• Portfolio Strategies
  • A Pseudo-Life Annuity: Guaranteed Annual Income for 35 Years

    by Robert Muksian

    A Pseudo Life Annuity: Guaranteed Annual Income For 35 Years Splash image

    A portfolio allocation mix of 60% stocks and 40% bonds combined with an annual withdrawal equal to 4% of the initial portfolio amount and increased annually by an inflation rate is recommended to retirees by practitioners and scholars.

    This strategy is based on research by Larry Bierwirth and William Bengen as a means of maintaining constant dollars of income during the remainder of one’s lifetime, or 30 to 35 years in retirement. The 4% initial withdrawal rate in particular has become the benchmark for retirees.

    Scholarly articles on this topic usually include a comprehensive literature search directing the reader to all the variations of asset mixes, modified withdrawal rates, or the combination of “safe savings rates” and “safe withdrawal rates.” The “drawback” to all of the research is that there will always be risk associated with any funds invested in stocks, and therefore no equity-based strategy can offer a guarantee of extracting the full amount of the initial retirement portfolio before death.

    As an alternative to the equity-based strategies, this article shows what an individual investor who had a $1 million portfolio on March 19, 2012, could have invested the money in to have virtually a 100% probability of not outliving his money and of leaving a legacy for his heirs at death. (Investors with lesser wealth can prorate the amounts as a percent of $1 million.)

    The Concept

    A bond is an investment vehicle that provides a guaranteed stream of interest income during a stated term. Bonds also offer additional cash equal to the face value of the bond at maturity, unless the issuer defaults. A bond is an “IOU” that is an interest-only debt until a maturity date, at which time the principal is repaid. The bond is comprised of two elements—the principal (“corpus”) and the interest payment mechanism (“coupons”). The cost of the bond is the sum of the present values of these two elements. Typical bonds issued in the U.S. pay interest semiannually; therefore, there are two coupons for each year of the bond’s duration.

    A bond’s yield, which is the coupon (interest) rate divided by the bond’s current price, often differs from the actual coupon rate. The yield can be higher than the interest rate—signaling that the bond is trading at a discount—or the yield can be below the interest rate—signaling the bond is trading at a premium. Unlike with equities, the stated principal, coupon and yield of a bond give an investor a specific dollar amount of return—assuming, of course, that the bond issuer does not default.

    Given this backdrop, suppose you had accumulated $100,000 in stocks and now wished to secure an annual withdrawal of $20,000 for each of the next five years. To avoid any market volatility that could affect this stream of income, you decide that a conversion from stocks to bonds is a viable alternative. Also suppose on that the date of conversion, bonds maturing in one, two, three, four and five years are available with 3% annual coupons and 3.5% yields to maturity after transaction costs. Based on the implied discounts, the total cost would be $98,603.25. This conversion would leave $1,396.75 to invest elsewhere. Then, during each year you would receive $600 in coupon interest (3% of the bond’s $20,000 face value) for each bond that has yet to mature. You would also receive the $20,000 face value for the bonds that matured at the end of each year.

    Suppose, however, that on the conversion date, the yield rate for each of the bonds was 2.5% instead. This conversion would be at a premium, with a total assumed cost of $101,425.04. Obviously, your $100,000 would be insufficient by $1,425.04 to fulfill your goal; an alternative is needed.

    The foregoing approach to portfolio security is referred to as laddering bonds. It is a process that can be used in an accumulation phase also, so as not to be locked into “current” yields for long durations, especially if prevailing interest rates are low and you think future yields will increase. However, there is always reinvestment risk when each bond matures; the future yield may be less than the maturing yield. Although bond laddering may be used for both accumulation and depletion of funds, this article is restricted to the discussion of depletion of funds.

    Zero-Coupon Bonds

    In the early 1960s, the idea of selling each part of the bond separately was introduced. That is, the corpus and coupons were separated. The corpus was sold as the principal and each coupon was sold as a “smaller” principal. These investments are stripped coupon bonds, often referred to as zero-coupon bonds or Separate Trading of Registered Interest and Principal Securities (STRIPS). However, because the Internal Revenue Service negated an initial tax advantage for STRIPS, the concept lost popularity for investments other than qualified retirement funds such as IRA accounts.

    A $20,000 zero-coupon bond maturing in five years with a 3.5% yield would cost $16,814.57 and one with a 2.5% yield would cost $17,663.62. Investing under either yield rate will provide proceeds (annual income) of $20,000 in five years. The purchase at either yield rate leaves a residual that could be at risk if invested in equities ($3,185.43 with the higher yield and $2,336.38 with the lower yield). Since the goal is to reduce risk to zero, we would want to invest the full $20,000 in bonds. Thirty-year U.S. Treasury STRIPS could be used, since they can be purchased in increments of $100. This enables the purchase of bonds with cumulative face values of $23,700 and $22,600, respectively, and these amounts could be the income received in five years (fully invested within $88.89 and $45.42, respectively, of the starting portfolio amount).

    The accepted absolute guarantee of that income is a bond issued by a stable government, and the “gold standard” has been the U.S. Treasury. The investor could look forward for any number of years, but this article is limited to 35 years. Using the Social Security earliest elective retirement age of 62, the funds would last to age 97. The probability of a 62-year-old male or female living to this age is about 4% or 9%, respectively.

    As of this writing, the Market Data Center of The Wall Street Journal website showed tables of Treasury bonds (Stripped Principal and Stripped Coupon) with maturity dates on the 15th of February, May, August, and November, the auction dates of 30-year Treasury bonds. The May 15 date was selected, and the asked price (% of face value) and asked yield (%) were extracted and are shown in Table 1. Since securities are sold at the “bid” and bought at the “ask,” the cost to the investor will include transaction fees charged by the broker. As a simplified test of the practicality of this analysis, I had three bonds priced on March 19, 2012. The bid price for a May 15, 2012, bond was 99.984% of face value. The bid price for a May 15, 2026, bond was 63.189% of face value. The bid price for a May 15, 2041, bond was 34.099% of face value. This analysis assumes that the investor pays the “asked price” shown in Table 1, not the bid prices above.

    Maturity Asked Price
    (% of
    Face Value)
    2012 May 15 99.987 0.09
    2013 May 15 99.780 0.19
    2014 May 15 99.098 0.42
    2015 May 15 97.918 0.67
    2016 May 15 95.797 1.04
    2017 May 15 93.413 1.33
    2018 May 15 90.589 1.61
    2019 May 15 87.409 1.89
    2020 May 15 83.871 2.17
    2021 May 15 80.554 2.38
    2022 May 15 77.208 2.56
    2023 May 15 73.761 2.75
    2024 May 15 70.244 2.93
    2025 May 15 66.659 3.11
    2026 May 15 63.277 3.26
    2027 May 15 25.000 3.36
    2028 May 15 57.710 3.43
    2029 May 15 55.498 3.46
    2030 May 15 53.292 3.50
    2031 May 15 51.042 3.54
    2032 May 15 48.940 3.58
    2033 May 15 46.942 3.61
    2034 May 15 45.047 3.63
    2035 May 15 43.282 3.65
    2036 May 15 41.646 3.66
    2037 May 15 40.014 3.67
    2038 May 15 38.385 3.69
    2039 May 15 36.907 3.70
    2040 May 15 35.577 3.70
    2041 May 15 34.196 3.71
    Source: J.P. Morgan Pricing Direct Inc. via www.sstbond.com.

    Since STRIPS are only available for 30-year maturities, the years 31 through 35 must be planned for at the initial purchase. The term “bond” in the following is to be interpreted as a sufficient number of multiples of $100 to achieve the amount to be purchased.

    In addition to the 30 bonds purchased for the annual income each year, one “extreme” option is to purchase five additional bonds on the initial date (March 19, 2012, for this analysis), to be reinvested in each of the next five years as follows. Assuming there will be a bond auction on May 15, 2012, you could purchase one bond that will mature in 2042 and purchase four bonds that will mature in 2013. In 2013 you could purchase one bond that will mature in 2043 and three that will mature in 2014. Continuing this process until May 15, 2016, there will be one excess bond to purchase for May 15, 2046. The negative aspects of this process are that the short-term yields are low and that there is a high cost to purchase the excess bonds in each of the first five years.

    The other “extreme” option is to purchase one bond maturing in each of the first 30 years and five additional bonds maturing in year 30 (2041) and then, assuming survival until then, purchase one bond for each of the following five years at that time. This alternative will have a smaller total initial cost and would be able to capture any increase in yields that might be available in 30 years.

    Within these extremes, other scenarios are available depending upon the investor’s judgment of reinvestment rate risk. For example, the five additional bonds could be purchased to mature in year 2016, or any other year in order to purchase five bonds for years 31 through 35. Another scenario: On May 15, 2012, purchase two bonds to mature in year 2016 (one for income in 2016 and one to purchase a 2042 maturity), two bonds to mature year 2021 (one for income in 2021 and one to purchase a 2043 maturity) and the same for 2026, 2031 and 2036.

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    Examples of Pseudo-Annuities

    To show examples of how you could build your own pseudo-annuity, I have created examples using STRIPS, laddered for 30 years, to provide 35 years of fixed maturity values.

    The ideal annual income is stipulated to be 4% of the initial portfolio and will be achieved by purchasing the principal (bond corpus) part of the STRIPS, which will be referred to as the bond. The number of bonds may be constant each year. The initial portfolio is $1 million. Other annual amounts would be prorated against this value. Any residual cash from the purchase is assumed to earn 4% per year over the 30-year period.

    The reference to each year implies a fiscal year from May 15 to May 14 the following year, and all purchases occurred on March 19, 2012.

    Plan A: Purchase Bonds for Years 2042–2046

    On March 19, 2012, purchase one bond for each of the years 2012 through 2041 and purchase five bonds to mature in 2013. In May 2013, use the income from one maturing bond to purchase a 2042 maturity, and use the income from four maturing bonds to purchase bonds maturing in 2014. Similarly, in 2014, the income from one maturing bond would be used to purchase a bond maturing in 2043, and the income from three maturing bonds would be used to purchase bonds maturing in 2015. In 2015, the income from one maturing bond would be used to purchase a bond to mature in 2044, and the income from two maturing bonds would be used to purchase two bonds to mature in 2016. In 2016, the income from one maturing bond would be used to purchase a bond maturing in 2045, and the income from the remaining maturing bond would be used to purchase a bond maturing in 2017. The income from this final bond would be used in 2017 to purchase a bond maturing in 2046.

    This plan would require the highest cost. The total cost on March 19 for the six bonds would be 5.99922 (6 × 99.987%, see Table 1) times the face value of the bonds. Using 4% of the $1 million, the six $40,000 bonds would cost $239,968, almost 24% of the fund, and the total cost would be $987,352. Although Plan A is a possible option, there are better plans that could be used for the 35 years of income.

    Plan B: Purchase Two Bonds Maturing at Five-Year Intervals

    This option involves having a fixed annual income from maturing bonds of $40,000 per year beginning on May 15, 2012, and terminating on May 15, 2046. Bonds worth $80,000 will be purchased to mature on May 15, 2016, 2021, 2026, 2031, and 2036. Forty thousand dollars will be used for income in each of those years, and $40,000 will be used to purchase bonds maturing in 2042, 2043, 2044, 2045 and 2046, respectively.

    The yield rates listed in Table 2 indicate that this can be accomplished at a purchase cost of $920,304, leaving residual cash of $79,696. This residual may be used to supplement the bond income with annual withdrawals and may be increased to offset, somewhat, the effects of inflation. Alternatively, it can be left to accumulate as a legacy. The withdrawals would begin with $3,045 in 2012, increased by 3% per year, and end with $7,177 in 2041 if the rate of return is 4%.

    Table 2 shows the results of this option, with a possible legacy amount of $258,483 on May 15, 2042, if the residual cash is not depleted by annual withdrawals and is not subject to required minimum distributions. However, if placed in equities, market volatility could affect the actual annual cash amount or the legacy amount.

    2012 May 15 0.09 40,000 39,995 920,304 3,045 76,650 43,045
    2016 May 15 1.04 80,000 76,638   3,428 75,759 83,428
    2021 May 15 2.38 80,000 64,443   3,974 71,915 83,974
    2026 May 15 3.26 80,000 50,622   4,606 64,012 84,606
    2031 May 15 3.54 80,000 40,834   5,340 50,656 85,340
    2036 May 15 3.66 80,000 33,317   6,191 30,071 86,191
    2041 May 15 3.71 40,000 13,678   7,177 0 47,177
    Growth of Residual Cash—May 15, 2042 258,483  

    Plan C: Purchase Six Bonds Maturing at Year 30

    Rather than purchase two bonds to mature every five years, another alternative would be to purchase six bonds to mature in year 30, on May 15, 2041. One of the bonds would be the income for the year, and the remaining five bonds would be used to purchase bonds maturing in 2042 through 2046.

    This option would provide $40,000 in annual income for 30 years. On the maturity date of the 30th anniversary, $200,000 from the additional maturing bonds would become available to purchase five bonds to mature in 2042 through 2046. The total cost of this option would be $855,770 with residual cash of $144,230. Assuming a 4% return on investment, this cash could supply additional annual income, beginning with $5,511 and increased by 3% per year to a final amount of $12,988 to mitigate the effects of inflation. If there are previously taxed investments that could deliver the same results, the cash could be left as a legacy amount of $467,795 on May 15, 2042, subject to required minimum distributions. As with Plan B, if left in equities, market volatility could affect these values.

    The results of this option are shown in Table 3.

    2012 May 15 0.09 40,000 39,995 855,770 5,511 138,719 45,511
    2022 May 15 2.56 40,000 30,883   7,407 127,948 47,407
    2032 May 15 3.58 40,000 19,576   9,954 85,389 49,954
    2041 May 15 3.71 40,000 13,678   12,988 0 52,988
    2041 May 15 3.71 200,000 68,392   0 0 200,000
    Growth of Residual Cash—May 15, 2042 467,795  

    The Decision

    In order to facilitate a decision, Table 4 provides a summary of the results of the three plans discussed here. Plan C provides the largest first year and final year annual cash flow. In addition, Plan C provides the largest possible legacy at the end of 30 years.

    Incorporating Life Expectancy Into the Plans

    Any stream of annual income is defined as an annuity, and there are two broad categories of annuities—life and certain (“fixed term”). Life annuities are usually obtained from insurance companies, but if an individual planned on creating his or her own life annuity, he or she would have to plan for a term that is to the end of a life table—to age 115 or 120—just as an insurance company does, with an accompanying reduction of the annual amount. The probability of survival to either of these ages can be considered to be 0%.

      Annual Income
    2012 – 2041
    Annual Cash
    First Year – Last Year
    Plan A 40,000 – 40,000 483 – 1,184 987,352 41,022
    Plan B 40,000 – 40,000 3,045 – 7,177 920,304 258,483
    Plan C 40,000 – 40,000 4,121 – 9,711 855,770 467,795

    A further problem would be that, because of the large number of bonds that would mature at 30 years, if the investor is still alive, the required minimum distribution RMD might necessitate a rather large withdrawal from the retirement fund. The term, 35 years, defines the stream of income as a pseudo-life annuity in that the number of payments is certain.

    Given a group of people at a given age, the life expectancy age is simply an indicator that a proportion of those people will die before reaching that age and the remainder will die after reaching that age. Then the selected term must extend beyond that age in the event that our investor is in the latter group. According to data from the U.S. Department of Health and Human Services 2004 U.S. Life Tables, life expectancies are shorter than the planned 35-year term for retirement ages of 55, 62, 66 or 70. For a person who will retire in 2012 at age 66, the probability of surviving 35 years is less than 2% for a male and less than 4% for a female—essentially 0%.

    There is a secondary consideration for laddered bonds in the withdrawal phase of retirement. If death occurs before 35 years, the remaining STRIPS would have to be distributed according to the rules for required minimum distributions (RMDs). This might necessitate the sale of STRIPS prior to maturity if there is no surviving spouse. The proceeds would depend upon the time to maturity and the yield rate at which the bond(s) would be sold. Those proceeds could be greater or less than the face value of the bonds.


    It is inconceivable that the U.S. government would ever default on its obligations and, consequently, it will always remain the safest of all investment venues. However, the trade-off for using U.S. Treasury STRIPS to guarantee 35 years of known annual income is that you gain stability but do not optimize returns. This trade-off is the price of the guarantee.

    For those investors who do not have inherent opposition to some volatility, having a guaranteed income equal to 4% of the initial portfolio each year plus a significant amount in a residual fund that could be exposed to equities could be achieved, as shown. The residual cash in all the plans is a “theoretical” amount in that transaction costs may reduce or deplete that cash.

    The transaction costs may necessitate the reduction of the maturity value of each STRIPS and the residual amounts of cash and or equities (perhaps not significantly), depending upon the purchase venue, such as Fidelity Investments or Wells Fargo Advisors. With the former, the investor would have to do all the calculations to ensure the best utilization of the money. With the latter, the adviser would determine all the purchases.

    This analysis shows that investors have several alternatives for guaranteeing acceptable, and known, retirement income for 35 years—essentially a pseudo-life annuity for those investors aged 55 and older.

    Click here for appendix with additional options for Plans B and C.

    Robert Muksian is a professor of mathematics at Bryant University in Smithfield, Rhode Island.


    David Wilson from MD posted over 4 years ago:

    I have an alternative that is a fraction of the complexity and is more predictable, conservative,stable, offers a higher return, flexibility, and protection on many levels.
    It is a whole life policy purposely structured for high cash value and retirement income. My plan, started atage 48, with a 1035 exchange of $54k and 8k annual premiums. It will provide in 20 yrs $378k of tax free cash with an annual dividend of $7500 and rising each year. Had I known and understood the power of this plan and started this 20 yrs ago, my premiums would have been halved, and the cash would easily be over $1 million with a death benefit twice that!
    One of the biggest benefits is the loan provision which provides for a "net zero" loan. I can borrow (4.7%) against the policy, not from it. Meaning, I am being paid interest and dividends on cash balance while money is loaned out essentially borrowing for free or even creating arbitrage situation. In fact, money is currently loaned out and utilized as downpayments on rental property which provides significant deductions and subsequent tax return to....pay annual premium!

    Ronald from ME posted over 4 years ago:

    Your higher return and other features comes at the cost of increased risk, so may not be suitable for more risk-averse investors. Insurance companies have gone bankrupt, and defaulted on their obligations in the past. Countries have also gone bankrupt, but most likely the risk of a US default on treasury obligations is less than the risk of an insurance company default.

    David from MD posted over 4 years ago:

    I will agree with you Ron that there are in fact no absolutes nor is there a "perfect" investment.
    My personal opinion is that the chance of my insurance company going bankrupt and defaulting on its obligations to policy holders is much less the risk incurred in a portfolio of bonds whose performance and solvency going forward in this current debt laden global economy is a risky and volatile proposition at best.
    You do understand that states have in place pools of money to back up insurance companies in case of failure in order to protect policy holders.
    Interesting tidbit from last market collapse. AIG, one of the biggest financial services companies in the world when it failed. It was the non insurance side of the business that failed. The solvency of the pure insurance side of the business was in tact.
    I appreciate your thoughts Ron but will gladly take my chances here.

    Craig from VA posted over 4 years ago:

    I am not sure the risk of forfeiture is the biggest concern. Using a life insurance policy as a distribution vehicle can be tax-efficient. However, the projected distributions you list are probably supported by dividends, which are not guaranteed. Life insurance ledgers project the current year's interest rate indefinitely into the future. Dividend crediting rates have been declining due to the low interest rate environment. How would whole life policy perform if dividends were credited below the current interest rate? This type of sensitivity analysis might help quantify the risk in the contract. To check the sensitivity of distributions, it might be important to understand how the distributions would be impacted if dividends were reduced by 50 or 100 basis points.

    David from MD posted over 4 years ago:

    I agree with you Craig 100%. As I stated there are no absolutes and no perfect investment. But, with ALL things considered, I feel, personal opinion, that it is the most efficient use of dollars for the basis of a retirement plan. Now, would I recommend, or do I suggest this being the end all to retirement/financial planning? No, of course not but it is the foundation, for me!
    I appreciate you thoughts!

    James from MA posted over 4 years ago:

    Maybe this approach is too complicated for me but - can someone explain how the $920,304 total cost in Table 2 is derived? Thanks j

    Barry from KS posted over 4 years ago:

    Anyone notice that the 2027 price is out of line?

    Binoy from CA posted over 4 years ago:

    The math seems wrong.
    At the given rates and with an outlay of $1 million, one cannot buy 30 years (let alone 35 years) of bonds that give off $40,000 income per year for the duration of 30 or 35 years.
    One needs $999,183 to purchase just 25 years of bonds that mature each year to give income of $40,000 per year as spendable income.

    ...I used $60.1 as the purchase price for maturity year 2027 which is also wrongly given as $25 in thee table.

    Daniel from PA posted over 4 years ago:

    The prices I am finding are not even close. Have they changed that much in three months or is there a much cheaper source than TDAmeritrade?

    Robert (Author) from RI posted over 4 years ago:

    Responses to:
    David from Maryland.
    I cannot make a meaningful response since I don’t know the exact particulars of your whole life policy. By definition, one cannot outlive a whole life insurance policy, but it begs some questions. Will you need to pay the 8K premium for life? If so, the $7500 dividend is wiped out. If not, the premium will be extracted from the cash value, thereby reducing the base for future dividends. As you project now, the dividend is about 1.98% of the 378K projected cash value. Your use of loans against the cash value may create a nice arbitrage, but if not repaid, with interest, at your death, the death benefit will be reduced by the outstanding balance. If your rental properties are still mortgaged, will that death benefit liquidate the debt? My experience has been that those with significant wealth use life insurance to protect against estate taxes, not retirement income, but you may have a good thing going. Best wishes.

    James from Massachusetts.
    The $920,304 amount of Table 2 was derived as follows. The “Asking Prices” were extracted from the website source and placed in an Excel spreadsheet as a table with 30 vertical cells. These values were used by a link from a calculation worksheet and as such were never touched manually. Barry from Kansas noticed the “out of line” price for 2027 and quite frankly, I am at a loss for an explanation. The 30-line table would be too long for the publication so I reshaped it into Table 1 by cut and paste in the worksheet, but somehow I must have “finger-poked” the 25.00 into the table. I do apologize for not catching the error prior to submission. The asking price for May 15, 2027 was 60.401 and that value was used in the calculations. James, the arithmetic is as follows. The May 2012 asking price in Table 1 is 99.987 meaning that a $40,000 maturity will cost 0.99987 times 40000 or $39,995. The May 2016 asking price was 95.797 so a $40,000 maturity will cost 0.95797 times 40,000 or $38,319 and for two of them $76,638 would be required. The May 2041 asking price is 34.196 and a $40,000 maturity would cost 0.34196 times 40000 or $13,678. As you can see the further out the maturity: the deeper the discount. This approach is also somewhat conservative in that the in 2016, 2021, 2026, 2031, and 2036, it will not take $40,000 to purchase the income for 2042 to 2046, but I did not address that because the “asking prices’ for those years would be unknown in 2012. The selected 30 line item calculations were transferred from the calculation worksheet to Table 2, again “automatically” so as not require and manual entry of numbers. (This is accomplished by visual basic programming behind the spreadsheet with the click of a button.) A Similar procedure was used for Table 3. Hope the foregoing is helpful.

    Binoy from California.
    I hope my response to James is helpful to you also. I have checked my calculations and get repeated results.

    Daniel from Pennsylvania.
    Apparently so. Relative to the values in Table 1, as of Friday, 6/22 the May 15, 2013 asking price is 99.883 with a yield of 0.12%, the May 15, 2027 asking price was 69.493 with a yield of 2.48% and the May 2041 asking price was 42.889 with a yield of 2.95. If I performed this analysis with the June 22 asking prices, the cost would be $969,956 for Table 2.

    B from NY posted over 4 years ago:

    If this is in an IRA account how does one calculate the RMD? Could I be forced to sell to take the RMD?

    Jim from RI posted over 3 years ago:

    It is an interesting approach. I think the risk of inflation would eat away at the purchasing power too much to make this an effective retirement plan though. I am still working and have twenty years to go until retirement but I think I might start a ladder for 20 years out once rates go above historic inflation levels.

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