But quite aside from the question of whether the return assumptions are realistic, should the rate that is used for discounting pension obligations be determined by the fund’s expected return, i.e. its investment policy? Actuaries certainly seem to think so. But when we apply some basic results from the theory of finance, we actually arrive at a very different conclusion. Thirty years ago, I sat on the board of an institutional mutual fund with Merton Miller. When the investment strategy and the funding assumptions of a particular US pension fund client were discussed, he commented wryly that they had obviously never heard of his and Franco Modigliani’s work. What he meant was that, according to the Modigliani & Miller (M&M) theorem, the discount rate that is used to determine the present value of future cash flows should depend exclusively on the market risk of those flows and be independent of how the investment required to generate the flows is financed. This is one of M&M’s basic results: investment and financing decisions can be separated (subject to some small print).

To apply this fundamental result to pension funds, let us first look at the usual pension promises from the viewpoint of a member. She faces a series of guaranteed payments for as long as she lives. The promise is absolute, i.e., there is no market risk associated with those payments. Consequently, we should calculate the present value of these certain future payments by applying a risk free rate over the appropriate horizon. The mortality risk of the member can be incorporated by multiplying the guaranteed payment with the probability of her being alive at the time of the payment; again, something that is quite independent of market risk. Given M&M’s theorem, the pension fund and its actuary should of course apply the same risk free discount rate when estimating liabilities. But they do not. Instead, they base the discount rate on the fund’s investment policy – improperly linking the financing decision to the investment decision.

What are the consequences of applying a higher discount rate? Obviously, the liabilities of the fund appear smaller, which allows for lower contributions or improved benefits or a combination of the two. But this advantage is an illusion. Let me illustrate this fact with a very simple example (inspired by a *paper* co-authored by the actuary quoted in the NYT article above). Consider a public employee who is promised a single payment of $100 to be received in twenty years. Also assume that the risk free rate will remain constant at 1% and that the expected return on a 50/50 equity-bond portfolio, which happens to be the pension fund’s policy portfolio, is a constant 4% p.a. At the risk free rate, the promised payment represents a current liability of $81.95; at the 4% rate, the liability drops to $45.64, a difference of $36.32.

The attraction of using a higher discount rate is obvious. But, naturally, we cannot just eliminate part of the liability by changing assumptions. It has simply been shifted elsewhere; thus, there will be some who gain and some who lose. The employee may gain if the actual return experience turns out better than expected and if the fund decides to improve benefits as a result. But if the return assumptions turn out to have been too optimistic, the employee will not lose since the payment is guaranteed. Instead, the shortfall will have to be borne by the tax payers in twenty years time. The beneficiaries in all cases are the current tax payers who only have to finance part of the liability represented by the promised pension payment. In other words, there is a transfer of risk from today’s taxpayers to a future generation of taxpayers and a corresponding transfer of wealth from future tax payers to current tax payers, something that I talked about in an earlier post in the context of the *Geneva pension reform*. Naturally, while the benefit to the current taxpayer can be determined precisely ($36.32), the cost for the future generation of tax payers will only be revealed later, since it depends on the success of the investment strategy.

The fact that actuaries have mistakenly linked investment and financing decisions in the determination of the discount rate that is applied to future liabilities is not a harmless assumption with minor consequences that can easily be corrected. Also the problem is not limited to public funds but rather more general. The systematic understatement of pension fund liabilities, in some cases over decades, means that a huge deficit has accumulated in most capitalised pension systems – usually hidden from view unless a dramatic event like Detroit’s troubles arrives. But these problems should not be used as an argument in favour of a pay-as-you-go system. Even a very poorly funded capitalised system is preferable to such a scheme whose assumptions tend to be even more unrealistic and that also tend to ignore the unfavourable demographic realities present in many countries.

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