Valuing Your Pension Benefits and the Asset Allocation Implications

    by William W. Jennings

    Valuing Your Pension Benefits And The Asset Allocation Implications Splash image

    A couple is approaching retirement. Two investment questions are foremost in their minds:

    • First, what should their asset allocation be—that is, what portion of their family portfolio should be allocated to cash, bonds, and stocks? Most professionals agree that the choice of asset allocation is an investor’s most important decision.

    • Second, do they have sufficient resources to meet their retirement income needs?

    You might expect that financial advisers consider the same resources when addressing these two questions. That is, the asset allocation should be based on a family portfolio that contains the same assets and resources that are used to consider its preparedness for retirement.

    Anyone who would expect such consistency would be wrong.

    The current professional standard is to include pension income, such as Social Security benefits, when addressing retirement preparedness, but to exclude the value of pension income from the family portfolio when addressing the asset-allocation decision.

    We join a growing group of commentators in arguing that this current standard is inconsistent. Pension income should “count” when addressing both questions.

    To be specific: Asset allocation should be based on the family’s extended portfolio that includes the present values of income from Social Security, military retirement, and defined-benefit pension plans. These pension values are essentially “bonds” in the family’s extended portfolio. And including these values will have dramatic investment implications. How do you value your pension benefits?

    In this article, we’ll tell you how to do just that—and we’ll discuss the investment implications of including pension benefits in your asset allocation.

    Valuing Pension Benefits

    Both pensions and high-quality bonds provide fixed payments that have a low risk of default. Most pensions pay a fixed dollar amount each month, although some make adjustments for inflation. Social Security makes payments that are fixed in real (inflation-adjusted) terms. In either case, the payments are fixed (in nominal or real terms) and relatively certain.

    But unlike a bond, pension benefits don’t have a stated current market value that you can simply look up and include in your asset allocation calculation. How, then, do you value pension income?

    If your pension benefits are a fixed dollar amount, a simple valuation method is relatively straightforward using an annuity table. You would simply multiply your current annual payment by the present value annuity factor that appears in Table 1.

    The annuity factor chosen should be the one that corresponds with:

    • The expected number of years the payments will last—for instance, if the payments are to last for your life, use your current average life expectancy, and

    • A discount interest rate equal to the current rate paid by a Treasury bond with a maturity equal to the number of years the payments will last.
    TABLE 1. Estimating the Value of a Stream of Fixed Pension Payments
    No. of Yrs. Annuity Factor
    2% 3% 3.50% 4% 5% 6% 7%
    5 4.71 4.58 4.52 4.45 4.33 4.21 4.1
    10 8.98 8.53 8.32 8.11 7.72 7.36 7.02
    15 12.85 11.94 11.52 11.12 10.38 9.71 9.11
    20 16.35 14.88 14.21 13.59 12.46 11.47 10.59
    25 19.52 17.41 16.48 15.62 14.09 12.78 11.65
    30 22.4 19.6 18.39 17.29 15.37 13.76 12.41

    Average Life Expectancies
    Age Female Male
    40 43.2 40.3
    50 33.6 30.8
    60 24.4 21.7
    65 20.1 17.6
    70 16.2 13.9
    75 12.7 10.6
    80 9.7 7.8
    85 7.1 5.5

    For example, a 75-year-old male has an average life expectancy of 10.6 years. Suppose he receives pension payments that total $6,000 annually. If the yield on a 10-year Treasury bond is 5%, the corresponding annuity factor for a 10-year annuity from Table 1 is 7.72. Multiplying the $6,000 annual payment by eight (to round up the annuity factor since life expectancy is 10.6 years) produces an estimated present value of about $48,000.

    If you are not yet receiving benefits, you must discount your age 65 benefits to a present value:

    PV = (Benefits ÷ (1 + Rate)No. Yrs to 65

    using the current Treasury bond rate, and the number of years until you reach age 65 for the exponential.

    For example, suppose a 60-year-old female expects to begin receiving $15,000 annually in benefits at age 65. Based on a 24.4-year average life expectancy, she will receive this amount for 19.4 years beginning in five years. If the 25-year Treasury yield is 5%, the present value at age 65 is about $186,900, [$15,000 × 12.46], where 12.46 comes from Table 1 for 5% and 20 years. The present value at age 60 is about $146,441 [$186,900 ÷ (1.05)5].

    Estimating the value of Social Security retirement benefits is a bit more complicated, and so we’ll have to go into that in a bit more detail.

    Valuing SS benefits: Singles

    This section presents an approach that estimates the present value of expected Social Security retirement benefits for singles. It assumes the beneficiary has an average life expectancy and will begin receiving benefits at age 65. Annual benefits are simply monthly benefits times 12.

    If you have yet to begin receiving benefits, you must use an estimate of your Social Security benefits at age 65. Social Security provides you with an estimate of your benefits each year in an annual statement sent to you. These statements will tell you your benefits at your Full Retirement Age, which varies depending on the year you were born. To use the table here, you must use a benefits figure that corresponds to age 65, which may require an adjustment to your Full Retirement Benefits figure. Table 2 allows you to make the adjustment; it shows the fraction of Full Retirement Benefits you would receive at age 65 based on your year of birth. [For more on this, see our article “Planning for Retirement: What to Expect From Social Security,” in the February 2002 AAII Journal, available at]

    Like the pension example above, you multiply your annual benefits by an annuity factor, in this case the annuity factor that appears in Table 3, based on your life expectancy and an appropriate discount rate (more on this below). The resulting figure will be an estimate of the value of your Social Security benefits, assuming payments will begin at age 65 if they have not yet begun, and assuming you have an average life expectancy.

    As an example, let’s look at George, who is 70 years old and has an average life expectancy. His annual benefits are $13,200 (12 times his monthly benefits of $1,100). Assuming the discount interest rate is 3.5%, the multiple from Table 3 is 10.79. The value of his Social Security benefits is $13,200 × 10.79 or about $142,000.

    (For the mathematically inclined, the sidebar “An Alternative Method” on page 25 presents another model that is useful for single individuals with shorter- or longer-than-average life expectancies.)

    TABLE 2. Fraction of Full Retirement Age Benefits if Benefits Begin at Age 65
    Year of
    Fraction of
    FRA Benefits
    At Age 65
    1937 or before 1
    1938 0.989
    1939 0.978
    1940 0.967
    1941 0.956
    1942 0.944
    1943-54 0.933
    1955 0.922
    1956 0.911
    1957 0.9
    1958 0.889
    1959 0.878
    1960 or later 0.867

    Why the difference between Table 1 and Table 3?

    Table 3.
    Estimating the Value of
    Social Security Benefits:
    Annuity Factors for Singles
    The major difference is that Social Security adjusts payments annually to reflect inflation. Consequently, the Table 3 factors discount the constant annual real benefits at today’s long-term real yield on inflation-adjusted U.S. Treasuries—TIPS (Treasury Inflation-Protected Securities). Like Social Security benefits, payments from TIPS are linked to consumer price inflation, and therefore TIPS yields (for your life expectancy) are the appropriate rate for you to use in valuing Social Security benefits.

    Potential Problems

    There are at least four potential problems that may apply to the way we have estimated Social Security benefits that you should be aware of if you use this approach:

    • If benefits have not begun, it assumes benefits begin at age 65;

    • It assumes there are no special circumstances that would reduce Social Security benefit payments (for instance, offsets due to other government retirement benefit payments);

    • The value of projected benefits are based, in part, on future earnings; and

    • It assumes average life expectancy.
    The first potential problem is minor. In other studies, we have found that, for singles and couples with average life expectancy, the present value of projected benefits is approximately the same whether benefits begin at 62, 63, 64, or any age through 70.

    The second potential problem can be handled by adjusting for any offsets for any individual to whom this may apply—people who work in jobs not covered by Social Security, who will be affected by the Windfall Elimination Provision and Government Pension Offset. [For more on this, see our previously mentioned February 2002 article.]

    The third potential problem is more of a concern, especially for people under age 50. The annual Your Social Security Statement that all individuals receive projects benefits assuming earnings will continue at the current real level until benefits begin. For someone age 50, this Statement may project benefits at Full Retirement Age of $1,200, while actual benefits might be $1,100 if you were to quit work today. Even if you continue to work, conservatism suggests that Social Security’s current value should not reflect the additional retirement benefits from future work. For people over 50, there probably is little difference between their initial benefits if they quit work early and their initial benefits if they continue to work. The bias is stronger for younger people, and if you are below age 50 you may want to adjust your estimated benefits to reflect this.

    The fourth and most important problem is that the model assumes average life expectancy. The value of Social Security is lower for individuals with shorter-than-average life expectancies and higher for individuals with longer-than-average life expectancies. Suppose Beth, for example, is age 60, exercises regularly, refrains from smoking, and comes from a line of long-lived ancestors. She might assume a 30-year life expectancy, which exceeds her average. If she will begin benefits at age 65, she could estimate the value of Social Security as the present value of her annual benefits beginning in five years and continuing for 25 years.

    Valuing SS: Couples

    Before we present our approach for valuing Social Security benefits to a couple, we must first describe spousal and survivor’s benefits [also discussed in the February 2002 article]. A spouse is entitled to the larger of 100% of benefits based on his or her earnings record, or up to 50% of the spouse’s benefits.

    But consider a couple’s choices if both spouses have an earnings record. The lower-earning spouse can receive benefits based on his or her own earnings record, with Full Retirement Benefits that start depending on the year in which they were born.

    Alternatively, he or she may receive spousal benefits based on the spouse’s earnings record. But the rules for Full Retirement Age spousal benefits are more complex. Spousal benefits are reduced by 25/36% for each month they are begun before Full Retirement Age. In addition, a spouse cannot receive spousal benefits unless the primary earner receives benefits. Finally, spousal benefits do not reflect Delayed Retirement Credits—if benefits are delayed, the primary earner receives a credit, while the spouse does not.

    Survivor’s benefits follow different rules. Survivor’s benefits are the larger of 100% of the primary worker’s monthly benefits, or 100% of benefits based on the surviving spouse’s earnings record. Unlike spousal benefits, survivor’s benefits reflect Delayed Retirement Credits.

    Table 4 estimates the present value of Social Security benefits as the product of an annuity factor and annual benefits using the higher earner’s benefits. The annuity factor includes an adjustment for the lower earner’s benefits:

    Annual Benefits × Annuity Factor = Present Value of SS benefits

    TABLE 4. Estimating Social Security Benefits: Annuity Factors for Married Couples—Husband and Wife Same Age
    Age 2.50% 3% 3.50%
    Annuity Factors for:
    30 7.32 4.09 5.84 3.32 4.68 2.7
    35 8.29 4.65 6.78 3.86 5.56 3.22
    40 9.39 5.3 7.87 4.51 6.62 3.85
    45 10.65 6.05 9.15 5.28 7.88 4.62
    50 12.08 6.96 10.64 6.22 9.38 5.57
    55 13.74 8.06 12.39 7.38 11.19 6.77
    60 15.67 9.5 14.47 8.92 13.4 8.39
    65 17.98 11.63 17.01 11.19 16.13 10.78
    70 15.48 9.34 14.76 9.05 14.1 8.77
    75 12.93 7.25 12.43 7.07 11.96 6.9
    80 10.44 5.43 10.11 5.33 9.8 5.23
    85 8.15 3.93 7.94 3.88 7.74 3.82
    90 6.28 2.85 6.15 2.82 6.03 2.79

    The process is similar to the one used for singles, and once again annual benefits are assumed to be at age 65. That means you may need to adjust the higher earner’s Full Retirement Age benefits to determine age 65 benefits by multiplying by the appropriate fraction from Table 2.

    The appropriate annuity factor to use is the sum of two figures in Table 4: a factor for the higher earner’s age 65 benefits, plus a factor for the lower earner’s benefits. However, the factor for the lower earner’s benefits must be adjusted by the ratio of the lower earner’s benefits to the higher earner’s benefits [i.e. lower benefits/higher benefits = couple’s ratio]. If this ratio is below 0.50, you should use 50% to reflect the 50% minimum for spousal benefits.

    This may seem a bit complicated, so let’s see how it works.

    As an example, consider Mark and Farrah. They are both 60 years old, and their Full Retirement Age is 66. However, they will begin receiving benefits at age 65, so they will receive only 93.3% of their Full Retirement Age benefits (from Table 2).

    They recently received their annual Your Social Security Statements. Mark’s benefit at Full Retirement Age is $1,200; Farrah’s is $1,000.

    Mark’s age 65 annual benefits would be:

    (93.3% × $1,200) × 12 = $13,435.

    Next, let’s determine the couple’s ratio: divide the lower earner’s Full Retirement Age benefits by the higher earner’s benefits:

    $1,000 ÷ $1,200 = 0.833.

    Since this is higher than 0.50 (the minimum 50% spousal benefits level), this is the couple’s ratio that will be used.

    The annuity factor is determined using Table 4. For a 60-year-old same-age couple and a 3.5% discount rate, the annuity factor for the higher earner is 13.4; for the lower earner the annuity factor is 8.39, multiplied by the couple’s ratio of 0.833, and then added to the higher earner factor for a total annuity factor of 20.39. The present value of Social Security benefits for this couple is:

    $13,435 × [13.4 + (0.833 × 8.39)] = $274,000.

    Table 4 assumes that:

    1. Each spouse has an average life expectancy, and
    2. The spouses are the same age.
    If they are in poor health or have a history of short-lived ancestors, then the factors will overstate the value to this couple, and vice versa.

    What if the husband and wife are different ages? Suppose he is 70 and she is 65.

    The appropriate factor is between the multiples for same-age couples at 65 and 70, but it is closer to the multiple at the wife’s age—she will probably live longer because she is younger and because women tend to live longer.

    Couples should adjust the factors from Table 4 accordingly. Even though the adjusted factor will only provide a rough estimate of Social Security’s value, it is better to include an estimate of its value than to ignore it and thus implicitly assume that its value is zero.

    Social Security Changes

    Based on current projections and absent changes in the system, the Social Security Administration anticipates huge Social Security deficits when the bulk of baby boomers retire. Undoubtedly, there will be changes in the system.

    We suspect there will be little, if any, benefit reduction for current retirees or those near retirement. The tables here, therefore, should prove most reliable for these groups.

    For younger individuals, the tables’ estimates may be too high. However, neither the expectation of changes nor the many assumptions embedded in the tables changes the fundamental reality that Social Security has value. Since current practice typically ignores the value of retirement income when calculating a family’s asset mix, it implicitly assumes the value is zero. The tables provide better estimates of the value of Social Security than the default estimate of zero.

    TABLE 5. Two Views of Mary's Asset Allocation
    Resource &
    Savings Vehicle
    Stocks in 401(k) $300,000 $300,000
    Bonds (CDs) in Taxable Acct $200,000 $200,000
    Social Security $0 $253,000
    Teachers’ Retirement $0 $253,000
    Total $500,000 $1,006,000
    Asset Allocation
      60% Stock 30% Stock
    40% Bonds 70% Bonds

    The Extended Portfolio

    To show how the valuation of retirement benefits will impact asset allocation decisions, let’s take a look at Mary, a 65-year-old with $500,000 in financial assets. She has $300,000 in stocks held in a 401(k) and $200,000 in bank CDs. In addition, she receives $1,500 per month in retirement income from Social Security and another $1,500 per month from teachers’ retirement.

    Table 5 presents two views of her current asset allocation. The traditional family portfolio contains only financial assets and does not adjust for taxes. According to this view, she currently has $300,000 in stocks, $200,000 in bonds, and thus a 60% stock exposure.Table 5 also presents an extended portfolio that contains the present value of pension income.

    From Table 3, the value of her Social Security benefits is about $253,000 or [($1,500 × 12) × 14.06], where 14.06 is the annuity factor for a single, 65-year-old single female, using a 3.5% TIPS yield for the discount rate. Her teacher’s retirement pension is calculated in the same way, since she taught in a state that, like Social Security, adjusts payments annually with inflation. The value of $1,500 per month from teachers’ retirement is also $253,000.

    The extended family portfolio contains $1,006,000 in assets and has about a 30% stock exposure, $300,000 ÷ $1,006,000.

    The two views present quite a difference in allocations!

    Investment Implications

    The above example illustrates many of the major lessons and investment implications:

    • Pension incomes—whether from Social Security, military retirement, or defined-benefit plans—are valuable assets. Clearly, pension income affects retirement preparedness. We believe the present value of pension income should be included in the family’s extended portfolio.

    • The value of pension income is essentially a bond in the family’s extended portfolio. Therefore, families with pension income have a smaller stock allocation in their extended portfolio than the stock allocation in their traditional portfolio. For example, Mary has a 30% stock allocation in her extended portfolio, while she has a 60% stock allocation in her traditional portfolio. Families should manage their extended portfolio. If they have been managing their traditional portfolio then they have a more conservative portfolio than they think they have and should have. Everything else the same, because pension income is essentially a bond, families with substantial pension income can invest a larger portion of their traditional financial assets in stocks. For example, Mary can invest a larger portion of her traditional financial portfolio in stocks than an otherwise identical person who does not receive a pension. This statement applies to families that are in retirement and to those that have not yet reached retirement.

    • There is not a minimum level of financial assets needed in order to satisfy a given level of retirement income. One real-world example brings home this point. Both members of a late-40s couple recently retired with high ranks from the Army. Despite a modest level of financial assets, they were able to retire. Anyone who ignored the values of their pension incomes missed the overwhelmingly largest assets in the family’s extended portfolio.

    • At the death of the first spouse, the surviving spouse should rebalance the portfolio. Suppose Sandy and Russ are 70 years old and receive, respectively, $1,300 and $900 from Social Security based on their earnings record. And further suppose Sandy dies unexpectedly. Several things may change. First, the expected value of Social Security benefits falls to about $168,000 ($1,300 × 12 × 10.79). Second, the family portfolio would lose the value of any other pension income she may have, such as income from a company pension. Third, life insurance proceeds, if any, would increase the size of the family portfolio. Even if Russ does not change investment goals or target asset allocation, the portfolio will change. The first two changes listed above would decrease the amount of “bonds” in the portfolio. The third would increase the cash in the portfolio. The impact on the stock allocation depends upon the relative sizes of the decrease in pension values and the increase in cash from life insurance. If the loss of pension value is larger (and his target asset allocation remains the same), Russ will need to sell stocks and buy bonds. If the cash from life insurance is larger (and his target asset allocation remains the same), he will need to use the insurance funds to buy additional stocks.

    • Return to the prior example, except assume Sandy is diagnosed with terminal cancer that shortens her life expectancy to one or two years. The portfolio implications are similar. The value of Social Security falls. The value of her other pension income may fall. They should rebalance their current portfolio to reflect the lower pension values and, if applicable, anticipated insurance proceeds.

    • The decrease in Social Security’s value from a sharp decline in life expectancy is different for singles and couples. Since Social Security provides no survivorship benefits for singles, its value to single individuals falls dramatically. Since Social Security provides survivorship benefits for surviving spouses, its value to a couple falls by less. If you are single, you may have to rebalance your portfolio more than a similarly situated couple as life expectancies change.

    • Unlike Social Security, most defined-benefit plans allow a payment option that provides 100% benefits to the surviving spouse. For example, suppose a husband retired from a company and he took a 100% joint life payout on the company’s pension. If he becomes terminally ill, the value of this pension will decrease modestly since this payout option will provide 100% benefits to his wife until her death. Thus, a change in life expectancy may require less rebalancing than you would otherwise expect.

    • Since the value of your Social Security and other retirement benefits are based on life expectancies, you will need to do some rebalancing each year as your life expectancy changes. But this may not be as dramatic as you may think. Unlike our assumptions earlier where life expectancy changed dramatically due to, for instance, a change in health, the value of pension income declines relatively slowly for those with average life expectancies. This implication applies to singles and couples who do not have a sharp decline in life expectancy but rather remain healthy long into their retirement. For example, consider a 65-year-old single female who has an average life expectancy of about 20 years. Assuming a 3.5% discount rate, the multiples and her life expectancies are:

      Age Multiple Life
      65 14.06 20.1 years
      75 10.09 12.7 years
      85 6.37 7.1 years

      As she ages from 65 to 75—half her original life expectancy—the value of the pension falls 28%. As she ages from 65 to 85—her original life expectancy—the value falls 55%. Two factors account for this slow decrease in pension value. First, each year she survives, her remaining life expectancy falls less than one year. Second, since near-term payments are more valuable than distant payments, the value of the pension falls slowly. For example, at age 65, the multiple is approximately the value of $1 per year for 20 years. At age 66, it is approximately the value of $1 per year for 19 years. The decrease in value is the value of the most distant payment, which is the least valuable payment.

    The bottom line is: Pension income is a valuable asset. When addressing retirement preparedness and when calculating the asset allocation, pensions’ values should be included as part of the family’s extended portfolio, and the family needs to carefully manage and monitor this extended portfolio.

       Details of Our Approach—and An Alternative Method
    The model used to derive the Social Security valuations estimates the present value of expected cash flows. Each year’s expected cash flow is the product of: probability of being alive × cash flow if alive. [ Calculation Details ]

    Single individuals can estimate the present value of Social Security benefits similar to the method used for estimating fixed pension benefits presented in Table 1, but using the TIPS [Treasury Inflation-Protected Securities] yield as the appropriate discount interest rate. Or, you can use a financial calculator to determine the present value of an annuity, again using your life expectancy for the number of years and the TIPS yield as the discount rate. Although it is not quite as accurate as our approach for those with average life expectancies, it has the advantage of estimating Social Security’s value for single individuals with shorter- or longer-than-average life expectancies.

    Unfortunately, a couple cannot estimate the value of Social Security benefits in this same manner. Even though a couple has a joint life expectancy, the size of each year’s Social Security payment depends upon whether one or both partners are alive. That’s why our Table 5 method uses expected cash flows, based on the assumptions described in the article.

    William W. Jennings, CFA, is deputy head for management education at the U.S. Air Force Academy. William Reichenstein, CFA, holds the Pat and Thomas R. Powers Chair in Investment Management at Baylor University, Waco, Texas. The opinions expressed are those of the authors and are not necessarily those of USAFA, USAF, or any other federal agency. The authors thank Steve Carney, Steve Fraser, and Dave King for their help. The authors may be reached at and

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