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Tontine pensions.

b. 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 mortality-gain 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 "annuity-payback mechanism." The annuity-payback mechanism has the added benefit of further reducing the noisiness of the payouts. We call the resulting product a "tontine annuity."

C. 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 annuity-payback mechanism.

1. Monthly Accrual of Fair Transfer-plan Payouts

In a tontine annuity, mortality-gain distributions would not be paid out immediately when other members die. Instead, mortality-gain 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 mortality-gain distributions in her account as a monthly mortality-gain 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 mortality-gain 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.

2. Annuity Payback

In addition to receiving a monthly mortality-gain 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 tontine-annuity distributions" to surviving members that are designed to cancel out the age-related increase in mortality-gain 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, risk-taking, and profits). To be sure, because the value of the assets in the tontine annuity fluctuates, monthly tontine-annuity 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 tontine-annuity 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 tontine-annuity 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 tontine-annuity distribution for the justturned-65-year-old member in Table 6 is $2133 ($2133.00 = $251,041.67/117.6939).

Alternatively, a tontine annuity could be designed to make monthly tontine-annuity distributions that mimic an inflation-adjusted variable annuity. That inflation-adjusted tontine annuity would make lower monthly tontine-annuity 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 tontine-annuity distribution for the hypothetical 65-year-old 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 not-adjusted-for- inflation tontine annuity.

In short, a tontine annuity could be designed to resemble an actuarially fair variable annuity or an actuarially fair inflation-adjusted 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.

3. 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 tontine-annuity 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)

4. 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 self-directed 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, risk-taking, 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 low-cost 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 high-cost 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, TIAA-CREF Financial Services has been offering a low-cost, tontine-like 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 one-life and two-life 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 fell out of favor at the beginning of the twentieth century, largely due to fraud and mismanagement of early tontine funds. (161) In today's post- ERISA world, however, it would be relatively easy for the U.S. Securities & Exchange Commission (SEC) and the U.S. Department of Labor's Employee Benefits Security Administration to regulate tontine annuities and the fiduciaries that would manage them. Moreover, private sector recordkeepers and custodians would help protect tontine annuity assets.

We live in an era in which new financial and lifetime income products are created all of the time. Indeed, GLWB funds were developed in Canada only recently, before spreading to the United States and other countries, (162) and as mentioned, a number of discount brokers have recently teamed up with insurance companies to offer low-cost variable annuities. (163) Accordingly, we anticipate that a number of discount brokers and insurance companies will want to develop new tontine annuity products and seek the regulatory approvals that might be needed.

5. Adverse Selection Is Always a Challenge for Annuities

To be sure, underutilization would be a problem for tontine annuities, just as it is for traditional annuities. All in all, as more fully explained below, people rarely choose to buy annuities voluntarily. In fact, over the years, there has been a significant decline in the annuitization of retirement savings by American workers. The shift from traditional defined benefit plans to defined contribution plans is a large part of the story, (164) as defined contribution plans typically distribute benefits in the form of lump sum distributions rather than as annuities. (165) Indeed, relatively few defined contribution plans even offer annuity options, and, in any event, not many participants elect those annuity options. (166) In short, the demand for annuities is lower than expected, a shortfall which has come to be known as the "annuity puzzle." (167)

There are many reasons for this low demand for annuities, but adverse selection is one of the most important reasons. (168) Basically, those who voluntarily purchase annuities tend to live longer than those that do not, and, consequently, annuities are not priced very well for those with normal life expectancies. (169)

a. Adverse Selection and Tontine Annuities

Adverse selection would also be a problem for tontine annuities. Just as the people who voluntarily purchase traditional annuities tend to live longer than those that do not, people who would choose to invest in a tontine annuity would tend to live longer than those who would not. To be sure, the tontine annuity would offer a better expected return than a commercial variable annuity, but coverage would nevertheless be skewed towards longer-lived investors. In short, as with traditional annuities, tontine annuities would be underutilized.

b. Solving the Adverse Selection Problem

In general, problems with adverse selection are solved with broad coverage. (170) For example, group health insurance premiums are low for large employers: they can generally ignore adverse selection as long as they provide healthcare coverage for virtually all of their employees. Similarly, Social Security and large defined benefit plan pensions can generally ignore adverse selection because they cover large numbers of employees. In short, the solution to adverse selection is to cover a broad group of individuals, and in the next Section, we show how a large employer could overcome the adverse selection against tontine annuities by adopting a "tontine pension" for a large group of its employees.

D. Tontine Pensions

While tontine annuities would be attractive investments in their own right, they are likely to be as underutilized as traditional annuities and other lifetime income products. (171) Individual investors generally underestimate their life expectancies and shy away from annuities and other lifetime income products. That is where pensions come in. Just as group health insurance spreads health risks over large groups, traditional defined benefit pension plans spread longevity risk over large groups: traditional pensions either provide annuity-like retirement benefits to their participants or purchase group annuities for them. (172)

Unfortunately, as we have seen, traditional defined benefit pensions in both the private and public sector are often underfunded, (173) and, in recent years, we have seen numerous plan sponsors freeze, terminate, or replace their plans. (174) Market volatility, shrinking labor forces, and increasing life expectancies have all exerted pressure on traditional defined benefit plans and their sponsors. It is no wonder that we have seen defined contribution plans supplant defined benefit plans in the private sector, and there is increasing pressure on public employers to also consider replacing their traditional defined benefit plans with defined contribution plans. For example, 50% of full-time private industry workers in the United States participated in defined contribution plans in 2011, up from 40% in 1989-1990; meanwhile, participation in defined benefit plans fell from 42% in 1989-1990 to just 22% in 2011. (175) All in all, the era of the traditional defined benefit plan is largely over. (176)

That is where tontine pension plans can come in. Like a typical defined contribution plan, a tontine pension would always be fully funded. Like a traditional defined benefit plan, however, a tontine pension would make annuity-like payments for as long as its retirees lived. This Section explains how a tontine pension would work.

1. A Simple Tontine Pension

An employer who wanted to provide a tontine pension for its employees would set up a defined-contribution-style pension plan, only instead of investing its contributions in stocks and bonds, the employer would invest in a tontine annuity for its employees. For example, each year, an employer might make contributions of 10% of its employees' salaries. Those contributions would be held in trust and invested in a tontine annuity, and allocated to the individual tontine pension accounts of the participants. The difference is largely in the payouts. Rather than being able to receive lump sum distributions (or periodic payments or a life annuity), each tontine pension plan participant would receive benefits based on the tontine principle. That is, the employer contributions for each participant, and the investment earnings on those contributions, would be held in a tontine annuity, and the "monthly tontine-pension distributions" would be the only kind of distributions made to retirees.

More specifically, starting at the participant's normal retirement age (or later, if she so elected), the balance in her tontine pension account would be paid out to her in the same manner as if she had purchased her own tontine annuity with the employer contributions made on her behalf. No other form of distribution would ever be permitted. For example, for a typical worker who had accumulated $250,000 at her retirement, her monthly statement would look just like the sample monthly statement for the tontine annuitant in Table 7.

In short, a tontine pension would provide lifetime retirement income in a way similar to a defined contribution platform. Essentially, the tontine pension is like a defined contribution plan that only pays benefits in the form of an actuarially fair life annuity. The difference is that rather than having the plan sponsor purchase annuities for each retiring employee or otherwise bear the risks and costs of providing the promised annuity benefits, with a tontine pension, the plan sponsor bears no investment or actuarial risks at all. The tontine pension would make distributions to retirees out of the funds accumulated in the underlying tontine annuity and in accordance with the fair transfer-plan and annuity-payback protocols. These monthly tontine-pension distributions could be designed to mimic immediate, level-payment annuities; (177) immediate, inflation-adjusted annuities; (178) deferred annuities; (179) or joint and survivor annuities. (180)

2. Tontine Pensions Compared with Other Pension Alternatives

a. Tontine Pensions Versus Traditional Defined Benefit Plans

A tontine pension could easily be designed to pay benefits that were, on average, comparable to those paid by a traditional, final-average-pay defined benefit plan. To be sure, the benefits paid by a tontine pension would vary from month to month because of fluctuations in the value of the underlying assets and the variability inherent in the indeterminateness of the deaths of other participants in the tontine pension. But, on average, benefits paid by a tontine pension would approximate an actuarially fair life annuity.

With a defined benefit plan, the variation in monthly payments is eliminated, but only because the plan sponsor (the employer) guarantees the promised payments. The plan sponsor bears all the contribution, mortality, and investment risks, and we have, of course, seen how poorly that has worked out, with thousands of failed plans in the private sector and numerous underfunded plans in both the private and public sectors. (181) While plan sponsors do a much better job growing investments than individuals, (182) plan sponsors do not always have the discipline to make the contributions that are needed to keep their traditional defined benefit plans fully funded. (183) On the other hand, tontine pensions would always be fully funded, just as defined contribution plans are almost always fully funded--through regular contributions equal to, for example, 10% of salary. (184)

In short, tontine pensions have two major advantages over traditional defined benefit plan pensions. First, unlike traditional pensions which are frequently underfunded, tontine pensions would always be fully funded. Second, unlike traditional pensions where the plan sponsor must bear all the investment and actuarial risks, with a tontine pension, the plan sponsor bears neither of those risks.

b. Tontine Pensions Versus Typical Defined Contribution Plans

So how do tontine pensions stack up against typical defined contribution plans? The answer is very well, indeed. Like a typical defined contribution plan, a typical tontine pension might start with employer contributions equal to, for example, 10% of salary. In the typical defined contribution plan, however, the participants are often allowed to direct the investment of their individual accounts, and payouts almost always take the form of lump sum and periodic distributions, rather than life annuities. (185) On the other hand, with a tontine pension, the plan sponsor could, and should, manage the investments, and benefits would be paid out only as a tontine pension that approximates an actuarially fair variable annuity.

To be sure, a plan sponsor could design a defined contribution plan where the plan sponsor manages all the investments and where benefits are only paid out in the form of a life annuity. But we know of no defined contribution plans like that, and we doubt that any employer with a defined contribution plan would have the discipline to design and continue such a plan in the face of employee expectations and demands (1) that the employees be allowed to direct their investments and (2) that the employees be allowed to receive the balance in their accounts as periodic or lump sum distributions rather than only as life annuities.

In fact, we believe that a tontine pension is reasonably analogous to a defined contribution plan with mandatory annuitization. There are a couple of key differences, however. First, with a tontine pension, those who survive until retirement would also benefit from the forfeitures of the accounts of those who did not. As far as we know, that does not happen with any defined contribution plans. Second, while a tontine pension would automatically provide benefits that approximate an actuarially fair life annuity, a defined contribution plan would have to purchase a lower-yielding commercial annuity to provide a mandatory annuitization benefit.

c. Tontine Pensions Versus Cash Balance Plans

A tontine pension is also similar to a cash balance plan with mandatory annuitization. In a cash balance plan, the sponsor credits hypothetical individual accounts with contributions of, for example, 10% of compensation. As with traditional defined benefit plans, the default benefit in a cash balance plan is a life annuity; however, cash balance plans typically allow lump sum and periodic distributions as well. (186) Indeed, we doubt that there are many cash balance plans that require benefits be taken in the form of a life annuity, and we doubt that there are many employers that would have the discipline to design or to continue such a plan in the face of employee expectations and demands that the employees be allowed to receive the balance in their accounts as periodic or lump sum distributions rather than only as annuities.

Moreover, because cash balance plans are defined benefit plans, like traditional pensions, cash balance plans are often underfunded. (187) On the other hand, with a tontine pension, the plan sponsor's contributions would be fixed at, for example, 10% of compensation, and the plan would then be fully funded with those actual contributions. The plan sponsor would then manage and grow the investments, and the tontine-pension distributions would approximate an actuarially fair life annuity.

3. Summary of the Advantages and Disadvantages of Tontine Pensions

In essence, a tontine pension would be like a traditional defined benefit pension plan, except that it would always be fully funded and the plan sponsor would never bear any of the investment or actuarial risks. Participants would receive monthly tontine pension benefits for as long as they lived, and a tontine pension could be designed to provide inflation-adjusted annuities, deferred annuities, or joint and survivor annuities. (188) Conceivably, individual participants could be allowed to make additional elective contributions to their accounts, just as they do now under 401(k)-type plans. (189)

The principal disadvantage of a tontine pension is that monthly payments would vary in amount. One source of variation is the randomness of member deaths, but the more individuals who participate in the plan, the less significant that noisiness would be. For a tontine pension that covers thousands of participants, the variation due to random deaths would be minimal. (190) However, there could still be considerable variation due to volatility in both the value of the underlying assets and the rate of return on those assets. (191)

Finally, as with traditional defined benefit plans, participants who live the longest would collect the most benefits, and those who died young might not even recover the amounts contributed on their behalf. Of course, that is the nature of traditional defined benefit plans, life annuities, and most other lifetime income products, so it is not a "disadvantage" unique to tontine pension plans.

III. Modeling a Simple Tontine Pension

In this Part, we design a model tontine pension for a large employer and then use a computer simulation to see what kinds of tontine pension benefits the participants could expect to receive.

A. The Parameters of the Simulation

Our computer simulation uses a pool of approximately 170,000 members (approximately 100,000 active employees and 70,000 retirees). The parameters of the simulation are as follows:

* The employer hires 3600 employees each year (300 each month).

* The employee's gender is randomly selected, equiprobably male or female.

* Each employee is hired on her 35th birthday and works continuously for the employer for 30 years until age 65, or earlier death. (192)

* Each employee is hired at a salary of $50,000 a year, and her salary increases 4.0% each year. (193)

* At retirement, each employee receives a tontine pension until death.

* In this simple simulation, nobody is married (so no joint and survivor annuity benefits are needed).

* The account balances of those who die are forfeited. (194)

* Every year, the employer contributes 10% of salary for every employee to the tontine pension. (195)

* Investment return: funds are professionally managed and earn 7.0% net of investment expenses each and every year, compounded annually. (196)

* Inflation is 3.0% each year. (197)

* Workers receive no payouts until age 65,198 and then retirees receive either uniform (fixed) annuity-type payouts or, alternatively, inflation- adjusted annuity-type payouts. (199)

* The mortality model is based on the Social Security Administration 2009 unisex mortality table. (200)

* Therefore, at equilibrium, approximately 3000 out of the 3600 initial hires each year reach age 65; approximately 100,000 are actively employed at any time; and there are approximately 70,000 retirees at any point in time.

B. Calculation of the Retirement Balance

At the outset, Table 8 shows how this tontine pension would work for workers ages 35 through 64. Column 1 of Table 8 shows the age of each worker from ages 35 through 64. Column 2 shows the salary of that worker each year. Column 3 shows the amount of the 10%-of-salary contribution that her employer makes to the tontine pension on her behalf each year.

Column 4 shows the account balance at the end of the year, not including the mortality gains that would result from the forfeitures from other members who died that year. (201) Column 5 shows the worker's probability of dying during that year. Finally, Column 6 shows the closing balance in the worker's account including the mortality gains that result from the forfeitures from other members who died that year. (202) The final row of Table 8 shows that a worker who lived (and worked) from age 35 through age 64 and retired at 65 would have a final pre-retirement salary of $155,933 (Column 2) and would have a starting retirement balance in her tontine pension account of $843,376 (Column 6).

C. Calculation of the Monthly Tontine-Pension Distributions

At retirement, the expected monthly payout is identical to the actual monthly payout of an actuarially fair annuity. As we have seen, the monthly payout of an actuarially fair annuity equals the account balance divided by the applicable monthly annuity factor. (203) For example, consider a worker who worked from age 35 through age 64 and retired on the last day of that year. We can see from the last entry in Table 8 that the closing account balance for that worker was $843,376. Assuming that she wants to draw level monthly tontine pension payments for the rest of her life, she should start by looking at Column 5 of Appendix Table 1, which shows that the uniform monthly annuity factor for the first month after she turns 65 is almost 118. Therefore, the first monthly distribution for a uniform tontine pension would be $7166 ($7165.84 = $843,376/117.6939).

Alternatively, if this retiree instead wanted inflation-adjusted payments for the rest of her life, Column 6 of Appendix Table 1 shows that the initial monthly annuity factor for the first month after she turns 65 is almost 152. Accordingly, the first monthly distribution for an inflation-adjusted tontine pension would be just $5549 ($5548.98 = $843,376/151.9876).

Figure 2 plots the expected payouts from these uniform and inflation-adjusted tontine pensions over time. The plot is for a member retiring on her 65th birthday. The uniform payout is the amount of the monthly payment in dollars. Ideally it is a constant $7166 per month for life--and that is what an actuarially fair life annuity would pay. (204) The actual payments would fluctuate a little bit around that value, but as the plot shows, the uniform payout curve is relatively smooth. Of course, that is what we would expect given that our model assumes a constant 7% rate of return and a constant 3% inflation rate. Consequently, monthly fluctuations result only from the randomness of deaths in the population, but with approximately 70,000 retirees at any point in time, those fluctuations are insignificant.

By contrast, the inflation-adjusted payout starts at $5549 per month and increases at an annual rate of 3% per year--that is what an actuarially fair life annuity with a 3% escalator would pay (and the model assumes a constant 3% inflation rate). Again, the actual payments will fluctuate a little bit around those values, but as the plot shows, the inflation-adjusted payout curve is also quite smooth.

D. Adequacy

All in all, we have shown how a large employer could use a tontine pension to provide retirement benefits for its employees. Given the assumptions in our model, Table 8 showed that our hypothetical retiree would have a final salary of $155,933 at age 64 and would have accumulated $843,376 by age 65. The latter sum would support a uniform tontine pension of around $7166 per month for life or an inflation-adjusted tontine pension that starts at around $5549 per month at age 65 and increases in later months.

It is relatively easy to determine how much pre-retirement income this 30-year, 10%-of-salary tontine pension would replace. For example, multiplying the uniform monthly benefit of $7166 by 12 months yields an annual tontine pension of $85,992 ($85,992 = 12 x $7166), and it is easy to see that the tontine pension would replace 55.1% of pre-retirement earnings in the first year of retirement (i.e., a "replacement ratio" of 55.1% (0.5514676 = $85,992/$155,933)). (205) Similarly, the inflation-adjusted monthly benefit would yield an annual tontine pension starting at around $66,588 ($66,588 = 12 x $5549) and a replacement ratio of around 42.7% of pre-retirement earnings (0.4270295 = $66,588/$155,933). (206) In addition to these tontine pensions, however, our retiree would almost certainly receive Social Security benefits, and those Social Security benefits would replace another 35% to 40% of her pre-retirement income. (207)

All in all, it seems that a 10%-of-salary tontine pension would generate a pretty substantial retirement benefit for the typical worker. Moreover, raising the tontine pension contribution rate (e.g., above 10%) or increasing the number of working years (e.g., above 30) covered by the tontine pension would result in retirees receiving even more benefits and having even higher replacement ratios.

E. Tontine Pensions in the Real World

Our model does a respectable job of showing how a tontine pension could work in the real world. To be sure, the assumptions of the model are somewhat rigid. In the real world, inflation is not always 3% per year, wages do not always increase by 4% per year, and investments do not always earn a 7% rate of return. Each of those parameters is highly variable, although their average values are probably pretty close to our assumed values. In general, that real world variability could easily result in retirees receiving smaller (or larger) monthly distributions from their tontine pensions. To the extent that that real-world volatility puts retirement income security at risk, it is worth reiterating that either raising the tontine pension contribution rate or increasing the number of working years covered by the tontine pension would result in retirees receiving more benefits and having higher replacement ratios.

IV. Replacing the California State Teachers' Retirement System with a Tontine Pension

In this Part, we consider how a tontine pension for a large employer would work. Given the strictures of ERISA and federal securities regulation laws, we acknowledge that it may be a challenge for a private pension plan sponsor to create a tontine pension under current law. (208) On the other hand, public employers are exempt from most of ERISA's pension regulations. (209) Accordingly, we believe that a state government could easily create a tontine pension that would not run afoul of federal law. As we have seen, such a tontine pension would be fully funded and would make annuity-like payments to retirees for as long as they lived. (210)

As most states already have pension plans that cover most of their employees, what we are really talking about here is the prospect of replacing an existing state pension plan with a tontine pension. In particular, some states might want to replace their underfunded traditional defined benefit pension plans with tontine pensions. For our example, this Part considers whether California might want to replace the $74 billion underfunded California State Teachers' Retirement System (CalSTRS) defined benefit plan with a tontine pension. (211)

A. Background on the California State Teachers' Retirement System

CalSTRS is the largest educator-only pension in the world, with a membership of 868,493 and assets of approximately $187.1 billion as of October 31, 2014. (212) One of the largest programs that CalSTRS administers is its traditional defined benefit retirement plan, where benefits are based on a member's years of service, age, and highest compensation. (213) Essentially, members receive an annual retirement benefit (B) that is equal to 2% multiplied by the number of years of service (yos) multiplied by final average compensation (fac) (B = 2% x yos x fac).

For the fiscal year that ended on June 30, 2013, the CalSTRS traditional defined benefit pension had 416,643 active members with an average annual salary of $61,153 and 269,274 retired members and beneficiaries with an average annual retirement benefit of $43,308. (214) Also, as of June 30, 2013, the CalSTRS defined benefit plan was only 66.9% funded, with an unfunded liability of almost $74 billion. (215) The normal retirement benefit cost, expressed as a percentage of total compensation, was 16.818%. (216) In addition, as of June 30, 2013, CalSTRS needed another 14.620% of total compensation to amortize its $74 billion unfunded liability over 30 years. (217)

B. Replacing the California State Teachers' Retirement System Defined Benefit Plan with a Tontine Pension

There are a variety of possible ways to replace a traditional pension like the CalSTRS defined benefit plan with a tontine pension. Perhaps the most likely approach would be to keep the current defined benefit plan for all current employees but to close entry to that plan and require all new employees to join a newly created tontine pension. (218)

A more interesting approach would be for CalSTRS to freeze its current defined benefit plan and add a new tontine pension for all future benefit accruals. (219) At retirement, beneficiaries would then receive the defined benefit plan benefits that they have already accrued, but they would not accrue any additional benefits under their traditional defined benefit plan; instead, future contributions would be made to a new tontine pension. Theoretically, CalSTRS would freeze its defined benefit plan and add a tontine pension with future retirement contributions set at, for example, 16.818% of compensation (i.e., the current CalSTRS defined benefit plan's normal cost rate). (220) Going forward, such a plan would be roughly as generous as the current plan, but CalSTRS would never again have to worry about underfunding as a result of future benefit accruals. To be sure, this way of replacing the CalSTRS defined benefit plan with a tontine pension would do nothing to reduce its $74 billion unfunded liability, and that obligation would still need to be met by the state of California.

We do not mean to suggest that replacing the CalSTRS defined benefit plan with a tontine pension would be politically easy. We merely suggest that a tontine pension could provide an alternative way of providing lifetime retirement income to California teachers, and we reiterate that unlike traditional defined benefit plans--which are often underfunded--a tontine pension can never become underfunded.

V. SOLVING THE TECHNICAL PROBLEMS OF CREATING A TONTINE PENSION

Finally, this Part addresses some of the technical issues raised by tontine pensions.

A. Taxation of Benefits

Presumably, tontine pension benefits would be taxed like other pension benefits. (221) Employer contributions to a tontine pension should be excluded from the income of employees; the tontine pension fund's earnings should be exempt from tax; and retirees should be taxed only when they receive their monthly tontine-pension distributions. At the same time, the employer should be allowed a current deduction for its contributions to the tontine pension. (222) We note that the prospectus for CREF suggests that CREF's tontine-like pensions and annuities are taxed in accordance with these principles. (223)

B. Legal Issues

Although not a certainty, it appears that tontine funds, tontine annuities, and tontine pensions are all legal. As previously mentioned, investigations of the insurance industry in New York led to the enactment of legislation in 1906 that all but banned tontines. (224) To be sure, the legislation did not specifically prohibit the sale of tontines; instead, it just made it difficult for companies to defer payments beyond one year. (225) Many states followed New York's lead, and tontines soon fell out of favor. (226)

Much has changed since the beginning of the twentieth century, however. In particular, financial products today do a much better job at recordkeeping, (227) and investment assets are usually held by independent custodians. (228) Also, most states have softened their views on lotteries and gambling. (229) Accordingly, there should be less suspicion about tontine financial products. In fact, today, only Louisiana and South Carolina have statutes that actually ban tontines. (230) All in all, it seems likely that tontine financial products could be designed in ways that would survive state regulatory scrutiny. Indeed, as we have seen, CREF is arguably a tontine, (231) and it operates in, and is expressly regulated, by the State of New York, as well as by the insurance regulators of certain other states. (232) Any state that wished to set up a tontine pension for its own workers could enact a statute to permit that state to do so.

Tontine financial products should also be able to withstand federal regulatory scrutiny. As long as tontine financial products maintain good records, make adequate disclosures, and ensure that the underlying investment assets are held by independent custodians, the SEC should be satisfied.

For some tontine pensions, ERISA may present some regulatory hurdles. However, unless they are "established or maintained" by an employers or a union, tontine funds and tontine annuities would not be "employee benefit plans" within the meaning of ERISA's section 4 coverage rule, and therefore would not be subject to ERISA. (233)

On the other hand, tontine pensions established by employers or unions would be "employee benefit plans" within the meaning of ERISA. (234) As mentioned above, government plans are exempt from ERISA, so state and local governments could set up tontine pensions for their employees without having to comply with ERISA. (235)

Conversely, private-sector tontine pension plans would be subject to ERISA. The next question is whether there are any provisions of ERISA that would prevent private employers from creating tontine pensions for their employees. To be sure, traditional pensions exhibit tontine characteristics; for example, those who live longer will accrue more (monthly) benefits than those who die younger. (236)

Nevertheless, several provisions of ERISA may pose regulatory challenges for private-sector tontine pensions.

For example, with respect to defined benefit plans, Internal Revenue Code section 401(a)(8) indicates that "forfeitures must not be applied to increase the benefits any employee would otherwise receive under the plan." (237) With a tontine pension, all participants are entitled to a benefit that approximates an actuarially fair annuity. Therefore, those who live longer will get more (monthly) benefits than those who die younger. Because this is exactly what happens under a traditional defined benefit plan, we believe that tontine pensions should not be viewed as applying forfeitures to increase the benefits of other employees in violation of section 401(a)(8), and accordingly, we believe that the Internal Revenue Service should be willing to issue guidance to that effect (e.g., a private letter ruling). Moreover, we note that defined benefit plans have always been allowed to invest in annuities for their employees. Accordingly, we believe that defined benefit plans would be permitted to invest in tontine annuities. Of course, employers might prefer to operate their tontine pensions on a fully funded defined contribution plan platform. In that case, section 401(a)(8) would not be applicable.

ERISA's vesting rules may also pose a regulatory challenge for tontine pensions. For example, could a tontine pension meet the three-year cliff vesting rule that generally applies to employer contributions? (238) How do we interpret the fact that a single worker with a tontine pension account would lose everything in her account at death, even if she had worked for the employer for more than three years? Is forfeiture at death allowed in a defined contribution plan investment?

One approach is to ask whether an employer with a defined contribution plan could use employer contributions each year to buy commercial life annuities for each employee. We believe an employer could do so. Because tontine annuities would work just like commercial annuities, an employer should be able to design a defined contribution plan that invests in tontine annuities for its employees, even if those tontine annuities become worthless at death. (239)

ERISA's fiduciary obligation rules could also pose some regulatory challenges for tontine pensions. (240) For example, pension plans must be operated for the exclusive benefit of employees or their beneficiaries, and plan fiduciaries must act prudently and diversify the plan's investments. (241) Again, we see no reason to be concerned about a pension operating as a tontine pension or investing in tontine annuities, and we believe that the government would issue guidance supporting our position. (242)

We believe that tontine funds, tontine annuities, and tontine pensions could be designed in ways that comply with applicable state and federal laws.

C. Dealing with Market Volatility

Unlike a traditional defined benefit pension plan that makes fixed or inflation-adjusted benefit payments, tontine pension benefit payments would be volatile. Monthly tontine-pension distributions would vary with fluctuations in the value of the underlying assets and with the variability inherent in the indeterminate timing of the deaths of the other participants in the tontine pension. The fluctuations attributable to the randomness of the deaths of other participants would largely disappear as long as there are enough participants in the tontine pension. (243)

In contrast, the volatility due to fluctuations in the value of the underlying assets will not disappear. This is the same problem that any investor with a defined contribution plan or variable annuity confronts. (244) For example, an investor who used the 4% rule to withdraw $40,000 from her individual account in 2007 when her stock portfolio was worth $1,000,000 could only withdraw around $20,000 in 2009 when that portfolio was worth just $500,000. An investor can minimize the effects of market volatility by investing conservatively in bonds, but the expected earnings on her portfolio could fall dramatically. (245)

Of course, planning for that market volatility can help mitigate its impact. Wise consultants with irregular earnings generally spend no more money in the months that they get commissions than they do in the months that they do not. Similarly, the investor discussed in the previous paragraph could have spent just $30,000 of the $40,000 she withdrew in 2007 and saved the other $10,000 to spend in 2009 when she withdrew just $20,000. That is, individuals can smooth their consumption by underspending in the good years so that they can spend more in the lean years. Smoothing products, even "smoothed income annuities" can be purchased in the marketplace. (246)

A tontine pension could itself be designed to provide smoother distributions. For example, monthly distributions could be smoothed over a one-year or even a five-year period. (247) When the tontine pension administrator determined that a certain monthly distribution would be higher than the average distribution over the prior five years, the distribution could be split. A basic distribution could go to the participant's bank account immediately, and the excess could go into a "holding account" for the participant. In a later month when the tontine pension administrator determined that the distribution would otherwise be lower than the average for the prior five years, the holding account could be tapped to provide a larger distribution. The funds in the holding account could be invested with all of the other assets held by the tontine pension, and presumably, at that member's death, any balance in her holding account could be paid to her estate.

In short, income smoothing could be accomplished either inside or outside of a tontine pension. In any event, the volatility in monthly distributions attributable to fluctuations in the value of the underlying investment assets held in a tontine pension is no worse a problem for tontine pensions than it is for defined contribution plans or variable annuities.

D. Gender Issues

1. In General

While insurance companies can typically price the annuities that they offer to men and women differently, pension plans cannot offer different pricing based on gender. (248) Pension plans cannot require higher contributions from women or pay women lower benefits. (249) Therefore, when an employee retires with a traditional defined benefit pension, the retiree will see the same monthly pension benefits for life, regardless of gender. For example, CalSTRS pays identical pensions to retired men and women teachers who have the same service records. (250) To be sure, defined benefit plan actuaries take the gender of participants and their partners into account when determining the contributions that the plan sponsor needs to make. Retiring women can expect to collect more monthly benefit checks than their male counterparts, but the monthly payments must be equal for men and women. (251)

Tontine funds and tontine annuities could account for gender. (252) However, a tontine pension, like a traditional pension, would not be permitted to discriminate based on gender because Title VII of the Civil Rights Act of 1964 forbids this type of discrimination. (253) A tontine pension can comply with this gender neutrality requirement by using unisex life expectancy tables, as this Article does with its model tontine pension. (254)

2. Employee Contributions

Title VII's gender-neutrality requirement somewhat undermines the attractiveness of allowing participants to make additional voluntary contributions to their employer-provided tontine pensions. To be sure, allowing employees to make supplemental contributions to their tontine pensions would enhance employees' retirement incomes, just as voluntary contributions to 40i(k) plans increase participants' nest eggs and their retirement income. However, tontine pensions would be a better investment for women than men, given their relative life expectancies. The typical man would be better off investing in a 40i(k) plan or IRA (where gender is irrelevant), or in a typical commercial annuity sold by an insurance company (where gender can be considered). (255)

3. Qualified Joint and Survivor Annuities & Qualified Domestic Relations Orders

Under ERISA, defined benefit plans (and some defined contribution plans) are required to provide a qualified joint-and-survivor annuity (QJSA) as the normal benefit payment for married participants, unless the spouse consents to another form of distribution. (256) These plans are also required to provide a qualified pre-retirement survivor annuity (QPSA) option in case the worker dies before retirement. (257) ERISA-covered pension plans also allow state courts to divide the pension benefits of married couples through qualified domestic relations orders (QDROs). (258) Although not covered by ERISA, many public pension plans provide similar spousal protections. (259)

Tontine pensions could also be designed to provide spousal protections. First, with respect to survivor benefits, rather than having a married participant forfeit her entire account balance at her death, a tontine pension could provide QJSAs and QPSAs. For example, when a participant dies, she might forfeit half of the balance in her account; the remaining half could be retitled in the name of the surviving spouse. (260) Second, a tontine pension could allow divorcing spouses to secure domestic relations orders that transfer a portion of the participant spouse's tontine pension to the other spouse. This could allow the transferred portion to be retitled in the name of the transferee spouse. (261)

CONCLUSION

In this Article, we showed how large employers could use tontine pensions to provide retirement income for their employees. We developed a model tontine pension and used that model to show the retirement benefits that a typical worker could earn with a 10%-of-salary tontine pension. Over the course of a 30-year career, we estimated that a typical retiree would earn a uniform tontine pension that would initially replace approximately 55% of her pre-retirement earnings. Alternatively, that retiree would earn an inflation-adjusted tontine pension that would replace approximately 43% of her pre-retirement earnings.

These tontine pensions have two major advantages over traditional defined benefit plan pensions. First, unlike traditional pensions, which are frequently underfunded, tontine pensions would always be fully funded. Second, unlike traditional pensions, where the plan sponsor must bear all the investment and actuarial risks, with a tontine pension, the plan sponsor would bear neither of those risks. These two features make the tontine pension a particularly attractive alternative for employers who care about providing retirement income security for their employees but want to avoid the risks associated with having a traditional pension.

Tontine pensions also offer a possible solution to the chronic underfunding of state and local pension plans. For example, we showed how California could replace its $74 billion underfunded CalSTRS defined benefit plan with a tontine pension and never again have to worry about underfunding attributable to future benefit accruals.

Finally, a tontine pension would closely resemble an actuarially fair variable life annuity, but could be run by a low-fee discount broker. No money would need to be set aside for insurance agent commissions or for insurance company reserves, risk-taking, and profits. This means that tontine pensions would provide significantly higher benefits to retirees than commercial annuities.

Caption: Figure 1: Normalized Mortality Gain from FTPs Versus Age for a Typical Long-Lived Male Member in a Simulated Tontine Fund (130)

Caption: Figure 2: Monthly Payout for a Typical Long-Lived Member, Uniform and Inflation-Adjusted

APPENDIX

Appendix Table 1 is based on the Social Security Administration's 2009 unisex life table. (262) For individuals aged 35 through 119, Column 1 shows their age (x,), Column 2 shows their life expectancy ([e.sub.i]), and Column 3 shows their death probability ([q.sub.i]). Column 4 shows the force-of-mortality probabilities that we derived, (263) and Columns 5 and 6 show the uniform and inflation-adjusted monthly annuity factors that we derived for the first month of each year starting with age 65. (264)

Appendix Table 1: Unisex Life Tables, 2009, with
Force-of-Mortality Probabilities, and Monthly
Annuity Factors (265)

                  Life                       Force-of-
               Expectancy       Death        Mortality
Age             (years)      Probability    Probability
([x.sub.i])   ([e.sub.i])    ([q.sub.i])    ([f.sub.i])

35               44.90         0.001261       0.001262
36               43.95         0.001332       0.001333
37               43.01         0.001420       0.001421
38               42.07         0.001527       0.001528
39               41.14         0.001653       0.001655
40               40.20         0.001796       0.001798
41               39.27         0.001955       0.001957
42               38.35         0.002133       0.002135
43               37.43         0.002332       0.002334
44               36.52         0.002550       0.002553
45               35.61         0.002786       0.002790
46               34.71         0.003041       0.003046
47               33'8i         0.003322       0.003328
48               32.92         0.003630       0.003637
49               32.04         0.003963       0.003971
50               31.17         0.004326       0.004336
51               30.70         0.004707       0.004718
52               29.44         0.005086       0.005099
53               28.59         0.005455       0.005470
54               27.74         0.005827       0.005844
55               26.90         0.006234       0.006253
56               26.07         0.006685       0.006708
57               25.24         0.007166       0.007192
58               24.42         0.007677       0.007707
59               23.60         0.008233       0.008267
60               22.80         0.008854       0.008893
61               21.99         0.009552       0.009598
62               21.20         0.010323       0.010376
63               20.42         0.011172       0.011235
64               19.64         0.012113       0.012187
65               18.88         0.013181       0.013269
66               18.12         0.014374       0.014478
67               17.38         0.015665       0.015789
68               16.65         0.017056       0.017203
69               15.93         0.018576       0.018751
70               15.22         0.020314       0.020524
71               14.53         0.022277       0.022529
72               13.85         0.024406       0.024708
73               13.18         0.026695       0.027058
74               12.53         0.029207       0.029642
75               11.89         0.032111       0.032638
76               11.27         0.035415       0.036057
77               10.66         0.038994       0.039774
78               10.08         0.042837       0.043781
79                9.50         0.047063       0.048206
80                8.95         0.051906       0.053301
81                8.41         0.057459       0.059175
82                7.89         0.063648       0.065763
83                7.40         0.070515       0.073124
84                6.92         0.078164       0.081388
85                6.46         0.086714       0.090706
86                6.03         0.096263       0.101217
87                5.62         0.106880       0.113035
88                5.23         0.118606       0.126251
89                4.87         0.131451       0.140931
90                4.53         0.145412       0.157136
91                4.21         0.160474       0.174918
92                3.92         0.176613       0.194329
93                3.66         0.193799       0.215422
94                3.42         0.211994       0.238250
95                3.20         0.230169       0.261584
96                3.01         0.248041       0.285074
97                2.84         0.265318       0.308317
98                2.68         0.281695       0.330861
99                2.54         0.296871       0.352215
100               2.40         0.312977       0.375388
101               2.27         0.330077       0.400592
102               2.14         0.348236       0.428073
103               2.02         0.367528       0.458120
104               1.90         0.388029       0.491070
105               1.78         0.409816       0.527321
106               1.67         o.432975       0.567352
107               1.56         0.457593       0.611739
108               1.46         0.483763       0.661189
109               1.37         0.511581       0.716582
110               1.27         0.541150       0.779033
111               1.18         0.572575       0.849977
112               1.10         0.605968       0.931323
113               1.02         0.641446       1.025675
114               0.94         0.679129       1.134717
115               0.86         0.719145       1.269917
116               0.79         0.761624       1.433908
117               0.73         0.806699       1.643507
118               0.67         0.851378       1.906349
119               0.61         0.893947       2.243816

                  Uniform         Inflation-
                  Monthly          adjusted
                  Annuity           Monthly
                Factors for     Annuity Factors
                 the First          for the
Age            Month of the     First Month of
([x.sub.i])        Year            the Year

35                  n/a               n/a
36                  n/a               n/a
37                  n/a               n/a
38                  n/a               n/a
39                  n/a               n/a
40                  n/a               n/a
41                  n/a               n/a
42                  n/a               n/a
43                  n/a               n/a
44                  n/a               n/a
45                  n/a               n/a
46                  n/a               n/a
47                  n/a               n/a
48                  n/a               n/a
49                  n/a               n/a
50                  n/a               n/a
51                  n/a               n/a
52                  n/a               n/a
53                  n/a               n/a
54                  n/a               n/a
55                  n/a               n/a
56                  n/a               n/a
57                  n/a               n/a
58                  n/a               n/a
59                  n/a               n/a
60                  n/a               n/a
61                  n/a               n/a
62                  n/a               n/a
63                  n/a               n/a
64                  n/a               n/a
65               117.6939          151.9876
66               115.1577          147.7118
67               112.5519          143.3919
68               109.8756          139.0295
69               107.1273          134.6252
70               104.3072          130.1821
71               101.4239          125.7133
72                98.4856          121.2309
73                95.4925          116.7370
74                92.4424          112.2306
75                89.3370          107.7160
76                86.1922          103.2135
77                83.0219           98.7408
78                79.8263           94.2984
79                76.6015           89.8822
80                73.3500           85.4962
81                70.0896           81.1612
82                66.8410           76.9009
83                63.6153           72.7270
84                60.4220           68.6490
85                57.2732           64.6789
86                54.1842           60.8317
87                51.1716           57.1238
88                48.2522           53.5709
89                45.4418           50.1868
90                42.7539           46.9828
91                40.2005           43.9682
92                37.7928           41.1509
93                35.5427           38.5397
94                33.4649           36.1461
95                31.5809           33.9883
96                29.8776           32.0468
97                28.3359           30.2968
98                26.9285           28.7046
99                25.6135           27.2223
100               24.3250           25.7781
101               23.0633           24.3718
102               21.8287           23.0032
103               20.6214           21.6719
104               19.4415           20.3777
105               18.2892           19.1201
106               17.1642           17.8985
107               16.0665           16.7122
108                4.9955           15.5605
109               13.9509           14.4422
110               12.9316           13.3561
111               11.9366           12.3004
112               10.9641           11.2733
113               10.0120           10.2718
114                9.0770            9.2926
115                8.1546            8.3307
116                7.2383            7.3792
117                6.3178            6.4282
118                5.3799            5.4680
119                4.0607            4.1685


(1) See Moshe A. Milevsky & Thomas S. Salisbury, Optimal Retirement Tontines for the 21st Century: With Reference to Mortality Derivatives in 1693, at 2 (May 28, 2013) (unpublished manuscript), available at http://papers.ssrn.com/abstract_id=2271259 (describing tontines as "[p]art annuity, part lottery and part hedge fund"). An annuity is a financial instrument (e.g., an insurance contract) that converts a lump sum of money into a stream of income payable over a period of years, typically for life. The person holding an annuity is called an annuitant. See infra subsection I.C.2.

(2) See, e.g., Tontine, WIKIPEDIA, http://en.wikipedia.org/wiki/Tontine (last modified Oct. 22, 2014) (click on Popular Culture), archived at http://perma.cc/3UD5-FFE6 (listing plays, movies, television episodes, and books that feature tontines).

(3) M*A*S*H: Old Soldiers (CBS television broadcast Jan. 21, 1980).

(4) See, e.g., The Simpsons: Raging Abe Simpson and His Grumbling Grandson in "The Curse of the Flying Hellfish" (Fox television broadcast Apr. 28, 1996) (depicting an episode in which Grampa Simpson reveals to his grandson Bart that he and Montgomery Burns were part of a World War II American army unit that stole priceless art from a German castle, which the last surviving unit member will inherit); see also The Wild Wild West: The Night of the Tottering Tontine (CBS television broadcast Jan. 6, 1967) (portraying Jim and Arte protecting a member of an investment group whose last surviving member would inherit the group's assets).

Having an incentive to kill someone to earn a profit is an example of what actuaries call a "moral hazard." See Moral Hazard, INVESTOPEDIA, http://www.investopedia.com/terms/ m/moralhazard.asp (last visited Jan. 16, 2015), archived at http://perma.ee/9DHX-FXK8 (defining "moral hazard" as "[t]he risk that a party to a transaction has not entered into the contract in good faith, has provided misleading information about its assets, liabilities or credit capacity, or has an incentive to take unusual risks in a desperate attempt to earn a profit before the contract settles").

(5) Milevsky & Salisbury, supra note 1, at 2.

(6) Id.

(7) Id. at 3; see also Moshe A. Milevsky, Portfolio Choice and Longevity Risk in the Late Seventeenth Century: A Re-Examination of the First English Tontine, FIN. HIST. REV., Oct. 22, 2014, at 1, 4-5 (explaining that the 1693 tontine was a wealthy person's investment because it required a 100pound contribution at a time when the average laborer made only 16 pounds per year).

(8) Milevsky & Salisbury, supra note 1, at 5; see also Milevsky, supra note 7, at 5 (noting that the structure of the 1693 tontine combatted moral hazard by freezing payments when only 7 members remained).

(9) See, e.g., Robert W. COOPER, AN HISTORICAL ANALYSIS OF THE TONTINE PRINCIPLE 6-9 (J. David Cummins ed., 1972) (discussing the English tontine's effect on early America). See generally Kent McKeever, A Short History of Tontines, 15 FORDHAM J. CORP. & FIN. L. 491 (2010) (discussing the early history of the tontine and its possible modern revival).

(10) Robert M. Jennings et al., Alexander Hamilton's Tontine Proposal, 45 WM. & MARY Q. 107, 110-11 (1988).

(11) See, e.g., COOPER, supra note 9, at 2-9 (tracing the early history of tontines in France, England, and the United States).

(12) See, e.g., id. at 10-17, 21-22 (discussing the rise of tontines in the United States, the defects inherent in the original tontine policies, and the abuses of the system that led to their demise); McKeever, supra note 9, at 507-11 (detailing the nineteenth century beginnings of tontine-like insurance policies in the United States and the legislative backlash to tontines).

(13) See McKeever, supra note 9, at 511 ("The contemporary assessment ... is that the tontine aspect of the standard insurance policies served as a distraction and scapegoat in coming up with remedies for the range of vices in the industry. The problem was not with the form, but with selfdealing management." (footnote omitted)).

(14) See COOPER, supra note 9, at 43-57 (discussing the findings of the Armstrong Committee, a committee created by the New York legislature to investigate the life insurance business, which led to legislation virtually banning tontine policies by forbidding insurance companies from deferring dividend payments beyond one year); see also Tom Baker & Peter Siegelman, Tontines for the Young Invisibles, REGULATION, Winter 2009-2010, at 26, available at http://object. cato.org/sites/cato.org/files/serials/files/regulation/2009/11/v32n4-4.pdf (describing anti-tontine regulations in New York and their effect on life and health insurance companies).

(15) See generally Michael J. Sabin, Fair Tontine Annuity (Mar. 26, 2010) (unpublished manuscript), available at http://ssrn.com/abstract=1579932 (explaining how a "fair tontine annuity" could function).

(16) Id. at 12, 22.

(17) Id. at 22.

(18) A variable annuity is an annuity that offers a range of investment options. Accordingly, the value of the annuity and the monthly payments will vary depending on the performance of the underlying investments. See Variable Annuities: What You Should Know, U.S. SEC. & EXCHANGE COMMISSION, http://www.sec.gov/investor/pubs/varannty.htm (last visited Jan. 16, 2015), archived at http://perma.cc/Z4BV-VXY2 (describing the basics of variable annuities).

(19) Nick J. Collier et al., Milliman, California State Teachers' Retirement System Defined Benefit Program--2013 Actuarial Valuation 10 (2014), available at http:// www.calstrs.com/sites/main/files/file-attachments/2013_db_valuation_report.pdf; see also infra Section IV.A (providing background on CalSTRS).

(20) The top risks for today's retirees include market volatility, taxes, longevity, healthcare needs, and unexpected events. Common Retirement Risks, AMERIPRISE FIN., https://www.ameriprise.com/retire/planning-for-retirement/retirement-risks (last visited Jan. 16, 2015), archived at https://perma.cc/QD7S-4UV7. See generally YOUNGKYUN PARK, EMP. BENEFIT Research Inst., Issue Brief No. 357, Retirement Income Adequacy with Immediate and longevity Annuities (2001), available at http://www.ebri.org/pdf/briefspdf/EBRI_IB_05-2011_No357_Annuities.pdf (discussing strategies for individuals with retirement income to manage three types of risk: investment income, longevity, and long-term care).

(21) Prudential, Should Americans Be Insuring Their Retirement Income? 3 (2013), available at http://research.prudential.com/documents/rp/InsuringRetirementIncome.pdf? doc=InsuringRetirementIncome&bu=SI&ref=website&cid=2.

(22) Id.

(23) See Jonathan Barry Forman, Making America Work 184-90 (2006) (giving an overview of the Social Security system); Staff of H. Comm. On Ways & Means, 113th Cong., Green Book: Background Material and Data on the Programs Within the Jurisdiction of the Committee on Ways and Means (Nov. 2014), http://greenbook.waysandmeans.house.gov/2014-green- book/chaptert-social-security/social- security-introduction-and-overview, archived at http://perma.cc/VN56-P3TT ("Social Security is a self-financed program that provides monthly cash benefits to retired or disabled workers and their family members, and to the family members of deceased workers.").

(24) For 2015, employees and employers each pay a Social Security retirement tax of 5.6% on up to $118,500 of wages, for a combined Old-Age and Survivors Insurance (OASI) rate of 10.6%--the lion's share of the total 15.3% collected for OASI, Disability Insurance (DI), and Medicare. Self-employed workers pay an equivalent combined OASI, DI, and Medicare tax of 15.3% on their first $118,500 of net earnings. See SOC. SEC. ADMIN., FACT SHEET: 2015 SOCIAL SECURITY CHANGES, available at http://www.ssa.gov/news/press/factsheets/colafacts2015.pdf; Social Security & Medicare Tax Rates, SOC. SECURITY ADMIN., http://www.ssa.gov/oact/progdata/taxRates.html (last visited Jan. 16, 2015), archived at http://perma.cc/CL9V-JVDX.

(25) See 42 U.S.C. [section] 402(a) (2012) (describing eligibility for old-age insurance benefits); id. [section] 414(a)(2) (defining a "fully insured individual" as, among other definitions, an individual having at least "40 quarters of coverage").

(26) Soc. Sec. Admin., Fact Sheet: 2015 Social Security Changes, supra note 24.

(27) Retirement Planner: Full Retirement Age, SOC. SECURITY ADMIN., http://www.socialsecurity.gov/retire2/retirechart.htm (last visited Jan. 16, 2015), archived at http://perma.cc/QX7T-S2TQ.

(28) Monthly Statistical Snapshot, June 2014, SOC. SECURITY ADMIN, tbl.2 (July 2014), http://www.ssa.gov/policy/docs/quickfacts/stat_snapshot/2014-06.pdf, archived at http://perma.cc/9EXJ-C8ZU. In addition, a means-tested Supplemental Security Income (SSI) program provides monthly cash benefits to certain low-income elderly, disabled, or blind Americans. Supplemental Security Income Home Page, SOC. SECURITY ADMIN., http://www.socialsecurity.gov/ssi/index. htm (last visited Jan. 16, 2015), archived at http://perma.cc/B2S6-4K8T. In 2015, the maximum federal SSI benefit for a single individual is $733 per month, and the maximum for a couple is $1100 per month. SSI Federal Payment Amounts for 201s, SOC. SECURITY ADMIN., http://www.ssa.gov/oact/cola/SSI.html (last visited Jan. 16, 2015), archived at http://perma.cc/D72T-6JQV?type=image. In June 2014, 2.1 million elderly Americans received SSI benefits from the federal government, and their average monthly benefit was $430.34. Monthly Statistical Snapshot, June 2014, supra, tbl.3.

(29) Jonathan Barry Forman & George A. (Sandy) Mackenzie, The Cost of "Choice" in a Voluntary Pension System, in NEW YORK UNIVERSITY REVIEW OF EMPLOYEE BENEFITS AND Executive Compensation [section] 6.01 (2013).

(30) Employee Retirement Income Security Act of 1974, Pub. L. No. 93-406, 88 Stat. 829 (codified as amended in scattered sections of 3,18, 26, 29, 31 & 42 U.S.C.). See generally JOINT COMM. on Taxation, Present Law and Background Relating to the Tax Treatment OF RETIREMENT Savings (2012), available at https://www.jct.gov/publications.html?func= startdown&id=4418 (providing information about the tax rules applicable to retirement savings arrangements).

(31) I.R.C. [section] 402(b)(1) (2012).

(32) Id. [section] 501(a).

(33) Id. [section][section] 72(a)(1), 402(b)(2). See generally IRS, PENSION AND ANNUITY INCOME (2015), available at http://www.irs.gov/pub/irs-pdf/p575.pdf (explaining the tax treatment of distributions from pension and annuity plans). In general, a participant's pension benefits will be fully taxable if the participant's employer contributed all of the costs for the pension without including any of the contributions in the employee's taxable wages. Id. at 11. On the other hand, if an individual made after-tax contributions to a pension or annuity, she can exclude part of her pension or annuity distributions from income. Id. More specifically, under I.R.C. [section][section] 72 and 402, the individual can exclude a fraction of each benefit payment from income. That fraction (the "exclusion ratio") is based on the amount of premiums or other after-tax contributions made by the individual. I.R.C. [section][section] 72(b), 402(c) (2012); see also IRS, supra, at 11-15 (explaining the calculation of the amount of pension payments that can be excluded from income). The exclusion ratio enables the individual to recover her own after-tax contributions tax free and to pay tax only on the remaining portion of benefits which represents income. IRS, supra, at 11-15. Taxpayers who began receiving annuity payments from a qualified retirement plan after November 18, 1996 generally can use the so-called "Simplified Method" to calculate the tax-free part of their benefits. Id. at 12- 13. Under the Simplified Method, the Code provides a table with a fixed number of anticipated payments that depends upon the annuitant's age as of the annuity starting date. Id. The taxpayer then divides her total after-tax contributions over the applicable number of anticipated payments and excludes the amount so determined each year. Id.

(34) I.R.C. [section] 404(a) (2012).

(35) Id. [section] 219(a). Almost any worker can set up an IRA with a bank or other financial institution. In 2015, individuals without pension plans can contribute and deduct up to $5500 to an IRA, although individuals over age 50 can contribute and deduct another $1000 (for a total of up to $6500), and spouses can contribute and deduct similar amounts. Press Release, IRS, IRS Announces 2015 Pension Plan Limitations; Taxpayers May Contribute up to $18,000 to their 401(k) Plans in 2015 (Oct. 23, 2014), available at http://www.irs.gov/uac/Newsroom/IRS- Announces-2015-Pension-Plan- Limitations-1.

(36) I.R.C. [section] 408A (2012). Unlike regular IRAs, contributions to Roth IRAs are not tax deductible. Id. [section] 408A(c)(1). Instead, withdrawals are tax free. Id. [section] 408A(d)(1). Like regular IRAs, however, the earnings on Roth IRA investments are tax exempt. Id. [section] 408A(d)(2).

(37) FORMAN, supra note 23, at 215.

(38) Id.

(39) Id.

(40) Final average compensation is often computed by averaging the worker's salary over the last three or five years prior to retirement. Alternatively, some plans use career average compensation instead of final average compensation. Under a career earnings formula, benefits are based on a percentage of an average of an employee's career earnings for every year of service by the employee. Id.

(41) In the United States, defined benefit plans are generally designed to provide annuities, i.e., "definitely determinable benefits ... over a period of years, usually for life, after retirement." Treas. Reg. [section] 1-401-1(b)(1)(1) (2012).

(42) Traditional defined benefit plans can easily become underfunded for three reasons: (1) the employers promise their employees additional benefits for past service, (2) the employers fail to make their actuarially required contributions, or (3) the assets held in the plan decline in value because of market volatility.

(43) Pension Benefit Guar. Corp., Helping Secure Retirements: PBGC Annual Report 2013, at 5 (2013), available at http://www.pbgc.gov/documents/2013- annual-report.pdf.

(44) S&P 1500 Pension Deficits Remain Above Year-End 2013 Levels, MERCER (Aug. 5, 2014), http://www.mercer.com/newsroom/sp-1500-pension-deficits-remain-above-year-end- 2013-level-so.html, archived at http://perma.cc/YV3Z-G97H; see also S&P DOW JONES INDICES, S&P 500 Corporate Pensions and Other Post-Employment Benefits (OPEB): The FINAL Frontier 4 (2014), available at http://www.spindices.com/documents/research/researchsp-500-corporate-pensions- and-opeb-the-final-frontier-2013.pdf (noting that companies in the S&P 500 were 87.9% funded in the fiscal year 2013, meaning they were underfunded by $224.46 billion).

(45) Standard & Poor's ratings Serv., U.S. State Pension Funding: Strong Investment Returns Could Lift Funded Ratios, But Longer-Term Challenges REMAIN 16-17 tbl.3A (2014), available at http://www.standardandpoors.com/spf/upload/Events_US/US_PF_Webcast_Pensarti.pdf; see also Alicia H. Munnell, Jean-Pierre Aubry & Mark Cafarelli, The Funding of State and Local Pensions: 2013-2017, ST. & LOC. PENSION PLANS (Ctr. for Ret. Research at Bos. Coll., Chestnut Hill, Mass.), July 2014, at 2 (2014), available at http://crr.bc.edu/wp-content/uploads/2014/06/slp_49.pdf (finding that a sample of 150 state and local plans was just 72% funded in 2013 (underfunded by $1.2 trillion)).

(46) Forman, supra note 23, at 215-16; Emp. Benefit Research Inst., Fundamentals of Employee Benefit Programs 64 (6th ed. 2009), available at http://www.ebri.org/pdf/publications/books/fundamentals/2009/06_DB- DC_RETIREMENT_Funds_2009_EBRI.pdf (describing the function and types of defined contribution plans).

(47) Defined contribution plans are also known as "individual account" plans because each worker has her own account, as opposed to defined benefit plans, in which the plan's assets are pooled for the benefit of all of the employees.

(48) Towers Watson, International Pension Plan Survey: Report 2011, at 15 (2011), available at http://www.towerswatson.com/en/Insights/IC-Types/Survey-Research- Results/2011/12/International-Pension-Plan-survey-2011 (indicating that lump sums distributions are "by far the most prevalent" form of distribution for defined contribution plans).

(49) See Six Ways to Save for Retirement, PROGRAM PERSP. (U.S. Bureau of Labor Statistics, Washington, D.C.), Mar. 2011, at 2-3, available at http://www.bls.gov/opub/perspectives/ program_perspectives_vol3_issue3.pdf (introducing and describing six types of defined contribution plans).

(50) I.R.C. [section] 401(k) (2012).

(51) BLS Examines Popular 40i(k) Retirement Plans, PROGRAM PERSP. (U.S. Bureau of Labor Statistics, Washington, D.C.), Nov. 2010, at 1, available at http://www.bls.gov/opub/perspectives/program_perspectives_vol2_issue6.pdf (asserting that there has been a "wide- spread movement towards defined contribution plans, such as 40i(k) and 403(b) ... in private industry and to a lesser extent, in State and local government").

(52) IRS, supra note 35.

(53) I.R.C. [section] 402A(b)(1) (2012) ("The term 'qualified Roth contribution program' means a program under which an employee may elect to make designated Roth contributions in lieu of all or a portion of elective deferrals the employee is otherwise eligible to make under the applicable

retirement plan."). Unlike regular 401(k) plans, contributions to Roth 401(k) plans are not excludable. Id. [section] 402A(a)(1). Instead, withdrawals are tax free. Id. [section] 402A(d)(1). Like regular 401(k) plans, however, the earnings on Roth 401(k) plan investments are tax exempt. Id.

(54) The Dow Jones Industrial Average hit 14,000 in October 2007, fell to around 7000 in February 2009, and rose to more than 17,000 in September 2014. Dow Jones Industrial Average, GOOGLE Finance, https://www.google.com/finance/qMNDEXDJX%3A.DJI&ei-bXBqUsidGJ C2lAOrxQE (last visited Jan. 16, 2015) (follow "Historical Prices" hyperlink, set daily price time period, then follow "update" hyperlink); see also infra subsection I.C.1 for a discussion of the so-called 4% rule.

(55) See The Dangers of Buying an Annuity When Interest Rates are Low, ANNUITY DIG., http://www.annuitydigest.com/blog/tom/dangers-buying-annuity-when-interest- rates-are-low (last visited Jan. 16, 2015), archived at http://perma.cc/R8Y9-TKJM (warning how interest rate fluctuations can cause annuities to become very expensive because fixed annuity payments are based on prevailing interest rates).

(56) David John Marotta, The False Promises of Annuities and Annuity Calculators, FORBES (Aug. 27, 2012, 8:54 AM), http://www.forbes.com/sites/davidmarotta/2012/08/27/the-false-promises-of- annuities-and-annuity- calculators, archived at http://perma.cc/85V5-9WLB (describing how inflation rates change the buying power of the variable annuity).

(57) See Jonathan Barry Forman & Amy Nixon, Cash Balance Pension Plan Conversions, 25 OKLA. CITY U. L. Rev. 379, 387 (2000) ("[A] cash balance plan is a defined benefit plan that looks like a defined contribution plan.").

(58) Id.

(59) See, e.g., About PBGC, Pension Benefit Guaranty Corp., http://www.pbgc.gov/about (last visited Jan. 16, 2015), archived at http://perma.cc/48R2-LALW (stating that PBGC's purpose is to protect and enhance retirement security for American workers and their families); About the Employee Benefits Security Administration, U.S. Department Lab., http://www.dol.gov/ebsa/aboutebsa/main.html (last visited Jan. 16, 2015), archived at http://perma.cc/ZQ68-L8TJ (introducing the Employee Benefits Security Administration's commitment to educating and assisting workers, retirees, and their families covered by private retirement plans); Tax Information for Retirement Plans, INTERNAL REVENUE SERVICE, http://www.irs.gov/Retirement-Plans (last visited Jan. 16, 2015), archived at http://perma.cc/ G6UF-Q4AT (providing a wide array of tax-related information and services for retirement plans). The IRS and the U.S. Department of Labor also have significant responsibilities with respect to IRAs and Roth IRAs.

(60) I.R.C. [section] 401(a) (2012) ("A trust created or organized in the United States and forming part of a stock bonus, pension, or profit-sharing plan of an employer for the exclusive benefit of his employees or their beneficiaries shall constitute a qualified trust under this section...."); Employee Retirement Income Security Act of 1974 [section] 403, 29 U.S.C. [section] 1103(a) (2012) ("Except as provided in subsection (b) of this section, all assets of an employee benefit plan shall be held in trust by one or more trustees.").

(61) See, e.g, Employee Retirement Income Security Act of 1974 [section] 101, 29 U.S.C. [section] 1021 (2012) (requiring the plan administrator to provide a summary plan description to plan participants, and annual, terminal, and supplementary reports to the Secretary of Labor).

(62) See, e.g., I.R.C. [section] 401(a) (2012) (outlining qualification requirements for qualified pensions, profit-sharing, and stock bonus plans); Employee Retirement Income Security Act of 1974 [section] 404, 29 U.S.C. [section] 1104(a)(1)(C) (2012) (requiring a fiduciary to diversify investments of the plan as warranted by the circumstances to minimize the risk of large losses). In addition, prohibited transaction rules prevent parties in interest from engaging in certain transactions with an employee benefit plan. See I.R.C. [section] 4975 (2012) (imposing a tax on prohibited transactions conducted with disqualified persons); Employee Retirement Income Security Act of 1974 [section] 406, 29 U.S.C. [section] 1106 (2012) (enumerating prohibited transactions for fiduciaries). For example, an employer usually cannot sell, exchange, or lease any property to the plan. Employee Retirement Income Security Act of 1974 [section] 406(a)(1)(A), 29 U.S.C. [section] 1106(a)(1)(A) (2012).

(63) I.R.C. [section] 411(a)(8) (2012); Employee Retirement Income Security Act of 1974 [section] 3(24), 29 U.S.C. [section] 1002(24) (2012).

(64) I.R.C. [section] 410(a) (2012); Employee Retirement Income Security Act of 1974 [section] 202, 29 U.S.C. [section] 1052 (2012).

(65) I.R.C. [section] 410(b) (2012).

(66) I.R.C. [section] 411(a) (2012); Employee Retirement Income Security Act of 1974 [section] 203, 29 U.S.C. [section] 1053 (2012).

(67) I.R.C. [section] 411(b) (2012); Employee Retirement Income Security Act of 1974 [section] 204, 29 U.S.C. [section] 1054 (2012).

(68) I.R.C. [section] 415 (2012).

(69) Id. [section] 401(a)(4).

(70) Id. [section] 412; Employee Retirement Income Security Act of 1974 [section] 302, 29 U.S.C. [section] 1082 (2012).

(71) See supra text accompanying note 21.

(72) 42 U.S.C. [section] 2000e-2 (2012); Ariz. Governing Comm, for Tax Deferred Annuity & Deferred Comp. Plans v. Norris, 463 U.S. 1073,1074-75 (1983) (per curiam) (finding that Title VII of the Civil Rights Act of 1964 prohibits an employer from paying lower monthly retirement benefits to a woman than to a man who has made the same contributions); City of L.A. Dep't of Water & Power v. Manhart, 435 U.S. 702, 711 (1978) (finding that Title VII of the Civil Rights Act of 1964 prohibits an employer from requiring female employees to make larger contributions to its pension plan than male employees because of mortality table differentials between the sexes).

(73) I.R.C. [section] 1 (2012); Rev. Proc. 2014-61, 2014-47 I.R.B. 860, 861 [section] 3.01.

(74) I.R.C. [section] 1(h)(1)(D) (2012).

(75) For example, home mortgage interest is generally deductible, and gains from the sale of a personal residence are often excludable. Id. [section][section] 121, iO3(a)-(h).

(76) For example, gross income does not include interest on any state or local bond. Id. [section] 103.

(77) See supra note 33 for a more in-depth explanation of how an annuitant can often exclude a fraction of each annuity payment from income under I.R.C. [section] 72 (2012).

(78) See I.R.C. [section] 101(a) (2012) (excluding life insurance proceeds paid by reason of death of the insured from gross income calculations).

(79) See, e.g., Gary C. Bhojwani, Allianz Life Ins. Co. of N. Am., Rethinking What's Ahead in Retirement 13 (2011), available at http://assets.knowledge.allianz.com/ downloads/Allianz_life_rethinking_what_s_ahead_in_retirementent_1154.pdf (outlining how annuities can generate guaranteed retirement income for life); Soc'y of Actuaries, Designing a Monthly Paycheck for Retirement 3-7 (2012), available at http://www.soa.org/ workarea/downloadasset.aspx/id-30089 (discussing the different options for generating retirement income and important factors to consider when deciding which one to choose); Anthony Webb, Making Your Nest Egg Last a Lifetime, Issue in Brief (Ctr. for Ret. Research at Bos. Coll., Chestnut Hill, Mass.), Sept. 2009, at 2-3, available at https://npers.ne.gov/SelfService/public/ howto/publications/MakingYourNesteggLast.pdf (examining alternatives and their tradeoffs on how to convert accumulated savings into a monthly paycheck). See generally Bonnie-Jeanne MacDonald et al., Soc'y of Actuaries, Research and Reality--A Literature Review on drawing Down Retirement Financial Savings (2011), available at http:// www.soa.org/WorkArea/DownloadAsset.aspxPid-19866 (reviewing existing literature advising retirees on how to draw down their financial savings).

(80) See, e.g., Jonathan Barry Forman, Optimal Distribution Rules for Defined Contribution Plans: What Can the United States and Australia Learn from Other Countries?, in NEW YORK UNIVERSITY Review of Employee Benefits and Executive Compensation [section] 3.03(2] (2012).

(81) Id. [section] 3.01.

(82) Id. [section] 3.0314].

(83) See William P. Bengen, Determining Withdrawal Rates Using Historical Data, J. FIN. PLAN., Oct. 1994, at 174-75 (explaining, using historical data, why retirees should withdraw no more than 4% of their retirement savings each year); see also Janemarie Mulvey & Patrick Purcell, Cong. Research Serv., R40008, Converting Retirement Savings into Income: Annuities and Periodic Withdrawals 17 (2008) ("[A] large body of research on safe withdrawal rates for individuals has determined that a real withdrawal rate in the neighborhood of 4 percent of the initial portfolio has a low chance of running out of money." (internal quotation marks omitted)); Benjamin Bridges, Robert Gesumaria & Michael V. Leonesio, Assessing the Performance of Life-Cycle Portfolio Allocation Strategies for Retirement Saving: A Simulation Study, SOC. SECURITY Bull., 2010, at 23 (examining the performance of life-cycle portfolio allocation strategies with varying exposure to stock and bond market risk based on observed historical U.S. asset returns).

(84) Bengen, supra note 83, at 175.

(85) This example is taken from Eleanor Laise, A Strategy for a Lifetime of Income, Kiplinger (Aug. 17, 2011), http://www.kiplinger.com/features/archives/krr-a-strategy-for- a-lifetime-of-income.html, archived at http://perma.cc/DP7N-QK9Q.

(86) Id.; see also Michael Finke, Wade D. Pfau & David M. Blanchett, The 4 Percent Rule is Not Safe in a Low-Yield World (2013), available at http://wsisonline.com/papers_files/The%204%20Percent%20Rule.pdf (advising against the 4% rule); Kelly Greene, Say Goodbye to the 4% Rule, Wall St. J., Mar. 3, 2013, http:// online.wsj.com/news/articles/SB10001424127887324162304578304491492559684, archived at http:// perma.cc/QA5Z-3HT3 (explaining that due to market forces eroding the value of retiree's nest eggs, the 4% rule puts retirees at risk of running out of money); Eilene Zimmerman, 4% Rule for Retirement Withdrawals Is Golden No More, N.Y. Times, May 14, 2013, http://www.nytimes.com/2013/05/15/business/retirementspecial/the-4-rule-for- retirement-withdrawals-may-beoutdated.html?_r=o, archived at http://perma.cc/YRQ9-32XV ("Many financial advisors are rejecting the 4 percent rule as out of touch with present realities.").

(87) Farrell Dolan, Applying the 4-Box Strategy to Retirement Income Planning: Generating a Lifetime of Income, Limra's Marketfacts Q., Fall 2009, at 84, 88, available at http://pjwalkercommunications.com/wp-content/uploads/2010/02/Market-Facts.pdf ("This single product solution offers a high cash flow and income is guaranteed for life."); Darla Mercado, Making the Case for Annuities, InvestmentNews (Mar. 25, 2012, 12:01 AM), http:// www.investmentnews.com/article/20120325/REG/303259969/making-the-case-for- annuities, archived at http://perma.cc/ZZ6X-KFFU (explaining that annuities remain an attractive option despite changes in the economy reducing their returns).

(88) See Immediate Annuities Update, Annuity Shopper, Winter 2014, at 18 tbl.5, available at http://www.immediateannuities.com/pdfs/as/annuity-shopper-2014-01.pdf (showing average monthly payout for 65-year-old man of $572, a total of $6864 per year).

(89) Id. (showing average monthly payout for 65-year-old woman of $534, a total of $6408 per year).

(90) Id. (showing an average monthly payout for 65-year-old man with 3% cost of living adjustment of $422 in the first year of his retirement, for a total of $5064 for the first year).

(91) See Jason S. Scott, The Longevity Annuity: An Annuity for Everyone?, FIN. ANALYSTS J., Jan.-Feb. 2008, at 43-44, available at http://corp.financialengines.com/employer/FE-LongevityAnnuity-FAJ-08.pdf (explaining the advantages of longevity annuities as compared to immediate annuities); Anthony Webb, Guan Gong & Wei Sun, An Annuity that People Might Actually Buy 2 (Ctr. for Ret. Research at Bos. Coll., Working Paper No. 7-10, 2007), available at https://www2.bc.edu/~sunwc/paper/ib_7-10.pdf (discussing calculations of the value of longevity insurance).

(92) E-mail from Hersh Stern, WebAnnuities Ins. Agency, Inc., to Jonathan Barry Forman (Feb. 7, 2012, 11:46 EST) (on file with authors). Alternatively, that 65-year- old man could have purchased a deferred annuity that starts at age 80 and pays $17,069.40 per year; at age 75 and pays $11,649.84 per year; or at age 70 and pays $8133.60 per year. Id. Companies do not offer inflation-adjusted deferred annuities, but some companies do offer fixed step-ups. Joseph A. Tomlinson, Income Choices, FIN. PLAN. (May 1, 2011), http://www.financial- planning.com/fp_issues/2011_5/income-choices-26728oi-i.html, archived at http://perma.cc/U35E-EXKR (comparing various investment strategies including systematic withdrawals, immediate annuities, deferred annuities, and guaranteed lifetime withdrawal benefits).

(93) See, e.g., Stephen C. Sexauer, Michael W. Peskin & Daniel Cassidy, Making Retirement Income Last a Lifetime, Fin. Analysts J., Jan.-Feb. 2012, at 76-77 (proposing a "decumulation benchmark" that would use about 88% of retiree savings to purchase a laddered portfolio of Treasury Inflation-Protected Securities [TIPS] for the first 20 years and a deferred life annuity purchased with the remaining 12%); Rick Wurster, DC 20/20: Pathways to a Secure Retirement, Rotman Int'l J. Pension Mgmt., Fall 2011, at 54, 58 (suggesting that an annuity providing 35% of real income replacement from age 85 would cost about 7.5% of a participant's average account balance at retirement).

(94) Finally, it is worth noting that workers might be able to buy deferred annuities in installments, starting at a young age. For example, a worker could use a portion of her retirement savings each year to purchase a deferred annuity that starts at age 65, or at the advanced ages of 70, 75, 80, 85, or even 90. Accordingly, this type of deferred annuity product could be used to provide retirement benefits that mimic the lifetime pensions provided by traditional defined benefit plans. See Moshe A. Milevsky, Real Longevity Insurance with a Deductible: Introduction to Advanced-Life Delayed Annuities (ALDA), N. Am. Actuarial J., Oct. 2005, at 109, 111 ("[T]he [Advanced-Life Delayed Annuity] is preferable to a pure endowment policy that would (mature and) pay a lump sum at age 80, 85, or 90 since it would continue to provide periodic lifetime income regardless of how long the annuitant lived beyond the endowed age."); see also Zorast Wadia, Longevity Risk of Retirement, Actuarial Dig., Spring 2012, at 4, available at http://publications.milliman.com/ publications/eb-published/pdfs/longevity-risk-and-retirement.pdf (proposing a new retirement paradigm combining aspects of a defined benefit plan and a defined contribution plan).

(95) See Moshe A. Milevsky & Ling-wu Shao, Annuities and Their Derivatives: The Recent Canadian Experience ("[GLWB funds] provide savers with (some of) the retirement longevity protection of a traditional annuity, without forcing them to surrender upside potential or liquidity."), in Securing Lifelong Retirement Income: Global Annuity Markets and Policy 50, 56 (Olivia S. Mitchell, John Piggott & Noriyuki Takayama eds., 2011).

(96) Mechanically, the investor or retiree deposits or rolls over a sum of money into a variable annuity with sub-accounts that are invested in a portfolio of stocks, bonds, and other generic investments. Depending on market performance, that investment portfolio grows or shrinks. In any event, at retirement, the annuitant begins taking guaranteed withdrawals from the account. Payouts come from the invested funds, but if those funds are ever depleted due to long life or poor investment returns, the guaranteed minimum kicks in. On the other hand, if the investment portfolio performs well, payouts can be increased. Tomlinson, supra note 92.

(97) Id.

(98) Cooper, supra note 9, at 1-2.

(99) Id.

(100) See, e.g., Ralph Goldsticker, A Mutual Fund to Yield Annuity-Like Benefits, Fin. Analysts J., Jan.-Feb. 2007, at 63, 65 (describing alternative tontine structures, such as the pooling of assets from multiple tontine cohorts, investing assets in variable-income securities, and establishing inflation-adjusted payouts); Paul Newfield, The Tontine: An Improvement on the Conventional Annuity?, J. Retirement, Winter 2014, at 37, 42 (delineating the advantages of tontines, or "pooled survival funds," over traditional annuities, which include the lack of a contingency reserve requirement and a higher expected return).

(101) This example is derived from Moshe A. Milevsky, Want Financial Security? Look to the Renaissance, Wall St. J., Apr. 21, 2013, http://online.wsj.com/article/SB10001424127887324532004578358110813542442.html?m od=ITP_journalreport_i,

archived at http://perma.cc/RF7H-5FU8.

(102) For example, Professor Suzanne Shu suggests that a tontine for one's fellow firefighters will be perceived as fairer than the typical commercial annuity that they could buy from an insurance company: with a commercial annuity, an early death seems to benefit the insurance company, but with a tontine, an early death benefits fellow firefighters. Shlomo Benartzi, Behavioral Finance and the Post-Retirement Crisis: A Response to the Department of the Treasury/Department of Labor Request for Information Regarding Lifetime Income Options for participants and Beneficiaries in Retirement Plans 15 (2010), available at http://www.dol.gov/ebsa/pdf/1210-AB33- 617.pdf.

(103) For background on tontine annuities, see, for example, Goldsticker, supra note 100; Milevsky & Salisbury, supra note 1; Michael J. Sabin, A Fast Bipartite Algorithm for Fair Tontines (May 22, 2011) (unpublished manuscript), available at http://ssrn.com/abstract=i848737; Sabin, supra note 15.

(104) See supra text accompanying note 101.

(105) Individuals who invest in annuity-like products have mortality gains and losses depending on when they die. Individuals who live longer than their peers get mortality gains from those who precede them, while individuals who die earlier than their peers suffer mortality losses. See David Blake, Annuity Markets: Problems and Solutions, 24 GENEVA PAPERS ON RISK & INS. 358, 371 (1999) (explaining that a mortality cross-subsidy "arises because some annuitants will die shortly after taking out an annuity thereby releasing a 'mortality profit' which insurance companies share with longer-surviving annuitants").

(106) The term "fair transfer-plan" is derived from Sabin, supra note 15, at 5.

(107) The situation is identical to a commercial annuity: once the premium is paid, there is no refund.

(108) That is, the underlying investments do not pay interest or dividends, nor are there any sales that result in gains or losses. We relax this assumption later in the paper. See infra subsection II.B.1.d.

(109) The life expectancies (e,) and death probabilities (9,) in Table 1 are derived from data provided to the authors by the Social Security Administration. E-mail from K. Mark Bye, Soc. Sec. Admin., to Jonathan Barry Forman (Nov. 12, 2013, 14:31 EST) (on file with authors). See infra Appendix Table 1 for a fuller version of the Social Security Administration 2009 unisex life table.

(110) Table 1 is drawn from Bye, supra note 109, and the authors' computations.

(111) The force-of-mortality probabilities in Table 1 were computed from the death probabilities ([q.sub.i]) in Column 4 of that table. See Sabin, supra note 15, at 10-12 (demonstrating how the force-of-mortality method is interpolated from the probability of death during a given year).

The explanation is as follows: at the outset, we make the simplifying assumption that the force of mortality is constant during each year of age. Next, suppose that the probability of dying during a specific year of age is 5%. Then, the probability of surviving the year is 1-0.05 = 95%. Now suppose the probability of surviving the first 6 months is 1-0.05/2 = 97.5%, and the probability of surviving the second 6 months is the same. Then, the probability of surviving the year is [(0.975).sup.2] = 95.063%. Now suppose the probability of surviving the first month is 1-0.05/12, and the same for the second month, third month, etc. Then, the probability of surviving the year is [(1-0.05/12).sup.12] = 95.113%. Generalizing this math, if the probability of surviving each of n periods within the year is 1-0.05/11, then the probability of surviving the year is [(1-0.05/n).sup.n]. As n grows to infinity, the probability of surviving the year becomes [e.sup.-.05] = 95.123%, where e is Euler's number (-2.71828). The probability of dying sometime during the year (i.e., the death probability) is 1-0.95123 = 4.877%, and the force-of-mortality probability is 5%.

Now, let us work it in reverse. Suppose the mortality table says that the death probability during a specific year is 5%. What is the force-of-mortality probability for the year? It is the value x that satisfies [e.sup.-x] = 1-0.05. The solution is x = -ln(1 - .05) = 5.129%, where "ln" is the natural logarithm.

Accordingly, the force-of-mortality probabilities in Table 1 were computed from the death probabilities in Table 1 by using the formula, [f.sub.i] = -ln(1 - [q.sub.i]). For example, for member 4, [f.sub.4] = -ln(- [q.sub.4]) = -ln(1 - 0.051906) = 0.053302. Of note, the force-of-mortality probabilities are fairly close in value to the death probabilities, except at older ages. See infra Appendix Table 1 (showing how the values in Columns 3 and 4 diverge as individuals live beyond age too).

(112) The explanation is as follows: our goal is to design a fair transfer-plan, one that provides fair bets to all of the members. This means we want the expected return (ERi) received by each member i to be zero. Mathematically, we want 0 = -[f.sub.i][s.sub.i+] [[summation].sub.j[not equal to]i] [f.sub.j][s.sub.j][w.sub.i]/1-[w.sub.j]) for each member i,

where: [f.sub.i] is the force-of-mortality probability of member i, [s.sub.i] is the contribution made by member 1, and [w.sub.i] is the fair transfer-plan weight for member i that we need to provide fair bets. See Sabin, A Fast Bipartite Algorithm for Fair Tontines, supra note 103, at 7-8 (explaining the underlying algorithm).

The formula above gives us a set of m equations, one equation for each member i. The solution to those equations is unique, meaning there is only one set of fair transfer-plan weights ([w.sub.i]) that solve those equations. The challenging part is that the equations are not linear because, in each equation, one unknown, [w.sub.i], is divided by another unknown, (1 - [w.sub.j]). That means we cannot solve the equations using the standard methods of linear algebra. Fortunately, however, we are able to solve these equations by using an iterative method designed specifically for them. More specifically, the iterative method uses a bisection algorithm. See id. at 12-13 (demonstrating the bisection algorithm method). While the explanation of how to create the computer program to solve that algorithm is too involved to explain here, we can easily show that the method works, as the fair transfer-plan weights ([w.sub.i]) in Table 1 do solve the pertinent equations. For example, for i = 3,[ER.sub.3] = 0:

- 0.032638 x $1000 = -32.638 + 0.013269 x $1000 x 0.146795/(1 - 0.053815)= 2.059 + 0.020523 x $1000 x 0.146795/(1 - 0.086183)= 3.297 + 0.053302 x $1000 x 0.146795/(1 - 0.713207)= 27.283 = 0

We can verify that similar equations for i - 1, 2, and 4 also work. Therefore, we can be certain that the fair transfer-plan weights ([w.sub.i]) in Table 1 accomplish our goal for a fair transfer-plan (i.e., [ER.sub.i] = o).

(113) Checking our answer, $187.64 + $300.51 + $511.85 - $1000.

(114) See supra note 105 and accompanying text.

(115) See, e.g., Sabin, supra note 15, at 14-16 (providing an example of a tontine that could be fair regardless of the participants' gender).

(116) See, e.g., supra text accompanying note 21.

(117) The life expectancies (e,) and death probabilities ([q.sub.i]) in Table 2 are derived from data provided to the authors by the Social Security Administration. E-mail from K. Mark Bye, Soc. Sec. Admin., to Jonathan Barry Forman (Dec. 3, 2014,10:03 EST) (on file with authors).

(118) Table 2 is drawn from Bye, supra note 117, and the authors' computations.

(119) Checking our answer, $398.27 + $398.27 + $203.47 = $1000.01 (error due to rounding).

(120) That is, [ER.sub.i] = 0 for both women and men.

(121) See supra notes 88-89 and accompanying text. We have much more to say about gender issues later in this Article. See infra Section V.D; see also Mary L. Heen, Nondiscrimination in Insurance: The Next Chapter, 49 Ga. L. REV. (forthcoming 2015) (manuscript at 61) (on file with University of Pennsylvania Law Review) (arguing that gender discrimination laws should be expanded to prevent insurance companies from selling gender-based annuities).

(122) Table 3 is drawn from Bye, supra note 117, and authors' computations.

(123) Checking our answer, $579.21 + $1265.16 + $2155.63 = $4000.

Intuitively, some readers may be wondering why, for example, member 2 (the $2000 contributor) would get more than twice as much as member 1 (the $1000 contributor). Asked differently, some readers may be wondering why member 2's fair transfer-plan weight ([w.sub.2]), 0.145278, would be more than twice as much as member is fair transfer-plan weight ([w.sub.1]), 0.066510.

Here, a slightly different example can help. Imagine a tontine fund with four otherwise identical 65-year-old men, except that while members 1, 2, and 3 each contribute $1000 to the tontine fund, member 4 contributes $3000. Now assume that member 1 dies, leaving members 2, 3, and 4 alive. Intuitively, it might seem that member l's $1000 contribution should be divided in proportion to the relative contributions ([s.sub.i]) of members 2, 3, and 4, in which case member 2 ([s.sub.2] = $1000) and member 3 ([s.sub.3] - $1000) would each get $200, one-fifth of dying member 1's $1000 contribution ($200 = $1000 x $1000/($1000 + $1000 + $3000)), while member 4 ([s.sub.4] = $3000) would get $600, or three-fifths ($600 = $1000 x $3000/($1000 + $1000 + $3000)). In fact, however, member 4 must get 100% of dying member 1's contribution, and he must also get 100% of member 2's contribution or 100% of member 3's contribution if either of them is the one who dies. Otherwise, member 4's expected return from the investment would be less than zero. After all, if member 4 dies, he will lose his entire $3000 contribution; therefore, in effect, he must get 100% of the contributions of any other member who dies.

In short, all other things being equal, members who make larger contributions to a tontine fund must get disproportionately higher mortality-gain distributions from the fund in order to receive a fair bet. The fair transfer-plan weights ([w.sub.i]) do the work. That is why, in Table 3, member 2's fair transfer-plan weight ([s.sub.2] = $2000; [w.sub.2] = 0.145278), is more than twice as much as member 1's fair transfer-plan weight ([s.sub.1] = $1000; [w.sub.1] = 0.066510).

(124) Here, a member's risk means the product [f.sub.i][s.sub.i] of his force- of-mortality probability ([f.sub.i]) multiplied by his contribution (s,), and the total risk means the sum of all members' risks. See Sabin, supra note 15, at 14 ("[A]n FTP exists if and only if no member holds more than half of the total risk of the pool."). Additional rules may be imposed that limit the total amount that a member may contribute. Id.

(125) See supra note 107 and accompanying text.

(126) See supra Tables 1 & 2 (using the Social Security Administration's 2009 unisex and gender-based life tables, respectively).

(127) Felicitie C. Bell & Michael L. Miller, Soc. Sec. Admin., Life Tables for the United States Social Security Area 1900-2100, at 14 fig.4a (2005), available at http://www.ssa.gov/oact/NOTES/pdf_studies/study120.pdf; Jonathan Barry Forman & Yung-Ping (Bing) Chen, Optimal Retirement Age, in New York University Review Of Benefits And Executive Compensation [section] 14.02 (2008) (outlining the effect of increased life expectancy on current pension plans).

(128) As a legal matter, the tontine fund agreement would need to specify how and when it would choose a new life table for use in its fair transfer-plan.

(129) See Sabin, supra note 15, at 24-25 (illustrating such a simulation).

(130) Id. at 25 fig. 5.

(131) See id. at 5 (noting that, in a fair tontine, "a surviving member's expected payout does not depend on the number of members in the pool, or the ages, genders, or contributions of the other members").

(132) In this example, two other members died on April 7, and this hypothetical member had $184.32 credited to her account ($184.32 = $135.41 + $48.91).

(133) This hypothetical tontine fund has approximately 5000 members of varying ages and genders who have made varying contributions. Mortality gains are based on a fair transfer-plan, and surviving members get a single payout at the end of the month.

(134) In the real world, it would certainly take some time for the tontine fund manager to discover and record deaths and to compute the resulting mortality gains. Accordingly, actual monthly mortality-gain distributions might be delayed for a month or two. It would be more accurate to say that the surviving member in Table 4 is entitled to, and will eventually receive, the $52.29 attributable to the April 12th death of the member whose account is shown in Table 5.

(135) This hypothetical tontine fund has approximately 5000 members of varying ages and genders who have made varying contributions. Mortality gains are based on a fair transfer-plan, surviving members get a single payout at the end of the month, and dying members forfeit the balance in their accounts on the date of death.

(136) Dow Jones Industrial Average, supra note 54. Monthly mortality-gain distributions would also fluctuate with changes in the dividend and interest yields on the underlying assets.

(137) The Dangers of Buying an Annuity When Interest Rates Are Low, supra note 55.

(138) See Marotta, supra note 56 and accompanying text. We will further discuss how tontine financial products can help investors deal with market volatility in Section V.C, infra.

(139) See Sabin, supra note 15, at 22-26; infra subsection II.C.2.

(140) This footnote explains how to compute a yearly annuity factor, which is the actuarial present value of a life annuity that pays $1 each year for life. The monthly annuity factor is approximately 12 times the yearly annuity factor.

We compute the annuity factor at each birthday by working backwards from the terminal age of the mortality table. For the 2009 Social Security Administration table that we use (see infra Appendix Table 1), the last entry is for age 119; thus the terminal age is 120, meaning that the table implies an individual always dies before her 121st birthday.

If the individual is alive at birthday 120, she receives $1. Since she does not survive to birthday 121, the only payment she receives is the single dollar at age 120, so the actuarial present value of the annuity is $1. Thus:

[a.sub.120] = 1.

If the individual is alive at birthday 119, she receives $1. In addition, if she survives to birthday 120, she will receive a future payment stream having an actuarial value of [a.sub.120]. Thus, at birthday 119, the actuarial present value of payments is

[a.sub.119] = 1 + (1 - [q.sub.119]) x [a.sub.120] / (1 + d),

where: [q.sub.119] is the probability of dying during age 119 (i.e., before birthday 120), which is given in the mortality table; and d is the discount rate (e.g., d = .07, or 7%).

Similarly, if the individual is alive at birthday 118, she receives $1, and if she survives to birthday 119, she will receive a future payment stream having an actuarial value of [a.sub.119]. Thus, at birthday 118, the actuarial value of payments is:

[a.sub.118] = 1 + (1 - [q.sub.118]) x [a.sub.119] /(1 + d).

Continuing in this manner, we calculate the annuity factor [a.sub.117] for birthday 117, [a.sub.116] for birthday 116, and so on, until we reach the birthday of interest. For example, for the 2009 Social Security Administration table and a discount rate of 7%, continuing until birthday 65 gives [a.sub.65] = 10.359. (That is, the actuarial present value of an annuity that pays $1 each year for the life of a 65-year-old

is $10.36 (at a 7% discount rate).) As mentioned, the monthly annuity factor is approximately 12 times the yearly annuity factor, and Column 5 of Appendix Table 1, infra, shows that the monthly annuity factor for the first month of the year in which our hypothetical retiree turns 65 is 117.6939, or about 12 x 10.359.

(141) Column 5 of Appendix Table 1, infra, shows the applicable monthly annuity factors for the first month of each year starting with age 65, when monthly tontine-annuity distributions are expected to commence.

(142) This hypothetical tontine annuity has approximately 5000 members of varying ages and genders who have made varying contributions. Mortality gains are based on a fair transfer-plan, and surviving members get a single payout at the end of the month, based on the applicable monthly annuity factor.

(143) Column 6 of Appendix Table 1, infra, shows the inflation-adjusted applicable monthly annuity factors for the first month of each year starting with age 65, when monthly tontine-annuity distributions are expected to commence.

This footnote explains how to compute a yearly inflation-adjusted annuity factor, which is the actuarial present value of a life annuity that pays $1 the first year and then increases future annual payments by the assumed inflation rate. The monthly annuity factor is approximately 12 times the yearly annuity factor.

The annuity factor is computed in a manner similar to the uniform case in note 140, supra, except that now it includes the inflation adjustment. Letting i denote the inflation rate (e.g., i = .03 or 3%), then:

[a.sub.120] = 1,

[a.sub.119] = 1 + (1 + i) x (1 - [q.sub.119]) x [a.sub.120] /(1 + d),

[a.sub.118] + (1 + i) x (1 - [q.sub.118]) x [a.sub.119]/(1 + d),

and so forth. For example, we can show that if the inflation parameter is set to 3%, then [a.sub.65] = 13.216.

As mentioned, the monthly annuity factor is approximately 12 times the yearly annuity factor, and Column 6 of Appendix Table 1, infra, shows that the inflation-adjusted monthly annuity factor for the first month of the year in which our hypothetical retiree turns 65 is 151.9876, or about 12 x 13.216.

(144) See infra Table 7.

(145) This hypothetical tontine annuity has approximately 5000 members of varying ages and genders who have made varying contributions. Mortality gains are based on a fair transfer-plan, and surviving members get a single payout at the end of the month based on the applicable monthly annuity factor.

(146) Of course, default investments could be offered to individual investors, just as target date funds are typically a default investment offered in self-directed 401(k) plans. See U.S. DEP'T OF Labor, Emp. Benefits Sec. Admin., Target Date Retirement Funds-Tips for ERISA PLAN FIDUCIARIES (2013), available at http://www.dol.gov/ebsa/pdf/fsTDF.pdf (providing guidance to fiduciaries of 401(k) and other employee-directed retirement programs regarding selecting and monitoring target date retirement funds).

(147) See Jonathan Barry Forman, The Future of 401(k) Plan Fees, in NEW YORK UNIVERSITY Review of Benefits and Executive Compensation [section] 9.02[2]-[3] (2007) (noting that large plan investors generally pay lower fees, have better portfolio allocations, and have professional investment advisors that pick better investment products); Alicia H. Munnell et al., Investment Returns: Defined Benefit vs. 401(k) Plans, ISSUE IN BRIEF (Ctr. for Ret. Research at Bos. Coll., Chestnut Hill, Mass.), Sept. 2006, at 6, available at http://www.hrpolicy.org/ members/downloads/2006/CRR_IB_09-2006.pdf (finding that professionally managed defined benefit plans outperformed individually managed 401(k) plans over the period 1988-2004).

(148) Indeed, experts estimate that the typical commercial life annuity has a 12% "load" factor due to the combination of administrative expenses and adverse selection; that is, the typical commercial life annuity provides benefits that are worth just 88% of an actuarially fair annuity (i.e., a "money's worth ratio" of 88%). See MARK J. WARSHAWSKY, RETIREMENT INCOME: RISKS AND STRATEGIES 66 (2012) ("[D]ue to a combination of administrative costs and selection effects, the nominal annuity is assumed to have a money's worth ratio of 0.88, that is, the couple faces a 12 percent load factor on their annuity purchase."). Put differently, the payouts from actuarially fair annuities would be around 15% higher than in current annuity markets. See James Poterba et al., The Composition and Drawdown of Wealth in Retirement, J. ECON. PERSP., Fall 2011, at 102 tbl. 3 (providing that the actuarially fair life annuity for a 65-year- old-man in 2008 was 9.95% and the AnnuityShopper price for a commercial life annuity was just 8.46%, thus indicating a load factor of 17.6%: 9.95%/8-46% - 1 = 17.6%); see also Jeffrey R. Brown et al., The Role of Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program ("[T]he expected present value of annuity payouts is typically below the purchase price of the annuity...."), in RISK Aspects of Investment-Based Social Security Reform 321, 321-22 (John Y. Campbell & Martin Feldstein eds., 2001); James M. Poterba & Mark Warshawsky, The Costs of Annuitizing Retirement Payouts from Individual Accounts ("The cost of such annuities, including both administrative and sales costs, the 'adverse selection' costs associated with voluntary purchase behavior, and return on capital for the insurance company offering the annuity policy, affect the retirement income that the participant receives for a given level of wealth accumulation."), in ADMINISTRATIVE Aspects of Investment-Based Social Security Reform 173, 173-74 (John B. Shoven ed., 2000); Benjamin M. Friedman & Mark J. Warshawsky, The Cost of Annuities: Implications for Saving Behavior and Bequests, 105 Q.J. ECON. 135, 152 (1990) (arguing that actuarially unfair annuity costs are a cause of lack of public participation in the individual life annuity market); Olivia S. Mitchell et al., New Evidence on the Money's Worth of Individual Annuities, 89 AM. ECON. REV. 1299, 1309 (1999) (finding that a typical retiree "would perceive a noticeable 'transaction cost' when purchasing an annuity from a commercial insurance carrier").

(149) Variable Annuity Expense Analyzer, CHARLES SCHWAB, http://www.schwab.wallst.com/ Tools/VAAnalyzer/public (last visited Jan. 16, 2015), archived at http://perma.cc/QW77-AE2K (noting the March 31, 2014 Morningstar survey); see also INSURED RET. INST., 2011 IRI FACT BOOK 56 figs.3-5 (2011), available at http://www.advisorsexcel.com/downloads/2011FactBook.pdf (showing that average total expenses for variable annuities in 2010 were 2.33%, compared with average total expenses for mutual funds that year of just 1.32%). The additional expenses associated with variable annuities include both so-called "mortality and expense" (M&E) charges and separately stated administrative expenses.

(150) Charles Schwab, supra note 149.

(151) The Vanguard Group, Inc. offers a variable annuity with a total expense ratio ranging from 0.46% to 0.77%. Tax-Deferred Retirement Savings with the Vanguard Variable Annuity, VANGUARD, https://investor.vanguard.com/annuity/variable (last visited Jan. 16, 2015), archived at http://perma.cc/YU8C-2UV6.

(152) See Spartan 500 Index Fund--Investor Class, FIDELITY, https://fundresearch.fidelity.com/ mutual-funds/summary/315911206 (last visited Jan. 16, 2015), archived at http://perma.cc/5U4239BX (offering 0.10% gross expense ratio); see also Alicia H. Munnell et al., Will Regulations to Reduce IRA Fees Work?, ISSUE IN BRIEF (Ctr. for Ret. Research at Bos. Coll., Chestnut Hill, Mass.), Feb. 2013, at 2, available at http://crr.bc.edu/wp- content/uploads/2013/02/IB_13-2-508.pdf (noting that many studies have found that actively managed funds underperform compared to index funds); Richard W. Kopcke et al., Fees and Trading Costs of Equity Mutual Funds in 401(k) Plans and Potential Savings From ETFs and Commingled Trusts (Ctr. for Ret. Research, Working Paper No. 2009-27, 2009), available at http://crr.bc.edu/wp- content/uploads/2009/11/wp_2009-27508.pdf (encouraging a shift from actively managed funds to exchange-traded funds or commingled trusts).

(153) See Our History, TIAA-CREF FiN. SERVICES, https://www.tiaa- cref.org/public/ assetmanagement/about/why/our-history (last visited Jan. 16, 2015), archived at http:// perma.cc/AD44-KSMY (describing the company's products and programs since establishment).

(154) Id.; see also Poterba & Warshawsky, supra note 148, at 191-98 (discussing the history and development of individual annuities offered by TIAA-CREF).

(155) See TIAA-CREF FIN. SERVS., 2013 ANNUAL REPORT: COLLEGE RETIREMENT EQUITIES Fund 7-30 (2013), available at http://wwwi.tiaa- cref.org/ucm/groups/content/ @ap_ucm_p_tcp_inco/documents/document/tiaao1007803.pdf (analyzing the performance of the eight account types).

(156) TIAA-CREF Fin. Servs., Prospectus: College Retirement Equities FUND 6 (2014), available at http://wwwi.tiaa- cref.org/public/prospectuses/cref_prospectus.pdf.

(157) Id. at 74-7S. Of note, TIAA-CREF annuities have been using unisex life tables since 1982. See Spirt v. Teachers Ins. & Annuity Assn, 691 F.2d 1054, 1066 (2d Cir. 1982) (holding that TIAACREF is subject to Title VII, thus forbidding the use of sex-based mortality tables to calculate benefits based on contributions), vacated on other grounds, 463 U.S. 1223 (1983).

(158) But see TIAA-CREF FIN. SERVS., supra note 156, at 76 (mentioning that mortality experience has "not historically had a significant impact").

(159) Id. at 73. For more details, see generally TIAA-CREF FIN. SERVS., COLLEGE Retirement equities Fund ("CREF") Supp. No. 1 B-41 to B-42 (2014), available at http://wwwi.tiaa-cref.org/public/prospectuses/cref_sai.pdf.

(160) TIAA-CREF FIN. Servs., supra note 156, at 73. Of note, rather than using a fair transfer-plan to share mortality gains from each dying member (as our tontine annuity would), CREF's method shares aggregate mortality gains and losses. Consequently, some participants will get a better deal, and some will get a worse deal than they would with a fair transfer-plan. Cf. Sabin, supra note 15, at 59-62 (discussing the bias present in group self annuities that give some members better payouts than others).

Also, while our tontine pension (discussed infra Section II.D) results in forfeitures by workers as well as retirees, CREF participants do not face any forfeitures at all until participants voluntarily elect to take their distribution in the form of a one-life or two-life annuity, and typically such elections are not made until retirement after age 59.5. TIAA-CREF FIN. SERVS., supra note 156, at 72-75.

Finally, we note in passing that tontine annuities and CREF annuities are not the only kind of "pooled annuities" that could share longevity risk among annuitants. See, e.g., Michel Denuit et al., Longevity-Indexed Life Annuities, 15 N. Am. ACTUARIAL J. 97, 99-100 (2011) (proposing longevity indexing as an alternative method to sharing longevity risk among annuitants and annuity providers); Catherine Donnelly et al., Exchanging Uncertain Mortality for a Cost, 52 INS.: MATHEMATICS & ECON. 65, 69, 71 (2013) (comparing pooled annuity funds with mortality-linked funds); John Piggott et al., The Simple Analytics of a Pooled Annuity Fund, 72 J. RISK & INS. 497) 499-S01 (200S) (discussing the effect of risk diffusion on payouts in group self annuities); Andreas Richter & Frederik Weber, Mortality-Indexed Annuities: Managing Longevity Risk via Product Design, 15 N. AM. ACTUARIAL J. 212, 216-21 (2011) (proposing mortality indexing as a tool for improving traditional annuities); Michael Z. Stamos, Optimal Consumption and Portfolio Choice for Pooled Annuity Funds, 43 INS.: MATHEMATICS & ECON. 56, 58-61 (2008) (discussing how pooling effectively insures against longevity risk); Raimond Maurer et al., Participating Payout Life Annuities: Lessons from Germany 1 (Pension Research Council, Working Paper No. 2012-03, 2012), available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2078114 (noting that "participating life annuities offer guaranteed minimum benefits" for life and "an additional non-guaranteed surplus" based on investment return, mortality, and costs); Roberto Rocha & Dimitri Vittas, Designing the Payout Phase of Pension Systems: Policy Issues, Constraints and Options 28-47 (The World Bank Non Bank Fin. Insts. Grp., Working Paper No. 5289, 2010), available at http://wwwwds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2010/05/04/00015834 9_20100504092303/Rendered/PDF/WPS5289.pdf (proposing several policy responses to various types of pension risks).

(161) See supra text accompanying notes 12-14.

(162) See Milevsky & Shao, supra note 95, at 50, 56 (discussing the creation of GLWB products in Canada and their subsequent spread to the United States).

(163) See supra text accompanying notes 150-151.

(164) See William J. Wiatrowski, U.S. Bureau of Labor Statistics, Changing Landscape of Employment-based Retirement Benefits 1 (2011), available at http://www.bls.gov/opub/mlr/cwc/changing-landscape-of-employment-based- retirement-benefits.pdf ("It is well documented that the prevalence of defined benefit plans is declining; in many cases, such plans have been replaced by defined contribution plans."); see also William J. Wiatrowski, The Last Private Industry Pension Plans: A Visual Essay, MONTHLY LAB. REV., Dec. 2012, at 3, available at http://www.bls.gov/opub/mlr/2012/12/art1full.pdf ("[Defined benefit] plans are becoming rare for workers in private industry.").

(165) Towers Watson, supra note 48, at 15.

(166) See, e.g., CARLOS FIGUEIREDO & SANDY MACKENZIE, AARP PUB. POLICY INST., Older Americans' Ambivalence Toward Annuities: Results of an AARP Survey of Pension Plan and IRA Distribution Choices 6 n.6 (2012), available at http://www.aarp.org/content/dam/aarp/research/public_policy_institute/econ_sec/2 012/survey-pension-ira-distribution-AARP-ppi-econ-sec.pdf (noting that the 54th Annual Survey of Profit Sharing and 401(k) Plans carried out by the Plan Sponsor Council of America found that just "16.6 percent of all plans surveyed offered annuities as a distribution option, while 60.2% offered installments"); BEVERLY J. ORTH, APPROACHES FOR PROMOTING VOLUNTARY ANNUITIZATION (2008), available at http://www.soa.org/library/monographs/retirement- systems/retirement2020/2008/november/mono-2008-m-rso8-01-orth.pdf ("[A] large percentage [of defined contribution plans] offer no [annuity] options.... [T]he vast majority of IRAs are never converted to an annuity."); Paul J. Yakoboski, Retirees, Annuitization and Defined Contribution Plans, TRENDS & ISSUES (TIAA-CREF Institute, New York, N.Y.), Apr. 2010, at 3, available at https://www.tiaacrefinstitute.org/public/pdf/institute/research/trends_issues/ti _defimedcontributiono410.pdf (finding that only around 19% of retirees with significant defined contribution plan assets but little defined benefit pension income annuitized a portion of their retirement savings).

(167) See, e.g., Shlomo Benartzi et ah, Annuitization Puzzles, J. ECON. PERSP., Fall 2011, at 143, 154-57 (discussing behavioral and institutional factors leading to the low demand for annuities); Franco Modigliani, Life Cycle, Individual Thrift, and the Wealth of Nations, 76 Am. ECON. REV. 297, 307 (1986) ("[I]t is a well-known fact that annuity contracts, other than in the form of group insurance through pension systems, are extremely rare."). See generally Menahem E. Yaari, Uncertain Lifetime, Life Insurance, and the Theory of the Consumer, 32 REV. ECON. STUD. 137 (1965) (analyzing the effect of the uncertainty of lifespan on consumer behavior).

(168) See George A. (Sandy) Mackenzie, Annuity markets and Pension Reform 55-57 (2006) (finding adverse selection and a lack of understanding of annuities to be potential factors that reduce the demand for annuities); see also Annamaria Lusardi et al., Financial Sophistication in the Older Population 12-16 (Nat'l Bureau of Econ. Research, Working Paper No. 17,863, 2012), available at http://papers.ssrn.com/sol3/papers.cfmPabstract_id=2010395 (identifying the lack of financial sophistication, especially among the older population, as a potential source of poor decisionmaking about retirement).

(169) See MACKENZIE, supra note 168, at 43 (explaining that, in the life annuities market, moral hazard would lead to healthier behavior, meaning annuitants would tend to engage in behaviors increasing their lifespan).

(170) See id. at 41 ("Universal mandatory annuitization of part or all of the balances in individual accounts would lower the average life expectancy of the annuitant population, and should lower the average premium for each sex.").

(171) See supra subsection II.C.5.

(172) See supra subsection I.B.2.a.

(173) See supra text accompanying notes 42-45.

(174) Id. Pertinent here, for example, the Pension Benefit Guaranty Corporation took over "111 newly failed single-employer plans" in Fiscal Year 2013. PENSION BENEFIT GUAR. CORP., supra note 43, at 5. Further, the City of Detroit went into bankruptcy in large part because of its pension debts. See Monica Davey et al., Detroit Ruling Lifts a Shield on Pensions, N.Y. TIMES, Dec. 4, 2013, at Al (discussing a bankruptcy judge's finding that Detroit public employees' pensions were not protected in a bankruptcy).

(175) Wiatrowski, Changing landscape of Employment-Based Retirement Benefits, supra note 164. More specifically, there were 683,000 private pension plans in 2011. U.S. Dep't of Labor, Emp. Benefits Admin., Private Pension Plan Bulletin 1 (2013), available at http://www.dol.gov/ebsa/PDF/2011pensionplanbulletin.PDF. These are ERISA-covered plans and do not include non-ERISA plans such as IRAs and Roth IRAs. Of these ERISA-covered plans, just 45,256 were defined benefit plans (with 40.9 million participants and $2.5 trillion in assets), while 638,390 were defined contribution plans (with 88.7 million participants and $3.8 trillion in assets). Id. at 3 tbl.A1. Of these defined contribution plans, 513,000 were 401(k)-type plans. Id. at 2.

Also of note, a recent study estimated that 92% of the new pension plans formed from 2003-2007 were defined contribution plans, as opposed to defined benefit plans. U.S. GOV'T Accountability Office, GAO-11-333, Private Pensions: Some Key Features Lead to an Uneven Distribution of Benefits 12 fig.2 (2011), available at http://www.gao.gov/ new.items/d11333.pdf. See generally CONG. BUDGET OFFICE, USE OF TAX INCENTIVES FOR RETIREMENT Saving IN 2006 (2011), available at http://www.cbo.gov/sites/default/files/ cbofiles/attachments/2011-10-14-TaxIncentives.pdf (examining participation and contributions to various types of retirement plans by differing groups of workers).

(176) See George A. (Sandy) Mackenzie, The Decline of the Traditional pension: A Comparative Study of Threats to Retirement Security 3 (2010) ("[M]any observers believe that the defined benefit plan cannot survive as an institution in the private sector."); EDWARD A. ZELINSKY, THE ORIGINS OF THE OWNERSHIP SOCIETY: HOW THE Defined Contribution paradigm Changed America 4 (2007) (noting "the shift from the defined benefit modality to the defined contribution format"); Barbara A. Butrica et al., The Disappearing Defined Benefit Pension and Its Potential Impact on the Retirement Incomes of Baby Boomers, SOC. SECURITY BULL., 2009, at 1 ("The percentage of workers covered by a traditional defined benefit (DB) pension plan that pays a lifetime annuity, often based on years of service and final salary, has been steadily declining over the past 25 years."); Janice Kay McClendon, The Death Knell of Traditional Defined Benefit Plans: Avoiding a Race to the 40t(k) Bottom, 80 TEMP. L. REV. 809, 812 (2007) ("Even before the increased legislative requirements, traditional defined benefit plans were dying."); Edward A. Zelinsky, The Defined Contribution Paradigm, 114 YALE L.J. 451, 454 (2004) (describing the "emergence of the defined contribution society" as a "revolution" in pension plan form).

(177) See infra Section III.C.

(178) Id.

(179) We note that a tontine pension is basically a kind of deferred annuity. For example, unless an unmarried participant survives until retirement, she would forfeit the balance in her tontine pension account (just like an unmarried participant in a traditional defined benefit plan). If she wanted to defer her payouts even longer, for example, until age 85, then her account would simply reinvest the mortality-gain distributions from dying participants until that time. Because of adverse selection, it might be necessary for such deferral elections to be made years in advance.

(180) For more on how to design such qualified joint and survivor tontine annuities, see infra subsection V.D.3.

(181) See supra notes 42-45 and accompanying text.

(182) See, e.g., Forman & Mackenzie, supra note 29, at 6-39 to 6-40 ("[T]raditional defined benefit plans generally outperform [individually managed] 40t(k) plans."); Forman, supra note 147, at 9-5 (noting that there were "numerous economies of scale associated with traditional pension plans"); Munnell et al., supra note 147, at 6 ("Preliminary data suggest that IRAs under-perform employer-sponsored plans.").

(183) See supra notes 42-45 and accompanying text.

(184) To be sure, employers sometimes cut their contribution rates to defined contribution plans, but such plans are still fully funded by the contributions that are made.

(185) See supra note 48 and accompanying text.

(186) See FAQs About Cash Balance Pension Plans, U.S. DEP'T OF LAB., http://www.dol.gov/ebsa/FAQs/faq_consumer_cashbalanceplans.html (last visited Jan. 16, 2015), archived, at http://perma.cc/YHH2-Q4S6 (noting that cash balance plan participants can receive these kinds of distributions).

(187) See Kevin Olsen, PBGC Sues to Take Over Dewey & LeBoeuf Retirement Plans, Pensions & Investments (May 15, 2012), http://www.pionline.com/artide/20120515/ONLINE/120519943/pbgc-sues-to-take-over- dewey-amp-leboeuf-retirement-plans, archived at http:// perma.cc/L5ZT-UTFW (describing an example of an underfunded cash balance pension plan).

(188) See supra notes 177-180 and accompanying text.

(189) But see infra subsection V.D.2 (providing reasons why participants might be reluctant to make such contributions).

(190) See supra subsection II.B.3.a.

(191) See supra note 136 and accompanying text.

(192) We chose 30 years as a reasonable career with the employer. Obviously, workers who work 35 years would earn proportionally more tontine pension benefits, and those who work 25 years would earn proportionately less benefits. Tontine pension benefits would also vary if workers started working before or after our assumed start age of 33 or retired before or after our assumed retirement age of 65.

(193) In that regard, for example, the CalSTRS defined benefit plan uses a 3.75% annual wage growth assumption. MILLIMAN, supra note 19, at 57 tbl.B.1.

(194) If we had assumed that living workers could leave, their account balances would go with them to their new employer's plan, and vice versa, so we ignore them.

(195) We use the very plausible 10% contribution rate. That rate has the added advantage that it is easy to extrapolate away from it. For example, if one thinks that 15% is a better contribution rate, one need only multiply most of our model's results by 150%. Nor must the contributions

necessarily come from the employer: the results would be exactly the same if the employer and employee each contributed 5% of salary, for a total of 10%.

(196) Our 7.0% investment return assumption is also fairly reasonable. For example, the CalSTRS defined benefit plan uses 7.5% as its estimate of investment return (net of investment and administrative expenses). MILLIMAN, supra note 19, at 57 tbl.B.1. While many public pension plans have even higher assumed rates of return and have historically achieved those higher rates of return, many analysts believe we are in a low return environment for the indefinite future. See James J. Rizzo & Piotr Krekora, Presentation on the Goldilocks Principle & Investment Return Assumptions at Florida Government Finance Officers Association 2013 Annual Conference 41 (June 25, 2013), available at http://www.fgfoa.org/Assets/Files/Jim_Rizzo_Presentation_PDF.pdf (finding that 6.78% was the average rate of return projected by 8 national investment consulting firms for public pension plan portfolios over the next 15 years, compared with the 8% rate of return that those plans commonly assume).

(197) For example, the CalSTRS defined benefit plan uses a 3.0% inflation assumption. MILLIMAN, supra note 19, at 57 tbl.B.1.

(198) To make the simulation less complicated, only the retirement phase (i.e., the payouts to those age 65 and older) was simulated. The account balance at age 65 was set equal to the expected value (i.e., the statistical average) of the account of a worker who survives to age 65. The number of workers surviving to retirement was set to its expected value from the Social Security Administration's 2009 unisex life table. Bye, supra note 109.

(199) That is, the expected value of payouts is either uniform or inflation- adjusted.

(200) Bye, supra note 109.

(201) It is calculated as the sum of the prior year's balance multiplied by (l plus the interest rate) plus the current year's contribution multiplied by the square root of (1 plus the interest rate).

(202) This is the expected value of the balance that results from mortality gains. See supra note 198. It is computed by taking the preliminary balance in Column 4 and dividing it by (1 minus the death probability) in Column 5. For example, the closing balance in the account of an employee at age 64 is $843,377 ($843,376.82 = $833,161/(1 - 0.012113)) (minor error due to rounding).

(203) See supra notes 140-141 and accompanying text.

(204) For comparison, an annuity purchased from a commercial insurer would make a fixed monthly payment but of a lower amount depending on the insurer's load charge. For a typical load of 10%, the monthly payment would fall to just $6449.40 ($6449.40 - $7166 x 90%).

(205) The replacement ratio is the ratio of income in retirement to income pre- retirement. The desired replacement ratio is almost always assumed to be less than 100% because of the elimination of work-related expenses, because some pre-retirement income was devoted to saving for retirement, and because Social Security benefits are taxed more favorably than earned income. See Aon Consulting, Replacement Ratio Study: A Measurement Tool for Retirement PLANNING 24 (2008), available at http://www.aon.com/about-aon/intellectual- capital/ attachments/human-capital-consulting/RRStudy070308.pdf (estimating that required replacement ratios ranged from 77% for a person earning $80,000 a year in 2008 to 94% for a person earning $20,000 that year).

(206) Because of the impact of the 3% inflation assumption and the passage of time on the monthly tontine pension annuity factors, our retiree could expect that her monthly tontine pension benefits for the 11 months following her initial month of retirement would be slightly larger than the $5549 that she would receive in the first month of that retirement year. Accordingly, she should receive an annual pension of slightly more than $66,588 at age 65 and have a replacement ratio of slightly higher than 42.7%.

(207) See VIRGINIA P. RENO & ELISA A. WALKER, NAT'L ACAD. SOC. INS., SOCIAL SECURITY Benefits, Finances, and Policy Options: A Primer 5 (2013), available at http://www.nasi.org/sites/default/files/research/2013_Social_Security_Primer_PDF .pdf (showing that the current Social Security system replaces around 42% of the pre- retirement earnings of a worker with "medium" earnings); see also PETER BRADY ET AL., INV. CO. INST., THE SUCCESS of the U.S. Retirement System 17-20 (2012), available at http://www.ici.org/ pdfZppr_12_success_retirement.pdf (showing how Social Security replacement rates vary over time for representative workers); CONG. BUDGET OFFICE, THE 2012 LONG-TERM PROJECTIONS for Social Security: Additional Information 16 exhibit 10 (2012), available at http://www.cbo.gov/publication/43653 (showing how replacement rates vary with pre-retirement earnings).

(208) por a more thorough discussion of the legal issues involving tontine pensions, see infra Section V.B.

(209) See Employee Retirement Income Security Act of 1974 [section] 4(b)(1), 29 U.S.C. [section] 1003(b)(1) (2012) (exempting government plans).

(210) See supra Section II.D. We recognize that many governments use their pension plans to provide disability benefits, and some also use their pension plans to provide retiree health benefits. However, for simplicity we have ignored both disability benefits and retiree health benefits in this Article.

(211) See MlLLIMAN, supra note 19, at 10.

(212) CalSTRS at a Glance, CalSTRS, http://www.calstrs.com/glance (last visited Jan. 16, 2015), archived at http://perma.cc/WPH6-72ML.

(213) See Retirement Benefits Calculator, CALSTRS, http://resources.calstrs.com/CalSTRSCom ResourcesWebUI/Calculators/Pages/RetirementBenefit.aspx (last visited Jan. 16, 2015), archived at http://perma.cc/L86P-VXGC (providing a list of factors used to calculate benefits). CalSTRS also administers a defined benefit supplement program, a cash balance benefit program, and CalSTRS "Pension2." For more details, see generally CAL. STATE TEACHERS' RET. SYS., OVERVIEW OF the California State Teachers' Retirement System and Related Issues (2014), available at http://www.calstrs.com/sites/main/files/file- attachments/overview_2014_v3.pdf.

(214) MLLLIMAN, supra note 19, at 10.

(215) Id.

(216) Id. at 18 tbl.1. Under the entry-age normal cost accounting method, the normal cost is calculated to produce a level cost over each employee's career (i.e., a level percentage of payroll). The normal cost generally represents the expected cost of projected benefits attributable to work performed and pension benefits earned in the current plan year. Id. at 15.

(217) Id. at 47 tbl.15.

(218) Qf. Jonathan Barry Forman, Public Pensions: Choosing Between Defined Benefit and Defined Contribution Plans, 1999 MICH. ST. L. REV. 187, 208-10 (discussing various ways to transition from a traditional defined benefit plan to a defined contribution plan, but noting the difficulties inherent in making this switch).

(219) See id. at 210 (describing this approach).

(220) See supra note 216 and accompanying text.

(221) See supra subsection I.B.1.

(222) To the extent that any employees make (or are deemed to make) any after- tax contributions to their tontine pension funds, they should be allowed to recover those contributions tax-free, just as they could with a typical pension or annuity. See supra note 33.

(223) See TIAA-CREF FIN. SERVS., supra note 156, at 81-87 (describing the tax implications of similar existing pension plans).

(224) See supra note 14 and accompanying text.

(225) COOPER, supra note 9, at 56.

(226) Id. at 57.

(227) Today, for example, there are numerous laws that govern the securities industry. The Laws that Govern the Securities Industry, U.S. SEC. & EXCHANGE COMMISSION, http://www.sec.gov/about/laws.shtml (last visited Jan. 16, 2015), archived at http://perma.cc/ EWG5-9VWW. Also, we have seen that ERISA imposes a number of recordkeeping and reporting requirements on pension plan sponsors. See supra subsection I.B.3.

(228) Investor Bulletin: Custody of Your Investment Assets, U.S. SEC. & EXCHANGE COMMISSION, http://www.sec.gov/investor/alerts/bulletincustody.htm (last visited Jan. 16, 2015), archived at http://perma.cc/8UQM-XJ6J.

(229) Chris Isidore, Seven States that Don't Have Lotteries, CNNMONEY (Dec. 17, 2013, 1:16 PM), http://money.cnn.com/2013/r2/17/news/economy/states-without-lotteries, archived at http://perma.cc/3CBZ-WLAV; Richard A. McGowan, A Short History of Gambling in the United States, Opposing Viewpoints in Context, http://ic.galegroup.com/ic/ovic/ViewpointsDetailsPage/ViewpointsDetailsWindow?displayGroupName=Viewpoints& disableHighlighting-false&prodId=OVIC&action=2&catId-&documentId- GALE%7CEJ3010079223&userGroupName=sacr73031&jsid=62916eoa4i7a2c9be8c6da4f4edc7ff c (last visited Jan. 16, 2015), archived at http://perma.cc/YQ73-5NHH.

(230) McKeever, supra note 9, at 514.

(231) See supra notes 153-160 and accompanying text.

(232) TIAA-CREF FIN. SERVS., supra note 159, at B-44.

(233) See Employee Retirement Income Security Act of 1974 [section] 3(3), 29 U.S.C. [section] 1002(3) (2012) (defining "employee benefit plan"); id. [section] 4, 29 U.S.C. [section] 1003(a) (2012) (imposing coverage on "any employee benefit plan").

Moreover, to the extent that any tontine annuities might be subject to ERISA, we believe that ERISA's insurance savings clause is relevant with respect to any tontine annuity viewed as an insurance product under the applicable state's law. In that regard, ERISA's preemption clause provides that ERISA "shall supersede any and all State laws ... [that] relate to any employee benefit plan"; however, the savings clause then exempts from preemption any state law "which regulates insurance, banking, or securities." Id. [section] 514(a), (b)(2)(A), 29 U.S.C. [section][section] 1144(a), (b)(2)(A). Congress generally left the regulation of insurance products to the states. Presumably, tontine annuities sold by insurance companies would be subject to regulation by state insurance regulators. But what about tontine annuities sold by a discount broker? Are these just investment products or are they insurance? We are unsure. However, because tontine annuities alone are not employee benefit plans, we believe that they are outside the scope of ERISA.

(234) In general, a tontine pension would be an "employee benefit plan.... established or maintained by" an employer or employee organization within the meaning of ERISA section 4. Id. [section] 3(3), 29 U.S.C. [section] 1002(3) (2012); id. [section] 4, 29 U.S.C. [section] 1003(a) (2012).

(235) See id. [section] 4(b)(1), 29 U.S.C. [section] 1003(b)(1) (2012) (exempting government plans).

(236) COOPER, supra note 9, at 61 (explaining the distribution of benefits over time in traditional pensions).

(237) I.R.C. [section] 401(a)(8) (2012).

(238) See id. [section] 411(a)(2)(B)(ii) ("A plan satisfies the requirements of this clause if an employee who has completed at least 3 years of service has a nonforfeitable right to 100 percent of the employee's accrued benefit derived from employer contributions."); Employee Retirement Income Security Act of 1974 [section] 203(a)(2)(B)(ii), 29 U.S.C. [section] 1053(a)(2)(B)(ii) (2012) (same).

(239) Another option is to begin by considering an individual with an IRA. IRAs are not subject to ERISA, but the Internal Revenue Code rules that govern IRAs are very similar to the ERISA rules governing defined contribution plans. For example, both IRAs and pensions receive favorable tax treatment, and both are subject to the prohibited transactions rules. See supra Section I.B. We do not believe that there is anything in the Internal Revenue Code that would prevent an individual from having her IRA invest in a tontine fund or in a tontine annuity. Nor do we think that ERISA would prevent a participant with a self-directed 401(k) plan from investing in a tontine fund or annuity.

Finally, there is no doubt that an employer can create a defined contribution plan, make contributions to that plan on behalf of its employees, and invest those contributions for the benefit of its employees. The question comes down to whether a plan sponsor can invest employer contributions in a tontine fund or tontine annuity knowing, as we do, that each employee will lose the balance in her account when she dies. We see no reason why a plan sponsor would be prohibited from doing so. (Granted, the spousal protection rules might impose forfeiture limits with respect to married participants. We discuss those rules infra subsection V.D.3).

(240) See I.R.C. [section] 401(a) (2012) (setting forth requirements for an employer's stock bonus, pension, or profit-sharing plan to constitute a qualified trust); Employee Retirement Income Security Act of 1974 [section] 404, 29 U.S.C. [section] 1104 (2012) (enumerating obligations of a fiduciary with respect to such a plan). See generally U.S. DEP'T OF LABOR, EMP. BENEFITS SEC. ADMIN., Meeting Your Fiduciary Responsibilities (2012), available at http://www.dol.gov/ebsa/ pdf/meetingyourfiduciaryresponsibilities.pdf (explaining to employers how to administer their retirement plans).

(241) I.R.C. [section] 401(a) (2012); Employee Retirement Income Security Act of 1974 [section][section] 403, 404(a), 29 U.S.C. [section][section] 1103, 1104(a) (2012).

(242) Cf. Selection of Annuity Providers for Individual Account Plans, 72 Fed. Reg. 52,021 (proposed Sept. 12, 2007) (to be codified at 29 C.F.R. pt. 2550) (proposing the establishment of a "safe harbor" for selecting annuity providers to distribute benefits from "individual account plans covered by title I" of ERISA).

(243) See supra subsection II.B.3.a.

(244) See supra notes 136-138 and accompanying text.

(245) According to one projection, over the next 10 years, the expected return on U.S. stocks will be 7.25%, while the expected return on U.S. Treasury bonds will be just 0.50%. See BNY Mellon, 10-Year Capital market Return Assumptions: Calendar Year 2013 (2013), available at http://us.bnymellonam.com/core/library/documents/knowledge/market _commentary/bny_mellon_10_Year_capital_market_return_assumptions_20i3.pdf (presenting 10-year capital market return assumptions based on social and economic changes).

(246) See Per Linnemann, A New DC Concept from Denmark, RETIREMENT INCOME J. (Sept. 4, 2013), http://retirementincomejournal.com/issue/september-5- 2013/article/a-new-dc-concept from-denmark, archived at http://perma.cc/M89E-DWN7 (discussing Denmark's success with "smoothed income annuities").

(247) TIAA-CREF allows participants to choose variable annuity payments that change monthly or yearly. See TIAA-CREF FIN. SERVS., TIAA-CREF RETIREMENT STRATEGIES: Helping You Reach Your Retirement Savings Goals 35-36 (2006), available at https://www.tiaa-cref.org/public/pdf/retire_strategies.pdf (explaining how to choose a retirement plan).

(248) See supra note 72 and accompanying text (explaining that Title VII of the Civil Rights Act prohibits pension plans from requiring higher contributions from women than men or paying women lower benefits than men).

(249) Id.

(250) See supra Section IV.A (providing background on CalSTRS).

(251) On the other hand, a defined contribution plan can distribute lump sums to its retirees with the knowledge that the commercial annuities available to the retirees from private insurers will differ based on gender. As noted above, a 65-year-old man who purchased a $100,000 annuity in January of 2014 could receive $6864 a year for life, while a 65-year-old woman would receive $6408 a year because of her longer life expectancy. See supra subsection I.C.2 (explaining lifetime annuities). But see Heen, supra note 121 (discussing why we should ban gender discrimination in the sale of commercial annuities).

(252) See supra Sections II.B-C (providing an overview of tontine funds and tontine annuities).

(253) See supra note 72 and accompanying text (explaining that Title VII of the Civil Rights Act prohibits pension plans from requiring higher contributions from women than men or paying women lower benefits than men); see also Spirt v. Teachers Ins. & Annuity Assn, 691 F.2d 1054, 1066 (2d Cir. 1982) (finding that defendants use of sex-distinct tables for calculating contributions to a pension plan constituted unequal treatment on the basis of sex), vacated on other grounds, 463 U.S. 1223 (1983).

(254) See supra note 200 and accompanying text. Unisex tables are not a perfect solution, because they are less accurate than gender-specific tables. Unisex tables would, however, ensure that same-age men and women who make identical contributions receive identical monthly distributions, which is what Title VII requires for pensions.

(255) Again, see Heen, supra note 121 for a discussion as to why we should ban gender discrimination in the sale of annuities.

(256) I.R.C. [section] 40i(a)(u) (2012) ("[A] trust forming part of such plan shall not constitute a qualified trust under this section unless ... the accrued benefit payable to such participant is provided in the form of a qualified joint and survivor annuity."); id. [section] 417(a) (permitting participants to elect to waive the qualified joint and survivor annuity form, but requiring the participant's spouse to consent in writing); Employee Retirement Income Security Act of 1974 [section] 20$(n)-(c), 29 U.S.C. [section] 1055(a)-(c) (2012) (same). A QJSA is an immediate annuity for the life of the pension plan participant and a survivor annuity for the life of the participant's spouse. Id. [section] 205(d)(1), 29 U.S.C. [section] 1055(d)(1). The amount of the survivor annuity may not be less than 50% nor more than 100% of the amount payable during the time the participant and spouse are both alive. Id., 29 U.S.C. [section] 1055(d)(1).

(257) Id. [section] 205(a), 29 U.S.C. [section] 1055(a). A QPSA typically pays an annuity that is equal to the survivor's portion of the QJSA. Id. [section] 205(e), 29 U.S.C. [section] 1055(e).

(258) I.R.C. [section] 40i(a)(i3) (2012); Employee Retirement Income Security Act of 1974 [section] 206(d), 29 U.S.C. [section] 1056(d) (2012).

(259) See Cal. Pub. Emps. Ret. Sys., Survivors & Beneficiaries FAQs: Your Retirement Application and Options Webinar, available at http://www.calpers.ca.gov/eip docs/about/video-web-center/videos/member-retirement/faq-survivore.pdf (explaining that some employers offer benefits to employees' survivors and detailing those spousal protections).

(260) The tontine pension of a married couple might be shared between the spouses along the lines of earnings sharing. See, e.g., FORMAN, supra note 23, at 205-06 (discussing the possibility of earnings sharing for Social Security).

(261) QDROs can present adverse selection and moral hazard issues. For example, what, if anything, should be done to prevent a dying spouse from getting a divorce and using a QDRO to transfer her tontine pension to her ex-spouse, rather than forfeiting it to the surviving members in her tontine pension plan?

(262) Bye, supra note 109.

(263) See supra note ill and accompanying text.

(264) See supra notes 141 & 143 and accompanying text.

(265) This data is derived from Bye, supra note 109, and authors' computations. The monthly annuity factors were determined using an interest rate of 7% and an inflation rate of 3%.

JONATHAN BARRY FORMAN ([dagger]) & MICHAEL J. SABIN ([dagger][dagger])

[C] Jonathan Barry Forman & Michael J. Sabin 2015.

([dagger]) Alfred P. Murrah Professor of Law, University of Oklahoma; BA. 1973, Northwestern University; M.A. (Psychology) 1975, University of Iowa; J.D. 1978, University of Michigan; M.A. (Economics) 1983, George Washington University; Professor in Residence at the Internal Revenue Service Office of Chief Counsel, Washington, D.C. for the 2009-2010 academic year; Member of the Board of Trustees of the Oklahoma Public Employees Retirement System, 2003- 2011.

([dagger][dagger]) Independent consultant, Sunnyvale, CA; B.S. (Electrical Engineering) 1977, University of Florida; M.S. 1979, Ph.D 1984 (Electrical Engineering), Stanford University; Member of Technical Staff, Bell Laboratories, 1977-1981; Assistant Professor (EECS), University of California Berkeley, 1984-1986.

This Article was presented at the Third Annual ERISA, Employee Benefits, and Social Insurance National Conference on Benefits Law at the Crossroads: Whither U.S. Employee Benefits and Social Insurance Law?, Marquette University Law School, Milwaukee, Wisconsin, March 28, 2014; at the Savings and Retirement Institute, Washington, D.C., May 8, 2014; to a panel of the American Bar Association, Section of Taxation, Committee on Employee Benefits, Washington, D.C., May 10, 2014; and at the international pension conference on Social Security Systems and Demographical Challenges, Poznan University of Technology, Poznan, Poland, October 16, 2014. A shorter version of this Article was published as Jonathan B. Forman & Michael J. Sabin, Tontine Pensions: A Solution to the Chronic Underfunding of Traditional Pension Plans, in SOCIAL SECURITY SYSTEMS AGAINST THE CHALLENGES OF DEMOGRAPHICS AND MARKET 55-70 (Marek Szczepanski, Tomasz Brzeczek & Malgorzata Gajowiak eds., 2014), available at http://jay.law.ou.edu/faculty/jforman/Speeches/2014TontinePension%28Poland%29.pdf.

Table 1: A Tontine Fund with Four Members of
Different Ages, Unisex (110)

                          Life
                       Expectancy       Death
Member       Age         (years)     Probability
(i)      ([x.sub.i])   ([e.sub.i])   ([q.sub.i])

1            65           18.88       0.013181
2            70           15.22       0.020314
3            75           11.89       O.032111
4            80           8.95        0.051906

          Force-of-       Fair
          Mortality     Transfer-
Member   Probability   plan Weight
(i)      ([f.sub.i])   ([w.sub.i])

1         0.013269      0.053815
2         0.020523      0.086183
3         0.032638      0.146795
4         0.053302      0.713207

Table 2: A Tontine Fund with Four Members, Gender-Based118

                                         Life
                                      Expectancy       Death
Member        Age         Gender        (years)     Probability
(i)       ([x.sub.i])   ([e.sub.i])   ([q.sub.i])   ([q.sub.i])

1             65           male          14.51       0.016182
2             6S           male          17.51       0.016182
3             65          female         20.19       0.010298
4             6S          female         20.19       0.010298

           Force-of-        Fair
           Mortality    Transfer-plan
Member    Probability      Weight
(i)       ([f.sub.i])    ([w.sub.i])

1          0.016314       0.330931
2          0.016314       0.330931
3          0.010351       0.169069
4          0.010351       0.169069

Table 3: A Tontine Fund with Four Members, Different
Levels of Contribution (122)
                                         Life
                                      Expectancy
Member       Age       Contribution     (years)
(i)      ([x.sub.i.)   ([s.sub.i.)    ([e.sub.i.)

1            65           $1000          17.51
2            65           $2000          17.51
3            65           $3000          17.51
4            65           $4000          17.51

                        Force-of-       Fair
            Death       Mortality     Transfer-
Member   Probability   Probability   plan Weight
(i)      ([q.sub.i.)   ([f.sub.i.)   ([w.sub.i.)

1         0.016182      0.016314      0.066510
2         0.016182      0.016314      0.145278
3         0.016182      0.016314      0.247530
4         0.016182      0.016314      0.540682

Table 4: Sample Monthly Tontine Fund Statement
for a Living Member133

Date      Amount       Balance     Description
           ($)           ($)

03/31                250,000.00
04/02     67.17      250,067.17    Proceeds from FTP
04/03     25.21      250,092.38    Proceeds from FTP
04/05     55.14      250,147.52    Proceeds from FTP
04/07    135.41      250,282.93    Proceeds from FTP
04/07     48.91      250,331.84    Proceeds from FTP
04/12     52.29      250,384.13    Proceeds from FTP
04/15    102.54      250,486.67    Proceeds from FTP
04/20    159.46      250,649.13    Proceeds from FTP
04/21    139.68      250,785.82    Proceeds from FTP
04/22     17.82      250,803.63    Proceeds from FTP
04/25    124.81      250,928.44    Proceeds from FTP
04/28     55.32      250,983.76    Proceeds from FTP
04/30     57.91      251,041.67    Proceeds from FTP
04/30   (1041.67)    250,000.00    Payout of FTP
                                     Proceeds

Table 5: Sample Monthly Tontine Fund Statement
for a Member Who Dies During the Month (135)

Date     Amount ($)    Balance ($)      Description

03/31                  250,000.00
04/02      67.17       250,067.17    Proceeds from FTP
04/03      25.21       250,092.38    Proceeds from FTP
04/05      55.14       250,147.52    Proceeds from FTP
04/07      135.41      250,282.93    Proceeds from FTP
04/07      48.91       250,331.84    Proceeds from FTP
04/12   (250,331.84)        0        Forfeited to FTP

Table 6: Sample Monthly Tontine Annuity
Statement for a Living Member
(for the First Month After the Member
Turned 65) (142)

Date        Amount       Balance       Distribution

03/31                  250,000.00
04/02       67.17      250,067.17    Proceeds from FTP
04/03       25.21      250,092.38    Proceeds from FTP
04/05       55.14      250,147.52    Proceeds from FTP
04/07      135.41      250,282.93    Proceeds from FTP
04/07       48.91      250,331.84    Proceeds from FTP
04/12       52.29      250,384.13    Proceeds from FTP
04/15      102.54      250,486.67    Proceeds from FTP
04/20      159.46      250,649.13    Proceeds from FTP
04/21      139.68      250,785.82    Proceeds from FTP
04/22       17.82      250,803.63    Proceeds from FTP
04/25      124.81      250,928.44    Proceeds from FTP
04/28       55.32      250,983.76    Proceeds from FTP
04/30       57.91      251,041.67    Proceeds from FTP
04/30     (2133.00)    248,908.67     Tontine-annuity
                                       Distribution

Table 7: Sample Monthly Tontine Annuity Statement
for a Living Member, with Investment Earnings
(for the First Month After the Member Turned 65) (145)

Date     Amount     Balance      Description

03/31               250,000.00
04/02     67.17     250,067.17   Proceeds from FTP
04/03     25.21     250,092.38   Proceeds from FTP
04/05     55.14     250,147.52   Proceeds from FTP
04/07    135.41     250,282.93   Proceeds from FTP
04/07     48.91     250,331.84   Proceeds from FTP
04/12     52.29     250,384.13   Proceeds from FTP
04/15    102.54     250,486.67   Proceeds from FTP
04/20    159.46     250,649.13   Proceeds from FTP
04/21    139.68     250,785.82   Proceeds from FTP
04/22     17.82     250,803.63   Proceeds from FTP
04/25    124.81     250,928.44   Proceeds from FTP
04/28     55.32     250,983.76   Proceeds from FTP
04/30     57.91     251,041.67   Proceeds from FTP
04/30    1000.00    252,041.67   Interest for
                                   the month
04/30   (2141.52)   249,900.15   Tontine-annuity
                                   Distribution

Table 8: Calculation of the Retirement Balance

                                   Preliminary
Age       Salary    Contribution      Balance

35       $50,000          $5000         $5172
36       $52,000          $5200       $10,920
37       $54,080          $5408       $17,294
38       $56,243          $5624       $24,349
39       $58,493          $5849       $32,144
40       $60,833          $6083       $40,743
41       $63,266          $6327       $50,218
42       $65,797          $6580       $60,644
43       $68,428          $6843       $72,107
44       $71,166          $7117       $84,696
45       $74,012          $7401       $98,512
46       $76,973          $7697      $113,665
47       $80,052          $8005      $130,273
48       $83,254          $8325      $148,468
49       $86,584          $8658      $168,396
5"       $90,047          $9005      $190,215
5i       $93,649          $9365      $214,102
52       $97-395          $9740      $240,247
53      $101,291        $10,129      $268,856
54      $105,342        $10,534      $300,150
55      $109,556        $10,956      $334,376
56      $113,938         $n,394      $371,812
57      $118,496        $11,850      $412,774
58      $123,236        $12,324      $457,604
59      $128,165        $12,817      $506,681
60      $133,292        $13,329      $560,438
61      $138,623        $13,862      $619,364
62      $144,168        $14,417      $684,024
63      $149,935         $H,994      $755,050
64      $155,933        $15,593      $833,161

           Death        Closing
Age   Probability       Balance

35      0.001261          $5179
36      0.001332        $10,935
37      0.001420        $17,319
38      0.001527        $24,386
39      0.001653        $32,197
40      0.001796        $40,816
41      0.001955        $50,316
42      0.002133        $60,774
43      0.002332        $72,275
44      0.002550        $84,912
45      0.002786        $98,787
46      0.003041       $114,011
47      0.003322       $130,707
48      0.003630       $149,009
49      0.003963       $169,066
5"      0.004326       $191,042
5i      0.004707       $215,114
52      0.005086       $241,475
53      0-005455       $270,331
54      0.005827       $301,910
55      0.006234       $336,473
56      0.006685       $374,315
57      0.007166       $415,753
58      0.007677       $461,144
59      0.008233       $510,888
60      0.008854       $565,444
61      0.009552       $625,338
62      0.010323       $691,159
63      0.011172       $763,580
64      0.012113       $843,376


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Title Annotation: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. 790-831
Author:Forman, Jonathan Barry; Sabin, Michael J.
Publication:University of Pennsylvania Law Review
Date:Feb 1, 2015
Words:26068
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