Wednesday, April 18, 2012

The Power of Single-Premium Immediate Annuities

Over the past few days I’ve been getting back into the programming spirit. This is all preliminary and subject to further checks and refinements.

This evening I’ve been looking at how partial annuitization impacts retirement outcomes. Borrowing on assumptions developed by Joseph Tomlinson, I assume a 65-year old couple can purchase an inflation-adjusted single-premium immediate annuity with a payout rate of 5.05%. 

Update: I did say this was preliminary and subject to further checks. In the comments, Joe Tomlinson pointed out that I was misremembering about the 5.05% payout rate for a real SPIA. That is for a 65 year old male, not a 65 year old couple. Thus my analysis applies to a single male. For a 65 year old couple, 3.88% is the payout rate. I've changed the figure below to point out that it is for a 65 year old male. And I've also added a new corrected figure for the 65 year old couple. My descriptions below are about the male case. For the couple, the results are much less impressive. However, it is still vital to remember that "failure" does not mean the same thing when annuities are included. With systematic withdrawals, failure means your income falls to zero. With annuities, failure means that your income falls to the annuity amount. With 50% annuitization of assets, that would mean your income falls to
100 x .5 x 3.88 / 4 = 48.5% of your original spending level once your financial portfolio runs dry.  For the couple, the advantages of annuities become less obvious, though I think this still reflects positively on them, especially if leaving a bequest is not an overly important consideration. Ultimately, to evaluate the tradeoffs for this couple, we may need to rely on the approach developed by Joe Tomlinson in his February 2012 JFP article. It accounts both for mortality rates and for how much relative importance the retiree puts on leaving a bequest. I'm also in the process of working on some other metrics to evaluate these decisions, though perhaps I should first do more careful checking before posting new material to avoid this sort of embarrassing backtracking :) 

They want to spend at a constant inflation-adjusted withdrawal amount representing 4% of their retirement date assets (the normal 4% rule assumption).

Also, while I usually base Monte Carlo simulations on historical averages, that especially isn’t fair for annuities. The annuity payout rate is based on the low current bond yields, and so I adjust the returns for stocks and bonds both downward by 1.52% so that real bond returns are calibrated to 1% instead of the historical 2.52%. This maintains the same historical equity premium, and I do not change either the standard deviations or correlations. I explained this issue more completely in Lower Future Returns and Safe Withdrawal Rates.

I’m making a retirement income frontier which shows the traditional failure rates for a 30-year retirement on the x-axis, and the median real wealth remaining after 30 years on the y-axis. I show the results for asset allocations between 0 and 100% stocks for two different strategies.

The blue curve represents traditional drawdowns from a portfolio to obtain the desired spending without annuitization. Because of the lower asset returns, failure rates are higher than my figures usually show. Stock allocations above 40% have the lowest failure rates, and these vary between about 20 and 30%. As for median remaining wealth, higher stock allocations support higher expected bequests.

The cyan curve shows what happens when the couple male annuitizes 50% of their wealth, purchasing an inflation-adjusted SPIA at their retirement date. That 50% is arbitrary and is not a maximum allocation to SPIAs or anything like that, I just wanted to see what happens in a basic scenario. This couple then withdraws the necessary amount from their remaining portfolio to top off the annuity and get their 4% spending power. With the 5.05% payout rate, this couple male is getting 2.5% of the 4% of spending from their annuity, and the remaining 1.5% of their spending comes from their portfolio.

The cyan curve shows that partial annuitization reduces failure rates across the board for all stock allocations. Even more than that, with partial annuitization, failure doesn't mean that income falls to zero. It just means that the portfolio is empty. You still have 62.5% (=2.5/4) of your original income amount from the SPIA even in the case of failure. Rethinking Safe Withdrawal Rates: The Meaning of Failure explains more about this issue.

I connected corresponding stock allocations with red dashed lines. The outcomes for remaining wealth are more mixed. With annuitization, stock allocations above about 50% would support lower bequests than the corresponding stock allocation in the no annuitization case, while stock allocations below 50% would support higher bequests.

But what is also rather important to note is that for a risk averse couple male, partial annuitization lowers the failure rates, which could make them more willing to use a more aggressive stock allocation for their remaining portfolio. Essentially, the SPIA acts like a super-bond, and so even 100% stocks with the remaining portfolio corresponds to something closer to an overall 50/50 asset allocation. Consider a couple willing to hold only 40% stocks if they don’t annuitize. With 40% stocks and partial annuitization, they can obtain both a lower failure rate and a higher expected bequest. And they could continue increasing their stock allocation to any level up to 100% to get higher expected bequests while still keeping their failure rates quite a bit lower than with the no annuitization case.

That, to me, suggests that partial annuitization really does have the potential to help retirees obtain better outcomes. I do have to acknowledge that this isn’t the full story. I assume a rather long 30 year period, and annuities will look more attractive as the period under investigation increases. When I wrote my somewhat negative column on GLWBs last December, I suggested that partial annuitization may be a better approach, and these preliminary results do suggest that a full investigation of this issue is in order.


  1. This is a very nice graph and very interesting results. It might be worth also testing at a lower annuity payout rate. I based my 5.05% on commercially availabe rates a single male age 65 with a life expectancy of 20 years. So looking at 30-year retirements would place the annuity in a favorable light. Commerical rates for 65-year-old couples as of late March were 3.88%. I also created a hypothetical annuity based on a 1% real rate and variable mortality with a 30-year life expectancy and that payout rate was 3.91%. So testing 3.9% or so might be worth doing. That would be slightly under the 4% target withdrawal rate so things might tilt differently than using 5.05%.

    With all of this it will be interesting to see if the analysis produces optimal mixes involving partial annuitization, or whether all-or-nothing approaches do better. Anyway, I think this type of analysis holds a lot of potential to improve our understanding.

  2. Thanks, Wade, great stuff again.

    I'm seeing comments on discussion boards that might indicate a vocabulary problem. When an article uses words like "failure" with other words like "wealth", people assume that the result is "out of money".

    The reality of a retirement with a SPIA is that "portfolio failure" and "loss of wealth" still leave a retiree with their annuity (and pension and Social Security). However the typical website reader who's skimming the headers misses the distinction and still equates "failure" with "indigent". To them, "loss of wealth" means "no more money".

    Yet the retirement never fails because the annuity still pays out. All wealth is not lost because the retiree still has monthly income. Maybe it's better to avoid words like "failure" and phrases like "loss of wealth". Other descriptions could be "investment depletion" or "cut back to annuity income" or "running out of investments".

    I'm trying to write my own post along those lines. It ain't easy.

  3. You can make your analysis more general by using a formula originally posted on the Bogleheads forum by gw. The approximately payout percentage of an annuity is 1/remaining-life-expectancy + assumed-interest-rate. For commercial annuities an assumed interest rate equal to the 10 year T bill rate is reasonably close.

  4. This is a great illustration of the bequest/income security tradeoff that comes from annuitization. Which leads to implication that those with a weak bequest motive (say a childless couple or one with financially secure children) will annuitize more of their retirement wealth compared to retirees with a stronger bequest motive. This also opens up the question of whether the child would prefer a non-annuitized parent who will either a) give them a larger expected bequest or b) saddle them with increased support in the event of a shortfall. The risk aversion/risk capacity of the bequest recipient is also an important consideration.

  5. Joe: Thanks. You are right. I've included a substantial revision and update above to reflect that the appropriate payout rate for a couple is 3.88% instead of 5.05%. That's my mistake.

    Doug (Military Guide): Exactly. The concept of failure is a big misleading idea in safe withdrawal rate studies, because it ignores any income outside of the financial portfolio. That means it includes any income from guaranteed sources like SPIAs that you might use part of your wealth to purchase. We really need to Rethink Safe Withdrawal Rates and Get a New Meaning for Failure.

    Anonymous: Thanks. I've seen that formula and I can also calculate annuity payout rates with a program I wrote, but the problem is I don't know the appropriate overhead costs to build in, so it is probably better for me to just use real quoted prices when I can.

    Michael: Thanks. Yes, this could be a research article idea: how the parents and children can work together to choose the best retirement income strategy for the parents taking into account potential intergenerational income transfers in both directions.

  6. This is great stuff, Wade. The second chart seems to point out the challenges when the annuity payout rate is at or below the target withdrawal rate. This type of analysis you're doing has a lot of potential.

  7. I think you might be underselling the value of annuities for dual life couples. For two 65 years olds, the median dual expectancy is 26.7; if you assume only a 30 year withdrawal period, a substantial fraction of couples will run completely out of money in the portfolio withdrawal case. In the partial annuity approach, they'll still have half their income, most probably, for a single survivor.

  8. Thanks Joe and ourbrooks.

    ourbrooks, that is a good point about the idea that less spending power may be needed after one spouse passes. I've been different takes on how much less it should be.

  9. I just don't see how the SPIA is a good deal at current interest rates. If a 65-year old couple gets a SPIA with 3.88% payout, how is that really reducing much risk of running out of money? I know history isn't perfect, but if a 30 year withdrawal rate of 4% has around 2% historical failure rate, the SPIA doesn't seem to offer much. Especially when you consider that there is no residual value of the SPIA and the average 30 year period will end with a big balance left over.

    I understand that averages don't do much good if you happen to be one of the unlucky ones, but how much of an opportunity cost are people willing to pay in order to protect against that tail risk. Especially if they view it as such a slim occurance.

    1. Hi, I think it's more a matter of partial annuitization.

      Just a couple things to keep in mind:

      For a couple, there is a decent chance that the second to die spouse will make it more than 30 years

      With low SPIA rates, that also means you should expect lower sustainable withdrawal rates. Interest rates are low now, so the historical averages don't apply for today's sustainable withdrawal rate

      I think we are really only talking about partial annuitization to help build a floor