Friday, October 19, 2012

Efficient Frontiers: Inflation Assumptions, Fixed SPIAs, & Inflation-Adjusted SPIAs

The other day, I posted about a new research paper called, "An Efficient Frontier for Retirement Income." This paper provides a framework for retirees to choose how to allocate their retirement assets between stocks, bonds, inflation-adjusted SPIAs, fixed SPIAs, and VA/GLWBs.

In the case study used the article, a 65-year old heterosexual couple requiring a 4% withdrawal rate to meet their lifestyle goals (and whose minimum spending needs were set equal to the lifestyle goal) was best served by combinations of stocks and fixed single-premium immediate annuities (SPIAs). At current product pricing levels, there is little need for bonds, inflation-adjusted SPIAs, or immediate variable annuities with guaranteed living benefit riders (VA/GLWBs).

I’ve received lots of great feedback and am now in the process of working through a variety of issues, one by one, to demonstrate about the robustness of these results to different assumptions and retiree situations.

Today, one of the results that really caught me off guard was that fixed SPIAs performed so much better than inflation-adjusted SPIAs. I was naturally more of an inflation-adjusted guy. In hindsight, though, the reason is obvious. I made a table to demonstrate why. I used commercially available SPIA rates that were available in April 2012 (this is a while ago, but I just haven’t gotten around to updating what I use). Those rates are at the top of the table:
 Comparing Fixed and Inflation-Adjusted SPIAs
Fixed SPIA Rate (%)
Inflation-Adjusted SPIA Rate (%)

Expected Inflation Rate (%)
Number of Years For Real SPIA Income to Match the Fixed SPIA

An important point to note is that the initial retirement date payout is 51% larger for the fixed SPIA than the inflation-adjusted SPIA ((5.84-3.875) / 3.875). After retiring, the fixed SPIA amount will always stay at the same nominal amount, whereas the nominal amount of the real SPIA increases along with the sequence of inflation experienced after retirement. For my simulations, I did have inflation fluctuate randomly around an average inflation rate of 2.1%, which represented the breakeven inflation rate expected by the markets as determined by comparing Treasury yields with TIPS yields.

If inflation is fixed at 2.1%, the table shows that the actual income amount provided by the real SPIA would not start to exceed the fixed SPIA amount until the 20th year of retirement. That’s a long time to wait. Granted, after 20 years, the real SPIA will continue providing a larger amount of income forever, but it is a long time to wait for that to happen. That is the fundamental intuition about why fixed SPIAs beat real SPIAs in my simulations

Granted, a very important point is that many people are worried about higher inflation in the future. The markets currently don’t expect that, but if you disagree, then you might like to use a higher inflation rate for your calculations about whether a real SPIA is worth the cost. What is important here is how long it will take for cumulative price increases of 51% to happen. If inflation averages 3%, then the real SPIA would provide more income starting in the 14th year of retirement. If inflation is 4%, then it would only take 10.5 years.

Your views about future inflation are quite important to this decision.
Note that higher inflation would also hurt the performance of the VA/GLWB strategy since its guarantees cannot be expected to keep pace with inflation, and it would also hurt bond mutual funds since the interest rate increases accompanying higher inflation would result in capital losses.

Higher inflation will not completely overturn the idea that the efficient frontier consists of stocks and SPIAs, but it could influence the result about whether the appropriate SPIA choice is a fixed SPIA or a real SPIA. Interestingly, it also allows some role for bonds especially in the portfolios on the frontier leaning more to the side of leaving a larger bequest.

Here is a figure of the baseline case for a 65-year old couple with lifestyle 
spending needs equal to 4% of retirement date assets. Everything is the same as in my original article, except that now the average inflation rate is 4% instead of 2.1%. Now, the frontier consists of combinations of stocks, bonds, and real SPIAs:


  1. Heh-- I remember in 2003-2004 when people spurned real SPIAs because Vanguard's was limited to 10% inflation per year, and everybody "knew" that wouldn't be enough.

    I wonder if market forces are distorting the relative values between fixed & real SPIAs. Insurance companies aren't any better than investors at predicting inflation rates, and they might be pricing in a generous safety margin for themselves... at least until the insurers start competing against each other for market share.

    1. Doug,

      Thanks. That is probably right. Troubles with hedging inflation plus lack of competition are probably the two keep factors driving this difference.

  2. I've also done the calculations on fixed vs inflation-adjusted SPIAs, and also found the long time before the breakeven point. But there are two extra considerations that are hard to incorporate into the modelling - that (1) in 20 years will I be competent to make decisions about purchasing another fixed annuity to make up the lag?, and (2) in 20 years will an insurance company sell me an annuity (somewhere around 85 the insurance companies assume they will be sued by the heirs for wiping out their inheritance)? Somehow the peace of mind knowing that the decision-making is done, and we can run on auto-pilot without concern about the future inflation rate, is worth something.

    1. Thank you, this is right. It's good to be flexible, but there is also value in making plans before cognitive decline sets in too strongly. Prof. David Laibson refers to annuities as "dementia insurance"

  3. Wade - fantastic paper, I hope it turns out to be the game-changer that it has the potential to be. I'm very glad your working out it's dependency on assumptions (inflation) or initial conditions (low interest rate environment). A comment and a question:

    Your post analyzing a 4% inflation environment seems misplaced to me. If I've got the assumptions correct, your analyzing a case where interest rates and annuity payouts are premised on 2% future inflation, but they're wrong (it's 4%). So it looks like your analyzing a case where all of these assets (bonds, SPIAs, etc.) are mispriced. I would have thought you'd want to analyze a case of a more normal, higher inflation/interest rate environment (where bond prices, annuity prices, etc. are premised on the higher rates).

    A question: I have always written off annuities not only because of their historically high fees (which seems to have changed) but also because of their inflexibility and permanence. You really can't change them (easily) for the rest of the term (often your lifespan). With a stock/bond allocation you can reallocate percentages if your situation changes, but once you commit to an annuity you're stuck. How do we take into account this loss of flexibility (i.e. option value) to annuities when we try to make the stock/bond/annuity decision for retirement.


    1. Thank you very much.

      You are getting at an important issue. But with what I'm doing thus far, the person buys annuities immediately. I don't have future annuity purchases and future annuity pricing build it. So this unexpected higher inflation shouldn't impact the annuity prices. It could impact bond returns though, in a way that I have incorporated, as higher inflation would raise bond yields and lower bond returns. That aspect is missing from the results in this blog post.

      And you ask a good question about how to value the loss of flexibility that comes with annuitization. This is an important question. I'm trying to work toward an answer here buy keeping track of the remaining reserve of a financial assets, which further gets at the idea that other things being the same (i.e. a given percentage of lifestyle goals are met) the retiree would choose the allocation supporting the highest remaining financial assets. It is an incomplete answer, but it represents my attend to account for the loss of flexibility with annuitization.

  4. Have you seen ?
    There is a fascinating suggestion that taking IRS RMD plus income is almost optimal in their model. Now that rule has some obvious issues, such as the fact that income will be very different for different portfolios and it's probably not sensible to encourage too strong an income bias (as the authors of the article point out in another context). Still, it would be interesting to know how something like IRS RMD + 2% would stack up as a withdrawal rule in your metrics. One other issue is that it leads to a good bit of year to year variability, especially for portfolios with substantial equity positions. One might also try smoothing that a bit over a three to five year window, sort of like the way pension funds do their accounting.

    1. I've not had a chance to read that paper yet, but that sort of result does tie in with an article I wrote over the summer, and also with an article I reviewed here recently:

      Basically, if the goal is to spend as large of percentage of wealth as possible, then an appropriate account for remaining life expectancy and acceptable failure rates is optimal. The RMD approach goes a long way in that direction.

      But it does create the variable income, which is another factor that must be considered. I like your smoothing idea.

    2. Oh I see, the CRR brief you linked to is a summary of an article the same authors released earlier in the year. I'll read this summarized version first. Thanks.

    3. (Same anonoymous as above responding to comment below as site won't let me do so directly.) Well, to some extent that depends on the amount of income, of course. But if you use RMD + 2 %, that's going to be similar to just life expectancy at younger ages but not at later ages because IRS tables assume a spouse 10 years younger. So it will be more conservative than life expectancy at older ages. Also, if you use a constant such as 2% instead of income, it should have less year to year variability than the life expectancy method. Consider the silly example of someone 100% in stocks. A 50% market drop produces almost a 50% year over year decline using life expectancy, but proportionately less if you have a 2% constant involved. Of course, that's too extreme, but you can see the idea.


    4. I read the CRR brief now, and when I get a chance I want to read the original paper they released earlier in the year. It sounds like their methodology is similar to the one used by David Blanchett and others in the article I describe linked in the above comments.

      I did include the RMD strategy in this article:

      and found that more often than not, spending amounts would actually increase over time. RMD plus portfolio income might get you toward a smoother or possible decreasing consumption path, which should provide greater "utility" as survival probabilities decline with age.

      The issue with these types of strategies is that while you never run out of assets, your spending will be volatile and unpredictable. Some sort of additional smoothing rules should be considered, though anything that does smooth by keeping consumption higher after a downturn does run a higher risk of wealth depletion. If dividends don't fall as much with a downturn, that does provide one source of smoothing.

  5. Wouldn't IRS RMD + interest and dividends just result in a total withdrawal similar higher withdrawals of the life expectancy method? The mixing of withdrawals and cash flow seems inconsistent to me.

  6. 'similar to the'

    opps, hit submit to soon

  7. If you frame annuities as an investment, then the payback period would be relevant. ("20 years is a long time to wait.") But annuities are longevity insurance and inflation-protection extends the coverage to inflation risk.

    To me, the goal of an annuity is longevity insurance. Purchasing an annuity allows me to share longevity risk and purchasing inflation protection shares inflation risk. In that case, break-even periods significantly less than 25 or 30 years are of little concern to me. I'm concerned about eliminating the worst possible outcome -- reaching old age with inadequate income -- so I buy insurance.

    I don't worry about when my car or home insurance will become profitable. This is the same logic that encourages people to claim Social Security benefits at age 62, isn't it?


    1. Dirk,

      Yes, you are right. That is certainly also the good argument for delaying Social Security. But at some point the if the pricing is so out of line, the insurance value of the inflation-adjusted annuities might not be worth the extra cost.

      I've been exploring this further, and it does seem that inflation-adjusted SPIA pricing is improving and this may be less of an issue. Also, it turns out that by actively trying to avoid the use of utility functions, I might have implicitly assumed an aggressive retiree rather than a conservative retiree.

      Another general problem is that the inflation-adjusted SPIA rate is not high enough to meet the lifestyle goal, which puts added pressure on the portfolio.

      This is still a work in progress...

  8. Here's a quote I got today for two annuities from Penn Mutual (66 year old man, single, in New York):

    $100K purchase straight immediate annuity: $562 payout monthly for life

    $100K purchase immediate annuity w/3% compound interest increase per year: $417 payout to start (interest added at end of each year)

    I couldn't figure out how to calculate the "break even" time in years of the lower payment plus interest, or the total amount I would receive after, say 10 and 20 years, in both scenarios.

    can you help?

  9. Figured this out in Excel. It takes about 13 years for the payments to equalize, and about 20 years for the total payout to equalize. Doesn't seem like the 3% increase is a very good deal: plus I'd rather have the money up-front when I can enjoy it more...

    1. Hi,

      I've been falling behind. About your questions, I'm calculating that in year 11 the 3% growth annuity is just slightly behind and will be ahead in year 12. I agree about the 20 years part.

      I can't really disagree with your decision about the choice between the two. It just depends on your unique needs. After inflation occurs for long enough, will the $562 still be able to meet all of your basic needs?

  10. Interesting that the graphs indicate that if you don't want anything left in your estate at the end then put 100% in real SPIA. It also doesn't address the case of a pension with no inflation adjustment in the mix. To me the big concern is not 3% or 4% inflation for 30 some years but what happened from 1968 to 1982 where the cost of living tripled with almost no market growth. That may have been caused by the oil embargoes and incompetent politicians but with climate change, population growth, competition for emerging markets...and even dumber politicians I can see that happening with either energy or food within my lifetime.

  11. I have been looking at two SPIA options -- one fixed in terms of payments and one inflation adjusted. The monthly payment from the inflation adjusted option "catches up" with the straight line option at around year 19; the total payout of the inflation adjusted option surpasses the straight line option around 25 years into the future. What I'm not grasping, however, are the comments above related to "that's too long to wait" and "I'd rather have the money up front and enjoy it." This seems paradoxical to me. Maybe I am missing some logic in how I think about this, but it seems to me as follows: If you select the non-inflation adjusted option, you are going to have to take the excess (each month or year) above your needed spending level and reinvest it right away as a buffer to offset the lesser payment at year 19 (and beyond) if you make it there. Presumably those purchasing annuity products are in reasonable health and expect some longevity. In other words, just like the commenter above, I would love to "enjoy" the higher payment of the non-inflation adjusted annuity in the beginning -- more $$ to spend. But what if I get to year 19 and now I have a shortfall each and every year that become worse with time? In a nutshell then, it seems to me like a wash. You take the inflation adjusted option and feel free to spend 100% or you take the non-inflation adjusted option and reinvest "for insurance" the amount it pays you above and beyond what the inflation adjusted product offers. Thoughts on this? Am I missing part of the argument or failing to see some angle I should?

    1. Thanks for writing. The way I basically look at how to implement this in practice is that for someone willing to take on some inflation risk, it may be better to ladder in fixed SPIA purchases over time, allowing more assets left to be left in the investment portfolio longer as a way to seek upside. It could backfire, of course.

      On the other hand, part of the reason the inflation-adjusted SPIA look expensive is because the markets are pricing in low future inflation. If you are really worried that inflation will be higher than what markets expect, then this would lead you to favor the inflation protection, as it wouldn't take as long for the inflation-adjustments to catch up with the fixed payout rate.