## Schwarzenegger’s pension math

August 30, 2010
interested in the value of a guaranteed real income, this sentence jumped out at me from Arnold Schwarzenegger's recent WSJ op-ed:

Since I’m interested in the value of a guaranteed real income, this sentence jumped out at me from Arnold Schwarzenegger’s recent WSJ op-ed:

Few Californians in the private sector have \$1 million in savings, but that’s effectively the retirement account they guarantee to public employees who opt to retire at age 55 and are entitled to a monthly, inflation-protected check of \$3,000 for the rest of their lives.

The problem is, I can’t make the math work. You can argue until you’re blue in the face about proper discount rates, but at the very least any pension plan should be able to invest its money to keep up with inflation. But let’s see what happens with a 0% real discount rate, not least because it makes the math easier.

California’s life expectancy is 77.9 years, so let’s say the average retiree lives for 23 years after retiring at 55*. If they earn \$36,000 a year in real terms for 23 years, that sums to \$828,000. And the minute you start assuming even the most modest of real investment returns, the less realistic Schwarzenegger’s number becomes: if you invest \$1,000,000 at a 5% yield while paying out \$3,000 a month with 2% annual inflation, that’ll support payments for 682 months, or about 57 years, taking our hypothetical retiree to the plump old age of 112.

To put it another way, I’m sure that any life insurer in the world would happily take Schwarzenegger’s bargain and accept \$1 million of public funds in return for the obligation to pay a 55-year-old California retiree \$3,000 a month, in real terms, for life.

The rest of the op-ed is misleading, too: see Paul Kedrosky’s elegant fisking of Schwarzenegger’s chart. But as ever in California, political rhetoric always tends to trump economic reality. California’s finances are indeed pretty gruesome, and it’s true that the state has been making pension promises it can’t afford for decades. But given how bad reality is, there’s no need to exaggerate it for the sake of politics.

Update: Many thanks to all my commenters. First, as many of them pointed out, life expectancy at age 55 is actually somewhere in the 25-28 year range, not 23 years. And especially thanks to DanHess, who actually found a private-sector quote:

I got some quotes for how much a million dollars will buy for a fifty-five year old in terms of a fixed annuity starting presently and going for life. They were generally in the range of about \$5000 per month, some a bit more, some a bit less.

I just got off the phone with the Vanguard annuity sales department, where I was told that for a 55-year-old, inflation adjustment knocks off approximately 30% to 35% off the payout of the annuity.

\$5,000 minus 1/3 for inflation adjustment brings you down to around \$3330 per month. But I’m not convinced that the inflation adjustment should be so expensive these days, given that any life insurer should be able to hedge the inflation risk very cheaply right now.

Finally, there’s the question of survivor benefits, which I admit I hadn’t considered. I don’t know exactly how California pensions work, but if they essentially end up being paid until both of two spouses have died, rather than until the recipient has died, then that obviously increases their value significantly.