Updated with correction
In his popular book "A Brief History of Time," Stephen Hawking introduces the complex world of (astro)physics to a larger audience. One of the phenomena it describes are black holes, massive stars that collapse under their own gravity and attract everything in vicinity toward the center. The book also describes the Event Horizon. This imaginary boundary close to a black hole is the point where gravity becomes so massive that even light cannot escape its grip, giving rise to the name "black hole."
This point of no return is an interesting concept that has been widely used in many other contexts. This article applies it to pension funds' balance sheets. The health of pension funds is often described by the funding ratio, which can differ dramatically across the world. Well-funded plans report ratios far above 100%, where other funds face a much more dire situation with ratios even below 30%.
The dangers of low-funding ratios
Other than being a measure of health, a funding ratio can also say something about the ability to recover. For instance, imagine a fund with a funded status of 50%. Although it only has 50% of assets to cover every monthly benefit payment, it pays out the full benefits every month, as all funds do. By doing so it effectively decreases the funding ratio even further, given the other 50% of benefits are paid by the remaining members. This, in turn, makes recovering to a funding ratio of 100% even harder. An outperformance of the investments against the liabilities could help, but a low ratio makes such a recovery much more difficult. In our example it would require the assets to make the same dollar return as the liabilities, although they are only half the size.
These two effects make it especially hard to recover from low funding ratios without the help of additional contributions from the corporate or government entity that is backing the fund. One could ask at which funding ratio the aforementioned effects become so strong that recovery is no longer a certainty. In other words: What is the event horizon, or the point of no return?
A quantitative approach
In a recent paper from the Rockefeller Institute at the State University of New York, it is argued that a funding ratio lower than 40% could be considered a good indicator of a deeply troubled U.S. pension fund. The Center for Retirement Research found that only four funds out of 150 in the U.S. had a funding ratio lower than 40%. These four funds were all broadly recognized to be deeply troubled.
In a recent project however, Ortec Finance took a more quantitative approach to determine whether a funding ratio of 40% could indeed be considered a point of no return, or whether this point could potentially be higher. Please note that, as in the Rockefeller paper, we only focused on the asset side of the balance sheet and did not take into account potential policy or recovery measures resulting in lower liabilities.
To determine the point of no return for pension plans we took two approaches. First we modeled a pension plan's balance sheet and projected it deterministically 20 years forward, based on a number of forward-looking economic assumptions regarding the development of interest rates, inflation and return on assets. We used a return on assets and discount rate of 7.25%, frequently used by public pensions across the U.S., and allowed for a contribution level that is slightly above the cost of new accrual. The projection is based on a pension plan with an average maturity. The analysis is performed by adjusting the initial funding ratio and assessing the development of the ratio:
The point of no return
The above graph shows that a funding ratio of 40% can indeed be considered a clear sign that a plan is deeply troubled. Even if a return on assets is able to keep up with the discount rate, the plan will see a rapid decline in funded status, which can only be stopped by very significant recovery contributions. We can also see that even a funding ratio of 60% leads to a decline in funded status, which will only accelerate over longer horizons. In that sense, a funding ratio of 60% can already been seen as a point of no return.
The economic environment is of course much more dynamic than the smooth deterministic returns used in this example. In order to get insight in the development of the funding ratio, actuaries and risk managers often fall back on stochastic analysis. In such analyses, a large number of realistic economic scenarios are created and then applied to the same balance sheet model as used above. This approach results in a large number of possible developments of the funding ratio under realistic circumstances, and can be used to further examine the behavior of the ratio. The analysis below shows the impact on the funding ratio for 2,000 forward-looking economic scenarios.
Event horizon at 60%
The graph shows an analysis of a semi-mature fund that is open for accrual, and has an initial funding ratio of 60%. The graph shows the development of the funding ratio through time across 2,000 different economic scenarios, divided in two confidence intervals of 50% and 95%. To assess whether the event horizon is indeed close to 60%, we highlighted the median over the scenarios in blue, which shows a steady decline to a level about 40%. Moreover, an overwhelming 70% of the scenarios end up in a situation that is worse than the starting point, underlining our conclusion that pension plans with funding ratios of less than 60% can be considered deeply troubled.
If we use this 60% level, rather than the 40% the Rockefeller Institute used, and apply this to the database from the Center of Retirement Research, we find the number of deeply troubled pension plans increases to 36 from just four.
Identifying deeply troubled plans
The point of no return can be used to identify plans that are deeply troubled, but it also has other applications.
For instance, we would suggest that plans take this point of no return explicitly into account when they define their risk appetite as a basis for their investment strategy. Once a plan falls below this level, the ability to recover decreases dramatically and is unlikely to succeed without significant contribution. The sheer size of the liabilities make it very hard for plans and their sponsors to adjust course once they hit this point, and it requires careful planning to avoid this black hole. It would also make sense for fund executives to draw up plans beforehand, so they know what to do once they reach such levels, such as requiring additional contributions to avoid a deeply troubled plan being drawn further into the black hole.
Finally, the point of no return depends on a number of variables and will differ across plans; hence we recommend performing such an analysis as part of the next strategic review.
Maurits van Joolingen is lead consultant at Ortec Finance, Rotterdam, Netherlands. This content represents the views of the author. It was submitted and edited under P&I guidelines, but is not a product of P&I's editorial team.