# WER: inputs & outputs

Withdrawal Efficiency Rate is a nifty metric designed by Blanchett, Kowara, and Chen in their 2012 paper “Optimal Withdrawal Strategy for Retirement Income Portfolios”. The goal is to build a metric that allows you to compare withdrawal strategies to determine which one is better. (Well, better along one axis of measurement, at least.)

In order to calculate a Withdrawal Efficiency Rate (WER) you need to run a bunch of Monte Carlo simulations. You need to simulate lifespans and market returns. So it seems obvious (at least when I say it out loud like that), that the results will be affected by the assumptions you use in your Monte Carlo simulation.

## Changing Longevity

In Scenario 1 we use the historical returns for a 60/40 portfolio, along with Hulstrom’s life table. The top three are VPW, EM, and the Retrenchment Rule.

In a previous post I noted that life tables can vary a fair amount. Hulstrom’s is the most aggressive (people die earliest). Let’s try with a middle-of-the-road life table, the National Vital Statistics Services 2011 life table.

There’s not much of a change here. The Retrenchment Rule and ECM have swapped places but they were so close before that’s not significant.

Now we’re using the most conservative life table, from Annuity 2000. This has people living the longest. VPW has dropped quite a bit and the Endowment (take a constant 5%) has jumped up. ECM has distanced itself from the Retrenchment Rule.

VPW’s drop is probably due to the fact that you run out of money after 35 years and with the Annuity 2000 life table there’s a decent chance that will happen every now and then.

Let’s try that again but “fix” VPW, to try to get a more realistic picture.

VPW does better now but still trails EM.

## Changing Returns

For the remainder of the post I’ll stick with the Annuity 2000 life table and “realistic VPW”.

The first thing we can do is use a more conservative Monte Carlo model. Reduce the average returns by -0.5% and increase the standard deviation by +2.0%. (This means a real average return of 4.7% instead of 5.2%.)

ECM moves into second place in this scenario. Which I guess makes sense, since it is supposed to be the more conservative option from McClung. EM remains at the top of the list, though.

What if we crank up the returns? Assume we had a 100% stock portfolio and use historical US returns. This is the ultimate rosy scenario.

Now let’s flip things around. Let’s try a 100% bonds portfolio and then reduce returns another 0.5%.

This mixes things up a bit. VPW has fallen quite a bit. The Sensible and Simple strategies, after languishing up till now, make an appearance. The Sensible strategy comes from gummy’s website. You take a low, inflation-adjusted amount (3%) and then a portion of any portfolio increases.

The Simple strategy is Blanchett’s “Simple Formulas for Complex Withdrawal Strategies”.

ECM, McClung’s conservative option, finally takes the top honors.

## Moving away from historical numbers

What about this low-yield world that’s causing us all so much angst? Let’s try stepping away from historical numbers and use Blanchett’s autoregressive model for low-yields.

But what about high valuations? Don’t we have to worry about that, too? Let’s also try Blanchett’s model for low yields and high valuations.

We see Simple raise its head again.

## PMT Interlude

ARVA, Retrench, and VPW are all based on PMT; they (mostly) just plug different numbers into the PMT formula. So it’s interesting to see their WER vary so much. ARVA is usually at the bottom of the pack; VPW near the top; and Retrench doing well but just outside the top tier.

ARVA does poorly because it has such a low discount rate (2% in these tests). If we override the suggestions of Waring & Siegel and use a higher discount rate it does better:

Still not quite as good as VPW, though that’s most likely due to ARVA being a bit more conservative about lifespans.

The Retrenchment Rule also does worse the VPW. It also is more conservative about lifespans. It uses a 110 year timespan for the PMT calculation versus VPW’s 100 year timespan.

Overall, McClung’s EM performs extremely well regardless of the Monte Carlo inputs. It never finished worse than second place and finished in first place in 4 out of 8 scenarios.

ECM also performed well but, at least based on these tests, it is hard to see an argument for using it over plain EM. Even in the scenarios where it “won” (scenarios 6 and 7) it only slightly outperformed EM.

Of all the PMT flavors, VPW fared the best, even with the replanning “fix” added in the ensure you don’t exhaust the portfolio if you live past 100. It’s worst performance came in Scenario 6 (100% bonds). VPW was 72% efficient in Scenario 5 (100% stocks) but only 61% efficient in Scenario 6 (100% bonds). That delta, an 11% drop, was the largest (by far) of any strategy.

That’s a little worrying but I don’t have any great insights into why VPW behaved like that.

Sensible Withdrawals made strong showing in Scenario 6 (100% bonds) but it has some weaknesses that don’t show up in WER testing. Because you only get the “bonus” when last year’s market did well, there are a lot of years when you only get the floor. If you set the floor too high (say, 4%) then you run into all the sequence of returns problems that the 4% Constant Dollar withdrawals have. If you set it lower (to say, 3%) to reduce the chance of the portfolio running out then a lot of years you only get that reduced amount.

One way of seeing this to look at McClung’s HREFF-4 metric. At a high level think of this as “how often do you get a 4% or greater withdrawal”. You can see that Sensible Withdrawals do pretty poorly on this score.

Blanchett’s “Simple” formula has one surprise showing. I don’t really have an explanation for that. Blanchett’s formula is an interesting academic exercise but I can’t see it having much real world use. It isn’t much simpler than the lookup tables it is supposed to replace. It performs ** okay** under most circumstances but never wows anyone. And it has some weird performance characteristics. As seen above, its WER is usually middle of the road.

But its HREFF-2 is astounding, nearly front of the pack.

And then its HREFF-3 turns mediocre again

That kind of variability is a bit worrying; I’d prefer something with more stable outcomes.

Finally, I should note that while there is always a first, second, and third place often the differences in efficiency are so small they are probably meaningless. For instance, take a look at Scenario 3 again

Endowment, Retrenchment, and VPW all have nearly identical results. They differ by only 1% or 2%. Even the difference between #1 and #5 is only about 5%. There is generally a clear grouping of “efficient” and “not efficient” strategies but there seem to be diminishing returns in trying to pick the “most efficient” strategy.