# Flavors of PMT-based withdrawals, part 2 of 2: Expected returns

Last time I said that PMT calculations for retirement need two inputs — the number of years of payout and the expected returns over the payout period — and looked at the first variable.

Now let’s turn our attention to the second variable: expected returns.

VPW uses the historical returns for global equities and bonds. This comes from the Credit Suisse Global Investment Returns Yearbook 2015, which covers the period 1900–2015. It is an extension of the research that Dimson, Marsh, and Staunton did for their groundbreaking book *Triumph of the Optimists*. You can tell VPW your exact mix of stocks and bonds but by default it will use an expected return of 3.4%.

VPW also expects this to be essentially static over the course of your retirement.

Ken Steiner says to use 4.5%:

To maintain a more comparable relationship between investment in annuities and investment in other securities, we now recommend using a 4.5% investment return assumption and a 2.5% inflation assumption for budget determinations.

Steiner also suggests updating this every year. For instance, in December 2014 he suggested 5%.

Siegel and Waring tell you to use TIPS rates:

r, which we’ve called the average real rate for the sake of simplicity, is actually the single real interest rate on the portfolio of TIPS constituting the ladder; this single interest rate is the present value-weighted average of the yields on the constituents

Right now TIPS rates are pretty low. They max out at 0.63 and drop as low as -.19. I’m too lazy compute the value-weighted average. It will be ** below** 0.43 (the real yield for a 20-year TIPS), so I’ll just use that for convenience.

They also tell you to update this every year based on current TIPS rates.

Even though 2 of 3 ask you to update expectations every year based on the current environment…keep in mind that none of the analysis below does that.

Those lead to very different withdrawals in Year 1

`VPW: $51,926`

Steiner: $58,747

Waring & Siegel: $35,448

If we assume constant 5% returns, let’s look at how each of them performs:

VPW and Steiner are pretty similar. VPW takes a more conservative stance, which means that its withdrawals are back-loaded; it takes out less early on but more towards the end.

Siegel & Waring’s approach is clearly far too conservative in this scenario. No retiree wants to see their annual income go from $35,000 at age 65 to $128,000 at age 95 because you played it too safe.

Of course, this assumes we get a constant 5% return.

If things are worse, if we actually see 2% returns, then Siegel & Waring’s inputs start to look better.

But that’s still not amazing. You spent 13 years taking home less money. Now that you’re 78 you’re ** finally** overtaking VPW & Steiner. I don’t think many retirees would make that tradeoff.

In fact, you’ll notice that all of the lines cross around the same point. And if you play around with the spreadsheet (changing the expected returns or the actual returns), the lines ** always** cross at the same point around year 13. That’s just how the math behind PMT works.

So the first lesson is: if you underestimate the returns it will take you 13 years to “autocorrect” via PMT. Likewise, if you overestimate returns, it will take the same amount of time.

When you add up mortality, declining health, and declining spending (as shown by Bernicke’s research among others) I think it is clear that you would rather have a falling slope than a rising slope. That suggests it is better to be too aggressive than too conservative.

Let’s try using some actual historical returns and see how the three different assumptions perform. I’ll use 2000–2015, which includes two bad bear markets and a “lost decade” during the 2000s. This seems like the kind of market when Siegel & Waring’s very conservative number would thrive.

Even here, it doesn’t seem like it has done that well over a 15-year period. As we saw above, after about 13 years it will start to outperform. But that’s a long, long time to wait. Let’s look at the two lowest points.

First in 2003 we see

`VPW: $27,102`

Steiner: $29,704

Siegel & Waring: $20,259

Then a few years later in 2009

`VPW: $23,172`

Steiner: $23,835

Siegel & Waring: $20,595

Siegel & Waring’s expected return numbers continually look overly conservative to my eye. And you don’t get enough “reward” for it. If I assume a 5% future returns from 2016–2030(which is approximately what John Bogle says we will see for the next decade) we get

So, yes, eventually Siegel & Waring see you withdrawing nearly 2x the other two. But you’re 94 years old at that point.

Looking over both variables — mortality and expected returns — it feels like Siegel & Waring did the best job with mortality and Steiner does the best job with expected returns.

If I compare this “combined Steiner + Siegel & Waring” against a “VPW where you replan at age 90” and plug in fixed 5% returns it looks like

This is telling us that VPW gives you more income in the middle part of your retirement in exchange for dramatic income cuts once you hit your 90s. The higher income in your 70s and 80s is nice but I think most people would prefer a smoother curve.

If we use historic rates (1966–1995, the worst retirement in history) it tells a similar story.

And checking against 1921–1950 (the best retirement in history) we see it again

In Siegel & Waring’s paper they note that you can give the curve any shape you want by playing with the the variables. There is definitely merit to that; we would rather have money in our early retirement — at least within limits.

You could build a “most aggressive” version of PMT that assumes 6% returns and uses median life expectancy (despite Steiner’s arguments against using it).

Over the 1950–1980 timespan it looked like this:

Substantially more in early life in exchange for quite a bit less in late life.

There are no right answers for what you use in these PMT calculations. It is an alchemic concoction of your risk aversion and fears about the future and your own longevity. But it is also clear that the numbers you use can have fairly substantial impacts: $142,000 a year versus $110,000 a year in some circumstances.

It probably isn’t wise to use someone else’s spreadsheet without digging deep into its bowels, understand why they made the assumptions they did, and agree with the underlying reasoning.