The Case for Stochastic Present Values

Abstract

The decision making tools and reporting requirements for DB plans have been the subject of extensive discussions in recent years. For public plans, the debate has been particularly intense. For the most part, there have been two camps: “traditionalists” and “financial economists.” Both camps’ positions have pros and cons that numerous publications have discussed in detail. Yet, no common ground has been found between the two camps. This paper presents an introduction to a solution that represents this common ground. The solution – an economic theory that encompasses both traditional actuarial and FE approaches - is based both on pension actuarial science and financial economics. The analytics of this theory have been developed sufficiently enough to be useful to practitioners. I am cautiously optimistic that this approach will eventually become an integral part of the mainstream in pension actuarial science and financial economics. The roots of this debate are as follows. For better or worse, the overwhelming majority of retirement plans endeavor to fund their financial commitments by virtue of investing large portions of their wealth in risky assets. Investors in risky assets must expect certain compensation for taking risk. Risk premium must exist, but not without risk. One may not use risk premium and, at the same time, ignore risk. Clearly, traditional pension actuarial practices are in violation of these principles. As these practices stand now, the riskier the asset allocation, the lower the present value of pension commitment. This logic makes little sense. However, the solution “financial economists” propose makes even less sense. They brandish the principle “risk premium does not exist without risk” and inexplicably turn it into “risk premium does not exist, period” as far as actuarial practices are concerned. This is precisely the wrong conclusion to reach. Forcing actuaries to disregard risk premium – one of the cornerstones of finance - is a terrible idea that has no basis in either actuarial science or financial economics. In this author’s opinion, the right conclusion is “use risk premium and take risk into account.” As a first step, we have to scrutinize one of the most important assumptions that both “traditionalists” and “financial economists” appear to take for granted. The assumption is that present value of a financial commitment is a deterministic object - a number. This assumption was adopted decades ago when risk management was in its infancy and computing power was prohibitively expensive. That time is long gone. The assumption that once was accepted for computational convenience has now become an impediment for the development of risk management tools for pension plans. It is crucial to recognize that the present value of a financial commitment funded by investing in risky assets is a stochastic object – a random variable. As soon as this recognition takes place, we can take risk into account explicitly and apply actuarial science and financial economics to develop the most efficient asset allocation, contribution and benefit policies pension plans need. The paper provides a roadmap to such development. The time has come for stochastic present values.