Pension Math and Investment Returns

While the private sector primarily utilizes a defined contribution scheme, where employers will contribute funds to a 401(k) account that an employee is in charge of managing, the public sector predominantly has a defined benefit pension system where fixed dollar amounts are promised during retirement.

To illustrate these concepts, let us consider the case of a 40-year-old who opts to retire at age 65, and then receives a defined benefit amount for the rest of his/her life.  For simplicity, looking at a single payment illustrates how projected investment returns considerably influence how much money needs to be contributed now.

Money contributed in 2013  è  Compounds for 25 years  è  Money for retirement in 2038

Suppose that upon retirement in 2038, the worker is supposed to receive a payment for $100,000.  State and local governments must contribute money now, in 2013, to ensure the retiree will receive $100,000 in 25 years.  The compound interest rate (also called the discount rate) reflects the state’s estimate of annual investment returns over the next 10-20 years.  You can also think about the discount rate as the expected rate of return (which in theory should be achievable with the asset mix the pension fund uses).  For example, if you believe that investing in stocks and bonds will generate a 6% annual return over time, then 6% would be the appropriate discount rate.

A high discount rate allows for smaller contributions now in the hope that significant appreciation will grow the amount to $100,000.  A low discount rate means that larger contributions must be made now.

Given that states are struggling to balance their budgets, many are using more aggressive assumptions in order to save cash now.  However, if actual investment returns fall short of these targets, states will have to contribute substantially more money in the future to compensate for this shortfall.  Despite lower interest rates and investment returns, many public pension plans have never adjusted the discount rate, exposing these plans to grave risk.

Let’s look at the difference between compounded returns of 8.25% vs. 6.50%.  Many state governments are using figures around 8.25%, while corporations are (by law) using a much more conservative 6.50%.

? contributed in 2013  è  25 years @ 8.25%  è  $100,000 in 2038       vs.

? contributed in 2013  è  25 years @ 6.50%  è  $100,000 in 2038

Required contribution using 8.25% rate:  $100,000 / (1.0825) ^25 = $13,782                                                           vs.

Required contribution using 6.50% rate:  $100,000 / (1.0650) ^25 = $20,714

Reducing the discount rate by 1.75% (from 8.25% à 6.50%) necessitates contributing a staggering 50% more money now.  It’s no wonder that states have generally opted to use a significantly higher discount rate, but in this “new normal” rate environment, they are likely deluding themselves.  Yet even at the high discount rates, states have promised far more in benefits than they will be able to pay, resulting in massive projected shortfalls.

For instance, New Jersey, only the 11^th most populous state, has unfunded pension liabilities of $55,000 million at an aggressively high discount rate.  Applying a more conservative discount rate, this number increases to around $100 billion, fundamentally compromising the state’s capability to provide any other desired services (e.g., education, human services, transportation, etc.).

Source:  http://www.policyprospectus.com/2012/08/a-primer-on-pensions.html

In order to shore up the pension system, state governments will need to adopt a combination of these politically unpopular, yet economically necessary, approaches to stave off a true fiscal crisis where everybody will lose out (defaulting on debt, huge cuts to state budgets, and not having cash to pay retirees):

1)  Employees contributing more to their pension plan to ensure its sustainability

2)  Gradually migrating from a defined benefit to a defined contribution system

Unfortunately, politicians who care about their self-interest above all else have “kicked the can” on pensions and other issues for years, and it takes statesmen to address difficult fiscal issues now in order to stave off financial ruin later.  When offering constructive ideas, the debate is often poisoned by public sector unions claiming that teachers, police officers, firefighters, clerical workers, etc. are being attacked, when in fact pension reforms are necessary to ensure the solvency of the very system they are relying on for retirement.

For any helpful discourse, it is paramount that both sides separate the individual from the union they are required to join.  The default response from certain interest groups has been to demonize the messenger without offering any meaningful proposals, but it is critical for people to see through that shallowness.  Hopefully these mathematical concepts and their applications were illuminating.