“Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans,” M. Iqbal Owadally and Steven Haberman, January 2004

“Efficient Gain and Loss Amortization and Optimal Funding in Pension Plans,” M. Iqbal Owadally and Steven Haberman, January 2004

Gold, Jeremy

As evidenced by the Vancouver Symposium (SOA 2003), a globe-circling intellectual battle line has been drawn between two schools of pension actuarial thought. Bach school is working to apply the concepts and tools of economics to the science and practice of pension actuaries. Professors Owadally and Haberrnan have brought us some of the best-written work from one side of the line of battle.

Because I hail from the other side, I am cautious about ascribing properties to the Owadally-Haberman school. Nonetheless, I think it is fair to characterize it as scheme-centric, statistical, and friendly to the inclusion of equities in defined benefit (DB) plans. My side may be counter-characterized as principal-centric (recognizing shareholders, plan beneficiaries, and taxpayers as principals), capital structure intensive, and not friendly to the inclusion of equities.1

Jon Exley (2003) has most sharply denned the divide between the two schools with respect to asset allocation:

“At first sight, deciding the asset allocation for a denned benefit pension scheme . . . might seem like an obvious application of portfolio selection theory. . . A natural way to proceed might be to . . . pick a strategy that maximises return subject to some acceptable degree of risk. . .”

“[We argue] that the basic flaw in traditional asset and liability modelling is that asset allocation of institutional funds should not be treated as a classical portfolio selection issue. The traditional models arc looking in the wrong direction. The machinery commonly applied by many practitioners is designed to solve the wrong problem. . . [We argue] that institutional asset allocation problems should be addressed … by the corporate nnancial theory of the nrm. This is an entirely different branch of economic theory that deals with issues such as optimal capital structures for Arms rather than individuals’ portfolio construction” (p. 29-31).

In terms of the economic literature, Exley (2003) is pointing us toward Modigliani and Miller (1958), Treynor (as Bagehot 1972), Jenscn and Meckling (1976), Miller (1977), Black (1980) and Tepper (1981), and away from Markowitz (1952) and Sharpe (1964) and their myriad successors. Certainly, he means no disrespect to the portfolio selection branch and its brilliant developers. Rather, he challenges DB plans, their sponsors, actuaries, and consultants to identify and apply the pertinent tools to the task at hand.

The present paper is clearly consistent with the portfolio selection literature. Owadally and Haberman define efficient methods of gain and loss amortization as those that offer the least volatile funding for a given level of contribution rate volatility or, equivalently, the least volatile contribution rates for a given funding volatility. Comments by section follow.


Section 1 lays out a clear beginning to a paper that remains clear and well-organized throughout. Owadally and Haberman begin by assuming that deterministic (demographic) actuarial assumptions are perfectly met and that inflation and returns on assets are stochastic. This readily brings us to focus on gains and losses arising from the economics of DB plans.

Asset returns and inflation (and from here on I will ignore inflation as, for the most part, do Owadally and Haberman) are hedgable in the capital markets. This is a critical divide for the two contending pension actuarial schools. The corporatefinance side argues that shareholders and taxpayers can take on or dispose of asset risks and rewards on virtually the same terms as those available to DB plans. Thus, I assert that the proper problem definition asks not how much equity risk principals2 shall take in their aggregate portfolios but rather where such risks shall reside (especially as to whether inside or outside of tax-sheltered plans; see Bader 2003a).

Asset hedgability should allow us to ask, and should incline Owadally and Haberman to address, the question of why DB plans generate any economic gains or losses. Because DB plans need not take unhedged economic risk, why should they? Owadally and Haberman create utility functions at the plan level without ever telling us whose utility should apply. In my view, this is where the scheme-centric view breaks down.

In section 1.4, Owadally and Haberman correctly note that expected losses and unfunded liabilities equal zero under their model. Gains and losses, therefore, must arise from deliberate asset-liability mismatches or, more crudely, from gambling at the scheme level.

Owadally and Haberman refer to a pension plan under a trust that is independent of the firm. While trust management may be independent (perhaps more so in the United Kingdom, less so in the United States), the financial outcomes of the trust fall upon plan principals and, under the no-default assumption applied throughout much of the paper, principally upon shareholders and taxpayers.

Owadally and Haberman identify benefit security as “one purpose of funding benefits in advance. . . .” The corporate-finance view of the matter is that benefit security is the paramount purpose of funding. In a model incorporating potential insolvency of the plan and its sponsor,3 we can argue that the efficient contract (here we define efficient in terms of maximizing the total value for the owners and the beneficiaries-subject to negotiated allocation thereof) includes full funding. Bader (2003b) demonstrates that underfunding is equivalent to borrowing from one’s employees (the sponsor puts its “bond” into the plan instead of cash) and that the employees’ inability to diversify firm-specific risk makes them inefficient (expensive) sources of financing.

Viewed from this corporate-finance perspective, the efficient funding and investing rules are quite straightforward: Fund fully and invest in bonds. Tepper (1981) makes this same recommendation based on Modigliani and Miller (1958) and Miller (1977) and the tax regimes of Anglo-American nations. That benefit-security and tax-arbitrage considerations lead to the same conclusion is coincidental; nonetheless, both point to full funding and no equities.

Thus, Owadally and Haberman must, as a prerequisite to their scheme-based utility function, justify the taking of any economic risk (asset returns, inflation, insolvency) at the scheme level. After explaining why economic asset-liability mismatches are desirable (and to whom), Owadally and Haberman might want to provide an economic rationale for their twin-smoothness criteria. Although most of the traditional actuarial literature points to smoothness as a desirable property of actuarial funding methods, as we move to integrate pension finance with the science of capital markets, we must develop anew any rationale for actuarial processes that smooth capital market returns. Until that rationale is proffered, I will iterate:

“Volatility is a property of markets; it is not a disease for which . . . [actuarial smoothing] is the cure. The volatility of denned benefit plan funding status and cost is real, and it is generated primarily by the mismatch of assets and liabilities. Assetliability matching can sharply curtail the volatility of financing gains and losses, and the purchase of deferred annuities can eliminate it” (Bader and Gold 2003, p. 12).


In section 2, Owadally and Haberman’s outline of a chain of work that includes Dufresne in addition to their own earlier work is clear and powerful and, within the portfolio selection and traditional actuarial disciplines, well worthy of kudos. In section 3, similar remarks may be made with regard to their simulation work, which adds to the credibility and the robustness of their reduced form section 2 model.


Owadally and Haberman incorporate a basic asset return model (preceding equation 7) with an asset allocation control variable (y^sub t^), a risk premium ([alpha]^sub t^ > 0), and an associated variance, [sigma]^sup 2^. They define a quadratic “cost” function (equation 8) reflecting a quadratic utility function.

Equations 9 and K) combine the quadratic cost model with a time preference parameter ([beta]) in order to develop what is described as an “objective criterion for the performance of the pension funding system. …” Equation 11 minimizes the cost of this system, solving for optimal control values for the annual contribution and the plan allocation to equities.

The adoption of a utility function and a time preference parameter may usually be justified in the context of portfolio construction for an individual investor whose preferences are thereby represented. In this instance, however, these parameters merely serve to substitute a cost of risk for the plan, which is different from the cost of risk for the very same assets and liabilities in the capital markets. The plan then develops an “optimal” exposure to capital market risks and passes these along to the shareholders of the plan sponsor. As such a shareholder, I would have to ask, “Why have you done this for (to) me? I have my own risk-reward and time preferences. To construct my own utility-maximizing portfolio, I must unwind what you have done. Furthermore, because investing in equities within a tax shelter is wasteful in the tax regimes of the United Kingdom, the United States, and Canada, I am left with an unnecessary tax burden, even after I unwind.”

In short, because the plan assets are generally available to the shareholders of the sponsoring corporation on the same terms as they are to the plan, and are thus hedgeable, the entire exercise is wasteful from the perspective of the firm’s owners. Under the reduced-form model, employees have no interest in the matter. Under a more comprehensive model (such as that alluded to in section S), the mismatch of plan assets and liabilities exposes employees to risk. This exposure will, in a transparent model, result in increased compensation costs that must, again, be borne by shareholders.


Owadally and Haberman have considered methods for amortizing “unforeseen economic experience” in DB pension plans without justifying why anyone should ever voluntarily expose themselves to such experience. It seems that those who advocate equity investment in DB plans continue to tell us that it lowers the cost of defined benefits. This view, although still apparently held by a majority of practicing actuaries, is now all but bankrupt intellectually. Even though it remains the case that various regulatory regimes for statutory funding and corporate accounting reward such equity investment, economic science rejects it.

The Society of Actuaries’ motto says “The work of science is to substitute facts for appearances and demonstrations for impressions.” To this, we should now add, paraphrasing Exley (2003): It must further be the duty of scientists to apply tools that are appropriate to problems that are well denned.

1 Except as justified by external (e.g., PBGC) guarantees and weak funding (Harrison and Sharpe 1983).

2 The immediate model ignores any insolvency risk to employees and, thus, so do I.

3 I agree with the authors that such default risk is beyond the general scope of the reduced form model discussed herein. Thus, I am not arguing about this aspect of the model but rather about their characterization of the purpose of funding, especially their view that smoothing employer cash flows is a significant economic reason to fund.


BADER, LAWRRNdK N. 2003a. “The case Against Stock in Corporate Pension Funds,”Pension section JVeios (February): 17-19.

_______. 2003b. Financing Corporate Pension Plans. Working paper presented in Proceedings o/ t/te Giitmann Symposium, Vienna, December.

BLACK, LAWRBNCR N., AND JKRKMY GOLD. 2003. “Reinventing Pension Actuarial Science,” The Pension Forum (January): 1-OS.

BLACK, FiS(UiKR. 19SO. “The Tnx Consequences of Long-Run Pension Policy,” FinancictZ .Analysts Jwtrnaf (July-August): 21-28.

EXLEY, JoN. 2003. “a Modern Perspective on Institutional Investment Policy,” in Asset and Z/iabiZity Management Toofs, edited by Bernd Scherer. London: Risk Waters Group Ltd.

HARRISON, MiCHAEL J., AND WiLLiAM. F. ShAReK. 1983. Optimal Funding and Asset Allocation Rules for Oenned-Benent Pension Plans. In Financial Aspects oF the DeJnitcd States Pension System, pp. 91-105. Kditcd by Zvi IJodie and John Shuvun. Chicago: University of Chicago Press. Online at http:// gobi.stanford.edu/faeul tybios/l)io.asp?Il)-6 1.

JENSEN, MiCHARL G., AND WiLLiAM II. MKCKUNC. 1976. “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure,” Journal of Financial Economics 3: 305-360.

MARKOWITZ, HARRY. 1952. “Portfolio Selection,” Journal of Finance 7-l(March): 77-91.

MILLER, MKRTON II. 1977. “Debt and Taxes,” JoURNAL of Finance: 32-2(May): 261-275.

MODIGLIANI, FRANCO, AND MERTON II. MiLLKR. 195M. “The Cost of Capital, Corporation Finance, and the Theory of Investment,” American Economic ,ReOietu 48-3(Ju:ic): 261-297.

SHARPE, WILLIAM F. 1964. “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” JounaL of Finance 19: 425-442.

SOCIETY OF ACTUARIES (SOA). 2003. Proccedings o/ The Great Controversy: UMrrent Pension vlctnariaZ Practice in LigHt o/Financial Economics Symposium, Vancouver, june.

TEPPER, IRWIN. 1981. “Taxation and Corporate Pension Policy,” Jbumafo/Futance: 36-1 (March): 1-13.

TREYNOR, JACK L. (using pseudonym, Walter Bagehot). 1972. “Risk and Reward in Corporate Pension Funds,” Financial Analysis Jbuma! (January-February).

* Jeremy Gold, F.S.A., M.A.A.S., M.C.A., Ph.D., is Proprietor of Jeremy Cold Pensions, 22 W. 26th St., New York, NY 10010, e-mail: jeremyg@alumni.upenn.edu.


This paper contains some intuitive and illuminating solutions to a number of mathematical problems. The authors also investigate sensitivities to the choice of stochastic investment models, and have brought considerable mathematical ingenuity to bear. all this is commendable.

We would welcome more discussion regarding the way corporate decisions are made and preferences defined. We are concerned that the authors’ concept of efficiency (Section 2) overlooks important aspects of corporate decision making. Section 1.4 states that “The pension plan financial management is separate from that of the company sponsoring benefits …” The authors then proceed to ignore any correlation between the well-being of the pension plan and of the sponsor itself. Setting such correlations to zero is a heroic assumption which turns out to be much more fundamental to the authors’ conclusions than is the choice of investment return distributions or amortization schedule. ? growing number of U.K. pension professionals are convinced that the “plan-centric approach,” ignoring all correlations with the outside world, is an unsound basis for decision making.

Consider first the variability in funding level. We agree with the authors’ assertion in section 1.4 that “one purpose of funding benefits in advance is to maximize the security of benefits.” However, the proposed steady state model assumes that the plan continues to pay benefits forever, and therefore benefits are totally secure. This is an unpromising start for a default risk model.

A plan member’s exposure to default consists of a sum at risk and a default frequency. The sum at risk is the difference between the funded sum and the cost to buy out promised benefits via deferred annuities. The funding surplus is a poor proxy, because the funding valuation basis takes advance credit for future risky asset returns (a consequence of the “unbiased” assumption in sec tion 1.4), unlike market annuity prices. Furthermore, a loss of benefits (ignoring the effect of any federal guarantee funds) only happens when a plan deficit coincides with corporate failure. A deficit alone does not trigger loss of benefits. Therefore, the covariance between plan strength and the sponsor’s financial strength is critical to any assessment of benefit security. Indeed, the covariance effect dominates any effect arising from funding variability unless the plan is stochastically independent of the sponsor’s fortunes. To say that plan management is separate from corporate management (Section 1.4) does not imply that the two entities are stochastically independent as the authors propose. For example, a corporation and its pension plan inevitably face the same level of interest rates and stock market prices. Few readers will accept the assertion (Section 1.4) that “variance [of the plan funding level] is a reasonable and tractable approximation [to plan security].”

We also agree with the suggestion in section 1.4 that “Another motivation for pre-funding pension benefits is to spread the required future pension contributions and hence reduce strain on the sponsor’s cash flows.” Corporations seek to avoid large pension flows at the same time as tight cash flows elsewhere in the business. Corporations might also worry about the impact of pension risk on their cost of raising capital to finance their core business. Variability of pension flows themselves is a small part of the picture. Variable funding contributions might even be a good thing if they naturally hedged some other aspect of corporate cash flow. Wise corporate risk managers are not concerned with the variability of pension flows in themselves, but instead with the effect of a pension plan on an already variable corporate cash flow.

As with the funding level, a covariance is required, but the authors argue instead that “minimizing the variability of the contribution … is also a reasonable objective.” Their assertion would be valid only if plan cash flow were independent of other corporate cash flows. The authors escape building a corporate model only by a heroic stochastic independence assumption regarding the cash flows of the pension plan and the sponsor.

It is surprisingly straightforward to analyze pensions even when a plan is correlated with the sponsor’s fortunes. We characterize the emerging literature as “business-centric” rather than “plancentric.” Only arbitrage arguments and clear thought are required in order to understand the key conclusions. No calculations are needed. Sharpe (1976) and Treynor (1977) set out the main findings. Non-zero correlations have a profound impact-implying that the same risk controls routinely applied to corporate balance sheets are also appropriate for pension plans.

Some difficult questions relating to discretionary benefits, default risk, and tax require more detailed modeling. Clear thinking and model complexity need not exclude each other. For example on the question of amortization, Chapman et al. (2001, section 6.9) deduce the following:

“Shortening the [amortization] period [from 10 years] to 5 years increases the percentage of scenarios where the company goes into liquidation . . . Note that both shareholders and employees are winners as a result of this change. . . . The losers are the Government, which receives less tax, . . . and holders of debt, who suffer a higher rate of default.”

Their approach is more useful for decisions than the corresponding findings of Dr. Owadally and Professor Haberman (see section 2). “Dufresne (1988) concludes that . . . spreading gains and losses over a period between 1 and 10 years is efficient. . . . Owadally and Haberman (1999) conclude that the . . . practice of amortizing gains and losses over 5 years is also efficient.”

The results of Chapman et al. (2001) are consistent with those of Sharpe (1976) and Treynor (1977), but conflict with the claims of Dr. Owadally and Professor Haberman. The current authors’ refusal to cite the business-centric literature is all the more remarkable because a written discussion of Chapman et al. was published in the British Actuarial Journal (IIaberman 2001).

The authors have presented some elegant mathematical results. Unfortunately, their usefulness is undermined by weaknesses in the assumptions. Their nemesis is the assumption of stochastic independence between the fortunes of a pension plan and its corporate sponsors. Had the authors investigated the effect of weakening this assumption, they would have recovered wellknown results from the 1970s finance literature.


CHAPMAN, R. J., TIM ,1. GORDON, CUKK A. SPEED. 2001. “Pensions, Funding and Risk,” British Actuarial Journal 7(4): 605686.

HABERMAN, STEVEN. 2001. Discussion on “Pensions, Funding and Risk,” British Actuarial Journal 7(4): 684-685.

SHARPE, WILLIAM F. 1976. “Corporate Funding Pension Policy,” Journal of Financial Economics 3: 183-193.

TREYNOR, JACK L. 1977. “The Principles of Corporate Pension Finance,” Journal of Finance 32: 627-638.

* Charles Cowling is Worldwide Partner at Mercer Human Resource Consulting, Clarence House, Clarence Street, Manchester M2 4DW, United Kingdom, e-mail: charles.cowling@mercer.com.

[dagger] C. Jon Exley is Senior Consultant at Mercer Investment Consulting, Wellington Plaza, 31 Wellington Street, Leeds LSI 4DL, United Kingdom, e-mail: jon.exley@mercer.com.

[double dagger] Nick Hudson is Senior Vice President at Stern Stewart & Co., 1 35 East 57th Street, New York, NY 10022, e-mail: nhudson@ sternstewart.com.

§ John Shuttleworth is a Partner at PricewaterhouseCoopers, Plumtree Court, London EC4A 4HT, United Kingdom, e-mail: john.l.shuttleworth@uk.pwc.com.

** Andrew Smith is a Partner at Deloitte, Stonecutter Court, 1 Stonecutter Street, London EC4A 4TR, United Kingdom, e-mail: andrewdsmith8@deloitte.co.uk.

[dagger][dagger] lan Sykes is Director at KPMG, 8 Salisbury Square, London EC4Y 8BB, United Kingdom, e-mail: ian.sykes@kpmg.co.uk.


The paper provides a closely argued and detailed consideration of how funding deficits and surpluses should be dealt with. However, by taking a plan-centric view of a pension plan, without incorporating the economie relationship of the plan to the owners of the sponsor (typically company shareholders) and the plan members, the paper is, therefore, unable to consider the economic impact of sponsor insolvency on members and contribution volatility on shareholder value. These features are of prime importance when considering pension plan funding.

The authors set out to find an efficient way of spreading gains and optimal funding. They adopt the objective of minimizing some combination of the variability of the deviation from the funding target and the contribution rate. The economic justification for choosing this combined objective is not made clear. Moreover, the two most important controls in determining plan funding, namely, the funding target and investment strategy, are assumed to be specified exogenously and, therefore, omitted from the analysis. For instance, the optimal solution of investing in hedging assets and paying the future service cost is excluded without further consideration.

The authors made an implicit assumption that the sponsor can never fail. This approach assumes away the possibility of any serious economic analysis because the main justification for providing advance pension plan funding via a separate trust (as opposed to the sponsor making advance provision via an unassigned savings vehicle) is to provide security in the event of corporate insolvency (see, e.g., McLeish and Stewart 1987).

The objective that appears to relate most closely to security is “minimizing the volatility of the funding level or of the unfunded liability.” However, this seems unlikely to be economically meaningful as:

* an unfunded plan would meet the funding volatility minimization criterion but clearly fail to provide the security of a funded plan, and

* a plan constantly funded at 50% clearly provides less security than a plan with a funding level that fluctuates between 120% and 100%.

Accordingly, we disagree with the authors that “variance is a reasonable . . . approximation” to “an ideal measure of security.”

In section 4, the authors introduce the idea of a cost function. This function is not justified in terms of how it affects the members or the ultimate providers of the pension, the shareholders (and other capital providers) of the sponsor. Indeed, using a Modigliani-Miller (1958) framework, where there is no insolvency, the cost to shareholders is fixed and so the cost function has no meaning for shareholders. Members will have no concerns over the funding level because the sponsoring company can always meet any deficit and, therefore, it has no meaning for them either. There is no attempt to reconcile the cost to the market value of instruments that could be used to achieve the desired goal and, given the structure of the model, it is difficult to see how this could be achieved.

In section 4.3, we are provided with the result that “the optimal proportion invested in the risky asset decreases as the f^sub t^ [the market value of the assets] increases.” Let us consider the converse. As the value of the assets decreases, the proportion of risky assets increases. From the members’ point of view, this says that the worse the security the more risk should be taken. It is difficult to reconcile this with the members’ interest in the security of their benefits. Economic feedback of an insecure pension promise into employee remuneration will not compensate members who have large accrued benefits or who are no longer employees.

The security aspect also affects the contributions. A plan in deficit effectively has a debt owed from the sponsor. The longer the period taken to remove the deficit (i.e., the smaller the adjustment contribution), the longer the members are at risk of sponsor default. Hence, the two objectives are contradictory.

The plan-centric view means that this paper is unable to address satisfactorily the issues raised by surpluses, deficits, and funding policy. Two possibilities arise: (1) that members and shareholders of the sponsor are essentially in conflict-a gain to one means a loss to the other-or (2) they can collaborate to realize value from a third party. In either case the approach of the paper is unable to help.

The points discussed above are a cause for concern, but even if they could be addressed, the most serious concern about the paper would remain: The approach adopted in this paper depends on a Markowitz (1952) style of portfolio selection. While portfolio theory is an important branch of finance, it is not appropriate to the problem being addressed in the paper. The area of finance theory that is applicable to pension funds and their sponsors relates to the theory of the firm as advanced by Modigliani and Miller (1958) and applied to pensions by Sharpe (1976), Black (1980), and Tepper (1981) and more recently Exley et al. (1997).


BLACK, FISCHER. 1980. “The Tax Consequences of Long-Run Pension Policy,” Financial Analysts Journal 36: 21-8.

EXLEY, C. J., S. J. B. MEHTA, AND a. 1). SMITH. 1997. “The Financial Theory of Defined Benefit Pension Schemes,” llritisli Actuarial Journal 3: 835-966.

MARKOWITZ, UAKRV. 1952. “Portfolio !Selection,” Journal of Finance 7: 77-91.

MCLEISH, DAVID .J. D., AND COLIN M. LSTEWART. 1987. “Objectives and Methods of Funding Denned Benefit Pension Schemes,” Journal of the Institute of Actuaries 114: 338-424.

MODIGLIANI, FRANCO, AND MKRTON II. MiLLRK. 1958. “The Cost of Capital, Corporation Finance and the Theory of Investment,” America?! Economic Re-view 48: 261-297.

SHARPE, W. (1976). “Corporate Funding Pension Policy,” Journal of Financial Economics 3: 183-193.

TEPPER, IRWIN. 1981. “Taxation and Corporate Pension Policy,” The Journal of !finance 36 (1): 1-13.

* Cliff A. Speed, F.F.A., works at Hewitt Bacon & Woodrow, Prospect House, Abbey View, St. Albans, Hertfordshire, ALI 2Q4, United Kingdom, e-mail: Cliff.Speed@hewittbaconwoodrow.com.

[dagger] Tim J. Gordon, F.I.A., works at Hewitt Bacon & Woodrow, Colmore Gate, 2 Colmore Row, Birmingham, B3 2QD, United Kingdom, e-mail: Tim.Gordon@hewittbaconwoodrow.com.


The contributors to the discussion of our paper have outlined a so-called “business-centric” approach to denned-benent pension funding. They claim that there is a fundamental division between this and the “plan-centric” approach. The truth about this division is more pedestrian. The plan-centric approach is embedded in the current regulatory and statutory reality of pension funding. Our paper confines itself to this reality. On the other hand, the contributors reiterate the “extended balance sheet” argument (which integrates the balance sheet of the pension plan into that of the sponsor) and would like to overhaul current pension legislation, regulation, and standards of practice. Their arguments ignore funding requirements, employee contributions, trust law, and discretionary benefits.

We address, in this paper, a purely practical issue concerning funding methods and amortization mechanisms and we suggest that spreading is better than amortization. The point of the paper is not to examine the purpose of pension funding and the overall suitability of actuarial funding methods. Nor are we promoting one asset allocation strategy over another. We are pointing out that, under the usual (and rather limited) objectives of actuarial funding methods, which are to minimize the volatility of contribution rates and funding levels around a normal cost and actuarial liability respectively, a contrarian investment strategy follows (which is expected), together with an optimal funding strategy involving spreading (which is new).

The discussions misrepresent a number of points. We emphasize that the first moment of the unfunded liability is zero, which enables us to look at volatility through the second moment. (We point out in the paper that the quadratic criterion is simplistic.) The funding valuation basis does not have to take advance credit for the risk premium in risky assets. It is quite possible to value liabilities at a suitable discount rate while calculating contributions and making funding decisions based on a higher expected rate of return on plan assets (Owadally 2003). Finally, our use of the term “efficient” does not mean that we simplify pension funding into a one-period portfolio selection problem.

The discussants assume that the pension plan is not a financial entity distinct from the corporation. This view turns accrued benefits into bonds and plan members into bondholders. It is difficult to see what level of funding is optimal under this scenario. Disregarding statutory funding requirements, an unfunded book-reserve system may even be optimal for the firm.

Several of the discussants refer to the “irrelevancy proposition” of Modigliani and Miller (1958). Under this theorem, the purchase or sale of financial assets by a company makes no difference to the shareholders of the company. This theorem is derived and hence applies under a series of strict conditions:

(i) all shareholders can buy or sell financial assets on the same terms as the company;

(ii) all shareholders have optimised their private portfolios.

Condition (ii) requires that all the shareholders have efficient portfolios in the Markowitz sense. In order to apply the theorem to the financial strategy of a defined benefit pension plan sponsored by the company, we must add the following two further conditions:

(iii) the assets of the pension fund belong to the company;

(iv) the benefits provided by the pension plan are marketable financial assets.

There are serious difficulties when we attempt to apply the Modigliani-Miller theorem to the financial strategy of the company pension plan. Is a company really in a similar financial position if it invests its pension fund entirely in bonds while simultaneously issuing a matching quantity of its own bonds, as the discussants appear to believe? If the assets of the pension fund did belong to the company, one could argue that the net gearing of the company would be unchanged. Pension fund assets, however, cannot be used to redeem the company’s loan stock if it gets into financial difficulties, so that condition (iii) does not hold. It follows that a financial strategy for the pension plan that results in higher gearing for the company would reduce the security of the retirement benefits.

Thus, a defined benefit pension plan is not in reality simply an extension to the balance sheet of the sponsor. It is by design independent, involving an independent fund, managed independently in the best interests of the plan members and, as such, the plan forms part of the remuneration package of the members. The investment of the funds is the responsibility, in the United Kingdom, of the trustees who are required to invest on behalf of the members and beneficiaries, as a prudent person would do.

Turning to the members of the pension plan, it is clear that the Modigliani-Miller conditions are not satisfied. These individuals have large amounts of their wealth tied up in defined-benefit pension assets that cannot be traded, so they cannot change their private portfolios in ways that could nullify changes to their pension benefits – thus, assumption (iv) does not hold. We argue that the financial strategy adopted by the pension plan affects the balance between the security of the termination benefit and the security of the retirement benefit. There are no market transactions members can perform that would alter the balance between these risks. Consequently, changes to the financial strategy of the pension plan will have real “first-order” consequences for the diversification of risk within each member’s private portfolio.

Our view is that the assumption of independence between the sponsor and the plan is crucial and the erosion of this assumption is partly the cause of the decline in defined-benefit pension provision. It must be recognized that defined-benefit pension risk is not born by stockholders alone, but is also borne by plan beneficiaries because of uncertain discretionary benefit enhancement and job mobility. In our view, a “consumer-centric” approach must be restored, whereby the defined-benefit promise is simplified and made explicit so that both employees and stockholders can cost it under standardized valuation models and identify the risks they take. This should then improve the quality of information available to investors and employees when they value company stock and employee contracts, respectively. This may involve the introduction of novel designs for defined benefit pension plans, such as variable benefit accrual rates (Khorasanee and Ng 2000).


KHORASANEE, M. ZAKI, AND ho KUNG Nu. 2000. “A Retirement Plan Based on Fixed Accumulation and Variable Accrual,” North American Actuarial Journal 4(1 ): 63-79.

MODIGLIANI, F., AND M. II. MILLER. 1958. “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review 48: 261-97.

OWADALLY, M.I. 2003. “Pension Funding and the Actuarial Assumption Concerning Investment Returns,” ASTIN Bulletin 33(2): 289-312.

Copyright Society of Actuaries Apr 2004

Provided by ProQuest Information and Learning Company. All rights Reserved