Friday, February 10, 2012

Annuities and Delayed Social Security

Today I’d like to feature Joe Tomlinson’s February 7th column for Advisor Perspectives, “An Innovative Solution to Retirement Income.”
He looks at two strategies which deserve more attention than they get: single premium immediate annuities (SPIAs) and delaying Social Security until age 70.
Though you must give up control of your assets, he notes that the current quotes for inflation-adjusted SPIAs are $446.95 per month for a $100,000 payment. That works out to $5,363 per year. That means you are locking in a 5.36% inflation-adjusted withdrawal rate for life. You’ve got to compare that with the alternatives for a systematic withdrawal plan based on safe withdrawal rates research. There’s the 4% rule, but if you think that is optimistic, you may be thinking more in terms of 3% or 3.5%. In this case, it may really make sense to consider some partial annuitization (no one says you have to annuitize everything).
Annuities may sound too good to be true, but very simply the reason that they work is because the insurance company can pay you assuming that you will live to your life expectancy. That is because they can average the uncertain lifetimes of individuals across a very large group of customers. Sorry for the crassness of this sentence, but those who die sooner end up subsidizing those who live longer. If you are planning only for yourself (and/or spouse), you sort of need to assume that you will live quite a bit longer than your life expectancy (you have a 50% chance of living longer than your life expectancy) in order to make sure you don’t run out of funds. That means you should be withdrawing less than possible if you knew exactly when the end would come. The insurance company can take advantage of these averages (their average customer will live to the expectancy, at least after making adjustments for the fact that there is some self-selection so that annuity buyers end up living longer than the general population) to be able to pay you more.
About the issue of whether it is a good idea to buy annuities when interest rates are low, I did make a figure which I hope can contribute something. I wrote a program to calculate annuity payouts. Insurance companies certainly use more sophisticated mortality data than me (I’m just using Social Security mortality data) and they also have more complicated ways to deal with investment returns (I just assume an interest rate) and that may mean the level of the line in this figure is not right. Perhaps it should be shifted up or down.  But I do think the slope is basically okay. And so it shows you how the annuity payout relates to the interest rate.  Again, these numbers may not be super accurate, so while I show that a 0% interest rate has an annuity payout of 5% and a 4% interest rate has an annuity payout of 7%, what is important is that the payout of an annuity is 40% higher when the interest rate is 4% than when it is 0%.  I think this can give some idea about the tradeoffs with buying an annuity now or with waiting (and hoping) that interest rates increase before buying an annuity:

Actually, I made that figure while on a business trip to Boston in October. I saved the figure then, but later I had some computer problems and lost the computer code for making it. So I can't remember all the assumptions I used in that figure.  I think it is an inflation adjusted annuity, perhaps for a 65 year old male.  There might be an overhead cost built in. But I'm not sure.  This is something I will come back to again with more clear explanations at some future time once I re-program it.
Meanwhile, the other important issue Joe discusses is the financial benefits from delaying Social Security. It reminds me of a chart I made once for an article, but never ended up using. This was based on a large sample of Social Security recipients in 2004. For these recipients of retirement benefits, I looked at everyone’s initial age for benefit receipt. The distribution looked like this:

Half of the recipients began at the earliest possible age of 62. Only about 3% of recipients began at age 66 or higher.  Joe explains why it makes a lot of financial sense to delay receipt to age 70.  It’s a great deal, the best inflation-adjusted annuity that money can buy. Yet people just don’t seem to be willing to do it.
Finally, he also discusses an innovative plan that would call for the government to make inflation-adjusted annuities available through Social Security offices.
Definitely have a look at his column for more about these helpful strategies.
If you are interested in annuities, Bob Seawright also recently wrote a very good column called “The Annuity Puzzle” for Research magazine. Mike Piper at the Oblivious Investor also wrote a good column about annuities in low-interest rate environments. Also make sure to read the set of comments started off with a good point made by Matthew Amster-Burton about how annuities could be even more attractive in low interest rate environments.
Finally, I was part of a student fieldtrip to Kyoto when it happened and then forgot to mention it, but I would like to thank the Finance Buff for making my blog into his “blog of the week” last week. As I owned a copy of his highly worthwhile book, Explore TIPS, before I knew about his online presence, it is a nice honor for me.


  1. The graph of annuity payouts vs interest rate is great, Wade, and it underscores what I was saying on Mike's blog: because the slope of the line on the graph is less than one, annuities get more attractive as interest rates decline.

    The reason should be obvious: interest rates have nothing to do with life expectancy. The point of buying an annuity isn't to lock in a great interest rate; you can always do that by buying bonds or CDs, without enlisting an insurance company's help. As interest rates rise, the retiree looking for a 4%+ withdrawal rate is more likely to be able to self-insure with a bond ladder and less likely to need to annuitize.

    And man, that Social Security piechart is really depressing.


    1. Buying an annuity in a low-rate environment is essentially like buying a long-term bond with a mortality credit on top. The only valid argument to not replacing the bond portion of your portfolio with an annuity (which provides a bond payout + mortality credit + longevity income insurance) is that interest rates are mean reverting. Over a decade in a low-rate environment makes the mean reversion argument a difficult one.

      Michael Finke

    2. Matthew and Michael,

      Thanks! I think what you are both saying sounds quite logical and correct.

      Veblenesque, I hadn't thought of you that way. Have you read The Worldly Philosophers? Veblen was quite a character.

    3. If we are thinking about replacing part of the bond allocation with annuities, doesn't it make just as much sense to build an annuity ladder?

      That way, you are dollar-cost-averaging into your "annuity portfolio" and taking advantage of the fact that payouts are higher for older purchasers...

    4. Yes, I think this sounds reasonable. It also leaves you less exposed to the interest rates on any one particular date.

  2. Wade –

    In your analysis of annuity payout A% versus interest rate I%, did you (a) assume that the I% holds throughout the annuity payout period? Or did you (b) consider the I% as being the interest rate AT TIME OF PURCHASE but future interest or market rates to be forecast by the actuaries?

    I would prefer approach (b), which I would expect the actuaries to apply, and would expect to produce a much flatter line than (a). I would think that at times of unusually high or low current interest rates, the actuaries would forecast some sort of interest rate “reversion toward the mean.”

    What interest rate mean, and how fast revert to what degree? I have no idea – but would sure like to see answers. If you used approach (b), how did you develop future interest rates?

    Dick Purcell

    1. Dick,

      I simply used (a). I applied an interest rate that is assumed to hold throughout the payout period. What you are saying certainly sounds right and probably would result in a flatter curve. Rather than assuming the fixed interest rate, I could put in a series to reflect mean reversion, if someone has some idea about a formula that actuaries might use for that.

      Thanks, Wade

    2. If the insurance company matches assets and liabilities, that would lock in the current level of interest rates. Re: mean reversion, I haven't studied it myself for bonds. Jeremy Siegel in his famous book on stocks says bonds exhibit mean aversion (pg. 33 2nd edition), but doesn't present evidence. My intuition is that rates are more likely to go up from here rather than down, but I'm hesitant to predict given that a luminary like Bill Gross got it spectacularly wrong last year.

    3. Joe,

      That's a good point. Then do you think it is reasonable to assume, basically, that the current (long-term) bond yield is the appropriate interest rate to use when calculating an annuity payout? I mean, will it provide a good enough of an approximation? Would the 30-year TIPS yield be good for an inflation-adjusted annuity?

    4. Wade and Joe --

      With stocks there's evidence of momentum short term and mean reversion longer term. Maybe for bonds Siegel meant aversion short term.

      Of course it's best to learn the approaches of actuaries who must study this to death (so to speak).

      But without hearing from the actuaries or analysis of interest-rate history, I'd bet Romney's $10,000 that for a decade ahead and beyond, historical mean is a better prediction than whatever the interest rate is today, and therefore don't buy approach (a). For a first cut, for 10 years ahead and beyond I'd use historical mean. For the first ten years, maybe use present rate, or maybe slope it toward historical mean (I'd slope it).

      If Romney can spare another $10k, I'll wager that this approach produces a considerably less steep line of annuity payout versus purchase-day interest rate than the line in the graph up in the blog.

      Dick Purcell

    5. Wade,

      I'll try a bit of reverse engineering using the Income Solutions(R) rates available from Vanguard. I did a quick look awhile back and, if I remember correctly, it looked like insurers were assuming a rate greater than Treasuries on fixed payout annuities (reflecting their ability to earn credit spreads), but building extra profit margin in on their quotes for inflation-adjusted annuities. I'm curious, and will try to take another look and send you some actual numbers tomorrow.

    6. Sorry, Wade, I shouldn't be just criticizing. This is a very valuable discussion, full of good focus and thinking -- blog, references, link, and the idea of your graph. It's just that I think there's real merit to the view that low interest rate time is good SPIA purchase time, and don't want the graph's line to be biased against that view.

      Seems to me the argument for low interest rate being good SPIA purchase time can be made purely on return rates. If you put your money in the SPIA, its "return" is determined by a mix of low current interest and the actuaries' anticipation of future better interest, whereas if you keep your money out its return is determined wholly by the current low-rate condition.

      Does that make sense to you??

      Dick Purcell

    7. Dick and Joe,

      Thank you. Dick, what you are saying does make sense. And it would make the slope flatter if insurance companies make allowances for higher future yields when yields are low. But that does sound risky for the insurance company to assume that. What Joe says makes sense too, that maybe insurance companies are matching assets with liabilities and so the current rate is mostly what matters.

      I didn't mean to scare anyone with the figure. I actually thought it could help bring some meaning to the discussion. People are worried that annuity payouts are too low now, and I was just trying to provide some quantification to understand that that maybe it is not as bad as people might think. It's not as though a zero interest rate leads to an almost zero payout, which is a thought that probably some people have in their mind.

      This may be where the Trinity study comes into play too, in that it is not helpful to plan retirements currently. We need to consider where we are starting from: low interest rates, low dividend yields, slightly overvalued stock markets. A 5% inflation-adjusted payout on an annuity sounds pretty good to me. I think I would be seriously considering that if I was actually anywhere close to retiring.

      Yes, there have been lots of great comments here. Did you see the first two by Matthew and Michael. They argue that annuities become even more attractive when yields are low. I think you may be arguing the same thing, but for a different reason.

      Joe, thanks for checking out some reverse engineering. What I had been doing was trying to calibrate my program to what annuity prices are currently on offer by adjusting the overhead cost. I was finding that I could match various annuity prices with my simplified assumptions by also adding an overhead cost of 15-20%, which I think is a typical estimate.

      The reason I care about this topic is I would like to simulate annuities as well in Monte Carlo simulations, which means that I need to have a nicely calibrated way to calculate annuity prices on my own.

    8. Wade, there's a good thread on annuity (SPIA) rates at Bogleheads, here:

      Right near the top, it shows Bob90245's graph of history of corp-bond interest rates and annuity payout rates, the same graph recommended by the other Anonymous below.

      To my shock, it shows that these things have been priced as if whatever interest rate prevails at time of purchase will be the interest rate for the rest of the annuitant's life. This makes me wonder whether or not the actuaries are actually doing any work. But it undermines most of what I've said above and supports your use of approach (a) in your graph.


      That Bogleheads thread also cites work of Milevsky suggesting that SPIAs should be bought over time, not all at once.

      Dick Purcell

    9. Thank you Dick. That is a good thread! And it links to another one from a couple years ago that may be equally as good. I need to read Moshe Milevsky's paper about it too.

      At least actuaries need to make sure they are getting the future mortality improvements estimated correctly. But I guess there isn't any particular reason to expect bond yields to mean revert. Along with Joe's point that insurance companies are asset/liability matching, that may explain the close relationship between current interest rates and annuity payouts.

    10. Wade –

      This gets more and more interesting. That earlier Bogleheads thread you cited has gems.

      1. An annuity pricing formulation presented by “gw” in that earlier thread blows away my reasoning for preferring approach (b) – but supports my approach (b) conclusion.

      To see it, scroll about 1/3 of the way down in this thread:

      In gw’s formulation, as Joe suggests the current interest rate at time of purchase is the interest rate that counts because the approach is matching of assets to liabilities, not any forecast of future interest rates. BUT – the dominant part of gw’s formulation is mortality, not interest rate, so as interest rates rise and fall “returns” of annuities purchased at that time should vary much less. (But this contradicts Bob90245’s graph, which shows actual historical annuity returns changing just as steeply as interest rates at time of purchase. What the Sam Hill??)

      2. At the very bottom of that earlier thread (at the link just above), there’s a post from dpbsmith that appears to me to blow away arguments for delaying SPIA purchase or doing it in steps over time. In too-brief summary, he says that every year’s SPIA payout has a mortality component, and the longer you delay the purchase the more years of that component you miss. I THINK THAT DPBSMITH POST IS A MUST-READ.

      Dick Purcell

    11. Dick,

      Thanks. Both of those threads have a lot of good stuff. I've got my figure re-created now, and I'm also making some other figures that I hope will be useful. I'm hoping to get a part 2 for the annuity pricing discussion finished for the blog in 24 hours or so. It's hard to get much done quickly during the weekend.


    12. I read dpsbmith's post now. That definitely looks like an issue which could benefit precisely from using Monte Carlo simulation, and it could be a good research topic.

    13. Wade --

      Did you see my Bogleheads post about Bob90245's Y axes?

      The annuity payout and interes-rate-at-purchase Y axes don't scale down to zero at the same level. If they did, they would show that proportionally, annuity payout rises and falls less than interest rate. So my advocacy of approach (b) for your graph was right.

      (My reason was wrong, but we won't mention that. It's not that the actuaries consider future interest rate reversion -- apparently they instead match liabilities with assets at time-of-purchase rates. The reason payout varies less than interest is that payout rate is partly determined by mortality.)

      Dick Purcell

    14. Dick,

      Without any mean reversion factoring, your (b) gets incorporated into my (a). My graph shows the combined effects of both mortality and interest rates. Since mortality is so important, it explains why the slope of the line is so much less than 1 as interest rates change. Annuity payouts are not fully responsive to changes in interest rates as my graph shows. I do not have a slope of 1 for the relationship between interest rates and annuity payouts. I think we are on the same page here now.

    15. Wade --

      All RIGHT!

      Took me a lot of circling to appreciate what you've done.

      I hope this discussion helps somebody else get a fuller understanding, because that relationship is very important for last-third-of life-decisions.

      Another important reason for max clarification of that relationship is to make extra sure there's no bias against the buy-SPIA-now decision. Buy-now has the huge advantage of getting people out of all this complexity before their coping with it all begins to decline.

      For that reason, I think any recommendation to delay SPIA purchase much past 60s has to have pretty strong financial-math support to overcome the complexity-when-old disadvantage and be responsible.

      Dick Purcell

    16. Thanks Dick! Your point about cognitive decline is quite important and I will include it in my follow-up for tomorrow. (Michael Finke, who commented above, has an important study showing both the cognitive decline and the fact that people fail to recognize they experience decline)

      I am slowly working my way through the Bogleheads threads when I get 5 minutes here or there during the daytime (I hope to really get to work when the family heads off to bed). But just a note, I think you may not have the correct reason for why dpbsmith argues to buy SPIAs sooner rather than later. About the mortality component, I think you might have it backwards. That by itself is a reason to delay. I thought dpbsmith's reason is because after he did some simulations, he found out that one could hardly be expected to do better with their own investments (spending down bond holdings) during the window when annuity purchases are delayed, so one might as well go ahead and annuitize. I need to read it again though.

    17. But Dick, this sentence of yours is really good:

      "This means that in general, low interest rate is best time to buy the SPIA, because low interest rate hurts SPIA payout rate less than it hurts prospects for money kept out of the SPIA."

      I do believe, also, that Matthew started off the comments here with this point.

    18. Dick,

      I got a couple more minutes in at Bogleheads. I think you are right afterall re: dpbsmith. He is talking about a loss of mortality credits by waiting.

      Also be sure to see the post by alec, where he discusses the idea that in waiting for interest rates to go up, your bond portfolio will also suffer capital losses as interest rates rise. This means you will have less to spend on the annuity, even if its payout is better. That is another good reason to go ahead and buy annuities, rather than waiting for interest rates to rise.

    19. I was hoping to find time yesterday to do some numbers, but we had house guests, so I will try today. Just some quick observations on this excellent discussion. As a financial planner, I'm reluctant to recommend SPIAs right now because I feel we're in a period where the Fed is artificially holding down rates to stimulate the economy, and I'm recommending fixed income portfolios with durations in the 3 to 5 year range. For a 65-year-old, a SPIA has a duration of about 13--like an 18-yr bond.

      I'll try to do some numbers on mortality leveraging showing the difference in payout rates between using a bond ladder (to life expectancy) vs. a SPIA---as a function of interest rates. I think it will show the SPIA advantage increases with increasing interest rates.

      I'm a bit dated, but 10 years ago I was the actuary in charge of the annuity product line for a big insurer. The SPIA business was small for us, as for most insurers, so we didn't burn up a lot of actuarial energy fine-tuning the pricing. We used current interest rates (not projected), did rough asset/liability matching, used annuitant mortality (to reflect some healthy lives selection) and projected mortality improvements. The GIC business was very big for my company, and there the actuaries and investment people did very sophisticated work on asset/liability matching, but our apporach on SPIAs was much rougher.

      One of the considerations about buying over time vs. all-at-once is weighing what make sense financially vs. the behavioral issue of trying to minimize potential regret.

    20. Joe,

      Thanks for sharing the actuarial details. It's quite helpful.

      Also, I'm about to make a new post where I tend to agree with those saying that SPIAs actually have more advantage when rates are lower than when rates are higher. But I haven't tried simulating it myself yet. I will be interested in your results and I'm open to having my mind changed. That could even be a good column topic.

    21. Joe –

      I note that in Wade’s blog above, above all these comments, his discussion of your column includes the following:

      "Finally, he also discusses an innovative plan that would call for the government to make inflation-adjusted annuities available through Social Security offices."

      As I understand it, what you discussed is a plan for the government serving as a middlemen for SPIAs offered by insurance companies. I like that but want to go a step further in the same direction: Get the Federal government to offer ITS OWN lifetime inflation-adjusted SPIA, eliminating “insurance-company survival risk.”

      I remember seeing this step recommended in a column in the New Your Times a year ago, Feb. last year:

      Paying for Old Age, by Henry T. C. Hu, professor at the University of Texas School of Law, and Terrance Odean, finance professor at the University of California at Berkeley.

      Loved it then, love it now. I think getting the government to do this is THE most important thing we could do for this whole retirement-finances field!

      Dick Purcell

    22. Joe,

      I was just having a look at the Wall Street Journal and see that you're quoted saying more or less the same thing as what you just wrote here.

      That's great, congratulations!

      Hmm... am I going to have to backtrack on my newest blog post where I argued somewhat confidently that it's not a good idea to wait for rates to rise?


    23. Wade,

      The way I look at it is that I think there is a greater chance that rates will be higher 3-5 years from now than lower, so I'd personally wait to "go long" and buy an annuity. But I realize there's a significant chance I might be wrong. Guesses about interest rates and bond investing are particularly perilous--take Bill Gross's decison to dump Treasuries in Feb. 2011, whereby he missed out on by far the best performing asset class for 2011.

    24. Just a note re: Dick Purcell's comment above. I too like the idea of going further with the government offering inflation-adjusted annuities as in the Hu, Odean proposal. I did a paper a couple of years ago on improving the retirement system that you might be interested in. It advocated for a much stronger role for the Federal government. It's on my website at or just shoot me an email at and I'll send it to you.

    25. Joe --

      Thanks! I'll visit your website.


  3. Thank you for the kind words, Wade.

    I should also note that the Government Accountability Office issued a major study last June making the same two points Joe Tomlinson’s article does. And, to be clear, Joe's article mentions the GAO study right up front. The study is available here:

    1. Bob,

      Thanks. I didn't read the GAO study yet. I need to do a lot more reading about annuities. I'm starting to get to it now finally though.

  4. Thanks for highlighting my article, Wade. For those interested, there will be a response from me to a reader's letter in the Feb. 14 Advisor Perspectives (free at where I compare Social Security delay to taking SS earlier and having more money invested in stocks. It turns out to be another way of demonstrating the benefits of SS delay, particularly for married couples.

    1. Joe, thanks. An active blog commenter named Larry has recently been asking about that sort of strategy. I hope he sees it. I'll add a link once it comes out on Tuesday.

  5. Instead of using devising a theoretical calc for Premium vs Yields, better to use actual data of actual market yields and the premiums at that time. See data from 2002 (tabs at bottom) Bob has also saved actual data for the US at
    He uses a static relationship between the two factors which I presume must have held for his data set.

    1. Thanks a lot anonymous! Those resources look great! I'm quite aware of Bob's great website, but I didn't know about this page. These might help me a lot with getting my program properly calibrated to the real world. Because I would like to calculate annuity prices in Monte Carlo simulations, I do need to have some sort of way to calculate prices myself. Thank you.