The Values of Shortfall and Surplus

You can look at it in lots of different contexts -- gambling, savings, personal finance, defined benefit plans. Which is bigger, the negative value of a 10% shortfall or the positive value of a 10% surplus? Of course, they are the same, 10% of something, but are they really?

From a personal finance standpoint, if you have a 10% surplus -- that is, 10% more money socked away than you need to meet your current obligations -- that is nice. But, if you have a 10% shortfall, that is really painful. The surplus gets you some comfort or some discretionary spending. The shortfall, on the other hand, increases your cost of money.

In defined benefit plans, it may be worse. And, the value of increasing surplus gets smaller and smaller (somewhat simplistically) as the surplus grows, but not so with the negative value of shortfall. Let's consider a fairly simple example. I'm going to assume that your defined benefit plan has a funding target of $100 million and assets of one of $80, 90, 100, 110, or 120 million. In other words, you have a Funding Target Attainment Percentage (funded status or FTAP) of one of 80%, 90%, 100%, 110%, or 120%. Let's ignore the Target Normal Cost and determine the one-year cost of paying down that unfunded liability (assume an effective interest rate of 5.00%).

At 80%, it's about $3.45 million. At 90%, it's about $1.73 million. At 100%, 110%, or 120%, it's $0. From a one-year funding standpoint, the negative value of shortfall is meaningful, but the positive value of surplus is not.

Suppose you are planning to terminate your plan. Absent the additional cost of annuities (insurance companies need to build in margin to manage their risks and to turn a profit), the surplus is generally worth about 15 cents on the dollar (less if you use it for a replacement plan), but the shortfall has a negative value of $1 on the dollar, unless you are going to get the PBGC to take over your plan.

Why do we care about all this? Until your plan gets into a restricted status (<80% funded) or an at-risk status (<60% funded), all oversimplified, each dollar of underfunding has the same negative value. But, overfunding has less positive value. So, when you are looking at your investment policy for your plan, when it is already fully funded, you should simply be looking to develop a strategy to keep the surplus there, but taking risks to grow the surplus is probably not prudent. It is only when a plan is underfunded that risk-taking may make sense. Again, absent the negatives that fall to a plan once it crosses below that 60% or 80% threshold, every dollar upside has the same value as every dollar downside. So, where a sponsor of an overfunded plan should be risk averse, the sponsor of an underfunded plan should be largely risk neutral. Frankly, the only scenario in which a sponsor should have a preference for risk is one where they are so poorly funded and the company's finances are so bad that they are making a bet with two possible outcomes: 1) the risk pays off and as a result the company is able to stay in business, or 2) the risk goes bad, and the PBGC takes over the plan.

Think about it. Then, think about your plan's investment policy. Does it make sense? Do you need help?