present value of pension obligations in the defined benefit plan and is either based on the ABO (PFL1), or the PBO (PFL2). The NDBPA (NDBPL) is the market value of assets (liabilities) invested in non-defined plans, NDB plans. MVE is the market capitalization of the firm. BVE is the book value of equity of the firm, allowing for any company stock investment depending on how the pension plan liability is defined. NFL is the total (non-pension) financial liabilities of the firm. The value of the put option is the estimates of the corporate guarantee and the value of the call option is the estimates of the pension fund net worth.

Table 3. Pension asset categories as reported in Money Market Directory, 2006–2008.

Description	Average Asset Allocation DB (%)	Average Asset Allocation DC Plan (%)	Assumed Beta	Indicated in JMB
Bonds	18.2	4.1	0.175	0.175
Corporate bonds	1.8	0.3	0.230	0.175
Government bonds	2.1	0.5	0.179	0.175
Municipal bonds	0.1	0.2	0.205	0.175
Inflation-linked bond	2.3	0.6	0.102	0.175
International bonds	1.0	0.2	0.175	0.175
High-yield bonds	0.6	0.0	0.175	0.175
General insurance	0.6	13.4	0.205	0.175
Convertible bond	0.2	0.0	0.205	0.175
Small-cap value	1.0	0.5	2.012	1.0
Small-cap growth	1.1	0.5	1.372	1.0
Small cap	5.0	1.3	1	1.0
Large-cap value	2.5	1.3	1.359	1.0
Large-cap growth	2.0	1.2	0.717	1.0
Large cap	8.1	1.2	1	1.0
Growth equities	2.1	1.6	1.044	1.0
Value equities	2.6	1.1	1	1.0
Indexed equities	8.5	8.2	1	1.0
International equity	12.0	2.1	1	1.0
Equities	16.9	8.6	1	1.0
Cash	2.04	2.5	0.06	0.06
Property	2.1	0.2	0.15	0.150
Company stock	1.9	35.2	Equity beta	Equity beta
Other investments	5.26	15.2	0.795	1.0

We use the CAPM to back out the systematic risk beta for various types of assets in pension funds. Relevant assumptions are consistent with Brealey et al. (2006) in capital market history in the 1926–2005 period. Specifically, we assumed the T-bill rate is 4.2%, the average market return is assumed to be 12%, and the average risk premium is assumed to be 7.8%. The average annual return rate for large-firm stocks is 12.3%, and 17.4% for small firms, the yield for long-term corporate bonds is 6.2%, yield for long-term government bonds is 5.8%, intermediate-term government bond yield is 5.5%, and the yield for US. Treasury bills is 3.8%. The high-yield bond is assumed to be 8%, which is between the large-stock and corporate bond. Municipal yields are assumed to the same as long-term government bonds. Inflation-linked bonds earn 5% ‘real’ return. Both capital guaranteed insurance and convertibles are assumed to yield 5.8% as long-term government bonds. The returns on small-cap value stock and large-cap stocks are assumed to be 17.4% ± 2.5%; The returns on large-cap value and growth stocks are assumed to be 12.3% ± 2.5%. This is consistent with the average annual difference between the returns on value stock and growth stock which have been about 5% since 1926. Betas of other equity classes, including index and international equities, are assumed to be 1.

Table 4. Estimates of pension asset and operating betas. (Averages with standard deviation in brackets).

Case	Operating Asset Beta Correct	Operating Asset Beta Error 1	% Overestimate for Error 1	Operating Asset Beta Error 2	% Overestimate for Error 2
Panel A: based on this study’s assumptions
(i): ABO	0.560 (1.432)	0.775 (1.403)	38.3	1.186 (7.331)	111.7
(ii): PBO	0.561 (1.432)	0.770 (1.394)	37.2	1.117 (6.221)	99.1
Panel B: based on JMB assumptions
(i): ABO	0.297 (0.287)	0.543 (0.537)	82.8	0.574 (0.599)	93.3
(ii): PBO	0.297 (0.287)	0.509 (0.334)	71.3	0.565 (0.551)	90.2
Panel C: t-statistics difference A-B
(i): ABO	4.005	3.477		1.775
(ii): PBO	4.005	4.142		1.909
(iii): ABO vs. PBO	−1.501	0.716		0.969

This table reports the average pension risk and overestimation of cost of operating assets for cases (i) (PBO), (ii) (ABO), and (iii) PBO., Beta of equity is estimated using capital asset pricing model, using data on three-year monthly stock return, obtained from the Center for Research in Security Prices, and the value-weighted return on all stocks on NYSE, AMEX, and Nasdaq as the proxy for market. Operating asset beta correct is the operation asset beta when correctly accounting for pension value and risk, operating asset beta error 1 is the operating asset beta ignoring pension plan altogether, and operating asset beta error 2 is the operating asset beta counting pension value but misrepresenting pension risk.

Table 5. Cost of capital estimates. (Averages with standard deviation in brackets.).

Case	Correct Cost of Capital Estimate (%)	Cost of Capital Estimate Error 1 (%)	% Overestimate for Error 1	Cost of Capital Estimate Error 2 (%)	% Overestimate for Error 2
Panel A: based on our assumptions
(i): ABO	7.448 (10.734)	9.341 (10.192)	25.5	12.218 (51.231)	63.8
(ii): PBO	7.842 (10.411)	9.317 (10.274)	18.7	11.730 (44.485)	49.2
Panel B: based on JMB assumptions
(i): ABO	7.088 (3.718)	7.712 (4.423)	8.9	7.929 (4.737)	11.8
(ii): PBO	5.993 (2.822)	7.479 (3.508)	24.8	7.822 (4.220)	30.5
Panel C: t-statistics difference A-B
(i): ABO	0.742	3.477		1.776
(ii): PBO	4.005	4.104		1.909
(iii): ABO vs. PBO	−1.501	0.662		0.969

This table reports the average systematic risk and overestimation of cost of operating assets for cases (i)–(iii). Beta of equity is estimated using capital asset pricing model, using data on three-year monthly stock return, obtained from the Center for Research in Security Prices, and the value-weighted return on all stocks on NYSE, AMEX, and Nasdaq as the proxy for market. Operating asset beta correct is the operation asset beta when correctly accounting for pension value and risk, operating asset beta error 1 is the operating asset beta ignoring pension plan altogether, and operating asset beta error 2 is the operating asset beta counting pension value but misrepresenting pension risk.

Table 6. Relation between pension risk and firm risk: simple regression: non-distressed firms (existing and new GAAP, standard deviation in brackets).

Panel A: Case i—ABO
	Asset Allocation/Financial Distress Assumption
	Book—Market Ratio		Return on Investments		Financial Leverage
	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46
Intercept	1.037 (0.097)	1.049 (0.091)	1.028 (0.109)	1.042 (0.093)	1.029 (0.096)	1.042 (0.087)
Pension risk	0.103 (0.097)	0.144 (0.206)	0.097 (0.146)	0.108 (0.229)	0.080 (0.116)	0.105 (0.213)
No. of observations	672	672	672	672	672	672
R-Squared	0.015	0.010	0.017	0.010	0.015	0.010
Panel B: Case ii—PBO
	Asset Allocation/Financial Distress Assumption
	Book—Market Ratio		Return on Investments		Financial Leverage
	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46
Intercept	1.035 (0.101)	1.045 (0.095)	1.024 (0.112)	1.032 (0.098)	1.030 (0.096)	1.039 (0.089)
Pension risk	0.119 (0.134)	0.262 (0.350)	0.154 (0.190)	0.249 (0.331)	0.078 (0.109)	0.191 (0.347)
No. of observations	672	672	672	672	672	672
R-Squared	0.030	0.025	0.037	0.027	0.018	0.017

This table reports regression results for the sample from 2004 to 2008 using the procedure described in Jin et al. (2006, p. 14). The regression being run for cases (i) and (ii) is Equation (9) with β_SOE = 0:

β_{E + N F L} = a + b β_{p e n s i o n 1} + ε

Table 7. List of control variables (following Jin et al. 2006, p. 15).

Variable	Calculation	Compustat Item No.
Market share by value	Calculated using market value and the industry classification codes	DATA24/DATA25
Market share by sales	Calculated using total sales and the industry classification codes	DATA12
Capital intensiveness	Current assets/total assets	DATA4/DATA6
Cash position	Cash and short-term investments/total assets	DATA1/DATA6
Financial leverage	Debt/total assets/	(Data9 + Data34)/DATA6
Growth rate	Log (total assets/lagged total assets)	Log (DATA6)/DATA6_lag)
Liquidity	Current assets/current liabilities	DATA4/DATA5
Return on investment	Net income/total assets	DATA172/DATA6
Firm size	Log (total assets)	Log (DATA6)
Research and development	Research and development expense/total assets	DATA46/DATA6
Advertisement	Advertising expense/total assets	DATA45/DATA6

Table 8. Relation between pension risk and firm risk: regression: non-distressed firms.

Panel A: Case i—ABO
	Asset Allocation/Assumption
	Book-Market Ratio		Return on Investments		Financial Leverage
	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46
Intercept	1.895 (0.392)	1.875 (0.385)	2.004 (0.384)	1.976 (0.382)	2.147 (0.570)	2.125 (0.566)
Pension risk	0.113 (0.100)	0.158 (0.162)	0.190 (0.188)	0.142 (0.213)	0.081 (0.092)	0.114 (0.161)
Market share by value	−0.246 (0.125)	−0.247 (0.124)	−0.211 (0.222)	−0.206 (0.216)	−0.151 (0.232)	−0.144 (0.224)
Market share by sales	0.130 (0.204)	0.148 (0.196)	0.152 (0.173	0.154 (0.160)	0.143 (0.168)	0.147 (0.160)
Capital intensiveness	0.239 (0.240)	0.257 (0.251)	0.185 (0.218)	0.219 (0.249)	0.152 (0.204)	0.176 (0.236)
Cash position	0.407 (0.779)	0.402 (0.770)	0.556 (0.726)	0.554 (0.721)	0.586 (0.754)	0.584 (0.738)
Financial leverage	−0.277 (0.171)	−0.296 (0.131)	−0.401 (0.187)	−0.422 (0.172)	−0.643 (0.324)	−0.660 (0.292)
Growth rate	0.414 (0.514)	0.395 (0.515)	0.571 (0.561)	0.564 (0.573)	0.506 (0.564)	0.493 (0.570)
Liquidity	0.001 (0.003)	0.001 (0.003)	0.001 (0.002)	0.001 (0.002)	0.000 (0.004)	0.000 (0.004)
Return on investment	−0.015 (2.188)	−0.054 (2.285)	0.191 (2.224)	0.067 (2.358)	−0.299 (2.012	−0.362 (2.101)
Firm size	−0.090 (0.049)	−0.087 (0.049)	−0.102 (0.052)	−0.097 (0.052)	−0.103 (0.060)	−0.098 (0.062)
Advertisement	−2.825 (2.135)	−2.787 (2.140)	−1.870 (1.756)	−1.838 (1.750)	−1.887 (1.078)	−1.851 (1.081)
Research and development	1.170 (2.207)	1.154 (2.097)	1.094 (1.765)	0.812 (2.061)	0.463 (2.070)	0.417 (2.037)
No. of observations	684	684	684	684	684	684
R-Squared	0.278	0.275	0.282	0.277	0.277	0.275
Panel B: Case ii—PBO
	Asset Allocation/Financial Distress Assumption
	Book—Market Ratio		Return on Investments		Financial Leverage
	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46
Intercept	1.887 (0.396)	1.864 (0.393)	2.000 (0.387)	1.965 (0.385)	2.152 (0.576)	2.128 (0.575)
Pension risk	0.116 (0.131)	0.264 (0.255)	0.111 (0.176)	0.326 (0.254)	0.101 (0.132)	0.195 (0.290)
Market share by value	−0.199 (0.152)	−0.207 (0.130)	−0.174 (0.240)	−0.169 (0.220)	−0.140 (0.227)	−0.105 (0.255)
Market share by sales	0.076 (0.234)	0.104 (0.207)	0.112 (0.217)	0.118 (0.182)	0.182 (0.178)	0.102 (0.208)
Capital intensiveness	0.216 (0.228)	0.250 (0.216)	0.147 (0.193)	0.192 (0.220)	0.100 (0.240)	0.165 (0.235)
Cash position	0.455 (0.838)	0.456 (0.835)	0.587 (0.793)	0.581 (0.798)	0.447 (0.783)	0.560 (0.724)
Financial leverage	−0.226 (0.242)	−0.247 (0.203)	−0.352 (0.242)	−0.384 (0.204)	−0.622 (0.300)	−0.648 (0.270)
Growth rate	0.404 (0.500)	0.385 (0.504)	0.577 (0.550)	0.571 (0.572)	0.509 (0.561)	0.505 (0.573)
Liquidity	0.001 (0.003)	0.001 (0.003)	0.001 (0.002)	0.001 (0.002)	0.000 (0.004)	0.000 (0.004)
Return on investment	0.096 (2.082)	0.062 (2.153)	0.306 (2.029)	0.176 (2.135)	−0.276 (2.007)	−0.342 (2.108)
Firm size	−0.092 (0.052)	−0.089 (0.051)	−0.104 (0.053)	−0.099 (0.053)	−0.104 (0.063)	−0.101 (0.063)
Advertisement	−2.916 (2.147)	−2.883 (2.071)	−1.904 (1.703)	−1.884 (1.601)	−1.832 (1.065)	−1.762 (1.070)
Research and development	2.312 (1.618)	2.516 (2.066)	2.011 (1.843)	1.847 (1.643)	0.449 (1.927)	0.384 (1.783)
No. of observations	684	684	684	684	684	684
R-Squared	0.284	0.281	0.291	0.286	0.276	0.278

Panel A: This table reports regression results for the sample from 2004 to 2008 using the procedure described in Jin et al. (2006, 14) and based on US GAAP. The regression being run is

β_{E + N F L} = a + b β_{p e n s i o n 1} + c o n t r o l var i a b l e + ε

. All results are estimated with company betas estimated using the market model and one lagged term and with the end-of-year pension data. The regression is run for each year, controlling for fixed effect at the industry level, and then the time series mean, and standard deviation of the regression coefficients are used to make inferences. The standard deviation, reported under each coefficient and in parenthesis, is further adjusted for potential time series correlation. Panel B: This table reports regression results for the sample from 2004 to 2008 using the procedure described in Jin et al. (2006, p. 14) in cases where the pension plan is subject to new GAAP (i.e., discount only accrued pension liabilities using risk–free rate). The regression being run is

β_{E C E + N F L} = a + b β_{p e n s i o n 2} + c o n t r o l var i a b l e + ε

Table 9. Relation between pension risk and firm risk: simple regression: distressed firms (existing and new GAAP, standard deviation in brackets).

Panel A: Case i ABO
	Asset Allocation/Financial Distress Assumption
	Book-Market Ratio		Return on Investments		Financial Leverage
	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46
Intercept	1.001 (0.287)	0.932 (0.206)	1.047 (0.145)	1.058 (0.126)	0.843 (0.167)	0.892 (0.162)
Pension risk	−0.386 (1.310)	0.603 (0.789)	0.098 (0.160)	0.130 (0.230)	0.676 (0.757)	1.066 (1.088)
No. of observations	75	75	75	75	75	75
R-Squared	0.055	0.037	0.075	0.069	0.229	0.260
Panel B: Case ii PBO
	Asset Allocation/Financial Distress Assumption
	Book—Market Ratio		Return on Investments		Financial Leverage
	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46
Intercept	1.018 (0.261)	0.968 (0.192)	0.989 (0.160)	1.050 (0.133)	0.841 (0.156)	0.904 (0.144)
Pension risk	−0.420 (0.969)	0.016 (0.971)	0.195 (0.254)	0.355 (0.353)	0.687 (0.754)	1.145 (1.028)
No. of observations	75	75	75	75	75	75
R-Squared	0.071	0.030	0.084	0.077	0.207	0.222

β_{E + N F L} = a + b β_{p e n s i o n 1} + c o n t r o l var i a b l e + ε

Table 10. Robustness check with impact of employer security removed from security risk.

Panel A: Case i—ABO
	Financial Distress Assumption
	Book-Market Ratio		Return on Investments		Financial Leverage
	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46
Intercept	1.895 (0.391)	1.865 (0.379)	1.913 (0.466)	1.877 (0.462)	2.147 (0.570)	2.126 (0.566)
Pension risk	0.113 (0.100)	0.053 (0.193)	0.108 (0.138)	0.157 (0.199)	0.081 (0.092)	0.114 (0.161)
Market share by value	−0.246 (0.125)	−0.167 (0.237)	−0.246 (0.159)	−0.255 (0.148)	−0.151 (0.232)	−0.144 (0.223)
Market share by sales	−0.246 (0.125)	−0.167 (0.237)	−0.246 (0.159)	−0.255 (0.148)	−0.151 (0.232)	−0.144 (0.223)
Capital intensiveness	0.239 (0.240)	0.287 (0.270)	0.235 (0.238)	0.273 (0.262)	0.152 (0.204)	0.176 (0.236)
Cash position	0.407 (0.779)	0.211 (0.864)	0.589 (0.696)	0.493 (0.841)	0.586 (0.754)	0.584 (0.738)
Financial leverage	−0.277 (0.171)	0.053 (0.675)	−0.300 (0.140)	−0.322 (0.136)	−0.643 (0.324)	−0.660 (0.292)
Growth rate	0.412 (0.514)	0.255 (0.250)	0.577 (0.562)	0.568 (0.575)	0.506 (0.564)	0.493 (0.570)
Liquidity	0.001 (0.003)	0.558 (1.246)	0.001 (0.002)	0.001 (0.002)	0.000 (0.004)	0.000 (0.004)
Return on investment	−0.015 (2.188)	−0.644 (1.665)	0.418 (2.239)	0.322 (2.380)	−0.299 (2.012)	−0.362 (2.101)
Firm size	−0.090 (0.049)	−1.335 (2.836)	−0.098 (0.057)	−0.093 (0.056)	−0.103 (0.060)	−0.100 (0.060)
Advertisement	−2.825 (2.135)	−1.199 (1.678)	−2.078 (1.951)	−2.048 (1.953)	−1.887 (1.078)	−1.851 (1.081)
Research and development	1.170 (2.207)	0.912 (2.112)	1.633 (2.025)	1.394 (2.438)	0.463 (2.070)	0.417 (2.037)
No. of observations	684	684	684	684	684	684
R-Squared	0.2788	0.275	0.254	0.287	0.277	0.275
Panel B: Case ii PBO
	Financial Distress Assumption
	Book—Market Ratio		Return on Investments		Financial Leverage
	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46	B_PL = 0.18	B_PL = 0.46
Intercept	1.887 (0.396)	1.864 (0.393)	1.894 (0.482)	1.857 (0.473)	2.152 (0.576)	2.128 (0.575)
Pension risk	0.116 (0.131)	0.051 (0.282)	0.106 (0.177)	0.285 (0.312)	0.074 (0.098)	0.195 (0.290)
Market share by value	−0.212 (0.141)	−0.038 (0.272)	−0.225 (0.204)	−0.202 (0.198)	−0.113 (0.272)	−0.105 (0.255)
Market share by sales	0.088 (0.222)	−0.019 (0.132)	0.085 (0.233)	0.188 (0.217)	0.095 (0.227)	0.102 (0.208)
Capital intensiveness	0.216 (0.228)	0.394 (0.143)	0.210 (0.224)	0.074 (0.389)	0.146 (0.192)	0.165 (0.235)
Cash position	0.455 (0.838)	0.291 (0.878)	0.525 (0.860)	0.572 (0.816)	0.574 (0.754)	0.560 (0.724)
Financial leverage	−0.225 (0.242)	−0.135 (0.335)	−0.242 (0.168)	−0.139 (0.345)	−0.622 (0.300)	−0.648 (0.270)
Growth rate	0.404 (0.500)	0.317 (0.534)	0.584 (0.552)	0.493 (0.631)	0.509 (0.561)	0.505 (0.573)
Liquidity	0.001 (0.003)	−0.079 (0.180)	0.001 (0.002)	0.131 (0.290)	0.000 (0.004)	0.000 (0.004)
Return on investment	0.096 (2.082)	0.122 (2.141)	0.583 (2.055)	0.328 (2.184)	−0.276 (2.007)	−0.342 (2.108)
Firm size	−0.092 (0.052)	−0.409 (0.725)	−0.099 (0.059)	−0.376 (0.605)	−0.104 (0.063)	−0.101 (0.063)
Advertisement	−2.916 (2.146)	−2.540 (2.426)	−2.137 (1.775)	−1.338 (2.684)	−1.832 (1.065)	−1.772 (1.072)
Research and development	2.312 (1.618)	2.649 (1.877)	2.508 (1.730)	1.891 (1.921)	0.382 (1.945)	0.384 (1.783)
No. of observations	684	684	684	684	684	684
R-Squared	0.284	0.281	0.301	0.293	0.280	0.276

This table reports regression results for the sample from 2004 to 2008 using the procedure described in Jin et al. (2006, p. 14). This regression being run is

β_{E_{C E} + N F L} = a + b β_{p e n s i o n 2} + c o n t r o l var i a b l e s + ε

. For case (iv), it is the extended model applicable to the combined entity of the firm and the sponsored SOE/SOE plan; i.e.,

β_{E_{C E} + N F L} = a + b β_{D B 2} + c β_{D C E} + c o n t r o l var i a b l e + ε

Table 11. Relation between pension beta and firm systematic risk: OLS regression (DB plan-surviving firms vs. DB plan-terminating firms).

Panel A: Surviving Firms (n = 283 Firm Observations)
	Pension Asset Allocation/Pension Liability Assumption
	Beta = ABO		Beta = PBO
	Equation (9)	Equation (10)	Equation (9)	Equation (10)
Intercept	0.133 (0.765)	0.087 (0.760)	2.047 (1.388) *	1.962 (1.381)
Pension risk	−0.122 (0.173)	−0.399 (0.204)	−0.251 (0.315)	−0.627 (0.552)
Market share by value	−0.003 (0.001)	−0.003 (0.001)	−0.003 (0.001)	−0.004 (0.001)
Capital intensiveness	−0.237 (0.434)	−0.232 (0.429)	−0.795 (0.788)	−0.811 (0.779)
Cash position	2.107 (0.949)	2.115 (0.942)	4.717 (1.722) ***	4.758 (1.711) ***
Financial leverage	−1.048 (0.345) **	−1.122 (0.349) ***	−1.011 (0.626) *	−1.114 (0.634) ***
Growth rate	−0.143 (0.297)	−0.176 (0.296)	0.195 (0.539)	0.146 (0.539)
Liquidity	−0.002 (0.002)	−0.002 (0.002)	−0.000 (0.004)	−0.001 (0.004)
Return on investment	−0.516 (0.907)	−0.386 (0.900)	0.140 (1.645)	1.710 (3.239)
Firm size	0.095 (0.077)	0.099 (0.077)	−0.063 (0.140)	0.144 (0.277)
Advertisement	0.574 (1.502)	0.389 (1.503)	−1.445 (2.725)	−1.334 (5.408)
Research and development	0.172 (0.719)	0.204 (0.715)	0.115 (1.304)	0.053 (2.573)
Idiosyncratic risk	−0.018 (0.036)	−0.015 (0.035)	−0.078 (0.065)	−0.153 (0.128)
No. of observations	450	450	450	450
R-Squared	0.065	0.069	0.076	0.068
Panel B: Terminating Firms (n = 167 Firm Observations)
	Pension Asset Allocation/Pension Liability Assumption
	Beta = ABO		Beta = PBO
	Equation (9)	Equation (10)	Equation (9)	Equation (10)
Intercept	4.008 (2.628) *	3.542 (2.603)	2.278 (1.674)	2.208 (1.650)
Pension risk	−0.660 (0.537)	0.269 (0.432)	0.155 (0.342)	0.136 (0.274)
Market share by value	−0.004 (0.001)	−0.002 (0.001)	−0.004 (0.001)	−0.005 (0.001)
Capital intensiveness	−1.576 (1.321)	−1.337 (1.312)	1.462 (0.842) *	1.611 (0.832) **
Cash position	14.650 (1.882) ***	14.938 (1.814) ***	−2.423 (1.199) *	−2.546 (1.150) **
Financial leverage	−0.793 (1.337)	−0.191 (1.243)	−3.103 (0.852) ***	−3.157 (0.788) ***
Growth rate	0.270 (1.350)	0.251 (1.339)	−0.235 (0.860)	−0.163 (0.849)
Liquidity	−0.002 (0.027)	−0.006 (0.027)	−0.009 (0.017)	−0.009 (0.017)
Return on investment	−2.484 (2.313)	−2.469 (2.298)	0.932 (1.473)	0.873 (1.456)
Firm size	−0.294 (0.268)	−0.315 (0.264)	−0.063 (0.171)	−0.047 (0.167)
Advertisement	−1.492 (5.105)	−2.672 (4.990)	4.634 (3.252)	4.644 (3.163)
Research and development	−9.246 (9.558)	−10.360 (9.587) ***	−6.736 (6.090)	−7.320 (6.077)
Idiosyncratic risk	−0.164 (0.113) *	0.269 (0.432)	−0.110 (0.072) *	−0.113 (0.071) *
No. of observations	450	450	450	450
R-Squared	0.446	0.430	0.227	0.229

Note: *** 1% significance level, ** 5% significance level; * 10% significance level. Panel A: This table reports regression results of the relation between pension beta risk and firm beta risk for the sample from 2006 to 2008 separately for those firms which continued to operate DB pension plans (283 firm observations) and those which terminated DB plans during the previous five years (167 firm observations). This table reports regression results for the sample from 2006 to 2008. The regression being run is either

β_{E + N F L} = a + b β_{p e n s i o n 1} + c o n t r o l var i a b l e s + ε

β_{E_{C E} + N F L} = a + b β_{p e n s i o n 2} + c o n t r o l var i a b l e s + ε .

Results are reported separately for pension risk defined in accordance with Equation (14) (all equity) and Equation (15) (after controlling for employees’ equity). All results are estimated with company betas estimated using the market model and one lagged term and with the end-of-year pension data. Standard deviations are shown in brackets. Panel B: This table reports regression results of the relation between pension beta risk and firm systematic risk for the sample from 2006 to 2008 separately for those firms which continued to operate DB pension plans (283 firm observations) and those which terminated DB plans during the previous five years (167 firm observations).

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Klumpes, P.J.M. Pension Risk and the Sustainable Cost of Capital. J. Risk Financial Manag. 2024, 17, 536. https://doi.org/10.3390/jrfm17120536

AMA Style

Klumpes PJM. Pension Risk and the Sustainable Cost of Capital. Journal of Risk and Financial Management. 2024; 17(12):536. https://doi.org/10.3390/jrfm17120536

Chicago/Turabian Style

Klumpes, Paul John Marcel. 2024. "Pension Risk and the Sustainable Cost of Capital" Journal of Risk and Financial Management 17, no. 12: 536. https://doi.org/10.3390/jrfm17120536

APA Style

Klumpes, P. J. M. (2024). Pension Risk and the Sustainable Cost of Capital. Journal of Risk and Financial Management, 17(12), 536. https://doi.org/10.3390/jrfm17120536

Article Menu

Pension Risk and the Sustainable Cost of Capital

Abstract

1. Introduction

2. Review of Literature and Proposed Model

3. Sample and Data

3.1. Sample and Data Collection Procedures

3.2. Data Description

4. Empirical Results

4.1. Pension Risk and Cost of Capital

4.2. Tests by Incorporating Various Control Variables for Operating Asset Risk

5. Robustness Checks and Filtered Tests

5.1. Financially Distressed Firms

5.2. Exclude Firms with Significant Company Stock in the Pension Plan

5.3. Filter Tests

5.4. DB Pension Plan Termination Decisions

5.5. Analysis of Surviving Firms

6. Conclusions

Funding

Acknowledgments

Data Availability Statement

Conflicts of Interest

Appendix A

Notes

References

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