# Updated Withdrawal Efficiency Rates

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 the initial paper they compare several well-known withdrawal strategies and introduce a new strategy of their own.

In *Living Off Your Own Money*, Michael McClung calculates WER. He includes some of the same strategies but also some new ones.

You can’t really compare raw WER values between various authors and papers. There are too many details that WER relies on that various authors will use different assumptions for: life expectancy, market behaviour, portfolio construction, the role of Social Security, and the exact parameters of withdrawal strategies.

But (if WER has any value), the *ordering* of strategies should be relatively stable.

Of course, any WER roundup won’t be conclusive. There will always be a new strategy someone has come up with. So it can be fun to extend the WER comparison to those new strategies.

Here is WER for three new strategies:

- longinvest’s VPW
- Pye’s Retrenchment Rule
- Blanchett’s “Simple Formula”

`VPW 0.816090`

EM 0.810883

Simple 0.784535

Retrench 0.770130

Endowment 0.723537

Constant 4% 0.705634

VPW, a PMT-based strategy, does well. Blanchett’s “Simple” formula isn’t supposed to be the “best” but is supposed to be “pretty good for a simple formula”; still it does pretty well.

The Retrenchment Rule does surprisingly poorly here. Since it is also based on PMT, it is surprising there is such a gap between it and VPW. What could be causing that?

I think there might be two things: the market simulation for the monte carlo uses lognormal returns that have a mean of 4.7% and a standard deviation of 13.82%. The mean of 4.7% is lower than the Retrenchment Rule “expects”. This means that the Retrenchment Rule starts at a higher level but will need to continually cut withdrawals.

That is (somewhat) by design: Pye seems to believe in having your cake up front, which I can understand.

But the math behind Constant Equivalent Withdrawals (which underpins WER) doesn’t like that and punishes it.

Imagine you start out at $70,000 a year for your withdrawal. And every year you have to cut that by $1,000. Your withdrawals would look like

` 70000,`

69000,

68000,

67000,

66000,

65000,

64000,

63000,

62000,

61000,

60000,

59000,

58000,

57000,

56000,

55000,

54000,

53000,

52000,

51000,

50000,

49000,

48000,

47000,

46000,

45000,

44000,

43000,

42000,

41000,

40000,

39000,

38000,

37000,

36000,

35000,

34000,

33000,

32000,

31000

But if you feed that into a Constant Equivalent Withdrawals (CEW) function it says you would rather have received a constant $43,879, even though 27 out of 40 years you received significantly more than that.

It might be that Pye’s strategy is being punished for what is explicitly trying to do.

Of course, WER isn’t the end-all, be-all of measurements. McClung came up with HREFF to provide another lens on the problem. Here’s the HREFF-4 for the strategies. (HREFF-4 means “a floor of 4%, so if you drop below that you get extra penalised”; this is to try to capture that once withdrawals drop **too** low people have to make cuts that are extremely painful.)

There’s nothing saying 4% is the perfect number for HREFF. It provides a different perspective but to do a fuller analysis you’d also want to look at HREFF-2 and HREFF-3.

`Simple 0.855833`

VPW 0.838219

Retrench 0.805118

EM 0.779211

Endowment 0.693739

Constant 4% 0.590613

Interestingly, both Blanchett’s “Simple” formula (3rd to 1st) and Pye’s Retrenchment Rule (4th to 3rd) see improvements here, while McClung’s EM seems to slide down the leaderboard a bit.