Wednesday, September 26, 2012

Efficient Frontiers for Other Retirement Spending Goals

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).

Since writing about this, I've been receiving lots of great feedback through blog comments, emails from readers, and a great discussion thread at the Bogleheads Forum. I'm now going to start trying to respond to some of the suggestions and requests for additional checks about the robustness of the results.

Today I will look at an issue raised by Mike Piper at Bogleheads. One of the things he asked about is how results may change if there is a change in retirement spending goals. This could be in terms of either the lifestyle goals or the minimum needs. I will look at a few further examples.

But first, today Mike wrote about the article at his blog. He is great at distilling complex issues down to their most basic level, and he also made a great point in his post. Here is what he said:

In other words, for individual investors, the takeaway is not that you should dump all your bonds in favor of stocks and/or fixed lifetime annuities. Rather, the takeaway is simply that a portfolio completely eschewing bonds in favor of lifetime annuities might not be completely-off-the-wall-crazy. And, given how far such a portfolio would be from conventional retirement recommendations, that’s very interesting.

Yes, he articulated that much better than me. Back to spending goals.
All of the details for the 65-year old couple are the same as in the article, including that they have a Social Security benefit equal to 2% of their retirement date financial assets. What I am changing now is their spending goals.

First, suppose the couple can meet their spending goals with a lower withdrawal rate. In the following figure, both the lifestyle spending goal and the minimum needs are 3% above Social Security instead of 4% above Social Security. We can see that the Stocks / Fixed SPIAs combo holds as the points on the efficient frontier.

Next, as I stated in the article, if the couple is in a really great situation and can meet their lifestyle goals with a 1% withdrawal rate of above Social Security, then the probability of not fully meeting the lifestyle goal is quite small. Goals are still fully met at the 10th percentile of outcomes in this case. The efficient frontier is basically one point: 100% stocks. This is a good place to mention again that the points on the efficient frontier are not always feasible for real world retirees. If a retiree is not comfortable with 100% stocks, then a constrained version of the efficient frontier could be created which disallows allocations that the retiree finds unacceptable. The figure is not so exciting, but I am providing it here again showing how it is still the case that stocks / fixed SPIA combos support higher financial asset holdings than stocks / bonds combos. Here it is:

Next, the couple is more pressed and must use a withdrawal rate of 5% above Social Security to meet both the lifestyle spending goal and the minimum needs. Though 5% is really more than can be considered as reasonably sustainable in the current economic environment and so the efficient frontier does not come close to fully meeting the goals, we can see that the Stocks / Fixed SPIAs combos still hold as the points on the efficient frontier.

The next interesting matter is if we make the minimum needs level lower than the lifestyle spending goal. This introduces some interesting new issues to consider about lifestyle vs. minimum needs, especially if the lifestyle goal is at an unsustainable level like 5%. I'll come back to this in my next post on efficient frontiers.


  1. Wade, thank you for the continued analysis. Very interesting to see those three, very different looking, efficient frontiers -- all still made up of stocks and fixed lifetime annuities.

    1. Thanks Mike. I'll keep working through lots of other scenarios too.

  2. Wade, thanks for the excellent work. Especially I like the way you present the results graphically.

    I suggest you try a mixture of the Generic Vanguard VA with no guarantees that changes the payout based on results over time (i.e., the Single Premium VA with 3.5% AIR). Everyone tends to discount this option in favor of the GLWB type, but your results with SPIAs suggest otherwise. Consider that the SPIA you model is (bond interest + mortality credits). The simple VA is (stock returns + mortality credits). Thus the same thing (mortality credits) that makes the SPIA replace bonds also makes the simple VA replace stocks. Backcast simulations indicate that the mortality credits tend to juice the stock returns as long as the costs of the VA are low (Vanguard).

    An educated guess is that a (X simple VA,(100-X) SPIA) line would go below the (stock, SPIA) line but wind up on the efficient frontier at the far right (near 100%) for high withdrawal simulations like the 5% + SS.

    1. John, thank you.
      I will plan to add immediate VAs to the mix as well.

  3. I think this is very interesting, but it seems to me that the greatest strength of this particular work is the same as its greatest weakness: The fact that it is so closely calibrated to the present economic situation. That makes the conclusions very valuable right now, but perhaps not so valuable under different conditions, such as higher interest rates. Unfortunately, this is not the sort of work that a reader can easily rerun for himself/herself when conditions change.

    1. Thank you.
      Your concern is valid. In the coming time, I will continue posting more results showing further variations. Though not posted yet, what I am finding is that this result is not very sensitive to the fact that interest rates are low now. Higher interest rates will help support better results for most every allocation, but the allocations that stay on the efficient frontier (stocks and fixed SPIAs) are looking to be fairly consistent and robust.

  4. For some reason, the site will not let me reply to your reply anonymously. I suspected that changes in interest rates would not affect most strategies too much. But I would expect the possibility of substantial changes with respect to inflation-adjusted annuities because their current pricing is historically odd.

  5. Wade, I thoroughly enjoy your research and will continue poring over your material going forward. Being a fan of Ed Easterling, at, the research indicates that the start date for investing in "stocks" matters. I use the quotation marks because I see the word "stocks" used so often in reference to the S & P 500 purchased on January 2 of a certain year, then in practice, the client ends up with a potpourri that changes frequently. Easterling's research is refreshing because he has reviewed 101 ten year rolling periods and shown that the timing of PE Ratio/Dividend Yield really do matter. AS he points out, this IS a secular bear market and that may matter to a 65 year old who places faith in a formula for the stock market based on an esoteric 70 year number for stocks, conveniently starting when PE ratios are at 10. I'm not sure where your PE starting point is for your calculations on stocks? Regardless of that fact your research is terrific, and you have made an excellent point about annuities being superbonds, which in some ways builds on the Wharton Research. Since many people are sitting in similar positions to a decade ago with respect to account values, today's 21.8 PE ratio and 2% or thereabouts dividend ratio does not indicate more than a 6% total return in stocks for an untouched portfolio over 20 years. Therefore, building a portfolio using deferred GWBs growing at a guaranteed 6% to 7% in the mix can replace part of the equity mix to provide more certainty.You do not like GWBs, but I see that as their value--simplicity and certainty based on the mortality credit, with the one sweetener of liquidity. SPIAs are like dental flossing. Dentists would like you to floss and brush 3 times a day, but will take one or two. If GWBs get people to floss (utilize mortality credit in some way), they will be better off than sitting there in a pile of bond funds and random equities at Vanguard. (I like Vanguard, just sayin'). Many people are uncomfortable with SPIAs. The quasi annuitization provided by GWBs may deliver somewhat less income than a staight SPIA but the certainty of the math calculation could one day be better for a retiree who is seven or ten years out from starting the income. I am surprised by one of your respondants in the related blog, referring to AIG as a provider of SPIAs.If one checks the record, American General (AIG owned) did not default on a single annuity. Obviously, AIG did not have its problems in the life insurance and annuity arena, and the track record for annuity payouts is beaten only by US Treasuries, historically. Again, thanks for your excellent work in pioneering key parts of a very large concept. I am a fan. And GWBs, are not so bad, my friend.


    1. Hi,

      Thanks. Yes, I have dabbled in the area of valuations in the past. My article on "safe savings rates" is very much connected to incorporating the market valuation level at the retirement date. The assumptions I use here are not connected to a specific PE10 level, but they are more conservative than history, and so suggest some overvaluation at present.

      I don't have a particular problem with GWBs, except that I think their benefits can be obtained more cheaply with a stocks/SPIAs combo. But in the past, I never looked at a using a deferral period. I always had retirement income start immediately. I'm now starting to look more at the role of deferral, which is what you are describing here with the guaranteed growth rates.

      Thanks, Wade