CHAPTER 16 Corporate Risk Management and Pension Asset Allocation Yong Li CONTENTS 16.1 I ntroduction 16.2 Background and Prior Research 16.3 Development of Hypotheses 16.3.1 Financial Reporting Risk 16.3.2 Contribution Volatility Risk 16.4 Re search Design 16.4.1 Em pirical Model 16.4.2 Measures of Explanatory Variables 16.4.3 Sample and Data 16.4.4 De scriptive Statistics 16.5 E mpirical Results 16.5.1 U nivariate Analysis 16.5.2 Results from Simultaneous-Equation Estimation 16.5.3 R obustness Tests 16.6 C onclusion References 38 366 367 369 369 370 371 371 373 375 376 380 380 381 384 385 365 © 2010 by Taylor and Francis Group, LLC 366 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling 16.1 INTRODUCTION The growing size of pension plans’ assets and liabilities* in relation to the market capitalization of sponsoring companies raises the possibility that firms’ overall financial position and prospects may influence not only its strategy for funding their pension liabilities but also its allocation of pension assets among alternative investment categories The oretical research prior to the 1990s has developed competing hypotheses to explain pension asset a llocation decision f rom a co rporate financial perspec tive (Sharpe, 1976; Treynor, 1977; Black, 1980; Tepper, 1981; Harrison and Sharpe, 1983) The t ax-based Black –Tepper h ypothesis i mplies t hat firms w ith o verfunded pension plans should invest in the most heavily taxed assets (such as bonds) to maximize their tax-savings because overfunded plans are less likely to default on their pension promises (Black, 1980; Tepper, 1981) The “pension put” hypothesis (Sharpe, 1976; Treynor, 1977) implies that firms with underfunded pension plans should invest more in riskier assets (such as equities) to maximize the value of the “put option” to default.† However, the competing theoretical hypotheses lack consistent support from the small volume of empirical research on pension asset allocation (Friedman, 1983; B odie e t a l., 1987; Peterson, 1996; A mir a nd B enartzi, 1999; Frank, 2002) The corporate asset allocation strategy over alternative asset investment categories (equities versus bonds) is not well understood based on findings from prior empirical literature Bodie et al (1987) cautioned that further empirical research remains to be fi lled before a cl ear picture of these important corporate pension decisions can emerge The objective of this chapter is to seek empirical regularities in the U.K firms’ r isk ma nagement o f pens ion a sset a llocation, a nd i ts i nterrelationship w ith t heir pens ion f unding a nd pens ion-related acco unting po licy over an extended period of FRS 17 adoption (1998–2002) The U.K pension fund i nvestment st rategy s e volved subst antially over t he pa st dec ades The issue of the new U.K pension GAAP (FRS 17: ASB, 2000) in 2000 has transpired the risks of providing defined benefit (DB) pensions to investors Pension trustees and managers started to attach greater importance to managing their pension risk exposures With the changing pension legislation * In m id-July 008, F TSE 00 c ompanies re cognized £ 14 bi llion p ension d eficits o n t heir balance sheets † Pension B enefit Gu aranty C orporation i nsures U.S fi rms’ p ension l iabilities i n f ull i n t he event of default The PBGC has a claim on 30% of the market value of the firms’ assets The PBGC’s insurance of pension benefits provide the firm a “put” option: it can shed its pension liabilities by giving the PBGC the assets in the scheme plus one-third of the firms’ assets © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 367 and a g lobal convergence toward t he fa ir-value-based pension accounting standards, changes in asset allocation strategy are taking place A new body of theoretical research concerning pension asset allocation has emerged over recent years (Sharpe, 1990; Leibowitz et al., 1994; Blake, 2003) These st udies de veloped a sset/liability or su rplus return models of portfolio diversification taking into account not only asset returns and variances but also changes in pension liabilities and their covariance with asset returns In light of these new theoretical insights on pension asset a llocation, this chapter develops and tests the hypotheses that U.K sponsors have managed t heir pens ion a sset a llocation w ith a n attempt t o m itigate t heir exposure to t he potential volatility risk of t he financial statements a nd/or cash flows during a period of accounting regulatory uncertainty Controlling for the endogeneity among asset allocation, pension funding, and the expected rate of return assumption choices, the empirical evidence based on the cross-sectional data on a panel of 279 firm-years during the period from 1998 to 2002, suggests that the relationships among asset allocation, pens ion f unding, a nd r elated pens ion r eporting ch oices a re, for m ost pa rt, co nsistent w ith t he co rporate r isk-management o bjective of hedging the cash contribution risks that stem from measuring pension assets and liabilities at a “fair value” basis The rest of this chapter proceeds as follows: Section 16.2 describes the institutional background and critically reviews the prior literature Section 16.3 de velops r esearch h ypotheses Section 6.4 de scribes t he r esearch methodology, variable specification, data, and descriptive statistics Results are presented in Section 16.5 and concluding remarks in Section 16.6 16.2 BACKGROUND AND PRIOR RESEARCH The productive deployment of pension plan assets directly reduces costs of f unding a D B pens ion p lan (McGill a nd Gr ubs, 1989) Pr ior em pirical research a lso e stablished t hat t he a sset a llocation i s t he ma in de terminant of the investment performance of a pension fund (Brinson et al., 1991; Ibbotson and Kaplan, 2000) Thus the decision to allocate plan assets among different investment vehicles represents a critical pension management decision by employer sponsors During the last four decades, U.K employer sponsors have invested the majority of their assets in equities (Blake et al., 1999) Davis (1991) observes that the U.K firms have maintained a substantially higher equity proportion than firms in the United States, Canada, Japan, and Germany However, co rporate st rategic a sset a llocations i n t he U nited K ingdom © 2010 by Taylor and Francis Group, LLC 368 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling evolved since recent years have seen rapid changes occurring in both the legislative and t he accounting regulation for final sa lary pensions in the United Kingdom The case of Boots group provides a perspec tive over the asset allocation decision undertaken by employer sponsors during a period of regulatory uncertainty In November 2001, the Boots group announced that its £2.3 billion pension fund, one of the U.K.’s 50 largest funds with 72,000 members, had switched 100% of its pension assets from equity into long-dated highquality bonds.* Duration-matching by investing in fixed-income investment products, such as bonds, can effectively reduce the likelihood of the accumulated assets falling short of the long-term pension liabilities (Blake, 2003) It is also noticeable that patterns of DB pension plan asset allocation in t he United K ingdom and United States have been relatively invariant over the last several years The average equity allocation for a typical U.K sponsor wa s 0% ( Urwin, 002) Rec ent U.S r esearch su ggests t hat t he actuarial smoothing in the valuation of pension assets and liabilities has contributed to t he high equity a llocations by sponsors (e.g., Gold, 2000; Coronado a nd Sha rpe, 2003) The U.K financial press a lso cla imed t hat the “fair value” approach as espoused by FRS 17-style pension accounting standard would lead corporate sponsors to shift t heir asset a llocation in favor of fi xed-income securities, in order to shield themselves against the potential volatility onto their financial statements (e.g., Financial Times, March 20, 2004) Very l imited empirical research s focused on ex plaining corporate asset allocation decisions Friedman (1983) presents evidence suggesting that less-profitable companies w ith h igher leverage a nd h igher e arnings variability tended to hold less in equities His results on asset a llocation seem to suggest that firms ma nage t heir pens ion f und a sset a llocations to counterbalance the risks across firms that are stemming from product markets or financial structure By contrast, Bodie et al (1987) find that the proportion of assets allocated to equities is negatively related to the level of funding and positively related to the size of the company In other words, underfunded plans tend to hold more equities and less fixed-income securities The n egative co rrelation be tween f unding a nd t he p roportion o f assets allocated to equities provides some support to the “pension put” hypothesis Thei r findings on asset allocations taken together suggest that * The bonds are a close match for the maturity and the indexation of U.K pension liabilities, which has a weighted average maturity of 30 years and 25% are inflation-linked © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 369 firms not manage their sponsored pension funds as if they are entirely separate entities from the sponsor (Friedman, 1983; Bodie et al., 1987) Nevertheless, U S.-based em pirical r esearch d uring t he 990s p rovides no e vidence supporting a t ax a rbitrage–based pension i nvestment strategy Motivated by t he i nconsistency a mong t heoretical a nd empirical st udies, F rank (2002) r eexamines t he ex tent t o wh ich t axes a ffect a firm’s decision to allocate its DB plan’s assets between equity and bonds within a simultaneous system of equations, which attempts to capture the joint corporate capital structure and pension asset allocation decision in such arbitrage strategy Contrary to prior empirical research, Frank (2002) finds ev idence consistent w ith firms t rading off t ax benefits a nd nontax factors as described by Black (1980) Motivated by t he release of U.S pension GA AP (SFAS 87), A mir a nd Benartzi (1999) investigate the possibility of a relation between firms’ pension accounting and investment choices during a post-pension accounting regulatory change period (1988–1994) in the United States They contend that SFAS 87 provides managers the opportunity to choose between recognition and disclosure In particular, they focus on the question of whether the r ecognition o f add itional m inimum pens ion l iability i n acco rdance with SFAS 87 affects asset allocation decision Indeed, they find evidence that companies closing to a recognition threshold will make an economic decision of allocating more plan assets into fixed-income investments Uncovering the existence of such a r elationship implies that SFAS 87 has potential economic consequences for firms, consistent with the corporate finance perspective The adoption of a “ fair va lue” approach i n pension accounting ( FRS 17), co nsistent w ith t he co rporate finance perspective, implies a short-term volatility mismatch between pension assets and liabilities It is possible that U.K firms may manage their pension asset allocation in a way so as to mitigate their pension risk exposures attributable to changing pension accounting regulation 16.3 DEVELOPMENT OF HYPOTHESES 16.3.1 Financial Reporting Risk The r elease o f n ew pens ion acco unting i nformation ( FRS 17) ma y a lter the nature or the perception of risks of employers’ pension exposure One common assumption was that the adoption of FRS 17 would expose U.K firms t o s ignificant ba lance sh eet v olatility U nder FR S 17, t he pens ion deficits or surpluses are required to be r ecognized on the corporate balance sheets once they arise By contrast, the former U.K pension GAAP © 2010 by Taylor and Francis Group, LLC 370 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling (SSAP 24: ASC, 1988) allows any surpluses or deficits to be spread over the employees’ future working time, typically 15 years If sponsoring firms were forced to recognize their past funding practices on a “fair value” basis onto the balance sheets, the desired positioning of the firm’s consolidated pension balance sheet may not be attainable solely t hrough pens ion ben efit r eductions, such a s p lan ter minations Consequently, plan sponsors a re ex posed to r isks of having potentially volatile financial statements Managers can mitigate such financial reporting risk by choosing a d ifferent mix of equities and bonds Investing in bonds has the advantage of obtaining a h igh correlation between assets and liabilities, thus reducing such financial reporting risks Following Bergstresser et al (2006), a sens itivity measure (PENRISK) is constructed to capture the variation in firms’ pension exposure to the potential financial reporting r isk PENRISK i s c alculated a s t he natural logarithm of t he r atio of t he ma rket va lue of pension a ssets to total net assets in a firm year.* Hypothesis ( H1): Ceteris p aribus, t he per centage o f a ssets invested in e quities d ecreases as firms’ ex posure t o t he po tential financial reporting risk increases 16.3.2 Contribution Volatility Risk Risky assets, such a s equities, are characterized by their volatile returns Financial theory suggests that the higher risk of equity investment is awarded b y t he h igher r eturn i t g enerates ( Markowitz, 952; Sha rpe, 1964) However, if the volatile return on the pension assets translates into changes in the required cash contribution, then risky assets will translate into more risky required contributions to the pension plan The main concern of “cash flow risk” managers is to minimize the volatility of changes in cash flows (Culp, 2001) Friedman (1983) finds some evidence that firms have incentives to time their pension contributions so as to smooth the reported earnings Prior to FRS 17, firms’ past pension funding practices are not reported on financial statements Shareholders and investors may judge the firm’s performance by its reported earnings rather than by more comprehensive c ash flow measures Coronado et al (2008) show that investors fa iled t o d istinguish be tween pens ion a nd o perating e arnings * Bergstresser e t a l ( 2006) s uggest t hat s uch a s ensitivity me asure c ollapses t he i nfluence of out liers a nd br ings t he d istribution of t he r atio c loser to t hat of a nor mally d istributed random variable © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 371 and capitalize them similarly The adoption of FRS 17 implies that investors a re beco ming m ore a ware o f t he r elative ma gnitude a nd po tential risks of DB pension provisioning (Klumpes and Li, 2004) Consequently, prudent va lue ma ximizing ma nagers fac e st rong i ncentive t o h edge t he riskiness of their future cash contributions By matching pension assets with liabilities, that is, allocating plan assets into bonds, sponsoring firms can effectively reduce the volatility of their pension contributions, thus achieve to hedge their cash contribution risks If the incentive is strong for sponsors to minimize the volatility of pension contributions, then it would be observed that firms with both extremely overfunded and underfunded plans invest in bonds because such extreme overfunding a nd u nderfunding a fford le ss flexibility t o ad just t he t iming of pension contributions than firms with moderate funding levels Pension plans with greater deficits are required to make deficit-reduction contributions and those with greater surpluses have to conform to the tax regulations.* By contrast, pension contributions are fairly predictable for moderate funding levels, but less predictable when funding levels become more e xtreme The contribution risk hypothesis thus predicts a nonlinearity relationship between variations in funding level and pension asset allocation, and provides an alternative risk-management explanation for the conflicting results from prior studies on the effect of pension funding on asset allocation.† This discussion leads to the second hypothesis: Hypothesis ( H2): Ceteris p aribus, t he per centage o f a ssets invested in equities increases as the funding level increases up to a specific point, then decreases as the funding level increases beyond this point 16.4 RESEARCH DESIGN 16.4.1 Empirical Model Accounting researchers have recognized the importance of analyzing the potential endogeneity in the choices made by firms along different dimensions (e.g., Beatty et al., 1995; D’Souza, 1998) Treating endogenous variables as exogenous, or excluding relevant choice variables, leads to biased * U.K corporate sponsors of defined benefit pension plans w ith a f unded status in excess of 105% were subject to taxation at a rate of 35% † Amir a nd B enartzi (1999) fi nd s ome e mpirical e vidence on s uch a non linear re lationship between pension funding and asset allocation However, their study does not control for the potential endogeneity between pension funding and asset allocation © 2010 by Taylor and Francis Group, LLC 372 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling and i nconsistent pa rameter e stimates Pr ior pens ion r esearch s n ot taken into account the simultaneity of pension asset allocation, funding, and r elated financial r eporting ch oices.* C ausality i s t herefore u nclear, and t he s ame c ross-sectional r esults c an be r ationalized by a va riety o f explanations It is possible that the corporate pension asset allocation policy is conditional upon firms’ long-term pension funding and their discretion over the l ong-term ex pected r ate o f r eturn o n pens ion i nvestments ( hereinafter “ ERR”) Pr ior U S.-based r esearch s dem onstrated t hat firm management s a ttempted t o eng age i n t he s moothing a nd sp reading of pension costs over time (Picconi, 2006) Corporate sponsors can exercise the discretion in the level of ERR assumptions to change the pattern and t he magnitude of pension liabilities, t hus mitigating t heir contribution volatility risk They could a lso increase t he a llocation of equities in their pension fund investment portfolio to justify the high level of the ERR assumptions Klumpes et al (2009) provide evidence that corporate pension termination decision is indeed not independent of their discretionary ERR choices Consequently, a simultaneous equations model is employed to control for the simultaneity and identify the impact of pension reporting risks on the pension asset allocation decision The hypotheses concerning corporate pension asset allocation decision are tested by employing a simultaneous model with three equations: asset allocation, funding, and pension actuarial assumption choices It is based on t he assumption t hat sponsors can adjust t heir asset a llocation, f unding, and related pension reporting choices simultaneously Specifically, the system of simultaneous equations is specified as follows: %EQUITYit = α + α1t FUNDit + α 2t FUNDSQit + α 3t PENRISK it +α 4t ERR it Φ1′ Χ1it + γ t + ε1t (16.1) FUNDit = β0 + β1t %EQUITYit + β2t ERR it + Φ′2 Χ2it + γ t + ε2t (16.2) ERR it = δ0 + δ1t %EQUITYit + δ2t FUNDit + Φ′3 Χ 3it + γ t + ε3t (16.3) * Mitchell a nd Smith (1994) employs si multaneous equations model approach to i nvestigate pension funding in the U.S public sector They attempt to control the simultaneity between the required per worker annual contribution (REQ), actual pension plan funding in the public sector (ACT), and average worker compensation package (AVEPAY) © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 373 where % EQUITY is the percentage of equity invested by corporate sponsors FUND is the reported stock funding level ERR is the level of reported expected rate of return on pension assets assumptions* FUNDSQ is the squared value of FUND PENRISK i s t he sens itivity m easure o f firms’ pe nsion ex posure t o reporting risk X1it, X 2it, a nd X 3it a re a v ector o f p redetermined co ntrol va riables i n three respective equations γt represents dummy variables for years 1998–2002 Equations 16.1 through 16.3 model pension asset allocations, funding, and ERR reporting choices, respectively ε1t, ε2t, and ε3t are error terms 16.4.2 Measures of Explanatory Variables Multiple p roxies a re de veloped t o co ntrol f or t he co mpeting t heoretical ex planations o n t he co rporate pens ion a sset a llocation dec ision o f Equation 16.1 The “pension put” hypothesis (Sharpe, 1976; Treynor, 1977) implies that firms for which the pension “put” option is more valuable (i.e., more in the money) will hold more of the most risky assets, presumably equities, and vice versa The “put” option is likely to be more valuable for underfunded plans, for unprofitable companies or firms with higher variability in their cash flows, or firms with more debt Consistent w ith p rior l iterature ( Friedman, 983; B odie e t a l., 987; Frank, 002), t hree p roxies u sed t o m easure t he va lue o f pens ion “ put option” to sponsoring firms include leverage (LEV), profitability (PROF), and firm r isk (STDCF) L EV is calculated as t he long-term debt d ivided by total tangible assets Higher leverage implies less debt covenant slack and higher probability of financial distress Thus the “put” option is more valuable to highly levered firms PROF is calculated as the mean return on shareholders equity over the preceding 10 years, which is a proxy for longterm p rofitability Less-profitable firms a re l ess l ikely t o f ulfill the fixed payments of retirees’ benefits and thus more likely to invest more in equities to ma ximize t he va lue of t he “put” option to default (Sharpe, 1976) STDCF is calculated as the standard deviation of operating cash flows over the preceding 10 years deflated by t he book va lue of equity Firms w ith * FUND me asures t he r atio of t he p ension pl an’s tot al a ssets to it s tot al prom ised b enefit obligations © 2010 by Taylor and Francis Group, LLC 374 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling higher va riability i n t heir c ash flows are likely to invest more in equity to maximize the “pension put.” Friedman (1983) finds a negative relation between firm risk, measured as income variability, and the percentage of assets invested in equities He proposes a “risk offsetting story” to interpret his finding The a rgument i s t hat r isky firms t end to offset t he r isks b y investing in less-risky assets in their pension plans, such as bonds The “ Black–Tepper” h ypothesis p redicts t hat firms sh ould o verfund their pensions because tax arbitrage enables firms to earn a tax-free rate of return on investments TAXST is included as a proxy for firm’s average tax rate TAXST is calculated as the total reported taxes minus the change in deferred taxes over the preceding 10 years deflated by beginning year total assets Firms with higher tax rate would gain more by investing the assets in fixed-income securities It is i mportant we a lso control for va rious economic determinants of pension asset allocation posited by prior research Prior U.S.-based studies find the plan demographics influences asset allocations (e.g., Amir and Benartzi, 1999; F riedman, 1983) The ma turity o f t he pens ion l iabilities may be an important determinant affecting the asset allocation decision by U.K sponsors in the current economic environment when most of the funds g radually ma ture a nd dema nd n ontrivial fixed benefit payments Firms with mature pensions may wish to invest more assets in bonds so as to achieve better asset/liability matching, thus reduce the likelihood of the assets falling short of obligations PRET, measured as the percentage of vested member over the total number of vested and non-vested members, is included as a control for the maturity of pension plan It is also argued that the U.K pension fund management is partially driven by t he herding behavior (Klumpes a nd W hittington, 003) This suggests that U.K pension funds often benchmark their investment performance against other funds’ performance and relevant market indices The co ntemporaneous ac tual r ate o f r eturn o n pens ion a sset po rtfolio (MKRTN) is included to control for this argument MKRTN is calculated as the actual rate of return on a weighted market portfolio with an equivalent asset mix The pension f unding regression (Equation 16.2) adopts t he empirical framework employed by Francis a nd Reiter (1987) to ex plain corporate pension f unding st rategy, wh ile controlling for t he endogeneity a mong asset allocation (%EQUITY) and ERR assumption choices The “financial slack” effect s em phasized t he pens ion f und’s u sefulness a s a so urce of corporate liquidity or as a store of temporarily excess corporate funds © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 375 (Myers and Majluf, 1984) Such slack could be kept in the form of either liquid assets, unused debt capacity, or pension assets The financial slack hypothesis predicts that the firms should overfund its pensions to build excess assets, which can accumulate at the pretax rate and be used when firms require f unds to finance positive NPV projects The proxy for t he rate of undertaking new investments (RUNI), measured as the sum total of capital expenditure plus R&D expenditure divided by total assets, controls f or t he “ financial slack” hypothesis of high-level funding Sharpe (1976) argues that “pension put” is of greatest value to underfunded pension plans, therefore risky firms should underfund their pensions to maximize the “put option” value STDCF is included as a proxy to control for the firm risk for the “pension put option” incentive of low-level funding The ERR regression (Equation 16.3) explains cross-sectional variations in r eported ER R l evels I n add ition, E quation 16.3 i ncludes t he l evel o f funding as a n add itional endogenous va riable Bodie et a l (1987) find a negative association between the size of the pension plan and the percentage of bonds allocated in the pension portfolio So a general control variable is included, plan size (LNSIZE), in all three equations.* 16.4.3 Sample and Data The main constraint on the sample size is the availability of detailed pension a sset c omposition.† The proprietary a sset a llocation d ata a re ndcollected f rom t he p rofessional p ublication “ Pension F und a nd Thei r Advisers” book (PFTA 1988–2004) The sample period consists of period over 1998–2002 During this period, U.K sponsors were subject to both legislative-imposed minimum funding solvency restrictions and differential pension accounting regulatory requirements To be included in the sample, t he sponsor first had t o be a p ublicly l isted F TSE 350 firm that sponsors a t l east o ne D B pens ion sch eme w ith co mplete pens ion a sset allocation data available Second, to increase the power of empirical tests, firms with more than 5% of their pension assets as “unclassified” are deleted.‡ Finally, firms with missing data required for analysis are deleted * A H ausman s pecification t est i s p erformed on t he e quation s ystem s pecified to check t he existence of endogeneity (Hausman, 1978) The result indicates that exogeneity of asset allocation decision (% EQUITY) can be rejected at 5% level † Frank (2002) also noted the obstacle to investigating DB investment policy is obtaining the asset allocation data necessary to compute percentage of bonds invested by pension funds ‡ Amir a nd B enartzi (1999) a nd Fr ank ( 2002) d eleted fi rms with 5% of th e a ssets th at a re “unclassified” in their studies © 2010 by Taylor and Francis Group, LLC 376 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling Following t he abo ve c riteria, t he co mplete a sset a llocation d ata c an only be obtained between 60 and 70 firms per year After eliminating outliers, the final sample comprises 279 firm-year observations All the data used for this study is collected from the financial statements of the sample firms, Datastream and “PFTA” book 16.4.4 Descriptive Statistics Table 16.1 presents t he descriptive statistics on t he distribution of pension a sset co mposition i n t he s ample A t t he en d o f 998, spo nsoring firms allocate 72.73% of their assets to equities and 15.12% to fi xedincome securities On average, sample U.K firms in vest s ignificantly more in equities than in bonds Th is evidence is consistent with the pension asset allocation of relevant population U.K firms on average invest about 49%–59% of their total pension funds in domestic equities and an additional 16%–22% in international e quities (Urwin, 002) The allocation to equities dropped nearly 8% in 2002 for the sample firms and an increase of nearly 4% allocated to bonds Overall the sample pension a sset a llocation d isplays a sl ow t rend t oward a g reater percentage of bonds among the overall pension asset composition during the study period (1998–2002) Panel A o f Table 6.2 p resents t he c ross-sectional d istribution o f %EQUITY b y y ear % EQUITY va ries s ignificantly a cross t he firms with a st andard de viation o f 3.66 f or t he poo led s ample T o ex amine t he TABLE 16.1 Distribution of Pension Asset Composition by Year Asset Category 1998 (n = 53) 1999 (n = 56) 2000 (n = 58) 2001 (n = 55) 2002 (n = 57) All (n = 279) U.K equity OS equity U.K fixed interest OS fixed interest Index bonds Property Cash Total equity Total bonds 54.54% 18.19 7.95 2.57 4.60 3.23 5.95 72.73 15.12 54.27% 18.26 8.37 2.52 4.57 3.03 5.68 72.53 15.46 51.65% 18.36 8.64 2.37 5.55 3.07 4.56 70.01 16.56 50.64% 22.77 8.02 2.26 5.52 2.01 2.87 71.21 15.80 44.20% 20.60 12.48 1.53 5.00 3.04 2.86 64.80 19.01 51.06% 19.64 9.09 2.25 5.05 2.88 4.38 70.26 16.39 Notes: This table presents the descriptive statistics on the distribution of pension asset composition of the sample U.K firms The asset investment categories are the U.K equity, the overseas equity, the U.K fixed interest, the overseas fixed interest, index-linked bonds, property, and cash © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 377 TABLE 16.2 The Distribution of Equity Investmentsa Quintile of Equity Investments 1998 (n = 53) 1999 (n = 56) 2000 (n = 58) 2001 (n = 55) Panel A: Equity investments ranked by quintiles every year (less equities) 35.00 37.00 30.00 30.00 70.00 69.00 68.71 66.71 75.00 72.62 75.00 74.40 77.00 77.40 80.00 80.25 (more equities) 88.00 91.00 91.00 90.00 Mean 72.41 71.73 71.50 70.43 Std 9.91 11.74 14.18 14.19 t test for quintiles −5.85*** −11.96*** −14.36*** −8.93*** versus Panel B: The distribution of changes in equity investments Annual Changes Two-Year Changes Statistic (N) (120) (80) Mean −1.36% −2.86% Std 6.75 9.86 Minimum −42.68 −42.66 10th percentile −6.00 −11.84 Median 0.00 −1.00 90th percentile 4.02 5.17 Maximum 22.00 22.00 2002 (n = 57) All (n = 279) 28.78 28.78 62.42 67.05 69.25 73.00 78.24 78.00 89.96 91.00 66.40 70.33 15.68 13.66 −6.96*** −18.13*** Thr ee-Year Changes (51) −4.70% 11.30 −38.66 −11.68 −3.09 6.33 22.00 Notes: Panel A p resents t he cr oss-sectional distr ibution o f %EQ UITY b y y ear o ver t he study period (1998–2002) Panel B presents the changes in %EQUITY over one, two, and three years a Equity investment is the percentage of the pension assets allocated to equities * indica tes significance at 10% level ** indica tes significance at 5% level *** indica tes significance at 1% level frequency o f a sset a llocation r evisions, cha nges i n % EQUITY a re c alculated over one, two, and three years Results in Panel B, Table 16.2 suggests that most firms maintain a constant allocation to equities Over a one-year period, more than 80% of the firms remained within five percentage points of their beginning allocation to equities Over a t hree-year period, 80% of the firms decreased their allocation to equities by less than 12%, or increased it by less than 7% Given the stability of equity allocation over the five-year study period (1998–2002), we focus on cross-sectional differences in asset allocation rather than time-series changes Table 16.3 provides m eans a nd st andard de viations f or t he ex planatory variables required for estimating Equation 16.3 by year The average © 2010 by Taylor and Francis Group, LLC Variable (N) FUND FUNDSQ ERR PENRISK LEV PROF STDCF TAXST PRET LNSIZE Descriptive Statistics on the Regression Variables by Year Statistics 1998 (n =53) 1999 (n = 56) 2000 (n = 58) 2001 (n = 55) 2002 (n = 57) All (n = 279) Mean Std Mean Std Mean Std Mean Std Mean Std Mean Std Mean Std Mean Std Mean Std Mean Std 1.144 0.167 1.337 0.403 8.430 0.778 −7.751 1.055 0.183 0.136 13.518 13.488 0.087 0.079 0.032 0.227 0.426 0.226 5.681 1.366 1.155 0.156 1.359 0.369 7.867 0.963 −7.561 1.074 0.188 0.128 12.502 14.105 0.224 0.672 0.027 0.029 0.421 0.217 5.881 1.323 1.110 0.131 1.249 0.298 7.325 1.053 −7.688 1.644 0.205 0.129 13.728 11.528 0.130 0.134 0.032 0.042 0.445 0.241 5.970 1.432 1.112 0.163 1.262 0.370 6.852 0.848 −7.723 1.688 0.221 0.146 9.498 10.307 0.155 0.170 0.025 0.021 0.490 0.263 5.947 1.397 1.086 0.151 1.202 0.331 6.578 0.746 −7.449 1.340 0.269 0.284 7.820 10.677 0.128 0.131 0.065 0.038 0.517 0.237 6.338 1.021 1.120 0.154 1.280 0.356 7.386 1.104 −7.624 1.367 0.215 0.182 11.296 12.226 0.146 0.330 0.024 0.033 0.462 0.237 5.979 1.309 © 2010 by Taylor and Francis Group, LLC 378 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling TABLE 16.3 ARR MKRTN SGR ∆ROA 13.989 47.867 29.054 1.818 0.09 0.05 6.12 0.82 0.26 0.04 19.424 25.908 10.702 0.926 0.08 0.05 5.58 0.89 0.14 0.05 11.734 19.527 11.708 2.340 0.07 0.05 5.14 0.87 0.02 0.08 8.532 20.392 −6.526 2.930 0.06 0.05 4.65 0.71 0.09 0.03 4.335 15.789 −1.114 0.880 0.06 0.04 4.33 0.65 0.18 0.07 11.484 27.998 8.450 12.157 0.07 0.05 5.15 1.01 0.13 0.06 Notes: This table presents the means and standard deviations of regression variables used multivariate analysis The variable definitions are as follows: %EQUITY is the percentage of pension fund portfolio invested in equities; FUND is the reported funding status under SSAP24; FUNDSQ is the squared value of FUND; ERR is the expected rate of return on pension assets assumption used in the estimation of pension expenses; PENRISK is the natural logarithm of the ratio of the market value of pension assets to total net assets; LEV is the firms’ leverage ratio defined as t otal short-term plus long-term debt, deflated by shareholders’ equity; PROF is the mean of return on shareholders’ equity over the preceding 10 y ears; STDCF is t he standard deviation of operating cash flows (earnings before extraordinary items plus depreciation expenses) over the preceding 10 years deflated by the book value of equity; TAXST is the total reported taxes minus the change in def erred taxes over the preceding year deflated by beginning year total assets; PRET is t he percentage of vested members over total number of vested and nonvested members, a proxy for the maturity of pension plans; LNSIZE is the natural logarithm of the market value of pension assets; ARR is the contemporaneous actual rate of return on pension fund investment; SGR is the projected salary growth rate assumption used in t he estimation of pension expenses; MKRTN is t he contemporaneous actual rate of return on a weighted market portfolio with an equivalent asset mix; RUNI is the capital expenditures plus R&D deflated by beginning year total assets; ∆ROA is the changes in operating earnings deflated by beginning year total assets © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 379 RUNI Mean Std Mean Std Mean Std Mean Std Mean Std 380 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling pension f unding ratio gradually declined from 1.144 in 1998 to 1.086 in 2002, r eflecting t he fa ll of t he eq uity r eturn s ince 000 O ver t he s ame period, the maturity of pension plans increased by nearly 22% The sensitivity m easure o f firms’ ex posure t o t he financial r eporting r isk s increased g radually o ver t he per iod 998–2002 a s ex pected I t i s a lso observed t hat firms’ profitability ( PROF) ex hibits a decl ining t rend b ut the LNSIZE exhibits stability over the entire sample period 16.5 EMPIRICAL RESULTS 16.5.1 Univariate Analysis Table 16.4 ex amines t he r elation be tween e ach o f t he ex planatory va riables i n E quation 16.1 a nd % EQUITY, u sing a n onparametric po rtfolio analysis Each independent variable is divided into five equal-size portfolios, where portfolio 1(5) contains firms with the lowest (highest) values The relation between the funding ratio of the pension plan (FUND) and equity allocation is consistent with the nonlinear relationship as predicted in hypothesis H2 The allocation to equities increases from 67.43% for the first quintile to 71.79 for the fourth quintile, and then it decreases to 68.24 for the fifth quintile Consistent with hypothesis H1, the measure of firms’ sensitivity to financial reporting risk (PENRISK) is statistically significant in ex plaining t he a llocation t o eq uities Firms w ith h ighest ex posure t o financial reporting risk (fift h quintile) allocate 65.77% of pension assets to equities, whereas firms with the smallest exposure (first quintile) allocated 75.99 to equities It i s f ound t hat a n egative a ssociation be tween t he ma turities o f t he pension plans and equity allocation Firms with the more mature pension funds (fift h quintile) allocate 55.46% of pension assets to equities, whereas firms with younger funds (first quintile) allocate 75.71% This evidence is consistent with prior findings in Amir and Benartzi (1999) and Peterson (1996) that firms with more mature aging distribution of plan participants allocate more in bonds than equities The effect of long-term profitability (PROF) a nd pens ion f und s ize (LNSIZE) a re st atistically s ignificant in e xplaining t he a llocation to e quities M ore p rofitable fi rms ( fi ft h q uintile) a llocate 6.93% t o equities, wh ereas l ess-profitable fi rms ( fi rst q uintile) a llocate 2.56% to eq uities F inally, fi rms w ith s maller pens ion f unds i nvest m ore i n equities The firms sponsoring smallest pension funds allocate 75.47% to equities, wh ile t he fi rms sponsoring la rgest pension f unds a llocate 67.75% to equities © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 381 TABLE 16.4 Mean Equity Investments by Quintile of the Explanatory Variables in Equation 16.1 Quintile of the Independent Variable Explanatory Variables Used to Form Quintiles (low)1 (high) t Test for Quintiles versus FUND PENRISK ERR LEV PROF STDCF TAXST PRET MKRTN LNSIZE 67.43 75.99 66.61 72.37 62.56 73.71 65.93 75.71 73.94 75.47 69.38 72.35 69.40 70.48 68.34 71.09 68.33 77.22 63.37 68.48 70.89 70.05 73.02 68.75 72.05 70.08 72.15 72.87 66.01 66.81 71.79 65.33 72.21 65.87 73.75 61.75 71.72 68.17 72.34 71.00 68.24 65.77 70.85 72.16 76.93 72.91 71.57 55.46 73.99 67.75 1.18 −4.58*** −1.19 −1.09 4.84*** −0.97 2.58** −4.87*** 1.15 −4.28*** Notes: This table presents the results from a nonparametric portfolio analysis of %EQUITY and exp lanatory va riables in Eq uation 16.1 E ach exp lanatory va riable is di vided into five equal-size portfolios, where portfolio 1(5) co ntains firms with the lowest (highest) values The variable definitions are as follows: %EQUITY is the percentage of pension fund portfolio invested in equities; FUND is the reported funding status under SSAP24; FUNDSQ is the squared value of FUND; ERR is the expected rate of return on p ension ass ets assumption us ed in t he estimation of p ension exp enses; PENRISK is the natural logarithm of the ratio of the market value of pension assets to total net ass ets; LEV is t he firms’ leverage ratio defined as t otal short-term plus long-term deb t, deflated by sha reholders’ eq uity; PR OF is t he me an o f r eturn o n shareholders’ equity over the preceding 10 years; STDCF is the standard deviation of operating cash flows (e arnings b efore extrao rdinary i tems p lus dep reciation expenses) over the preceding 10 years deflated by the book value of equity; TAXST is the total reported taxes minus the change in deferred taxes over the preceding year deflated by beginning year total assets; PRET is t he percentage of vested members over total number of vested and nonvested members, a p roxy for t he maturity of pension p lans; LNS IZE is t he na tural loga rithm o f t he ma rket val ue o f p ension assets; ARR is t he contemporaneous actual rate of return on pension fund investment; SGR is the projected salary growth rate assumption used in the estimation of pension exp enses; MKR TN is t he co ntemporaneous ac tual te o f r eturn o n a weighted market portfolio with an equivalent asset mix; RUNI is the capital expenditures plus R&D deflated by beginning year total assets; ∆ROA is t he changes in operating earnings deflated by beginning year total assets * indica tes significance at 10% level ** indica tes significance at 5% level *** indica tes significance at 1% level 16.5.2 Results from Simultaneous-Equation Estimation Table 16.5 presents results f rom t hree-stage least squares (3SLS) estimation o f t he s imultaneous eq uation m odel ( Equations 16.1 t hrough 16.3) © 2010 by Taylor and Francis Group, LLC Explanatory Variable FUND %EQUITY ERR FUNDSQ PENRISK LEV PROF STDCF TAXST RUNI PRET ∆ROA ARR SGR Three-Stage Least Squares (3SLS) Regression Results of Pension Asset Allocation (Equation 16.1) %EQUITY (Equation 16.2) FUND Pred Sign Est Coef t-Stat + 15.551** 1.86 + — — + + + ? 0.037 −6.416** −0.054* 0.061 0.006** 0.004 0.645 0.86 −1.79 −1.42 0.52 2.06 0.03 0.85 — −0.056*** −3.17 Pred Sign Est Coef t-Stat + — 0.629*** −0.032** 4.26 −1.90 + 0.002** 0.079*** −0.601* −0.233 2.27 2.62 −1.57 −1.04 — © 2010 by Taylor and Francis Group, LLC (Equation 16.3) ERR Pred Sign Est Coef t-Stat — + −1.433*** 0.834 −3.87 0.47 + 0.116** 2.20 — — — + −0.109 −0.164 0.001 0.781*** −0.34 −0.15 0.38 14.96 382 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling TABLE 16.5 ? — −0.002 −0.023 Included 0.1086*** −0.21 −0.98 — −0.058 Included 0.2475*** −2.79 — −0.048 Included 0.7446*** −0.89 Notes: This table presents the three-stage least-square (3sls) estimate of the system of three regression equations, that is, Equations 16.1 through 16.3 for %EQUITY, FUND, and ERR, respectively The variable definitions are as follows: %EQUITY is the percentage of pension fund portfolio invested in equities; FUND is the reported funding status under SSAP24; FUNDSQ is the squared value of FUND; ERR is the expected rate of return on pension assets assumption used in the estimation of pension expenses; PENRISK is the natural logarithm of the ratio of the market value of pension assets to total net assets; LEV is the firms’ leverage ratio defined as total short-term plus long-term debt, deflated by shareholders’ equity; PROF is the mean of return on shareholders’ equity over the preceding 10 years; STDCF is the standard deviation of operating cash flows (earnings before extraordinary items plus depreciation expenses) over the preceding 10 years deflated by the book value of equity; TAXST is the total reported taxes minus the change in deferred taxes over the preceding year deflated by beginning year total assets; PRET is the percentage of vested members over total number of vested and nonvested members, a proxy for the maturity of pension plans; LNSIZE is the natural logarithm of the market value of pension assets; ARR is the contemporaneous actual rate of return on pension fund investment; SGR is the projected salary growth rate assumption used in the estimation of pension expenses; MKRTN is the contemporaneous actual rate of return on a w eighted market portfolio with an equivalent asset mix; RUNI is t he capital expenditures plus R&D deflated by beginning year total assets; ∆ROA is the changes in operating earnings deflated by beginning year total assets * ,** ,*** indicates significance at 10%, 5%, and 1% level, respectively © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 383 MKRTN LNSIZE YEAR Adjusted R2 384 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling for t he pooled sample Panel A, Table 16.5 reports results f rom estimating E quation 6.1, t he a sset a llocation m odel o f t he p rimary i nterest Consistent wi th H 2, th e e ffect o f f unding l evel o n a sset a llocation f ollows a n onlinear r elationship The coefficient on FUNDSQ is negative and s ignificant at 5% level This finding su ggests t hat t he s ample firms with ex tremely o verfunded a nd u nderfunded pens ion p lans a llocated more pension assets into bonds than equities This allocation strategy can minimize the cash flow risk caused by volatile pension contributions, as extreme underfunded plans have stronger incentive to avoid the accelerated funding requirements and overfunded plans have stronger incentive to avoid exceeding the full-funding limits The coefficient on PENRISK is of negative sign as predicted, and significant at 10% level This ev idence is s upportive o f H1, wh ich p redicts firms that are sensitive to risks of volatile financial statements allocate less pension assets into equities Another interesting finding is the significant positive relationship b etween firms’ l ong-term p rofitability ( PROF) a nd the eq uity a llocation The “pension put” hypothesis predicts that lessprofitable firms should be i nvesting their pension portfolio in equities to maximize the value of the “put” option By contrast, this finding suggests that sample firms with higher long-run profitability have allocated higher percentage of their pension assets in equities, consistent with the univariate analysis This result appears to provide some support for “risk-offsetting” st ory adv ocated b y F riedman (1983) t hat t he l ess-profitable firms face higher risk to default on fi xed payments, thus prefer bonds to equities Finally, t he results i n Table 16.5 su ggest t hat t he maturity of sponsored pension fund is statistically significant in explaining pension asset allocation decision Other things being equal, the percentage of pension assets allocated to equities decreases as the pension fund maturity increases 16.5.3 Robustness Tests The pooled time-series, cross-sectional regression assumes the coefficients are consistent ac ross t ime a nd firms a nd t he residuals a re i ndependent To assess the sensitivity of the results to data choices and model specification, t he a sset a llocation m odel i s r eestimated u sing fixed effects panel regression to control for firm-specific factors that may affect pension asset allocation d ecision The u ntabulated r esults f rom fixed-effects regression a re consistent w ith t he 3SLS e stimates a s fa r a s t he ma in va riables on pension funding (FUND) and the sensitivity measure on firms’ financial report r isk (PENRISK) a re concerned The coefficient on PENRISK © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 385 remains negative and significant at 5% level, and the coefficient for FUND is p ositive a nd sig nificant The coefficient f or F UNDSQ i s n egative a nd significant at 5% level In summary, the sensitivity test indicates that the findings are not driven by dependence among observations or the set of control variables included 16.6 CONCLUSION This chapter examines the U.K firms’ risk management of their pension fund a sset a llocation, a nd its i nterrelationship w ith t heir pension f unding and pension-related accounting policy over an extended period (1998– 2002), during which the new U.K pension accounting standard (FRS 17) became effective C ontrolling f or t he en dogeneity a mong pens ion a sset allocation, funding, and the actuarial assumption on pension investment return, the empirical evidence suggests that pension asset management is consistent with a risk-offsetting explanation Firms manage their pension risk exposure in order to minimize cash contribution risks associated with the adoption of “ fair va lue” based pension accounting r ules The results also support the view that U.K trustees and managers have incorporated their co rporate r isk-management p ractices i nto t he a llocation o f t heir pension assets REFERENCES Accounting S tandards C ommittee 1988 SSAP 24, Accounting for th e C ost of Pensions London, U.K.: ASC Accounting S tandards B oard 2000 FRS 17, Retirement B enefits L ondon, U K.: ASB Amir, E a nd S B enartzi 1999 A ccounting recognition and the determinants of pension ass et allo cation Journal of Accounting, Auditing & Fin ance 14(3): 321–343 Beatty, A., S Cha mberlain, and J Magliolo 1995 M anaging financial reports of commercial banks: The influence of taxes, regulatory capital, and earnings Journal of Accounting Research 33(2): 231–261 Bergstresser, D , M D esai, a nd J R auh 2006 E arnings ma nipulation, p ension assumptions, and managerial investment decisions The Quarterly Journal of Economics 121(February): 157–195 Black, F 1980 The tax consequences of long-run pension policy Financial Analysts Journal 36(4): 25–31 Blake, D 2003 UK pension fund management after Myners: The hunt for correlation begins Journal of Asset Management 4(June): 32–72 Blake, D , B N L ehmann, a nd A T immerman 1999 A sset allo cation dynamics a nd p ension f und p erformance Journal of B usiness 72(4): 429–461 © 2010 by Taylor and Francis Group, LLC 386 ◾ Pension Fund Risk Management: Financial and Actuarial Modeling Bodie, Z., J O L ight, R Morck, and R A T aggart, Jr 1987 F unding and ass et allocation in co rporate p ension p lans: An em pirical in vestigation, in Z Bodie, J Shoven, and D Wise, eds., Issues in Pension Economics, Chicago, IL: University of Chicago Press, pp 15–44 Brinson, G P., B D Singer, and G L B eebower 1991 Determinants of portfolio performance II: An update Financial Analysts Journal 47(3): 40–48 Coronado, J L., O S M itchell, S A S harpe, and S B Nesbitt 2008 F ootnotes aren’t enough: The impact of pension accounting on stock values Journal of Pension Economics and Finance 7(3): 257–276 Coronado, J L and S A Sharpe 2003 Did pension plan accounting contribute to a stock market bubble? Brookings Papers on Economic Activity (1): 323–371 Culp, C L 2001 The Risk Management Process New York: John Wiley & Sons Davis, E P 1991 The development of pension funds; an international comparison Bank of England Quarterly Bulletin 31: 380–390 D’Souza, J M 1998 Rate-regulated enterprises and mandated accounting changes: The cas e of elec tric utilities a nd p ost-Retirement b enefits o ther t han p ensions (SFAS No 106) The Accounting Review 73(3): 387–411 Dye, R A 1988 E arnings ma nagement in a n o verlapping g enerations mo del Journal of Accounting Research 26(2): 195–236 Financial Times 2004 London, U.K., 20 March Francis, J R and S A Rei ter 1987 D eterminants of corporate pension funding strategy Journal of Accounting & Economics 9(1): 35–59 Frank, M M 2002 The impact of taxes on corporate defined benefit plan asset allocation Journal of Accounting Research 40(4): 1163–1190 Friedman, B 1983 P ension f unding, p ension ass et allo cation a nd co rporate finance: Evidence from individual company data, in Z Bodie and J Shoven, eds., Financial A spects o f t he U nited S tates P ension S ystem, Chicag o, IL: University of Chicago Press, pp 107–152 Gold, J 2000 A ccounting/actuarial b ias ena bles eq uity in vestment b y defined benefit pension plans Pension Research Council Working Paper, WP2001-5, Wharton School, University of Pennsylvania (May), Philadelphia, PA Harrison, J and W Sharpe 1983 Optimal funding and asset allocation rules for defined benefit p ension p lans, in Z B odie a nd J S hoven, eds., Financial Aspects o f t he U nited S tates P ension S ystem, Chicag o, IL: U niversity o f Chicago Press, pp 92–106 Hausman, J A 1978 S pecification t ests in eco nometrics Econometrica 46: 1251–1273 Ibbotson, R G and P D Kaplan 2000 Does asset allocation policy explain 40, 90, or 100% of performance? Financial Analysts Journal 56(1): 26–34 Klumpes, P and Y L i 2004 P ension accounting, in C Cl ubb and A R AbdelKhalik, eds., The Blackwell Encyclopedic Dictionary of Accounting London, U.K.: Blackwell Klumpes, P a nd M W hittington 2003 D eterminants o f ac tuarial val uation method changes for pension funding and reporting: Evidence from the UK Journal of Business Finance & Accounting 30(1/2): 175–204 © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 387 Klumpes, P., Y L i, a nd M W hittington 2009 D eterminants o f p ension c urtailment decisio n o f UK firms Journal of B usiness F inance & A ccounting (forthcoming) Leibowitz, M L., W K ogleman, a nd L N B ader 1994 F unding tio r eturn Journal of Portfolio Management 21(1): 39–47 Markowitz, H M 1952 Portfolio selection Journal of Finance 7(1): 77–91 McGill, D M a nd D S G rubbs 1989 Fundamentals o f Pr ivate P ensions Homewood, IL: Richard D Irwin Mitchell, O S and R S Smith 1994 Pension funding in the public-sector Review of Economics and Statistics 76(2): 278–290 Myers, S C a nd N M ajluf 1984 C orporate financing and investment decisions when firms have information that investors not have Journal of Financial Economics 13: 187–221 Pension Funds and Their Advisers 1998–2004 L ondon, U.K.: AP I nformation Services Peterson, M.A 1996 Allocating Assets and Discounting Cash Flows: Pension Plan Finance In Pensions, Savings and Capital Markets, P Fernandez, J Turner, and R Hinz (eds.) Washington, DC: U.S Department of Labor: Pension and Welfare Benefits Administration Picconi, M 2006 The perils of pensions: Does pension accounting lead investors and analysts astray? The Accounting Review 81(4): 925–955 Sharpe, W F 1964 C apital ass et p rices: A t heory o f ma rket eq uilibrium under conditions of risk Journal of Finance 19: 452–442 Sharpe, W F 1976 C orporate p ension f unding p olicy Journal of F inancial Economics 3(2): 183–193 Sharpe, W F 1990 Liabilities: A new approach Journal of Portfolio Management 16(2): 5–11 Tepper, I 1981 Taxation and corporate pension policy Journal of Finance 36(1): 1–13 Treynor, J 1977 The principles of corporate pension finance Journal of Finance 32(2): 627–638 Urwin, R 2002 The r ole o f eq uities in p ension f unds L ondon, U.K.: Watson Wyatt © 2010 by Taylor and Francis Group, LLC ... Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 367 and a g lobal convergence toward t he fa ir-value-based pension accounting standards, changes in asset allocation strategy... Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 379 RUNI Mean Std Mean Std Mean Std Mean Std Mean Std 380 ◾ Pension Fund Risk Management: Financial and Actuarial... 5%, and 1% level, respectively © 2010 by Taylor and Francis Group, LLC Corporate Risk Management and Pension Asset Allocation ◾ 383 MKRTN LNSIZE YEAR Adjusted R2 384 ◾ Pension Fund Risk Management: