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

North American Actuarial Journal, Apr 2004 by Gold, Jeremy, Cowling, Charles, Exley, Jon, Hudson, Nick, Et al

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

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.