What’s your retirement target?

Are you targeting a set amount at retirement? Or are you targeting a certain monthly income?

Either way you probably need to be able to convert from one to the other.

So how do you convert a lump sum to a regular income and vice versa?

*Have you read the important notes? It’s a condition for reading the blog. *

I’m gonna bet that you use the 4% rule of thumb. Given a lump of money if you peel off 4% every year you may be able to give yourself an income for life (with inflationary increases). And conversely if you target a certain income then the corresponding lump sum is 25x the income.

### Lifetime Income Illustrations

The Department of Labor (DoL) have been talking for years about giving those of us with a 401(k) or 403(b) plan an illustration of what income our account value might be able to eke out over our lifetime.

The recent SECURE act of 2019 provided for two illustrations and finally the rules for calculating these illustrations have been released. A happy day for actuaries everywhere!

So every year when you get your annual statement from your pension administrator you’ll receive two income illustrations a bit like the following.

### The Example

The above example from the DoL assumes a participant with an account balance of $125,000 and the illustration provides a monthly income of $645. Annualized this is $7,740 per year.

Let’s do some quick math and calculate the implied withdrawal rate here. 7,740/125,000 implies a withdrawal rate of **6.2%**

**Hot damn!**

That is one juicy withdrawal rate. Right? Knocks the socks off the plain old 4% – yeah?

I know what you’re thinking – *what are those folks at the DoL smoking? *

## The Assumptions

You may have guessed that we’re not comparing like-with-like. We need to dig into the assumptions in more detail to reconcile what’s going on.

Firstly note that the example illustration above assumes that payment starts at age 67. That’s right, even if you are a 25 year old diligently saving into your 401(k) your lifetime income illustration will assume that payment won’t start until age 67. These are the DoL rules and supposedly age 67 was chosen to jive with the start of social security payments for many retirees.

Another weird thing is the account value of $125,000 is not assumed to change in value between now and the date you are age 67. So no more investment returns, dividends, interest – it’s frozen for the purpose of this illustration.

This assumption has come in for some criticism and I expect it will change in the future. Most retirement projection tools will forecast your retirement balance with an assumed expected return and so these lifetime income illustrations will look quite inconsistent with all other projections. I believe the DoL chose this method for simplicity and to avoid the risk of assuming an investment return that participants might unrealistically rely on.

The DoL is only assuming that your money has to last from age 67 to death. Depending on whether you’re male or female that might be 25 years. Therefore the high implied withdrawal rate of 6.2% seems to be more in perspective given this relatively short payment period.

However there are a couple of other important assumptions that need discussing…

## More Assumptions

One key difference between the DoL assumptions and the 4% rule is the income illustration assumes that you exhaust all your principal at death. Yup – you are so good at money management that you can perfectly time your last withdrawal to your deathbed. This is in contrast to the general FIRE methodology of wanting to maintain preservation of principal.

This isn’t as crazy as it sounds from the DoL. It’s standard practice in creating any kind of actuarial reserve (ooooh fancy! Now I’m calling your humble 401(k) balance an ‘actuarial reserve’. Well la-di-da!) to assume that all the principal gets spent. If you are pooling all the risks of exhausting your money in retirement among many pension participants, or insured policyholders, then this is reasonable. If you are a lone investor then you don’t have the benefit of pooling to spread the risk, and so it’s natural to want to preserve your principal.

This assumption from the FIRE community neatly sidesteps the issue of mortality. (And wouldn’t we all like to do that!). By assuming a withdrawal rate that has shown to be historically viable the lump sum is assumed to last in perpetuity. The DoL on the other hand takes current actuarial mortality tables and calculates a true annuity.

A second key difference is that the DoL assumes the monthly payments are fixed in nominal terms. The payments do not receive any inflationary increases.

This is unlike the 4% rule of thumb where annual withdrawals are assumed to receive a fat increase for inflation.

This is an assumption that has received criticism, and again I think simplicity was the DoL’s goal in spurning inflation. I have some sympathy with this since it adds another layer of complexity to present results in terms of current or future dollars.

We now come to perhaps the largest difference between the DoL’s illustration and the 4% rule of thumb.

## Investment Return

The 4% rule is derived empirically from past investment data. Whether it remains viable in the future is a moot point, however the assumption essentially relies on future real investment returns being around 4%.

As I said above the DoL’s illustration before retirement at age 67 assumes zero increases, but in payment the DoL instructs you to assume the **10 year Treasury constant maturity yield**. Yep, I know, that’s low.

Really low.

Currently it’s around** 0.67%** (nominal). Here’s a chart showing historical rates.

So this is a massive deviation from the 4% rule. The Lifetime Income Illustrations essentially assume that you plow all your 401(k) into Treasury bonds upon retirement. It’s a low risk strategy, and a very low return strategy.

The DoL’s justification is that this is supposed to mimic the pricing seen from insurers on annuity products. I can understand the DoL wanting to give people a simple and understandable rate to use that provides a risk-free pension illustration, however for any reader of a FIRE blog this will be unrealistically conservative.

However for fun, let’s convert all this to a comparable withdrawal rate.

## The DoL's Withdrawal Rate

The example above taken from the DoL’s paper is really no good for us. It assumes the pension starts at age 67, and while I don’t want to be ageist I don’t think 67 can be justified as early retirement these days.

So I created my own spreadsheet to reproduce these calculations. It’s available for email subscribers to play with the assumptions.

Firstly I assumed $1m in savings. The classic FIRE calculation is of course that if you have $1m saved, then based on the 4% rule of thumb you might expect $40k of annual income (adjusted for inflation).

I then assumed a retirement age of 40. *Want to see an earlier age? *Download the tool and try it yourself.

I plugged in the current 10 UST yield of 0.67% and cranked-out the numbers. Here is a snapshot of the tool. It ain’t pretty but it does the job (much the same description can be applied to actuaries).

So based on the DoL assumptions if you retired age 40 with $1m in your 401(k) you could withdraw $26,316 a year for life. In other words a withdrawal rate of **2.6%**.

This is pretty low, and given we are using a return assumption based on Treasuries, should not come as a surprise.

However, recall that the DoL assumes a fixed pension and not increasing with inflation. So things are even worse.

## Allowing for Inflation

We need to re-run the calculations using the real return for the 10y UST. Doing this will be equivalent to assuming the payments increase with inflation. (If this isn’t obvious to you, don’t worry it’s an actuary trick).

The easiest way to get the real yield on the 10y UST is to look at the yield on the 10y TIPS (inflation protected Government bond). You can see from the snapshot below it’s currently **-0.93%**

Yes, I know using a negative return is weird. But <shrug> we are living in weird times.

When re-run with the new assumption of -0.93% I get an annual income of $18,000 (compared to $26k above). This implies a much lower withdrawal rate of **1.8%**.

This is the closest analogy I can get to the 4% rules with the DoL prescribed assumptions. Instead of enjoying a 4% withdrawal in retirement, if you follow the DoL illustration you will be restricted to only 1.8% withdrawal rate!

### Let's summarize these differences in a handy-dandy table!

Lifetime Income Illustrations | 4% Rule of Thumb | |
---|---|---|

Pre-retirement investment return | None | None |

Post-retirement investment return | 10 year UST | None explicit, but implied 4% real return |

Assumed retirement age | 67 | None |

Mortality | Prescribed actuarial table from IRS | None – implied perpetual income stream |

Methodology | Assumption based projection | Empirical based on past data |

Inflation escalation? | None | Yes |

**Author Bio:** I started actuary on FIRE as I did not see any actuaries taking a prominent role in the personal finance area and wanted to remedy a shortage of actuary jokes and write for those that appreciate rigor with fancy charts. In my regular day job I advise corporate US on investment and retirement strategies. I’m a qualified actuary, investment adviser and have a PhD in mathematics and reserve the right to have the occasional math post.

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