Annually Recalculated Virtual Annuity: A Test Drive

I thought I'd try my hand at the Waring and Siegel Annually Recalculated Virtual Annuity (ARVA) (The Only Spending Rule Article You Will Ever Need M. Barton Waring and Laurence B. Siegel, 2015) as an alternative to other retirement spending models to see how it works.
There are a lot of opinions these days on how one should spend or withdraw in retirement. This is just another way of getting at the same thing and I wanted to see what it looked like if I tried to interpret it my own way.  The advantage with this method, which is a bit simpler than I make it look, is that the risk of running out of money goes way down (not zero as long as one is accepting portfolio risk). On the other hand it also makes budgeting a little more unpredictable than something like a 4% rule. It is an approach that falls somewhere within the growing family of dynamic spending rules and actuarially sound budgeting methodologies. Me? I think that life is unpredictable so I am supportive of almost all adaptive methods...within reason. 

Key Inputs
- Current age (at any given point -- annually, say)
- Expected longevity using SS table or other method (at any given point )
- Expected real rate of return after inflation (at any given point)
- Value of endowment to be spent (at any given point)

- The test-drive blind is run blind to other income sources like SS.
- Assume there is an endowment big enough to even do this math

The W&S ARVA Steps (see the big white dots in the nearby chart)

1.  Estimate how long you think you might live in general terms. The recommendation is to not use an average or median or 30 years. That might lead to an optimistic or misleading result. Note that at the median, half the people will keel over before you and half after. And look at the average on the chart; there is an awful lot of real estate to the right of that number. The point here is not about precision, it's that one needs to internalize the fact that longevity is uncertain (though it does follow a recognizable probability distribution across a large enough population) so maybe being conservative is wise. For one's own individual case, though, there might be specific health information that would make the expectation very different than the general pool. (do you smoke by any chance?)
2. Based on #1 pick a conservative age further out than "the average." One does not have to build a probability density function like I did, just pick a number or maybe a range. I picked 95-100 for "the plan" in my illustration just to be really conservative but also realistic. The oldest human made it to about 120 but I don't think I'll make it that far so I cut it off at 100.
3. Use the Excel PMT function to calculate a spend rate.  Key inputs are: the expected real rate of return, number of years, and current endowment. One does not have to chart out all values for different age or return expectations like I did here. I did that just to illustrate what it looks like for various different assumptions.  Then, get a handle on the real rate of return after inflation. While you are doing that note that past real returns were probably lower than you thought they were (especially if one does not perseverate on the last half of the 20th century) and many if not most analysts in 2015+ think that returns for both bonds and equities will be lower for the foreseeable planning horizon. Note also that the PMT function is more or less an inside out version of what Moshe Milevsky said (in his 7Equations book) was an old Fibonacci formula for "how long will my money last" except here it's solved for "how much" given the "how long." Same problem, different direction. 
4. Determine the safe spend rate for that year. Play around with the assumptions if necessary.  In this test-drive I looked at a range that went from an optimistic young death age (really? a young death age is optimistic?) and high real returns to a conservative worst case (really? a worst case is living to see one's great great grandchildren?) old age of 100 and low real return expectations.  The best spend rate came in at over 5% and the worst was just a skitch under 3%.  That means that if I were to pick age 95, and I do, and a middle of the road return expectation (for this illustration anyway), the spend rate comes in at a little under the standard 4% rule which I guess makes some sense. On the other hand, note that if in the real-life execution of this plan one turns out to have been too conservative in the final sense, then one better have a legacy plan as well as reconcile oneself to the idea that there was a long stretch of unnecessary self-denial over the years. Personally, I think that an adaptive method combined with a long retirement horizon makes the  trade-off (conservative approach vs legacy/self-denial) manageable. That's because running out of money has infinite disutility as someone once said. In those later years I can loosen up as the assumptions start to come in. See the quote at the end.
5. Next year: do it all over again because every one of the key inputs will have changed (people seem to like certainty in retirement but as Dirk Cotton recently posted: "certainty is absurd"). And while you are doing that, you (like me) should have a vague sense of gratitude. That's because we both have an elegant problem in the sense that we are among a very small minority of Americans that have the luxury of being able to do the math at all. A ridiculously  and shamefully large number of aging Americans are painfully underfunded for retirement.

"Early retirement behavior matters most. The first five to 10 years of retirement have an outsized impact on long-term success. Spending less during these years offers a better likelihood of positive outcomes over the entire retirement horizon…A flexible drawdown strategy leads to better retirement outcomes. The best simulated results came from strategies that increase the drawdown percentage later in retirement."
Savings to Income by Luke F. Delorme, Research Fellow AIER

ARVA on a Chart: