Schwarzenegger’s pension math

By Felix Salmon
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:

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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.


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ER, what happens when you figure in the cost of guaranteed health benefits, etc, too, Felix?

==Bob D.

Posted by REDruin | Report as abusive

You have to consider their life expectancy at age 55, not birth. Nationally, this is 24.66 for men and 28.07 for women as of 2006, according to the SSA. tml

Posted by clawback | Report as abusive

Felix, you might research this? What is the hypothetical annuity payout on $1M for somebody retiring at age 55? (Of course annuity payouts are generally NOT inflation-protected.)

Consider also that life-expectancy at birth is not the same as life-expectancy for somebody who is already 55. Moreover, there may be additional riders (surviving spouse payments, rebate of money payed in for early death) that increase the value of the benefit.

Finally, I would question your assumption of 2% inflation. In longer-term projections these days I work from an assumption of 3% to 4% inflation. Real returns on Treasuries are probably negative over the next ten years.

Posted by TFF | Report as abusive

Hi Felix – I might be wrong, but I think the 77.9 year figure is life expectancy at birth, which is generally a lot lower than life expectancy at 55. According to this link ( hirlifetables2004.pdf) life expectancy in California is 85.4 years for a 65 year old. Not sure what the expectation for a 55 year old is, but presumably they’d be expected to make it into the low to mid 80′s which likely puts them over $1MM in total payments on a real basis (i.e. you’d need at least some outperformance of inflation on the investments, but not much as you point out).

Posted by mt16 | Report as abusive

Where on earth are you going to get 5% yield these days?

Posted by TWAndrews | Report as abusive

“…But as ever in California, political rhetoric always tends to trump economic reality…”

Why are you limiting the geography to California, Salmon?

Posted by ottorock | Report as abusive

It’s a minor point, but you’ve made this mistake twice now:
(Life expectancy from age n) is not equal to (life expectancy at birth) – n. It will usually be a bit larger (unless the country has unusually high infant mortality).

Also, you could have proven your point (without making silly assumptions) by simply finding the commercial price of a lifetime annuity. A UK one is about £100,000 per £5200 annual income (so a ratio of about 20:1).

Posted by 3mta3 | Report as abusive

Felix wrote:

“But given how bad reality is, there’s no need to exaggerate it for the sake of politics.”

Heartily agreed.

Reminds me that I held similar sentiments after watching “An Inconvenient Truth”

Posted by high_al | Report as abusive

Felix, why do you keep conflating the rate of return on assets with the proper discounting rate for liabilities? If you are guaranteed a series of guaranteed payments by a state government that you view as risk-free, you should discount that at the risk-free rate. What the pension fund thinks it can return is irrelevent.

Posted by Beer_numbers | Report as abusive

3mta3, is that commercial lifetime annuity indexed for inflation? Does it have the same survivor benefits?

In any case, at this point we’re quibbling about a relatively small amount. At a 20:1 ratio, that $3000/month annuity would cost $720,000. Not so far from a million?

Incidentally, Schwarzenegger’s numbers are almost identical to the ratios I’m targeting for my own retirement. It is conservative, but then the current economic climate demands conservative projections.

Posted by TFF | Report as abusive

Felix – have you tried getting a couple of major insurance companies to give you a quote for your hypothetical employee?

My suspicion is that a lifetime annuity for a 55-year old with annual inflation adjustment and survivor benefits could very well be yielding 3.6% these days.

Please keep in mind that 30-yr T-bonds are yielding 3.7% with no inflation adjustment available, TIPS are yielding only 1.6% above inflation, S&P 500 dividends are yielding only 1.9%, and the Shiller 10-yr real S&P PE is close to 20 which indicates long-term total returns of only about 2%.

CA and other pension funds are staring at the same issue as many current retirees where the historical yield benchmarks are almost meaningless. Anybody who is trying live off of interest and dividend income these days needs to have a ton of money set aside. They need to be in things like junk bonds to provide historical return levels.

The magic 8% return number hasn’t been in effect for a decade now which is why pension funds are running into deep doo-doo. We have used up many of the premiums built into that number over the past 15-years, so it is unlike to be operative for a while. Schwarzenegger is one of the very few voicing the reality that the pension funds don’t want to acknowledge since they would be insolvent then.

Posted by ErnieD | Report as abusive

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.

Now 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. Getting an exact quote from them takes more time than I care to spend, but that is the gist.

So we are looking at something in the range of $3300 per month, inflation adjusted, on a million dollars for 55 year old.

Felix, are you going to publish a correction to this post, as print journalists would?

Posted by DanHess | Report as abusive

The figures that apply for someone having reached Age 55 have been brought up elsewhere in the comments, but if you want to estimate how many years left an American has left once they reach any given age, this tool will do the math for you!

Posted by politicalcalcs | Report as abusive


Were there survivor benefits for the annuity? If not, I would guess that would knock off at least another 5% – 10%.

Posted by ErnieD | Report as abusive

I too suspect they were pricing in survivorship. Which is hardly unreasaonable: I bet virtually everybody with a dependent spouse takes it.

One way of framing the question, then, would be–how much would it cost you at age 55 to buy from Vanguard or Fidelity (say) a (a) stream of $3,000 monthly payments (b) for life with (c) inflation protection and (d) survivorship benefits. I suspect a million ain’t far off. Medical is of course extra but for a UC pension, that’s a line item in the state budget, not part of the pension fund; I think this is true of other state pensions as well.

An interesting sub-question is who is more likely to default: Vanguard/Fidelity, or the state of California?

Re the appropriate inflation rate, wouldn’t the TIPS guaranteed rate be a pretty good point of departure?

Posted by Buce | Report as abusive

I live outside the US and don’t know anything about relevant US laws, but should taxes figure here?

Posted by m_m | Report as abusive

Update appended. Dan, do you really think that print journalists are more likely to publish corrections/updates than bloggers are?

Posted by FelixSalmon | Report as abusive

In this case, I think the actor/governor is right in both cases. The math and the philosophy.

Why dont state workers have retirement plans that parallel the private sector? Is there any reason why someone who works for the state government, the dead weight load of taxes in micro econ, should be entitled to a more comfortable and secure retirement than your average wage slave that pays all the taxes?

Posted by Ken_H | Report as abusive

Beer_numbers’ point is well-taken, as far as it goes. But California pension obligations are unfunded. It is an error to ask what is the current market price of an annuity unless you are actually going to put on the hedge or sell the liability. Absent these intentions, you are not risk-neutral and have to compare the real-world expected liabilities to the real-world expected real discount rate. And it is unreasonable to assume that the current IR term structure, whether real or nominal, will be stationary for 30+ years.

What is reasonable? As it happens, 5% – 2% = 3%: remarkably close to the real rate at which the British government was able to borrow over most of the 18th and 19th centuries (it did a little better at the end of this period, but lets not assign California the best credit rating in history. After all, the discussion would be moot if they weren’t contemplating default on their pension obligations.)

As others have noted, the conditional life expectancy is somewhat longer than the conditioned; lets call it 85, so as to get a round 30 year annuity. Discounting 360 monthly payments of 3,000 at a monthly rate of 3%/12 = 0.25% gives a present value of about $712,000. Survivorship benefits might increase this slightly, but remember that the 85|55 assumption was somewhat conservative. Considering the creditworthiness of California compared to that of the pre-war British empire, this figure seems more like a maximum than a minimum.

Posted by Greycap | Report as abusive

Thanks for the update, Felix! The quotes I got are without survivor’s benefits.

As for fact-checking, it is a little bit of an issue with blogs, no, with no editor around? Here is an interesting bit about how a questionable blog post went on a national tour, cycling into much major media including print before one iota of actual reporting got done.  /2010/08/its_always_a_sad_reporting.htm l

One more thing… You wrote, “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.”

How would one hedge against inflation cheaply these days? The plainest inflation hedge is TIPs but they are very dear right now and offer little real return. Derivatives? Like what?

Posted by DanHess | Report as abusive

Darn. I saw something right up my alley, was so excited to answer and now I am late to the show.

I work at a life insurer in the corporate benefit funding department and our numbers for a 55 yo female would be 830K for a life only policy (life expectancy 30 years) 3,000 with a 2% COLA. If you gave us a million with the same plan we would start the pay out 3,616 and adjust upwards on an annual basis. Pretty good deal in uncertain times.

Posted by tcolemanuf | Report as abusive

So to bring it back to the original question, we’ve determined that the public pensions described by the governor are worth between $700,000 and $1,000,000 depending on how you wish to value them. You might only be willing to pay $700,000 for the pension (since there is some risk it will not be paid), but the actual funding necessary to meet the stated obligations is likely to be closer to $1,000,000 (paid over many years, naturally, not all up front).

As the governor asked, how many private-sector employees have that much saved up? It is a pretty nice pension.

Relevant questions:
(1) How is it funded? Wholly by the state? Or do employee contributions play a significant role?

(2) Is this in addition to Social Security or in place of Social Security? A full Social Security pension is about 2/3 of that, I believe, though it doesn’t kick in until age 65. If the public pension replaces Social Security, then it saves California from paying that portion of the FICA taxes.

When I worked as a teacher, I was on track for a pension even better than that. I could have retired in my early 60s with a pension equal to 80% of my final salary (commonly boosted by gimmicks). However this was largely funded by a 11% payroll deduction, with the town savings on Social Security making up the difference. Frankly, I’m happier managing my own retirement.

Posted by TFF | Report as abusive

DanHess, I’m a novice when it comes to hedging, but couldn’t you short Treasuries and buy the matching TIPS? The implied inflation is the difference in coupons, which this hedge would lock in.

Posted by TFF | Report as abusive

I can’t see any problems with Schwarzenegger’s numbers. Annuity rates are typically in that ballpark for the stated situation. It’s amazing how poorly even the best financial journalists understand the world of personal finance. In this case, even worse than an ex-World Champion bodybuilder. Don’t feel bad though, I’ve had Professors ask for advice on these issues before now. The world needs more financial education.

Posted by FifthDecade | Report as abusive

I agree with commenters who find no problem with Arnold’s numbers. I get an actuarial P.V. in the neighborhood of 700-800k, which including even moderate expense loading probably brings it close to $1m.

Posted by Mike_N | Report as abusive

I wanted badly to find a piece on pension padding in California that was in the news last month, which is one reason Arnold is squirming. I agree that Unions have a place to protect the employees, but when they abuse, it has to be stopped.

The story was about a lead supervisor for the state making 3 times his income by working overtime.. time and a half, etc in the last 2 (or 3) years so that his pension was inflated to more then his original salary and how he encouraged his colleagues and staff to do the same. All legal, yet a burden on the taxpayers for certain.

That abuse will be awfully expensive unless loopholes are closed and caps are put in place. Here is a recent story to remind you how pensions are being padded. 64UC20100707

Posted by hsvkitty | Report as abusive

No-one seems to be questioning the presupposition of Schwarzenegger’s remark, which is that if public employees are getting a $3000/mo annuity, then that’s too much and they ought to have some of that taken away from them. He wants people to envy them, and to wish that they were getting less. Shouldn’t we be wanting everyone to have more?

Posted by curiosus | Report as abusive

hsvkitty, pension padding is widespread (not just California) and a serious problem. It penalizes not only the taxpayers, but also those poor schmoes who don’t play the game. As a teacher, I was contributing 11% of my paycheck to a retirement system that was in dire straits because my (now retired) colleagues contributed at a 5% rate for their entire career and padded their annuity at the end. That is a big part of my reason for leaving public education.

curiosus, I don’t think the size of the annuity is as big a problem as the age. If those workers were receiving $3000/month at the age of 65, rather than at 55, then it would be a very different picture.

I’m still curious to find out more about how those benefits are funded (payroll deductions at what %) and whether they supplement or replace Social Security. Anybody familiar with the California system?

Posted by TFF | Report as abusive