Playing around with an EOYS free boundary sustainability metric

EOYS stands for what I want to call getting to the "edge of your seat" and is more or less what Patrick Collins suggests one do when one's retirement consumption portfolio starts to approach the boundary between feasible and infeasible a little too closely or maybe a little too fast[1].  Most of the following is just me parroting or trying to internalize what he is saying and then expressing it in some software and in a metric designed to gauge risk or sustainability in a way that might be more useful than probability of lifetime ruin. Or at least maybe this can be something that augments the sense of sustainability over time. I recommend the paper over this post; this is just me teaching me the concept.  Also much of this may be of no interest to those that are substantially over or under funded.

To visually paraphrase part of his paper, I have illustrated the basic idea like this:

To quote directly:

"Although penetrating the boundary is not an event that generates an explicit signal—there may be many thousands of dollars remaining in the portfolio at the time the boundary is breached—it nevertheless is an event that the investor should not take lightly. In terms of portfolio management, it is perhaps the single most critical piece of information that the investor should know. The existence of the feasibility condition puts a premium on intelligent monitoring. It is crucial to know how likely it is that even a one standard deviation move to the downside of the forecasted mean return could prove to be an economically non-survivable event. The investor needs to know whether they are in trouble, not whether their equity position has outperformed the S&P 500...This is a solvency question; or, in terms of the free boundary problem, it is the amount of wealth that separates the region of feasibility from the region of infeasibility. It is not a future oriented prediction; it is a question of the adequacy of current resources. Determining shortfall risk and quantifying solvency by locating the free boundary are both important components of risk assessment, and both provide important feedback regarding asset management dangers and opportunities."

In the paper, Collins uses the price of a SPIA to stand in as a proxy for the FB and measures the ratio of wealth to an annuity cost ratio (WACR) as a key metric, though he points out that "The WACR is a solvency benchmark; it is not a recommendation to buy an annuity contract."  He also uses an assumption that a ratio of 1.1 might be what I am calling EOYS though this is arbitrary.  Another arbitrary assumption is when he looks at the projected left tail of a net wealth process and uses the 20th percentile as a guide post.  I'll roll with both of these for this post. Since he looks at the age or years it might take for the net wealth process to hit the boundary and to determine whether the "investor has sufficient time to delay annuitization" or hold the option to annuitize a little longer, I'll do the same thing. 

Assumptions 

This won't be terribly rigorous, I just wanted to see how it looks.  I'll use the same FRET tool (here and here) and approach I mentioned before although working with its "wealth unit" approach feels a little weird. I think using traditional simulation might be better especially since the constant spend is maybe over-emphasized here but this is what I have for now and a generalized metric might even be preferred sometimes. Also looking at a real-time current estimate with real values for the portfolio and real annuity quotes would be useful in a real-life situation. For a quick illustration, though, I'll look at three made up scenarios:

	net
	real		const.	disc.
scenario	return	sd	spend	rate
1	5.0%	15%	4.00%	2%
2	5.0%	15%	4.00%	4%
3	5.0%	15%	3.50%	4%

Other embedded assumptions include: start age 60, longevity distribution similar to SOA annuitant mortality, 10% load factor, 5000 iterations, max 200 portfolio periods.

Legend -- in the charts below:

- black line is projected median net wealth process in that year
- grey lines are the 5th and 95th percentile
- blue line is the 20th percentile and the line of interest
- red solid line is the loaded-annuity cost projection
- red dotted line is the solid line times a 1.1 EOYS factor - the other line of interest


Scenario 1 - 5% net real return, 15% sd, 4% const spend, 2% discount rate

EOYS number of years: 0-1.  This is in and below the zone right from the start. This is mostly due to the spend rate, volatility and disadvantageous annuity pricing.  I have not modeled, and probably won't though it'd be interesting, a reversion of discount rates over time.

Scenario 2 - annuity discount rate up to 4%

EOYS number of years: 9.  Given the setup, this has about 9 years before it hits the zone and 15 until it exits below the zone. The change in this case was driven by the change in the discount rate.

Scenario 3 - decrease spending to 3.5%

EOYS number of years: 27.  This lasts 27 years before it hits the zone at which point it may not matter. The spend rate is the key here and this looks sustainable...until we check again tomorrow, anyway

Conclusion

Ok, so not very realistic nor do I think I got everything ticked and tied in the math and software[2]  but at least I can, for my own purposes, understand the principle a little better now that I've gone through the motions. I think I may at some point have another tool here to help me get a decent sense of retirement sustainability and risk. 


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[1] Monitoring and Managing a Retirement Income Portfolio, Copyright: Patrick J. Collins, Ph.D., CFA, Huy Lam, CFA, Josh Stampfli, MS EESOR [2015]

[2] The most egregious of my errors and lack of effort in this area, given that I am working in wealth units rather than real dollars, is in applying the concept of inflation consistently across the blue and red lines.  And that's before I even get to the question of whether the annuity pricing can be done in this wealth unit way in the first place.  For now I'll tell myself that: a) at least I am getting a price, any price, for a given year in the future, b) if I'm underpricing the annuity, which I probably am, it is something I can figure out later and at least I have a "zone" to work with now, c) this is not a formal tool used for commercial or academic purposes, it is just a concept prototype so it doesn't really matter...yet, and d) this would just be an early warning "process metric" anyway.  If a red flag arises I would be getting formal quotes and/or doing more sophisticated analysis of the lifestyle liability.  What I want to know on any given day is what is the distance from -- and speed of approach to -- a "boundary" in today's terms not 5 years from now.