
Reducing Backloading in a Tontine Fund
Unfortunately, it is impossible to reduce the backloading that is inherent in a tontine fund. The longer a member lives, the more she would recieve, as her monthly mortalitygain distributions would generally increase with her age and her increasing death probability ([g.sub.i]). (139) In the next Section, however, we will discuss how this backloading problem can be solved by adding an "annuitypayback mechanism." The annuitypayback mechanism has the added benefit of further reducing the noisiness of the payouts. We call the resulting product a "tontine annuity."

A Tontine Annuity
In this Section, we propose a tontine annuity that closely resembles a variable annuity. A tontine annuity is constructed by adding two enhancements to a tontine fund. First, as already discussed, to reduce noisiness, we would build in a monthly payment period; and, second, to eliminate backloading, we would add an annuitypayback mechanism.

Monthly Accrual of Fair Transferplan Payouts
In a tontine annuity, mortalitygain distributions would not be paid out immediately when other members die. Instead, mortalitygain distributions would be accrued within the individual accounts of the surviving members. If a member is alive at the end of the month, she would be paid the accrued mortalitygain distributions in her account as a monthly mortalitygain distribution (e.g., see Table 4). If she is not alive at the end of the month, she would receive nothing, as the balance in her account, including any mortalitygain distributions that accrued that month, would have been distributed to surviving members when she died during the month (e.g., see Table 5). Thus, a member would receive payments on a monthly schedule just as she would if she had instead purchased a variable annuity from an insurance company.

Annuity Payback
In addition to receiving a monthly mortalitygain distribution, each surviving member would also receive a portion of her original contribution at the end of each month that she is alive. Our approach is to make "monthly tontineannuity distributions" to surviving members that are designed to cancel out the agerelated increase in mortalitygain distributions inherent in simple tontine funds like the one in Figure 1 (i.e., the backloading).
It turns out that a tontine annuity constructed in this way closely resembles an actuarially fair variable annuity (i.e., one without insurance agent commissions or insurance company reserves, risktaking, and profits). To be sure, because the value of the assets in the tontine annuity fluctuates, monthly tontineannuity distributions would still be volatile. But if we pretend that the underlying investment assets grow at a fixed, assumed rate of return, then the tontine annuity would provide monthly payouts that are approximately constant for life.
Moreover, it is relatively easy to determine the proper amounts of these monthly tontineannuity distributions. The monthly payout of any actuarially fair annuity is simply equal to the account balance divided by a monthly annuity factor. The monthly annuity factor is the premium for an actuarially fair annuity that pays $1 per month for life. These monthly annuity factors can easily be calculated from a mortality table and depend only on the age of the annuitant and the assumed interest rate. (140)
For example, Table 6 shows a sample monthly statement for a member of a tontine annuity who lives through the first month after turning age 65 and who had exactly $250,000 in his account at the end of the prior month. The only difference between the monthly statement in Table 4 and the monthly statement in Table 6 is that instead of receiving a monthly mortality gain distribution of just $1041.67 (as in Table 4), our hypothetical member would receive a monthly tontineannuity distribution of $2133. That $2133 is computed by dividing the account balance on the last day of the month (i.e., $251,041.67 on April 30th) by the applicable monthly annuity factor (i.e., U7.6939). (141) That is, the monthly tontineannuity distribution for the justturned65yearold member in Table 6 is $2133 ($2133.00 = $251,041.67/117.6939).
Alternatively, a tontine annuity could be designed to make monthly tontineannuity distributions that mimic an inflationadjusted variable annuity. That inflationadjusted tontine annuity would make lower monthly tontineannuity distributions in the early years but greater distributions for those who live to later years. For example, if inflation is assumed to be 3% per year, then the first monthly tontineannuity distribution for the hypothetical 65yearold in Table 6 would be just $1651.72 ($1651.72 $251,041.67/151.9876), (143) but distributions in subsequent months would be larger and would eventually exceed the payout level of the notadjustedfor inflation tontine annuity.
In short, a tontine annuity could be designed to resemble an actuarially fair variable annuity or an actuarially fair inflationadjusted variable annuity. These tontine annuities would still be volatile because of fluctuations in the value of the underlying investment assets, but backloading would be eliminated.

Adding in Investment Income
In the simple tontine annuities we have considered so far, we have assumed that contributions do not earn any interest. In the real world, however, each member's contributions would be invested, and the member's balance would grow (or shrink) according to its investment performance. Accordingly, account balances at the end of each month would tend to be higher, and monthly tontineannuity distributions would also tend to be higher. For example, if the tontine annuity in Table 6 had earned $1000 of investment interest in that month, the balance in the account at the end of the month would have been $1000 higher, and, consequently, the monthly tontine distribution would have been $8.52 higher$2141.52 instead of the $2133, as shown in Table 6 ($2141.52 = $252,041.67/117.6939). (144)

Managing Investments
Investments in a tontine annuity would most likely be managed collectively for the entire pool, but it would be possible to design a tontine annuity which allows members to direct their own investments, just as people often do with their selfdirected 401(k) plans and IRAs. (146) Pertinent here, rates of return are likely to be much higher if the investments are managed by professionals rather than allowing individuals to direct their own investments. (147)
In theory, a tontine annuity could be managed by a discount broker, and no money would have to be set aside for insurance agent commissions or insurance company reserves, risktaking, or profits. Those commercial insurance charges can be quite hefty. (148) For example, a recent Morningstar survey of 2037 variable annuities showed an average administrative fee in 2014 of 1.33% of assets under management, and that fee is on top of the cost of managing the underlying investments, which itself can easily run another 1.0%. (149) To be sure, some discount brokers have recently teamed up with insurance companies to offer lowcost variable annuities. For example, Charles Schwab & Co., Inc., markets variable annuities with insurance charges that range from 0.60% to 0.65% (again, not including the additional administrative expenses involved in managing the investments), (150) and The Vanguard Group, Inc. offers a variable annuity with an insurance charge of 0.57%. (151) Again, these insurance charges do not include the additional administrative expenses involved in managing the underlying investments.
We are confident that discount brokers would be able to offer tontine annuities at even lower costs. As there are no insurance guarantees associated with tontine annuities, we believe that discount brokers could offer these products with total annual costs, perhaps, as low as 0.30% of assets under management, depending on the nature of the underlying investments. That means retirees would get significantly more benefits than they do with today's highcost variable annuities. For example, imagine a tontine annuity that invested entirely in an S&P 500 stock index fund. We know that most discount brokers offer an S&P 500 index fund with expense ratios of 0.10% or less, (152) and we believe that the tontine annuity management and recordkeeping functions could be performed for as little as 0.20% of assets under management. That means total costs could be as low as 0.30% of assets under management.
In that regard, TIAACREF Financial Services has been offering a lowcost, tontinelike product for years. (153) Created in 1952, the College Retirement Equities Fund (CREF) was the world's first variable annuity. (154) Today, CREF operates eight investment accounts that differ by objective: stocks, bonds, money market, and social choice; (155) and CREF keeps its costs for managing those accounts at between 0.395% and 0.465% of assets under management. (156) CREF participants choose which fund to invest in; and later on, they choose from among a variety of distribution options, including onelife and twolife annuities. (157) When a retiree selects a life annuity, the annuity payments will depend on both the investment experience of the chosen accounts and on the mortality experience of the other participants. (158) Basically, within each investment account, CREF periodically adjusts the annuity payments so that the present value of the aggregate amount expected to be paid out over the participants' remaining lifetimes matches the current value of the assets in the account. If participants in the fund "live longer ... than expected, the amount payable to each will be less than if they as a group die sooner than expected." (159) In short, like a tontine, the mortality risk falls on the annuitants and is not guaranteed by CREF (or TIAA). (160)
As mentioned, tontines were popular at the end of the nineteenth century, but they...

Tontine pensions.
Author:  Forman, Jonathan Barry 
Position:  II. Tontine Pensions B. A Tontine Fund 3. Two Problems with Tontine Funds b. Reducing Backloading in a Tontine Fund through Conclusion, with footnotes and appendix, p. 790831 
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COPYRIGHT GALE, Cengage Learning. All rights reserved.