Readers of my last blog entry, Annuities and Delayed Social Security, provided many valuable comments, prompting me to now write a follow-up post. Most of the discussion centered on a chart showing the relationship between annuity payout rates and interest rates. That chart was actually a last minute addition, as I saw the picture on my desktop and decided it might be worthwhile to include.

Now I’d like to discuss more about how annuities are priced and whether it is a good idea to wait to buy an annuity. I will limit the discussion today to inflation-adjusted single premium immediate annuities (SPIAs).

I will provide a modified version of the chart which I showed before. This is an inflation-adjusted SPIA for 65-year olds. For mortality data, I used the Social Security Administration’s Period Life Table from 2007. The interest rates are in real terms (such as the 30-year TIPS yield). Formulas for the calculations can be found below in Appendix 1. I charge a 15.5% overhead charge on the annuity (see more about overhead charges in Appendix 2). Also, before I showed interest rates up to 10%, but since these are real yields, the chances of seeing that are about the same as seeing pigs fly. So I stop at 5% this time. [Nominal interest rates can be higher because they consist of real interest rates plus a premium for expected inflation. Real interest rates do vary over time, but I think the chances of ever seeing long-term TIPS yields above 4% again are very low.] The chart looks like this:

Are Annuities (SPIAs) Okay When Interest Rates are Low?

Long-term TIPS yields are currently under 1%, which means that current annuity payout rates for 65-year old males are a little above 5%. Females get lower payouts because they live longer.

Should someone wait for higher interest rates to buy a SPIA?

There can be valid reasons to wait for buying an annuity, which I will address more below, but regarding the issue of whether it is worthwhile to wait specifically for interest rates to rise, I currently don’t think that sounds like a very good idea.

Who knows if TIPS yields will rise? They may continue falling. Even if TIPS yields do rise to 3% or so, this would result in only about a 20% increase in the annuity payout. Only 20%? That sounds like a lot. But as Boglehead dpbsmith argues at “with interest rates so low, are annuities effectively dead?”, if you are also investing conservatively like the insurance company, you will probably burn through your assets at a fast enough rate that you really don’t even get any benefit from the increased annuity payout rate since you have less assets by the time you do buy your annuity. He argues as well that, actually, by waiting you miss out on some of the mortality credits available by having had the annuity earlier. In the same thread, Boglehead alec also makes a good point that if you are waiting for interest rates to rise, and then they do rise, you will probably experience capital losses on your bond portfolio and so, again, you don’t get any benefit from the higher payout rate since you have less assets by that time. Joe Tomlinson did point out in the comments at my previous blog entry that this could be counteracted a bit by using shorter term bonds for your bond portfolio.

As well, as Matthew Amster-Burton, Dick Purcell, and others like Boglehead jbaron (at “Rates on annuities”) have argued, SPIAs actually become more attractive when interest rates are lower. You don’t buy annuities because they are good investments, you buy them because they provide a guaranteed income for life. This is insurance against living longer than your assets. And you have to compare SPIAs to the alternatives. A bond portfolio will also have more measly returns when interest rates are low. That is basically the alternative for an inflation-adjusted annuity. With low rates, the mortality credit component of the annuity payout becomes even more important, making annuities even more attractive relative to the alternatives like a bond ladder, etc. Another way to say it is, annuities are hurt less by low interest rates than alternative portfolio choices.

So don’t compare annuities to what might have been if interest rates had been higher, compare them to what is possible and available now. Now we are stuck with low rates. Trying to wait for rates to increase is going to eat away at your assets in the mean time, and there is nothing you can really gain from the effort. Low interest rates strengthen, not weaken, the case for purchasing a SPIA.

More generally, should I wait to buy an annuity?

I will now provide another figure which I think explains a lot of the reasoning behind why some argue that it is good to wait as long as possible to buy an annuity. This chart varies annuity payouts by age of purchase, rather than by interest rate. It is made assuming a 1% real yield. Again, these are inflation-adjusted annuities with the same assumptions as before:

Are Annuities (SPIAs) Okay When Interest Rates are Low?

As you can see, the longer you wait, the higher is your annuity payout rate. It really starts accelerating in one’s 70s, because that is when mortality rates start picking up and survival rates drop more quickly. Remaining life expectancies start dropping quickly, and so as you do make it longer, you can get a higher payout by waiting to make the annuity purchase.

But this is not the whole story. For one thing, though the payout rate is higher, you have less time to collect. The life expectancy is getting shorter. That is the big reason why the payout is bigger. There really isn’t anything to be gained in that particular regard.

Another important point made by Dick Purcell is that you may not want to wait too long to make complicated financial decisions like this, because cognitive abilities decline as one ages and it could be easier for one to be swindled by some unscrupulous salesman selling some other type of annuity (not a SPIA) with all sorts of punishing fees.

One other issue is that as you wait longer for the higher payout, you end up using your other assets in the mean time. Boglehead dpbsmith argues that by waiting, you miss out on some mortality credits (though they are quite small before one’s 70s) and so you probably won’t gain from waiting. I’d like to run some further simulations about this point one of these days. It sounds like a good research topic.

And then again, there are valid reasons to hold off buying an annuity, or at least to stagger one’s purchases by purchasing small SPIA chunks over time. Boglehead bobcat2 provided some reasons, such as the possibility that interest rates could increase (though I argued against this reason above), the possibility that one could be run over by a bus the day after buying the annuity, the opportunity to spread annuity purchases across insurance companies to reduce the impacts of a company failure and to help keep annuity purchase amounts under state guarantee limits, and the opportunity to maintain more flexibility and control over ones assets.

In this regard, it does seem quite reasonable to me for one to make multiple annuity purchases over rather than buying all at once. This is probably a case where valid arguments can be made for both sides and there is no one-size-fits-all answer.

Of course another important point to emphasize is that it is probably very rare that the best course of action would be to annuitize all of one’s assets. I’m mostly talking about partial annuitization here.

One other possibility worth mentioning is a deferred annuity. That is, someone aged 65, for instance, who purchases an annuity now which doesn’t begin payments until a later date. This is different from what I discussed previously when someone just waits until later to buy the annuity. The following chart is purely hypothetical since inflation-adjusted deferred annuities don’t exist yet. It is too hard for insurance companies to hedge the long-term inflation risk. But buying an annuity now which doesn’t begin payments until a later date gives a higher payout than waiting to buy the annuity at that date. The difference is just the probability of living that long. You get a lower price today because you may not make it until the time that annuity payments begin.

Are Annuities (SPIAs) Okay When Interest Rates are Low?

Appendix 1: Formulas for calculating annuity payout rates

The Actuarial Present Value (APV) for an inflation-adjusted SPIA is:

Are Annuities (SPIAs) Okay When Interest Rates are Low?

where SURVt is the probability of still being alive to age t, conditional on having made it to the age in which the annuity was purchased (separated by gender), and r is the expected real return for the annuity company’s investments, which I am representing here as fixed over time at the value of current long-term real interest rates (such as the yield on 30-year TIPS).

When a deferred annuity is purchased (such as a 65 year old purchasing an annuity which begins payments at 85), then I replace SURV with zeros for the years that no annuity payments are made.

The Annuity Payout Rate is then:

Are Annuities (SPIAs) Okay When Interest Rates are Low?

where annuitized assets for the charts is $100, and overhead is the overhead charge in decimal form.

Appendix 2: About the Overhead Charge

Insurance companies are businesses. They need to meet their business expenses as well as make a profit. Besides this, there are a couple reasons that they can’t just offer annuities priced using the 2007 Social Security Administration Period Life Tables. First, mortality rates can be expected to improve in the future as they have in the past. For instance, the figure below shows that single-year mortality rates for 75-year old males dropped from about 9% to 5% during the 20th century:

Are Annuities (SPIAs) Okay When Interest Rates are Low?

 So people who are 65 today will probably have lower mortality rates when they turn 75 than the 75-year olds in 2007. The insurance companies must adjust for that, though perhaps if they have a life insurance business too then the two business components might hedge one another. But also, insurance companies must deal with adverse selection. That is, the people who buy annuities tend to know they are in good health (people with terminal illnesses have no particular reason to buy an annuity) and may expect to live longer than the average person. Insurance companies must also adjust for this.

John Greaney at the Retire Early homepage has an interesting analysis of these SPIA charges. He compared annuity rates from the Principal Group with actuarially fair annuity rates and found that compared to population averages, it seems that Principal charged an overhead cost to account for all the above factors of about 22-29%. Allowing for corrections for adverse selection (which annuity companies don’t get to keep and it isn’t really a cost for you either… if you expect you might live longer than average then you would need to be making adjustments for this no matter what retirement income strategy you choose), he finds the costs were 9-16%.

I too had played around with those Principal numbers as a way to try to calibrate my annuity pricing program to annuity prices in the real world. I was generally using 10-year Treasury bond yields (compared to higher yielding corporate bonds like John used), and I was usually finding that an overhead charge of 15-20% (compared to John’s 22-29%) would get me a matching annuity price. I’m not sure whether it is better to use Treasury bond yields or corporate bond yields, but at least here is a range of possible overhead charges.

This was a calibration exercise for me to match my results to some existing numbers, and I used 15.5% here because it happens to be the overhead charge that gave me a match for whatever was the last example I had looked at. That is the charge taken by the insurance company when they sell the SPIA, relative to the actuarially fair numbers. John is much more critical about these charges than I am and makes good points about corporate greed and excess, but I think that SPIAs are more transparent and understandable than many of the other types of annuities out there. If you want a guaranteed income for life in addition to the best deal out there (which is waiting to 70 to start Social Security), then you must understand that you’ve got to pay something for it. SPIAs seemingly provide the best possible actual option available.


  1. Avatar Anonymous on February 14, 2012 at 6:45 am

    Wade –

    Thanks for making that point about the advantage of going from investment to SPIA before one’s analytical powers begin to decline, and citing me as somebody making that point. Along with the danger of unscrupulous annuity salesmen, I’d add the danger that most companies selling SPIAs offer them only without inflation adjustment –- without even mentioning inflation.

    But the danger I had in mind is in the alternative if one delays going to SPIA –- INVESTING. And there, what concerns me most is not salesmen or even the financial industry –- it’s the EDUCATION ESTABLISHMENT, which we should be able to trust, the universities teaching “investment” and the institutions that provide “fiduciary” credentials based on investment training copied from the universities.

    Under cover of the dreadfully misleading labels “expected return” and “risk,” they teach university students and fiduciaries to think investments should be chosen based on comparison in technical return-rate specs for the single year instead of best prospects for the investor’s future dollar needs and goals, and to think that a gamble within an asset class is equivalent to investment in the whole asset class. The resulting investment advice is commonly better for the financial industry than for the investor.

    This education establishment has made almost all of the ocean of investment “information” and advice, including “fiduciary” investment advice, so misdirected and misleading that I think the number one reason to go to SPIA upon retirement is to avoid investment misinformation and misguidance as one ages.

    Of course, there are superb financial planners, investment advisors, investment professors. But in a field of such complexity, dominated by misconceptions and misguidance shaped and presented with labels of deception, how are we average folks to identify them?

    Dick Purcell

  2. Avatar Anonymous on February 15, 2012 at 7:24 pm

    I object to the categorization of annuity pricing factors (by John Greaney at the Retire Early homepage) as overhead or fees. It feels like a concerted effort to bad mouth the product, while in fact their pricing is pretty good.

    Why derive pricing from the general population in the first place? They are irrelevant. Only healthy people buy annuities. The starting point for evaluating pricing is the buyer-population’s survival. You can see the difference in the table at

    Using the correct mortalities you can play around with your own assumptions about overhead using the third tab of this spreadsheet. Input your profit taking in column I. You will see how easy it is to end up in the red.

  3. Avatar Wade Pfau on February 20, 2012 at 6:11 am

    Yes, I agree that you can’t really blame the annuity company about adverse selection. And anyone shopping for an annuity probably has a higher than average remaining life expectancy, so they have to plan for a longer life no matter which approach they take.

  4. Avatar jobjob on May 13, 2012 at 5:14 pm

    Nice writing, Wade.

    My worry with an inflation-adjusted annuity is that it carries insurer risk. In fact, the risk that the insurer goes out of business may be the highest exactly in a high-inflation scenario, when it’s the most useful.

    Is there a product that carries ONLY longevity protection? I think this would look like a pool of retiree’s money with mixed allocation (equities, bonds, other) with a payout that varies (depending on the market), but that continues for life (and no left-overs for heirs). So this product would have market risk (variable yearly payouts), just like if you invest directly, but no insurer risk (payouts are from pool with no rate guarantees) and no longevity risk.

    • Avatar Wade Pfau on May 14, 2012 at 6:05 am

      Thanks. It sounds like you are describing a Notional Defined Contribution pension used in some countries like Sweden and Italy.

      It is similar to a DB pension in that inflows occur over time and it can be pay-as-you-go, but it is similar to DC in that payouts are related to market returns, mortality changes, etc.

    • Avatar jobjob on May 15, 2012 at 4:54 pm

      That sounds similar, though I understand that “pay-as-you-go” suffers when the demographic ratio of retirees to workers shrinks. This makes sense for a government as it avoids locking in unrealistic, defined benefits.

      What I’d love to see is a financial institution offering a “market annuity.” Let’s say that you have N expected years the day you start withdrawals. Then your first year you get 1/N as a payout. Subsequent years, you get 1/N plus any growth of the pool.

      The problem with a regular annuity is that if the insurer cannot know future growth rates. If the insurer guesses to low, he wins and I lose. If the insurer guesses to high, I MAY win, but if the insurer goes out of business, I lose.

      With the “market annuity”:
      1) the insurer cannot go out of business,
      2) I get exactly the market returns (minus management fees),
      3) I’m insured against longevity risk.

    • Avatar Wade Pfau on May 16, 2012 at 7:13 am


      I am not sure if I understand your proposal.

      What is the risk being insured by the annuity? Where is the risk sharing? Will payments decline if the market drops?

      I’m having trouble seeing how this is different from someone just withdrawing 1/N from their portfolio of assets for the rest of their life.

      Thanks, Wade

  5. Avatar jobjob on May 16, 2012 at 4:06 pm


    The only risk with the “market annuity” is market risk: unknown growth rate of the underlying investment.

    If you withdraw 1/N from a regular portfolio, then you have longevity risk (though your children benefit if you die early).

    With the “market annuity,” you transfer funds (with the pool of insurees) from those who die early to those who live longer than N years.

    The point is that the payout rate depends on the market rather than being set initially.

  6. Avatar jobjob on May 16, 2012 at 4:08 pm

    (Typo: “with the pool” –> “within the pool”.)

  7. Avatar Wade Pfau on May 17, 2012 at 1:10 am


    Would anything change if we replace the 1/N in your formula with:

    1 / remaining life expectancy


    • Avatar jobjob on May 17, 2012 at 11:14 am

      Hmm, you’re saying pay out “initial investment x cumulative growth / remaining expectancy”? It seems that would make later payments grow quite a bit for those that survive long. Yes, that would change the formula.

      Let me rephrase a bit. If I knew that I would live exactly N years, and I start with D dollars, then WITHOUT an annuity I would:
      Year 1: withdraw D/N
      Year 2: withdraw ((remaining D) * growth)/(N-1)
      Year 3: withdraw ((remaining D) * more growth)/(N-2)

      With the “market annuity” I would get the same payouts as above for the first N years, but:
      1. I could die early and the insurer’s pool gets “remaining D”,
      2. I could die late, and get yearly payouts P (after year N) that are roughly what my payout was in “year N” (or perhaps some adjusted average payout), times growth of the pool.

      (The exact formula for P would have to be such that the pool cannot run out of money, guaranteeing there is no insurer risk: somehow unitize my contribution.)

    • Avatar jobjob on May 17, 2012 at 12:31 pm

      Perhaps this is simpler version:
      I pay D dollars to a “market annuity” and I have a life expectancy of N years.
      It pays out, just if I had an individual investment account:
      Year 1: withdraw D/N
      Year 2: withdraw ((remaining D) * growth)/(N-1)
      Year 3: withdraw ((remaining D) * more growth)/(N-2)
      As people die early their remaining money is moved to a pool X.
      Everyone alive past their individual N gets a yearly payout from X in proportion to their initial contribution, D.

    • Avatar Wade Pfau on May 18, 2012 at 6:52 am

      In your explanations, what I mean too is that each year the N changes to adjust for your remaining life expectancy. As you actually survive past each age, your remaining life expectancy decreases by less than 1. You could also have a cap on how high the withdrawal can get, such as 20%, for very high ages.

      I guess I’m still not seeing what the risk pooling part is in your description. What I am describing is something done on a personal basis, not with an annuity.

    • Avatar jobjob on May 18, 2012 at 12:02 pm

      The risk pooling part is “pool X” above. Everyone lives as if they will die after exactly (the originally estimated) N years. Those who live longer keep living approximately as before, using money from those who died early. (Adjusting N by less than 1 is what you’d do WITHOUT pooling, per your recent articles.)

      So, my proposed pooling is similar to a regular annuity, except you’re likely to get better returns (pro), there is no risk of the insurer going out of business (pro), but the yearly payout is variable (con, if you dislike uncertainty).

  8. Avatar jobjob on May 21, 2012 at 2:46 pm

    Wade, sorry if this thread is getting tedious, but I think I there’s demand for this product, and I don’t think it’s out there. So let me try one more time to clarify what I think is a simple, yet powerful idea.

    A regular annuity transfers money from the short-lived to the long-lived. However, returns are poor compared to market (the insurer must set the rate lower than expected market growth to minimize his own risk, then pockets the difference). Also the insurer could go out of business.

    To get better return, and not worry about an insurer getting out of business, imagine 100 millionaires getting together at age 65. They each put $1M in a pool, then withdraw according to remaining N (expected life expectancy). Simple. Longevity risk addressed (except for the last few guys.) No fat margin for an insurer.

    The market annuity is essentially the above, but with some tweaks:
    * allow different starting amounts
    * make small adjustments in payout as N varies with time
    * let people join at different ages
    * remain open for people to join at any future time
    * small management fee

    Do I make sense?

    • Avatar Wade Pfau on May 22, 2012 at 6:47 am

      I’m still not sure I’m following. With your explanation:

      “To get better return, and not worry about an insurer getting out of business, imagine 100 millionaires getting together at age 65. They each put $1M in a pool, then withdraw according to remaining N (expected life expectancy). Simple. Longevity risk addressed (except for the last few guys.) No fat margin for an insurer.”

      I don’t see what is being pooled. What is different from the case that one millionaire just withdraws 1/N from his own wealth. How are funds transferred from the short-lived to the long-lived?

      How is the money invested? Insurance companies have to make low risk investments by regulation, it is not that their returns are poor compared to the market. Fixed annuity fees are not too high, maybe somewhere around 5-10% before counting for adverse selection. But adverse selection is still going to be a problem with this approach, and an actuary will have to be hired by the participants to figure out everyone’s appropriate N, and a fund manager will still need to be hired. So there are going to be fees still.

      Perhaps what you are describing is more like a variable annuity where payout is based on how the market performs relative to a set return level.

      I’m sorry, I’m just not grasping quite what you have in mind yet.

  9. Avatar jobjob on June 3, 2012 at 2:11 pm

    Lol. I’m such a beginner. Yes, I think I have been describing a variable annuity without the extras: no guaranteed minimum, no survivor benefit.

    From my readings, it seems like such variable annuities, *without* extras, have hefty fees around 1.25% per year. I’m surprised it’s so high. Wouldn’t this be very simple to manage? Just like an index ETF charge 0.1-0.2% per year in management, shouldn’t a vanilla variable annuity have smilar low fees? Is there a lack of competition?

  10. Avatar Anonymous on January 9, 2014 at 8:26 pm

    SPIAs? How about an inflation-indexed one I got through Vanguard Mutual Funds some years ago? Good rate too and from the largest insurance company in the world at that. Fortunately I didn’t part with much and the American taxpayers bailed me/them out. Yes, I am speaking of AIG of course.

    If it would be foolish to invest a large proportion of one’s wealth in the stock of one company, why isn’t it foolish to entrust the funds to one insurance company? Because it’s contracual? That won’t mean much if the company goes bust as, technically, AIG did.

    • Avatar Wade Pfau on January 9, 2014 at 10:55 pm

      I agree that it’s not a good idea to put it all into a contract at one company. Spread it out and try to stay below the state guarantee association levels if possible.

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