# Deconstructing safe withdrawal rates in a low yield world

Traditional research on Safe Withdrawal Rates (SWR) tells us that the safe rate is around 4% when using constant dollar withdrawals. A common objection is that current conditions — when yields on Treasuries are at record lows — is unprecedented in American history, making the findings of previous SWR research suspect.

But there has been unfortunately little critical analysis of this claim. If a 4% SWR isn’t safe then what is? 3.7%? 3%? 2%? 1%?

## Enter the autoregressive bond yield model

In January 2013 Blanchett, Finke, and Pfau published “Low Bond Yields and Safe Portfolio Withdrawal Rates” to try to provide some answers. The paper is a major step forward and better than the usual “I don’t think 4% is safe so I’ll apply an arbitrary downward revision based on my gut feel”.

What Blanchett et al does is, conceptually at least, straightforward and, in retrospect, an obvious approach. They interrogate the historical record to see what the relationship is between bond yields, the return on cash, the return on stocks, the return on bonds, and inflation is. You end up with a pile of regression coefficients that describe their historical relationships.

we introduce a model that takes into account current bond yields and allows them to “drift” toward a higher value during retirement using an autoregressive model.

You can then plug in current yields and generate next year’s returns for stocks, bonds, and inflation. This isn’t a prediction; this is model for use in Monte Carlo simulations. The numbers you get include a random component, so you’ll get slightly different numbers every time.

It is a clever idea and their approach generated some actual data (as opposed to pointless hand wringing).

• The probability of success for a 4% initial withdrawal rate over a 30-year period for a 40% equity portfolio is 48.2%.
• The safe withdrawal rate is 2.4% for a 60% equity portfolio over a 30-year period with a 95% probability of success.
• The safe withdrawal rate is 1.9% for a 60% equity portfolio over a 30-year period with a 99% probability of success.
• The safe withdrawal rate is 1.3% for a 60% equity portfolio over a 40-year period with a 99% probability of success.

All of those numbers are obviously a far cry from the results seen in traditional SWR research.

So what’s underpinning them? What does a sequence of returns look like that generates these SWRs?

## A mistake in the published paper

In their paper Blanchett et al. provide everything you need to recreate their model in their appendix, which is pretty cool. However, my implementation gave me results that were very far off from theirs. After a lot of double-, triple-, and quadruple-checking I finally emailed Blanchett. A quick email exchanged helped me track down the problem.

Some of the coefficients were printed in the wrong order in their paper.

The numbers in two columns βc and βy should be swapped. The βc for bonds is .446 and the βyi for bonds is .678. And so on for stocks and inflation.

(Needless to say, I felt pretty chuffed that I was the first person to find this error in their paper.)

Now that I had recreated their model, I was able to start digging into their results to understand them better.

## The contributions of their assumptions

Despite the title being about low yields, in the paper the authors say the results are due to three factors:

1. their model incorporates today’s actual yields
2. they reduce the expected return on equities by 2%
3. they assume a 1% fee

(They don’t mention it in the paper but they also assume that the “bond” portfolio of the portfolio is actually 20% cash. So a 60/40 portfolio is actually 60% equities, 32% bonds, and 8% cash.)

They don’t tell us how much each one contributes to the resulting lowering SWR. We can rerun their analysis, varying the parameters, to understand the contribution of each of the three.

## Checking for “model bias”

First let’s set all of the assumptions to align with those of traditional SWR research. That means no fee, no reduced expectation of returns, 60% equities, 0% cash, and a starting yield that is the same as the historic average (5.5%). This will help us tease out any potential “model bias” (positive or negative).

Traditional SWR research gives a probability of success in the mid- to high-90s for the above assumptions. The Low Yield model, with traditional assumptions, gives a probability of success of 93–96%. That matches up with previous research so it doesn’t appear to have any intrinsic bias up or down.

## One by one

Now, let’s set everything back to the defaults for Blanchett et al. and vary things one at a time, to see how they affect the probability of success.

(Note: don’t get too carried away with the precision below. This is based on a Monte Carlo analysis of 1,000 iterations and the numbers will vary by 2–4% in a given run.)

Our base is a 60% equity portfolio, 1% fees, 8% cash, -2% reduced equity expectations, and 2.5% bond yields. That gives a 62% probability of success.

If we get rid of the cash and keep all of our fixed income assets in bonds, the probability of success goes up to 63%.

If we get rid of all fees, the probability of success goes up to 74%.

If we set the bond yields to their historic norms, the probability of success goes up to 75%.

If we don’t reduce equity expectations, the probability of success goes up to 75%.

`61%  PoS: 1% fees; 2.5% yield; 20% cash; reduced equity+2%  PoS: get rid of cash drag+12% PoS: reduce fees from 1% to 0%+13% PoS: bond yields revert back to 5.5%+13% PoS: equity expectations revert back to 10%+`

Already we can see that low yields have probably been unfairly targeted as the only villain here. The cash drag is fairly minimal but the other three seem to contribute equally to the lowered success rates.

Let’s change things to be a bit more reflective of the average boglehead. We’ll get rid of the cash. We’ll also reduce the fees substantially and set them 0.054%, which is what a 60/40 portfolio of VTSAX and VBTLX would be. There are some small fees due to bid/ask spreads but also there are earnings from security lending. The true costs of the Vanguard funds can be determined by looking at how much they trail their index. In general, this difference is less than their ER, so we can feel confident we’re not subject to any hidden costs.

Even in a low yield world with reduced equity returns, the probability of success is 76%.

The authors’ fee assumption isn’t totally crazy. You don’t have to look hard to find people spending 1% or more on advisors and other investing costs. Here’s an example of a recent thread from bogleheads.org of someone who paying even more than Blanchett et al. assumed: https://www.bogleheads.org/forum/viewtopic.php?f=1&t=199160&newpost=3048712

Still, let’s see how things look for someone who has bought into John Bogle’s “cost matters” hypothesis and only has very low cost index funds: 76%. If you think those costs are artificially low, I’ll use the actual dollar-weighted costs of my portfolio: 0.19%. That gives a probability of success of 74%.

This is a far cry from the 95% success rates we’ve seen from traditional SWR research, so it does appear there is a fair amount of truth in concerns about current yields and equity returns. But I’d also argue that things haven’t changed so much that there is a clear case for throwing away the 4% number as a planning guide if you were using it before.

It seems that the biggest lesson is that in a low yield (and low return) world costs matter even more.

Next time I’ll look at what a sequence of returns in a low yield world looks like and whether it has any impact for a realistic (i.e. variable) withdrawal strategy.

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