By Stephen G. Brush (History and IPST) and James J. Griffin (Physics)

Professor Saul Gass (UMCP, now retired), in an article published in the May 2001 issue of The Faculty Voice, pointed out that the process by which the State of Maryland determines the specific value of a pension may produce some unexpected (and possibly disappointing) outcomes. Most people's only quantitative knowledge of their own pension is the Basic Allowance amount reported annually by the State Retirement and Pension System of Maryland (SRPS) to every participant. If a sixty year old with 30 years of experience works for another 10 years till age 70, he could retire with 40 years service instead of 30 years. Then his Basic Allowance will always grow by at least 33%. But if he wishes to provide for a surviving spouse, then his actual 40 year pension at age seventy may be substantially less than 133% of the 30 year pension he could receive at age sixty.

We here attempt to clarify this and other issues, first by describing how to estimate one's own pension benefit, and then by reviewing that description to show why the results come out the way they do. We first summarize the options that the system offers and present an abbreviated table of several Option Factors by which the "Basic Allowance" (Maximum Pension) must be multiplied to obtain the actual pension in various situations. With this information one can estimate at least roughly the amount of any specific pension.

Here we consider only the "old" Maryland Employees and Teachers Retirement System, not the "new" Maryland Employees and Teachers Pension System established in 1980. Our discussion is thus specifically relevant only to people who were hired before 1980 and elected to stay in the old system after 1980. Still, we hope that the general discussion might be helpful to any prospective retiree.

For simplicity, "he" means ""he or she." In fact the amount of the pension itself does not depend upon the sex of the retiree, nor of the beneficiary, despite the fact that the mortality tables from which its factors are calculated are different for males and females. The system uses weighted averages of life expectancy, based on the percentage of males and females in the system. (At the moment it is 45% male, 55% female).

Thus,

Maximum Pension = (Average Final Salary) multiplied by (Years of Service) divided by 55 or, as an algebraic equation,

M = (SY)/55.

M is the practical key to computing your retirement pension because it is the quantity always multiplied by an Option Factor to determine the actual amount of your pension. It is also the legal key because it is the amount that the retirement system promises to pay you from your retirement date until your death, if you do not elect an optional form of payment.

The calculation of pensions for the various other options depends on the "Present Value" of your pension at retirement. The "Present Value" of your pension, although never mentioned in the documents distributed to participants, is the actuarial equivalent cash value of your pension upon retirement. Since this is a "defined benefit system" neither your annual pension nor its present value; rather, both depend upon the fixed benefit promised you, as specified by the Maximum Pension amount, M, defined above.

Roughly speaking, the Present Value (V) is just the total amount of money the System would have to set aside now to pay you if you lived the expected number of years after retirement, according to standard mortality tables. Its actual computed value takes account of the fact that the cash for future payments can be invested to yield interest until the payments come due. We will explain below how to estimate the Present Value of your pension. The Present Value is the benchmark for fulfilling the legal and fairness requirement: that every alternative retirement arrangement offered to you ought to have the same (i.e., an actuarially equivalent) present value.

Keep in mind that if you choose to receive this Maximum Pension, all benefits will end upon your death. It offers no guarantee that the pension will return at least its Present Value to you, nor even the value of your own contributions (with interest) should you suffer an early death. If you retire one day and die the next, the System's obligation to you is zero. Furthermore, it provides nothing for a surviving beneficiary. If on the other hand, you live longer than actuarially expected, your maximum pension continues until your death, whether or not your total payments exceed the present value of your pension at retirement.

Alternative Options 1 through 6 do allow you to receive such benefits, but you have to pay for them. This extra "premium cost" (which can be thought of as an insurance premium to cover the expense of the added benefit) is paid for by a reduction in the pension from the Maximum Pension amount. This reduction is defined for each Option by an AOption Factor@ discussed further below.

Indeed, many of us have always thought that this Maximum Pension would be our actual pension upon retirement, having been misled by the phrases "Basic Allowance" or "Retirement Benefit." Big mistake! It is in fact the largest pension (Cost of Living Adjustments aside) that we can possibly receive; the pension we actually elect will very likely be significantly lower than M.

For any of the six standard alternative pension options your pension is the product of two factors: the Maximum Pension described above, and an Option Factor, which depends on your age at retirement and (for the dual-life options, #2, #3, #5, and #6) upon the age of your beneficiary. The Option Factor is always less than 1, so the actual pension is always less than the Maximum Pension. The pension is augmented each year by a cost-of-living percentage increment, capped or full depending on which of two contribution rates (plan A or plan B, as discussed just below) you chose to make.

If one wishes a guarantee that at least the Present Value of one's pension, or the value of his own contributions to the pension fund (with interest), will be paid to him, or to his beneficiary, even if he were to die before that had been achieved by his regular pension payments, Options #1 and #4 are available. They are "Single Life Options" because their actuarial cost depends upon only the age of the retiree. Note that by law a married retiree can select a single life option only with the spouse's permission.

Let's call this pension P₁, where the subscript "1" means Option #1. It is calculated by multiplying the Maximum Pension by a factor, to be called F₁, which depends on your age at retirement. (P₁ = MF₁) The values of F₁ for selected ages are given in Table 1.

We note again that the Present Value is the actuary's estimate of the immediate cash equivalent value of the stream of payments promised by the pension. Clearly it depends upon the life expectancy assumed for the retiree population, so it is a weighted statistical average for everyone who retires at that age rather than a precise figure for any particular retiree. It also depends upon the rate of interest that one assumes the cash would generate while waiting to be paid out to the retiree; the System currently assumes that this rate is 7%. We do know that it is proportional to the individual's Maximum Pension, and we can summarize the other factors in a single factor A, called the Service Annuity Factor:

The Service Annuity Factor is given in Table 1 for a selection of retirement ages.

In the example above, your Present Value is

Option 4: Guarantees the full return of the member's accumulated contributions (with interest), C. If the retiree dies before receiving the full guaranteed amount, the remainder is paid in a single sum to the beneficiary (ies). The reduction in pension associated with this choice is just C/V times smaller than the reduction for Option 1. Because the Option #4 factor (F₄) depends upon three variables (Age, C, and V), the Option #4 factor is awkward to tabulate. Furthermore, the value, C, of the member's contributions with interest is not regularly provided by the System. However, each participant's current C and V values are supplied (see the answers provided there for Options #1 and #4) in his Estimate of Service Retirement Allowances. This estimate can be obtained by filing Form MSRA-9, "Application for an Estimate of Service Retirement Allowances,." with the Maryland State Retirement Agency within one year of the retirement date envisaged, but not later than six months before that date. We recommend that everyone do so every year, requesting information on all, in order to accumulate a file of true data for future retirement planning purposes.

Option #2: The retiree's entire pension will continue to be paid to the beneficiary for the remainder of the beneficiary's life. (In the Tables, this is called "100% B.")

Option #3: One-half of the retiree's pension will continue to be paid to the beneficiary for the remainder of the beneficiary's life. (This is called "50% B.")

In Options #2 and #3, payments cease upon the death of the surviving beneficiary.

Option #5: The retiree's entire pension will continue to be paid to the beneficiary for the remainder of the beneficiary's lifetime. If the beneficiary dies before the retiree, the pension will increase ("Pop Up") to the Maximum Pension (M) for the remainder of the retiree's life. ("100% + PopUp")

Option #6: One-half of the retiree's pension will be paid to the beneficiary for the remainder of the beneficiary's life. If the beneficiary dies before the retiree, the pension will "pop up" to the Maximum Pension (M) for the remainder of the retiree's life ("50% + PopUp")

Special Option #7: Provides for personalized arrangements to suit special needs. A special option benefit must be approved by the Board of Trustees. No continued health coverage for the surviving spouse is available under option 7.

Once during each year after retirement, the appropriate COLA adjustments will be applied to every pension option, as discussed above .

This policy ignores good financial advice about retirement: find out what your pension would be, and whether it is adequate for your needs, before you retire. If it isn't adequate you may have to delay retirement for a few years until your expected pension would be adequate (in your own opinion). But the Maryland State Retirement Agency does not provide you the information you need to make such a judgment.

It is our opinion that for planning purposes one should be able to obtain reasonably accurate hypothetical estimates of what his pension would be under the various options, for several possible retirement dates and with reasonable assumptions about future salaries. (These estimates would not of course be legal commitments; not only is the future salary unknown, but the mortality tables on which the factors are based could change in the future.) We see no reason why the Agency refuses to offer this information.

A more modest proposal is: since the System already provides an estimate of your Maximum Pension in your annual participant report, why not also include every year an estimate of your pension for each of the options? (The birth date of your beneficiary, is already listed in each year's report.) By providing these additional six numbers each year, the System could inform each participant how much he could expect to get under each option, based on his then-current averaged three highest years' salaries. This would be a helpful client service, and would forestall complaints from those who feel they were not adequately informed about the consequences of their option choices. It would also allow each participant to collect a file of estimates over a period of years and extrapolate the trend to future years.

In addition, or at least as an alternative, the Retirement System should offer pension-estimating software on its web site, which would allow each individual to calculate the pension that would result from whatever hypotheses and personal data that he himself inserts into a Q&A format. Then we could all ask "What if ...?" on the web and get accurate answers for any assumptions we might present.

At a very minimum, the Retirement System should present on its web-site (or on the COMAR website), and on paper to anyone who asks and is willing to pay reasonable costs, the complete current table of Option Factors. Even a selection from it for ages at, for example, 5 year intervals, would be better than nothing. In the meanwhile, we recommend to our colleagues that for several years before retirement, you should submit Form MSRA-9, checking all option boxes, and retaining the responses for use in future planning.

Start with Option Factor #1, which depends only on the age at retirement. Suppose you plan to retire at age 67. Look in Table 1, and you find that the Factor is .9190 for age 65 and .8831 for age 70. So in your case it would be somewhere about half-way between those numbers, about .90. More precisely, it would be about 2/5 of the distance between those numbers. The difference is .9190 - .8831 = .0359. Multiply that by 2/5 and you get .0144. Subtract this from .9190, which gives .9046. This is not precisely correct (the actual value according to the Table is .9056) because the Option Factor decreases faster as retirement age increases; but it should be accurate enough to give you an idea of what your pension would be if you select this Option and compare it with the other Options.

Now we can answer, for Option #1, the question at the beginning of this article: if you retired at age 70 after working in the Maryland System for 40 years, how much greater would your pension be than if you retired at 60 after working 30 years? Let's be pessimistic and suppose that you didn't get any raise at all for the 31st through 40th years, so your average final salary is the same in both cases, say $55,000. Then at age sixty your Maximum Pension would be $55,000 multiplied by 30 (years of service) divided by 55, or $30,000. At age seventy it would be $55,000 multiplied by 40 (years of service) divided by 55, or $40,000. Your age 60 pension under Option #1 would therefore be $30,000 multiplied by the Option #1 factor for age 60, 0.9457, or $28,371. For retirement at age 70, it would be $40,000 multiplied by the Option #1 factor for age 70, 0.8831, or $35,324, or 1.24 times as much. You won't get 1.33 times as much for working 1.33 times as many years, but you will still get significantly more -- even if you received no raise in salary during your last 15 working years.

But if you wish after your death to have your pension continue undiminished until the death of your (same-aged) spouse, then the factors from Table 2 at ages 60 and 70, respectively are 0 .8224 and 0.7453 for Option #2, and your pension would be $24,672 for age 60 retirement , and $29,812 for the age 70 retirement (only 1.21, not 1.24, and not 1.33, times as great ), as compared with the maximum pension amounts of $30,000 and $40,000 respectively. Thus electing an ongoing pension for a surviving spouse by Option #2 reduces your pension by 17.8% from its maximum value for the age 60 retirement, and by 25.5% for the age 70 retirement.

Table 1: Factors for Single Life Annuity (Option #1) and Service Annuity Factors based on Present Value

For the dual-life options (#2, 3, 5 and 6) the calculation is more complicated because the Option Factor depends on both the age of the retiree and the age of the beneficiary at the time of retirement. In Table 2, we present the factors for selected age combinations, which allow one easily to choose two values of the age difference between the retiree age (R) and beneficiary age (B), one value larger and the other smaller than the actual difference. The actual Factor at any age will then lie between its values for those two differences. (Note that the age difference of retiree and beneficiary, R-B, remains constant as the retiree's age increases.) Then a simple interpolation can give a rough estimate of the actual Option Factor.

Table 2: Factors for Dual-Life Options

A striking feature of Table 2 is that for every option, the Option Factor decreases as the age at retirement increases (just as we have already found for Option #1). The second notable feature is that for every dual-life option, the Option Factor increases as the beneficiary's age at retirement increases.

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This very rational structure produces some seemingly counter-intuitive consequences, as we now discuss. We first note one often-overlooked but crucial feature of a fixed annual benefit pension: Its Present Value (roughly the cash-now dollar equivalent of the stream of promised fixed future payments under some assumed interest rate, 7% at present in our pension plan) diminishes steadily towards zero as long as the participant's age increases. Just suppose that you promise to pay a man $1000 per month as long as he lives. It is qualitatively obvious that it is a lot more valuable and expensive a promise if he is 20 years old than if he is 99. (This is true despite the fact that a precise assessment of its value may require the computational expertise of an actuary equipped with an appropriate mortality or life expectancy table.) In the same way a pension system's promise to pay you a certain annual amount until you die has a cash-now value which diminishes steadily as your age increases.

This fact about the value of a promised stream of pension payments tends to undercut the common psychological expectation that, as one ages and his contributions to a retirement system accumulate, the resulting pension ought to be growing in value proportionately. In fact at a great enough retirement age, the Present Value of any pension must fall towards zero, as the remaining time over which it will be paid dwindles towards zero.

Given that the Present Value of the Maximum Pension (M) defines the actuarial value of the pension, and that the Present Value of the adjusted pension plus that of any added benefit (to a beneficiary) must be the same as the Present Value of the Maximum Pension, how could the System arrange this for the alternative payout options offered to a given individual?

First: Calculate the Present Values (V) of both the added benefit and of the Maximum Pension M upon retirement. Second: Reduce M by an Option Factor, F, chosen to make the sum of the Present Value of the reduced pension and the Present Value of the added benefit equal to the Present Value of the Maximum Pension. Stated in other words: the System creates a hypothetical "insurance policy" which provides the added benefit, computes an actuarially-fair annual "premium cost" for that policy, and reduces each of the annual pension payments by an amount whose Present Value is equal to the premium cost of the policy.

In this context, we can see why the Option #1 reduction factor, F₁, diminishes steadily as the retirement age increases, as it in fact does in Table 1. Note first that the fair premium cost of ensuring the return of the Present Value of the pension as a fraction of V itself must increase with retirement age, since an early death (i.e., before V has been paid out), which triggers the added benefit, becomes statistically more probable as the retirement age increases and the remaining life expectancy decreases. In addition, the expected number of pension payments, from which the premium cost must be subtracted, is diminishing as the retirement age increases. To meet this increasing premium cost per pension payment, the Option #1 factor must decrease as the retirement age increases, as it does in Table 1.

For the dual-life options, similar reasoning applies: the greater the retirement age, the greater the probability that the retiree will die before the beneficiary, thus triggering the added cost of the survivor's benefit. Since all of the payments in any of the dual-life options are proportional to the Maximum Pension amount, their Present Values at retirement are proportional to the Present Value of the pension at retirement (i.e. to the V of the Maximum Pension). Then as the retirement age increases, the increasing probability of triggering the benefit increases the premium cost for the benefit, while the diminishing life expectancy decreases the expected number of pension payments from, which it must be recovered. The result is that the Option Factor for each of the 6 options decreases as retirement age increases.

Thus we find that the decrease of all the Option Factors with increasing retirement age flows directly out of the requirement that all of the alternative options must have the same Present Value at retirement. Fairness itself dictates what may seem intuitively to be an unfair result!

In summary, at the qualitative level, the Retirement System may be surprising and/or disappointing, but it is not irrational. And it surely would be less surprising/disappointing if the Maryland State Retirement Agency would accept as one of its responsibilities the obligation to explain, clearly and completely, exactly how your pension is calculated.

This discussion has been a factual and qualitative one, addressing what the system offers and whether a factor should be expected to go up or down with a change in a given variable, but sidestepping the quantitative question of "How much? That would require, among other things, looking at the mortality tables used to calculate the Option Factors and comparing the "premium costs" of our system with those calculated independently using the same principles but different mortality tables. For now we attempt only to explain the practical consequences of the system we have.

We thank the following for valuable advice and criticism: George Callcott, Sherylynn Matesky, J. Howard Pleines, Eric Slud, Francis Stack, Lydia Vogler.