Mitchell’s Musings 9-19-2016: Measurement for What?

17 Sep 2016 9:14 AM | Daniel Mitchell (Administrator)

Mitchell’s Musings 9-19-2016: Measurement for What?

Daniel J.B. Mitchell

I am going to take up defined-benefit pensions in this musing, but let’s start with a simple example. Suppose I wish to have $1,000 thirty years from now. How much should I put aside today as a lump sum to have that target amount in thirty years?

Clearly, the answer has to depend on what I think I will earn over the thirty-year period with my lump sum. But it is hard to be sure what the earnings rate will be unless I invest in something that is relatively riskless and that has that thirty-year duration.  Let’s suppose that there is such an asset in the marketplace and it carries an annual yield of 4%. As it turns out, if I put aside about $308 today and invest it in that asset, I will have my $1,000 in thirty years.[1]

However, suppose I were to invest in a reasonably prudent mix of stocks and bonds which are not as secure as the asset yielding 4%/annum, but which I believe – based on advice of experts – can be expected to yield 6%/annum. “Expected” is not the same as a sure thing, but the experts, looking at past long-term history and what they can see looking ahead, think 6% is a reasonable expectation. Of course, the experts note as a proviso that they could be wrong and that the actual result might turn out to be more or less than 6%.

As it turns out, if I were willing to take the risk that the 6%/annum target might not be achieved, I could put aside only $174 today to get my hoped-for $1,000 in thirty years.[2] That is, if things work out as expected, my $174 will grow with compound interest at 6% and become the target $1,000. And had I instead put aside $308, I would find myself thirty years from now with an “extra” $771.

Suppose further that in the period before I made the decision on how much to put aside today, expert advisors had been telling me that one could expect 7%/annum on average over a thirty-year period. But at the moment of decision, they told me that in view of recent adverse developments, they now believed 6% was more realistic. What would happen if I chose to believe that my advisors were being overly pessimistic due to recent developments (panicking) and that it would be better to keep the 7%/annum assumption? In that case, I would put aside only $131 today.[3] If keeping to 7% turned out to be correct, I would have my $1,000 in thirty years. But if my advisors were correct with their downward revision and the actual return was 6%, I would be short by about $254.

The most obvious point of this tale is that the more I put away today, the more likely it is that I will have at least $1,000 in thirty years. Put another way, if I follow what a low long-term rate of return implies in deciding how much to put away, I increase the odds of at least achieving my target. Note that there are really two steps implied. First, I assume a low rate. Second, because I assumed a low rate, I decide to put more money away today. These are separable events.

Suppose we translate these numerical examples into pension terms and suppose that actual rate of return turned out to be exactly the advisor-forecast of 6%/annum. The liability of my plan is $1,000 thirty years from now. If I had discounted that liability by 6% and had – as a result - put away $174 today, the plan would turn out to be fully funded. (My current ratio of assets to discounted liabilities = 1 or 100%.) If I had put away $308, the plan would be overfunded by 77%. ($308/$174 = 1.77) If I had put away only $131, my funding ratio would be only 75%. ($131/$174 = .75) I would be underfunded by 25%.

I have gone through this arithmetic because the University of California (UC) defined-benefit pension is officially underfunded and the UC Regents – as plan trustees – periodically mull over what to do about it. The plan uses a methodology which estimates the discounted value of its liabilities to future retirees by using the same discount rate as the rate officially estimated by the UC Regents to be their long-term expected annual rate of return.  Currently, the officially expected rate of return is 7.25%/annum.[4] However, it is clear from public statements of the Regents’ chief investment officer and his staff that they (the CIO and his staff) believe a 6-ish long-term rate is more realistic going forward than a 7-ish rate.

Moreover, there is at least one outside advisor on the Regents’ Committee on Investments who is arguing that even if the 6-ish rate is a reasonable expectation of the long-term return, the discount rate that should be applied to the liability of the plan is a 4-ish number.[5] That 4-ish number, in his view, seems to equate to what the State of California pays on long-term general obligation bonds. (The state in fact pays less than that because its bonds are tax-exempt, but if you adjust the yields to the equivalent taxable rate, they would have a 4-ish return.) His argument is that if the state’s pension liabilities are as firm as its bond liabilities, the same rate would be used for both.

There are two different issues here. The first is whether the Regents should lower their official expectation of a return to the level their own expert is telling them is appropriate (i.e., from a 7-ish expectation to a 6-ish rate). Presumably they should, unless they truly believe he is being panicked by recent developments and that the old official 7-ish assumptions are still valid. But if they instead believe what their expert is saying to them now, that belief will tell them that the plan is more underfunded than current methodology indicates. So the corollary is that if they lower the official expected return, they should also up the contributions to the plan appropriately. Again, as in our earlier example, there is a two-step process here. First, a change in the assumption and, second, acting on that assumption.

If they don’t take the second step, the plan would gradually have a lower and lower asset balance relative to liabilities and would someday become a pay-as-you-go arrangement. That is, each cohort of employees would – at some date in the future - end up being “taxed” to pay the pensions of previous cohorts. As a practical matter, without the availability of earnings from a large investment pool of assets, the pay-as-you-go cost would be very high.

Another issue, however, is whether it makes sense to have a lower discount rate than the expected earnings rate, as the outside expert is arguing. Lowering the discount rate for liabilities will up the measured value of those liabilities and thus lower the measured value of the funding ratio. If more contributions result, the likelihood of at least having the assets needed to pay those liabilities goes up. But note that measured value is not the same as actual value. The actual value will depend on actual future earnings. If you believe those earnings to be 6-ish, and yet you fund on the basis of 4-ish, your plan assets will gradually rise relative to liabilities and will do so indefinitely. Presumably, at some level of overfunding, the contributions would be halted.[6]

A key point about a pension plan – which differentiates it from the $1,000-in-thirty-years example – is that a pension plan goes on indefinitely; there is no finite maturity. On a regular basis, estimates of liabilities and expected future rates of return should be adjusted iteratively. There really isn’t a behavioral reason to pick a number such as 4% for discounting on the grounds that pension liabilities are in theory similar to state bond liabilities. The 4% vs. 6% differential might be taken to be an indication some measure of risk to employees. That is, other things equal, employees might be willing to contribute more to a plan which guaranteed an outcome rather than one that produced only an expected outcome. (But there is much research to suggest that ordinary folks have big problems in evaluating risk.)

Just blowing up the measured liability relative to assets by assuming a lower discount rate than the assumed earnings rate might well have perverse results. It could make the current underfunding problem seem intractable and lead to Regental paralysis and no solution. The purpose of computing the funding ratio is managerial, not theoretical. You make the calculation to help guide management decisions.

The best outcome, and the one most feasible, would be for the Regents a) to lower their expected earnings rate (and their liability discount rate) to what the CIO and his staff are suggesting is reasonable, and b) to modify their funding plan to accord with that rate, used as both the projected earnings rate and the discount rate. And they should follow that approach periodically and make iterative adjustments as needed.


[1] $308.32 x (1.04)­­­30 = $1,000

[2] $174.11 x (1.06)30 = $1,000

[3] $131.37 x (1.07)30 = $1,000

[4] The rate was recently lowered from 7.50%.

[5] You can hear the September 9, 2016 meeting of the committee at The comments of the outside advisor are at approximately 1:29 on the audio recording.  

[6] We know in fact that when the plan became overfunded in the 1980s as officially measured, contributions were halted for two decades. So there is evidence that actual contribution behavior responds to the measured value of the funding ratio. We know in fact that – with a long lag – when the official measure of the ratio came to show underfunding, contributions were resumed. There may well be asymmetry between the reaction to overfunding and the reaction to underfunding. And, as noted below, a high measured level of underfunding could cause paralysis.

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