#### St. George’s Thesis

How was your week? Productive I hope. I spent most of my spare time drafting my pièce de résistance for the Pension Series as a guest post for one of my favorite blogs and bloggers. I’m excited, so stay tuned for the announcement as to when and where you can find it. Unfortunately, it means I’m short an article because I (stupidly) don’t keep any posts in the bank.

However, I am about to let you in on a little blogging secret. Facebook provides an endless amount of material to write about. As proof of this point, about 10 days ago George, one of my awesome Golden Albatross Facebook Group members, asked the following sizzler of a question related to pensions and inflation-adjusted Cost of Living Allowance (COLA):

*Basically, if my pension is say $50k *[a year]* with no COLA provided by my employer, what do I have to have saved in an IRA to be able to grow my pension with cost of living for the next 30 years? (50k+4%)+4%)+4%)etc. For 30 years…)
*

He was essentially asking how to build his own inflation-adjusted COLA. It was a great question, the importance of which I grasped intuitively since I’ve recently blogged several times about the nefarious effect that inflation can have on a pension. But the potential math associated with George’s question made my head hurt. As much as I like to masquerade as some sort of evidence-based statistics-loving nerd (which I mean in both the nicest and most envious way possible), the truth is my knuckles scrape the ground when I walk. Fortunately, they are furry, so the pavement doesn’t do much damage. Didn’t I mention I was a liberal arts major in one or two of my previous posts?

#### Context is Everything

All joking about my potential chromosomal linkage to our Simeon cousins aside, the idea behind George’s question is nothing new to the Financial Independence (FI) space. In fact, one might argue it’s one of the fundamental ideas that drives the FI community. It’s the idea of replacing the guaranty of a Defined Benefits Pension (DBP) with some sort of Do-It-Yourself (DIY) hack. Whether it’s the examination of the value and limits of purchasing an annuity to replace the steady income that a DBP historically provided workers by bloggers like Darrow Kirkpatrick at Can I Retire Yet. Or the thousands of articles written by bloggers like the Mad Fientist, Michael Kitces, JL Collins, Mr. Money Design, and Ern McCracken about Safe Withdrawal Rates (SWRs) from investments. Everyone is striving for the same goal: creating a reliable income stream in retirement much like a DBP.

The difference in George’s question though is that he has a potential DBP coming his way in the not so distant future, so he is not looking for a way to replace the entire income of a pension. He just doesn’t have an associated COLA to accompany the pension. This means inflation will eat away at the value of his pension on an annual basis making his hypothetical $50K less valuable each year. For instance, if George simply started taking his hypothetical $50K pension this year, without an inflation-linked COLA, in 40 years at a 2% annual inflation rate, the purchasing power of his pension would equal $22,644.52 in today’s dollars. Ouch! That’s over a 50% reduction in value. Thus, George is astute to inquire as to how to amass his own pot of money that he can use to create his own inflation-linked COLA.

Given my above-mentioned lack of math skills, answering George’s question wasn’t going to be easy. My extensive research (i.e. 10 minutes on Google) turned up zero articles addressing George’s topic (I did find some awesome DIY Coca-Cola recipes though). I’m not surprised since it’s a somewhat complex question about a DBP, which not many experts look at these days. However, if you think about it, this question has greater application than simply building a DIY inflation-linked COLA for a DBP. If answered, then we’ve identified an inflation defeating investment mechanism for any personal finance product that needs one! I know it’s not world peace, but it possibly opens up some methods for people without pensions to build some fixed income streams and protect them from inflation in retirement.

#### A Closer Examination

Let’s examine this math problem a little closer. The mathematical complexity isn’t centered on how to execute the COLA payments. That’s simply a matter of George checking the Consumer Price Index-Urban (CPI-U) from the Bureau of Labor and Statics (BLS) either monthly or annually once he’s in retirement. He can then withdraw the appropriate percentage from the investment account he set up for the COLA replicating mechanism.

The real problem is figuring out the initial amount George would need amassed and invested in that COLA replicating mechanism by the time his pension starts. In other words, based on the Initial Dollar Value (IDV) of George’s pension ($50K) he needs X invested at retirement to kick off an SWR that matches CPI-U inflation. Solve for X! Secondary, but also associated with that problem, is what inflation rate to use as an average? Finally, there’s the question of portfolio allocation to produce that CPI-U inflation rate matched return. I guess I meant to solve X, Y, and Z. Uggghh.

As much as I love a good algebra equation, I felt this called for the skills of a polymath. Fortunately, I keep one on retain… er … what I really meant is there’s one in my Facebook Group. For some reason known only to himself, Big Ern McCracken is a member of my Golden Albatross Group, for which I am grateful. For those who don’t know Big Ern, he runs the Plutus Award nominated website called Early Retirement Now. He has written, among other things, the definitive series of posts within personal finance circles on the efficacy of the 4% Rule (or as he calls it the 4% Rule of Thumb). Thus, once I wrapped my head around George’s question, I knew if anyone possessed the ability to solve for X, Y, and Z it was Ern.

#### Ern’s Solution

Ern was game. In fact, he knocked out an initial answer in less than 12 hours, and by 24 hours provided a complete response. Most of that delay was due to the time difference of me living in Hawaii. Luckily, for everyone reading this, Ern gave me permission to reprint his answers here. Thus, I’ve pasted them below in sections using *italics*. I’ve interspersed my comments in the non-italicized text when I felt context was needed.

Without further delay, let’s get to Big Ern’s most elegant solution to George’s question:

*There is no 100% accurate answer. But I can give you a rule of thumb number.*

No worries, none of the problems we solve on this website actually have a 100% accurate answer — mostly because I’m doing the math. In fact, we are lucky to get within 50% accuracy.

*I normally work with a 3.5% safe withdrawal rate (SWR). That means, in the worst possible case, you’ll need 1/0.035=28.57 per dollar of COLA adjusted payment stream. So, a portfolio of $28.57 invested in an 80/20 portfolio should generate a $1 per year COLA pension. *

Right, based on Ern’s previous research on SWRs, the maximum sustainable rate of withdrawal someone can use to take money annually from an investment account with a low probability (less than 3%) of the account running out of money is only 3.5%. This is good through all market conditions. To effect a 3.5% SWR requires George invest $28.57 for each nominal dollar he needs to spend from his COLA reproducing investment mechanism.

But George is not looking to spend 3.5% annually from his COLA reproducing investment mechanism. If he was, then in the worst case he would need almost $1.5mil invested ($50K x $28.57) at retirement. Fortunately, George is looking to spend at the same rate as inflation, which will hopefully be a lot lower than 3.5%. Thus, Ern needs to determine what value to use for future inflation. Finally, note that Ern’s chosen portfolio allotment is 80% stocks / 20% bonds for this scenario. Let’s see if that will work for Z.

*I also estimated that assuming a 2% annual inflation rate a non-COLA pension is worth only about 60-70 cents on the dollar (see link), also worst possible case. Roughly 60 cents on the dollar for a 60-year horizon and 70 cents on the dollar for a 40-year horizon.*

Ah, so Ern prefers to use 2% as his projected annual inflation rate (see the inflation section below as to why). We now have Y. Separately, through his previous research, Ern determined that a 2% annual inflation rate’s effect on a non-COLA pension drives the value of that pension down to as little as 60 to 70 cents on the dollar. In other words a haircut in the value of the pension by 30% for a 40-year retirement, and 40% of the value for a 60-year retirement. Thus, depending on George’s lifespan in retirement he needs to recoup 30% to 40% of the value of his pension through his inflation-linked COLA generating investment mechanism over the same time period.

*So, you’ll need around 0.3 to 0.4 times $28.57 to make up for the non-COLA pension, so $8.6 to $11.4 per dollar of annual non-COLA pension in reserves, invested in at least 80% equities, to fund your own COLA payments. *

Hang with me here, because this is the most important part. I double checked this with Ern too, so I know the example below is accurate. What Ern means with this statement is if George retired with a $50K (non-COLA) annual pension, then George needs approximately $8.6 x $50K = $430,000 to $11.4 x $50K = $570,000 invested in an 80/20 stocks to bonds mix the first day of retirement in order for him to pull out 2% annually as a do-it-yourself COLA. Thus X = $430K to $570K depending on how long George intends to live!

While to some that may appear an eye-watering amount, it’s much better than the worst case 3.5% SWR driven $28.57 x $50K = $1.5mil I referred to above. In fact, I doubt it’s a coincidence that $430K and $570K are 30% and 40% of the approximately $1.5mil figure. So, the even more simplistic Grumpus Maximus rule of thumb for figuring this out assuming a 3.5% SWR and 2% annual inflation rate would be:

- $28.57 x Pension’s Initial Dollar Value (IDV) = Worst Case Amount (WCA)
- 40 year Retirement Scenario: WCA x 0.30 = X
- 60 year Retirement Scenario: WCA x 0.40 = X

Certainly, these amounts are doable, but only if you start early and plan ahead. 30% to 40% of most pension amounts is probably significant. Honestly, running this scenario has given me a new appreciation of a) why DBPs are so rare, and b) why inflation-linked COLAs built into those DBPs are even rarer. This stuff is expensive! No wonder the private and public sectors in the U.S. have pushed so hard to reduce DBPs.

#### A Word On Inflation Rates

If your one of my regular readers, hopefully, you’ve come to see, like me, that inflation is a pernicious sucker. It can literally suck the life out of the largest pensions, if not accounted for. Thus, in the name of thoroughness for this post, I asked Ern what drove him to use a 2% inflation rate. I looked through his blog but did not see a post with an obvious answer. As a point of reference, 2% is the post-Great Recession rate. Yet, 3.22% is the historical average since the end WWI. Granted, that average trended downwards over most of last and this century, but even a little change upwards in the inflation rate for this scenario could seriously impact the calculations. Ern wrote me back with the following answer:

*I use 2% because 1) that’s the prevailing long-term forecast of a lot of professional economists in academia and Wall Street (including myself), 2) it’s the inflation target of the Federal Reserve, 3) it’s close to the implied inflation rate derived from the TIPS *[Treasury Inflation Protected Securities]* vs. nominal Treasury bonds, 4) the 3.22% long-term historical is tainted by the experience of the 1970s that – hopefully – will never repeat itself.*

Fair enough, and all sounds logical. However, I wrote Ern back (again) and asked him how to make the calculations in case George wanted to use the 3.22% historic inflation average to discount the non-COLA pension. I told Ern that I suspected a 3.22% inflation rate probably bumps the numbers up to approximately 40% to 50% of the SWR rate for the initial value of the pension — but I didn’t know how to calculate it. Here was Ern’s final answer:

*To run this with 3.22% I’d have to run the whole simulation again, but if I had to give you a ballpark estimate I’d probably agree and apply a haircut of 40-50% of the original numbers using the 2% inflation forecast.*

Just so you are all tracking, Ern and I were talking about applying 40% to 50% haircut to the value of George’s initial $50K pension based on a higher inflation rate which would bump up the numbers in our calculations to look something like this:

- 40% scenario (40 years of retirement): $11.40 x $50K = $570K
- 50% scenario (60 years of retirement): $14.29 x $50K = $714K

Remember these are ballpark figures, but a 3.22% inflation rate means George would need to save even more money prior to retirement. Exactly what I expected.

#### Conclusion

Unfortunately, the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (commonly, but mistakenly, referred to as the Nobel Prize in Economics) was already awarded this year. Who is this Richard Thaler guy anyways? What’s he ever done other than redefine how we look at the discipline of Economics? Anyhoo, it gives me, George, and Ern time to prepare speeches and our tuxedos for next year. Actually, I keep my tux prepped and ready to go at all times. Maybe I can wear it to the next Fed meeting when Janet Yellen mistakenly invites me as a reward for all of Big Ern McKracken’s hard work.

In all seriousness though, I would like to thank Ern for collaborating on this subject with me. Let’s be honest I didn’t have a hope in hell of figuring out George’s question otherwise. Thank you to George for asking a tough but fun question to delve into as well. If you have a pension/FI related question, don’t hesitate to ask by emailing (grumpusmaximus@grumpusmaximus.com), commenting on the blog, or catching me on Facebook. If its a tough enough question, it will probably get featured at some point. Just make sure you have your tux or ball gown ready though. You never know when the Riksbank committee will come a calling.

Excellent post! This is a hard problem! You have the double uncertainty of market returns and inflation uncertainty. One issue works in your favor though: Sequence of Return Risk. Because you hardly withdraw anything in the beginning and only slowly transition into the withdrawals you would be less worried about SoRR. Maybe even go to 100% equities to have the maximum inflation hedge! My tuxedo is always ready to go if that phone call from Stockholm ever comes! 🙂

Thank you Ern. Obviously I couldn’t have written this article without your math skills. I’ve enjoyed delving into this subject with you and hope to do something similar again in the future! Now, where did I put my bow tie and cuffs links?