Harvesting-Rate Efficiency Metric

In McClung’s Living Off Your Money, he introduces the Harvesting-Rate Efficiency Metric (HREFF) as a way to try to help readers compare variable withdrawal strategies.

With constant dollar withdrawals, the primary metric in studies is whether you run out of money; the “probability of success”. With variable withdrawal schemes, that’s less meaningful. Many of them can, technically, never run out of money. But you might only be withdrawing $100 a year. How do you capture that?

Many variable withdrawal schemes also try to use your capital “efficiently”: that is, they’d rather increase your income while you’re alive than leave you with a $6 million portfolio when you die. So looking at final portfolio values, another common metric in constant dollar studies, is not useful.

CEW

It is far from universal, but it is increasingly common to see studies use variable withdrawal schemes and compare them using Certainty Equivalent Withdrawals (CEW). CEW is pretty cool — it takes a variable stream and cashflows and turns it into a single number. (I’m going to skip over the math & economics behind that; just take my word for it for now.)

Here’s how CEW works is practice. Which is set of annual withdrawals is “better”?

  • $100 — $10 — $40 — $20 — $70 — $35
  • $29 — $31 — $32 — $28 — $31 — $27

The first one gives you more money when everything is said and done: $275 versus $178. But people don’t like uncertainty and the future isn’t given the same weight as the present. It depends on how risk averse you are, but for most people the second choice wins out. You’d rather have a steady set of cashflows than one that bounces around.

The CEW (with a risk aversion factor of 4) for the first one is $15; the CEW of the second one is $29.

HREFF

CEW is nice because it provides a building block for comparing variable withdrawal strategies. McClung’s insight is that CEW alone isn’t sufficient. Most people treat their income as “layered”: you need $X for the bare necessities (a place to live) and $Y for simple things that make life nicer (cable TV) and $Z for every day luxuries (vacations).

Imagine that you need $30,000 a year to pay for your house and other basics. If you receive less than $30,000 you’re going to be under some financial stress.

Now imagine you have a choice of 2 different income streams:

  • $30 — $30 — $35 — $35 — $35 — $35
  • $29 — $29 — $40 — $40 — $40 — $40

You’d pick the first one. The second means you’ll spend two years only getting $29,000 and that’s not enough to pay your bills.

Sure, the second one gives you more money total ($218 versus $200). It even has a higher CEW ($34 versus $32).

But it meant your electricity got cut off, or you had to drive your car without insurance, or you couldn’t pay property taxes.

HREFF is an attempt to improve CEW by adding the concept of a floor, to help understand how often you’ll be left eating cat food.

HREFF Parameters

An unfortunate side effect of CEW and the improvements that HREFF added is there are a number of tweakable parameters. In one sense that is good, because it allows the results to be more realistic by tuning the parameters to reflect your personal preferences. But it also means no single chart is “definitive”.

  • gamma: a person’s risk aversion. A risk-tolerant person might have a gamma of 2 or 3. A risk-averse person might have a gamma or 6 or 7.
  • HREFF floor: is your minimum budget 2%? 3%? 2.75%? This will vary from person to person, obviously.
  • epsilon: how big the “penalty zone” is for withdrawal variability. By default, the penalty zone is small so long as the floor is being met.

Let’s see what (if any) differences we can spot by changing those parameters.

This is based on a 1,000 iteration Monte Carlo analysis assuming the historical mean & standard deviation of a 60/40 portfolio.

Epsilon

First, let’s try changing epsilon (the “penalty zone”). This should increase the penalty felt by more variable schemes.

The ordering stays the same until epsilon 10,000. At that point RMD takes the top spot and gummy’s Sensible Withdrawals climb out of the cellar, but all other positions stay the same. EM and Floor-to-Ceiling are always at the top.

With the exception of gummy’s Sensible Withdrawals and RMD, the absolute efficient metric also doesn’t vary much as epsilon changes. Guyton-Klinger is about 65% efficient at epsilon 10,000 and at epsilon 30, for instance.

Gamma

Gamma is a measure of how risk averse you are.

This shows a bit more impact than changing epsilon. (Which is what I would have expected.)

  • RMD goes from middle of the pack to first place, when gamma=1
  • Floor-to-Ceiling works better for more the more risk averse retiree. It is middle of the pack when gamma=1 but near the top at higher values for gamma.
  • VPW is always in 2nd or 3rd.
  • EM is always in 1st unless gamma=1, in which case it drops to 3rd behind RMD and VPW.
  • The second grouping — Sensible Withdrawals, Constant Dollar, Constant Percentage, and Decision Rules — don’t seem much affected by changing gamma. They’re always in the same order.

Floor

This it the minimum withdrawal rate you need to pay the basics in life. If a withdrawal strategy gives you less than this in a year, then it is heavily penalised.

This shows the most variation.

  • Floor-to-Ceiling does a good job when the floor is high (3 or 4). When the floor is allowed to be lower then it becomes less efficient. This is because Bengen’s floor is quite high (meaning it almost always will give you 3% or 4%) but the ceiling is quite low (meaning it won’t always be that efficient as the portfolio gets larger). The “margin of victory” with a floor of 4 is substantial, however.
  • RMD does well at low level (1 or 2) but increasingly poor as the floor increases. The RMD table is very conservative early on (only a 3.6% withdrawal at age 70) meaning it struggles to provide a high floor for much of the early part of retirement.
  • gummy’s Sensible Withdrawals do surprisingly poorly…I don’t have an explanation for it. Is it just leaving too much upside on the table?
  • Constant percentage does surprisingly well. It is never a top performer but for such a simple strategy it holds its own.
  • Decision Rules do…okay. They seem to perform best with a floor of 4. Or, perhaps a better way to phrase it, they don’t drop off as much as others do.

There’s a fourth, “hidden” parameter in HREFF: the market returns you’re using. This is the same thing I talked about in WER: inputs & outputs.

Here’s HREFF-3 with a variety of Monte Carlo simulation parameters. The parameters used were:

  • “Conservative” 40% bonds, 60% stocks, which has returns adjusted downward to more closely match historical global returns instead of US returns
  • Historical 100% bonds, 0% stocks
  • Historical 40% bonds, 60% stocks
  • Historical 0% bonds, 100% stocks
  • Blanchett’s “low yields and high valuations” model that attempts to model current conditions, rather than historical averages.

This confuses the issue even more. Several strategies bounce around quite a bit. Constant dollars wins a few scenarios but comes in much lower in others, for instance. It appears to do better when stocks aren’t contributing much (either because they aren’t in the portfolio or because stock returns are expected to be poor). Floor-to-Ceiling also seems to do best in adverse scenarios.

A guess about what might be happening here: those strategies are living on the edge. They’re less dynamic and instead of cutting withdrawals they run the risk of exhausting the portfolio. Most of the time you die before that happens and that gamble works out. So they look okay in extreme markets.

(Maybe that means there’s room to extend HREFF to include some notion of “if my portfolio gets too small, I’m going to freak out not matter how good the income streams are”. Maybe that’s something Milevsky’s “risk quotient” could try to capture? Or it may be overloading a metric that already is complex.)

Let’s apply a simple weighting (first place = 20 points, 20th place = 1 point) and add it up across scenarios.

Stout & Mitchell   82     
Floor-to-Ceiling 79
EM 79
ECM 79
RMD 68
VPW 65
Constant Dollar 64
Clyatt's 95% Rule 63
Walton's Tilt 1/3 59
Decision Rules 54
Blanchett's Simple 53
Vanguard 48
Constant % 44
Ingliss Feel Free 33
Pye's Retrenchment Rule 29
gummy's Sensible Withdrawals 20
Walton's Inverted 16
ARVA 10

That’s not a great metric — it doesn’t distinguish between winning by a little and winning by a lot— but it allows us to get some sense of how often a strategy “won”.

Surprises:

  • Bengen’s Floor-to-Ceiling does well, coming in second.
  • Constant Dollar does better than expected; it is in the top 50%.
  • Pye’s Retrenchment Rule does surprisingly poor, given that it is also a PMT-based strategy. Possibly because it never increases withdrawals? (It only cuts them when the market has done poorly.)

Hmmm…I feel like I walked away with more questions than answers. HREFF has some promise but it also clearly requires a lot of interpretation and analysis.

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