On why the 4% rule was always a little bit of a head fake

It seems like an awful lot of people, myself included, have taken shots at the 4% rule (or should we call it what he later said was 4.5%?), many but not all of them for the right reasons.  Google "Bengen and 4% rule" for background on what it was and why it was so I don't have to write it up and so that here I can just take my new tool out for a spin and mention a few thoughts about why, in general it (4%) worked ok.  And also why it had unexamined risk. I believe much of this has been touched upon in the literature already.


My Opinion on 4%

Here are a few reasons, in my opinion, that it worked out as a generally good rule of thumb for it's time:

1. It was "dealt a hand" of historical data. Using history means you are working with what was dealt by the universe over the time being surveyed.  It's not that it was necessarily good or bad data, just specific to an era in history in a particular place.  That specific data used for the 4% study made it work out that 4% happened to survive the tests that Bengen devised in good faith. 
2. It assumed a certain age.  In fact many studies assume a certain age, usually 65.  That assumption is fine but is an arbitrary choice that should -- "in theory should" but often doesn't and doesn't in the particular case of the 4% rule -- put in play a force of mortality that, when examined, constrains or expands the period over which a plan must be successful.  Early retirees have a different set of probabilities than 65 year olds, for example. On the other hand 65 might be easier to plan than 50 because one can use a shorter "fixed" horizon, though 30 seems a common practice -- which makes age more or less irrelevant because of the next point. In his paper it looks like Bengen does not really have a hard start age assumption. Rather he says a typical client would be somewhere around 60-65. This is an understandable simplification.  Early retirees are a more modern phenomenon but worthy of study as well.[1]
3. It assumed a fixed period[1]. This is really kinda the same as the previous point just in different guise.  A fixed period more or less assumes someone is alive over a whole period. If you are 5 or 95, one is still analyzing over 30 years. But over 30 years the cumulative probability of a 4%spend net-wealth-process failing is not zero, it is just relatively low.  Forget the specific "person" for a minute now. If the "period" being examined were to be 1000 years, a generic "net wealth process with a 4% draw and modest net returns" would have a material, probabilistic risk of failing at some point. A 30 year horizon just happens to be the first and easy part of that curve. In fact, for many people the slice in question can be either shorter or longer than 30 and for early retirees quite a bit longer...not to mention the fact that: a) except for US counties plagued by the opioid crisis the longevity assumptions keep rising with modern health care and b) longevity assumptions push out a bit each year anyway as a person survives to the next year...up to a point.

The Setup

Now let's look at this with my risk approximation tool I'm calling "JPA" for short.  Since I can't speak for what hand the universe will deal markets going forward, I will instead suggest two scenarios that are focused on different ages (and different expectations for longevity as well) and therefore different "durations:"

A. 65 years old, 4% spend, longevity expectation more or less set using the SS 2013 life table (averaged across everyone, so lower than healthier wealthier cohorts), 4% net real returns, 10% volatility, and a plausible set of "other" assumptions not detailed here.

B. 50 years old, 4% spend, longevity expectation set using the equivalent of the SOA annuitant mortality table (averaged across healthier wealthier people, so a longer expectation), 4% net real returns, 10% volatility, and a plausible set of "other" assumptions not detailed here.

The Test Drive - Scenario A

Plugging scenario A assumptions into three tools -- JPA, Kolmogorov equation, and my hacked MC simulator -- I get these results for ruin risk:

JPA	0.037
K-eq	0.039
MC sim	0.030

These are pretty consistent.  This is a plausible result and makes peace with the thought that the 4% rule works because the risk here appears quite low and under 5% if 5% is a meaningful threshold which it might not be.  The low risk is a function of the late-ish retirement age and the shorter duration over which it needs to work. In this and the following chart note that the cumulative risk of the net-wealth process does not change. This is what A looks like when charted out using JPA:

The Test Drive - Scenario B

Plugging scenario B assumptions into three tools -- JPA, Kolmogorov equation, and my hacked MC simulator -- I get these results for lifetime ruin risk: 

JPA 0.261 K-eq 0.261 MC 0.330

The MC is a little higher but high risk all around.  This is a plausible result because we are not only planning over a longer life time we also shifted the expectation out even more because we used a longevity expectation based on a pool of people that live longer.  I don't know if this risk is high enough to freak out and do something, all I know is that it is "higher."  This is what B looks like when charted out using JPA. Look for the expanding longevity probability "horizon:"

Thoughts on 4%

The 4% rule was good work and necessary. It just suffers from some predictable faults: it used a fixed period and it used one particular slice of world history.  The risk was still there, though, just hidden.  The risk is (and was) even higher if one were to retire earlier and/or have a longer longevity expectation...even higher still if there were to be some reason we might not think we will be dealt the same hand that the universe has dealt before.  On the other hand the fixes are still all the same: spend less or more cautiously especially if an early retiree, allocate wisely and maybe even tactically if one has the skill, work longer or do side-hustles, reduce fees and taxes, find a pension, etc. etc. etc. That, as far as I can tell, has not changed. 

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[1] Actually what he wrote was: "...Do so by computing the shortest portfolio life acceptable to the client (generally the client's life expectancy plus 5 or 10 years, depending on the conservatism of the client)." and " determine the highest withdrawal rate that satisfies the desired minimum portfolio life. For a client of age 60-65, this will usually be about 4 percent. " So 65 with a mean expectancy of 82 would be somewhere around 92-65 = 27 years and 60 would be 92-60 = 32.  This is why I implied that he said age 65 and 30 years. If you consider this carefully you will see that I am unfairly setting up a little bit of a strawman just to knock it down.
http://www.retailinvestor.org/pdf/Bengen1.pdf