###### CERF Blog

Let’s think about the structure of the perfect retirement investment vehicle. The perfect vehicle would have annual payouts that exceed what could be achieved by buying bonds or other asset classes. The perfect vehicle would hedge against so-called “longevity risk” which is the risk of outliving your money. The perfect vehicle would have annual payments that were indexed to a broad price index so that the retiree was hedged against the ravages of inflation. One product that has each of these features is an indexed deferred life annuity (IDLA). That is, you make an investment of cash and at a future date (the deferral date) the annuity begins making payments to you. These payments are adjusted for inflation and continue as long as you are alive.

Examples of IDLAs include Social Security and some public sector defined benefit plans (those that offer benefits indexed for inflation). A major difference between Social Security and defined benefit plans is that the latter are funded by participant contributions while the former is a “pay-as-you-go” system. An important issue for state and local governments is the economic viability of public sector plans.

The key parameters that define a defined benefit plan are a) the combined employer and employee contribution (savings) rate and b) the crediting rate for years of service. A typical structure for a public sector plan is that employee and the employer make annual contributions to the pension fund totaling, say, 10% or 20% of employee annual income. These contributions are invested in portfolios of stocks, bonds, real estate and other assets by professional money managers overseen by the trustees of the fund. At retirement, the employee then receives annual pension benefits according to a formula something like the following: years of service multiplied by the annual crediting rate multiplied by ending salary. Thus, if an employee worked for a county for 30 years and the crediting rate is 2%, then the pension benefit in the first year of retirement would be 60% of ending salary, and this amount would be adjusted upward each year by the rate of inflation. For people who stay with one employer for a very long time, this type of plan can offer substantial retirement security. On the other hand, for job hoppers the defined benefit plan doesn’t work out nearly so well.

Even for the long-term employee, the plan won’t work out so well if the pension fund is unable to meet its obligations. Key determinants of the viability of a plan include the basic parameters defining contributions and benefit payments, as indicated above. Other critical factors are the tenure of employees, the longevity of retirees, and the rate of investment return on the pension fund. Over the past fifty years or so, public pension plans have achieved an average annual investment return of about 8%. To assess economic viability on a macro level, the trustees of a fund must estimate the present value of the future benefits to be paid (they rely on professional actuaries to make this computation) and compare that to the value of the pension assets. A plan is “under-funded” if the present value of the liabilities exceeds the value of the assets.

Although varying widely across various states and municipalities, most public sector plans are underfunded by a considerable margin. Shortfalls between assets and liabilities can be made up by increasing the employee and/or employer contribution rate, but very large adjustments in the contribution rate may not be feasible. A further problem is that a key assumption driving the present value of plan liabilities is the assumed rate of return on plan assets. To an economist, it seems strange that one would use an asset return to discount your liabilities, because it means that the value of the liabilities would change whenever you adjust your mix of assets! Putting that aside, a perhaps bigger problem is that plan trustees are currently assuming future investment returns in the 7-8% range, similar to the long-term historical performance, even though current levels of long-term bond yields are near all-time lows.

It is interesting to investigate the effects of lengthening longevity and lower expected investment returns on plan viability. A convenient way to do this is to build a “probability of ruin” model that estimates the probability that a plan will fail given its key assumptions – contribution rate, crediting rate, longevity and investment return.

**Probability of Ruin**

Building a good probability of ruin model requires taking account of uncertain investment returns and mortality. Fortunately, economist Moshe Milevsky has developed such a model in his scintillating book *The Calculus of Retirement Income*. By using this model we can see that the design of the typical public sector plan outlined above was reasonable when it was put into place a few decades ago.

The following table lays out the results of the model for a variety of assumption sets. Each of Columns A, B and C assume the same plan terms – 20% annual combined employer and employee contribution rate and 2% annual crediting rate. The columns vary on the investment return and longevity assumptions. Column A represents reasonable return and longevity assumptions as of thirty years ago; that is, expected real return on a 50% equity and 50% bond portfolio equal to 5% per year, and expected remaining life at retirement years of 15 years. The individual case examined is that of an employee with 30 years of tenure who retires at age 65. Note that the ruin probability at 5% is pretty low. That is, the plan was reasonably well structured as of 1980. Columns B and C show the effects of more contemporaneous assumptions. Both columns assume an expected investment real return on a 50/50 stock/bond portfolio of 3% per year, rather than 5% (while 5% was a reasonable prediction back in 1980, it is arguably not so today). The ruin probability is much higher at 25%. Finally, Column C reflects current investment return expectations (3%) combined with the greater retiree longevity that is expected today compared to 1980. In this case the ruin probability is 36%. The good news is that this means there is a 64% chance the plan will not fail, at least not for the current 20-30 year retirement iteration. But the nature of a pension plan is that it involves a series of retirement length periods. If you repeatedly play a game where you flip a coin with probability .64 of a head, you will eventually get a tail.

Table 1

A B C

Contribution Rate 20% 20% 20%

Annual Crediting Rate 2% 2% 2%

Investment Return 5% 3% 3%

Years of Service 30 years 30 years 30 years

Longevity in Retirement 15 years 15 years 20 years

Probability of Ruin 5% 25% 36%

In order to get ruin probabilities down to the levels they were when these plans were originally set up, plan parameters must change. An obvious candidate is to increase the combined employer and employee contribution rate. In order to reduce the ruin probability in Column C to the level in Column A, the contribution rate must be increased to more than 30%. Alternatively, other plan features such as the crediting rate or inflation indexing formula may be adjusted.

So, the answer to the question posed in the title is yes, these plans can survive, but it will require adjustments in contributions or benefits which as a practical matter may not be politically feasible. The problem here, as in the case of Social Security, lies in guarantees that may have been reasonable at one time but are not robust to changes in circumstances. Perhaps a better strategy is to avoid guarantees altogether and, instead, rely on the power of risk sharing. Next month we’ll discuss an ancient financial instrument that may provide a superior retirement vehicle – the tontine.