Putting an adaptive PWR up against changing longevity estimates

Here is another "on a roll" type post.  While I still had it fresh in my mind I thought I'd run PWR analysis ("perfect withdrawal rate" links here, here, here, here and here)[1] through an "adaptive" cycle of changing longevity and then compare it to my old self-made rule of thumb [RH40 = age adjusted spend rate estimate = age/(40-age/3)]. I showed in past posts (not linked here) that RH40 is a good proxy for a conservative constant risk (5% fail rate) spend estimate and that it even won some CRRA utility games (for high risk aversion) in some of the spend games I did a while back (not linked here either). It stands in here because: a) it tracked well with both programmatic simulation and analytic simulation when they were set to pretty conservative assumptions, b) it is easy to remember and apply, and c) generally it keeps fail rate risk on a forward estimated basis around a constant 5%, which I like.  The basic idea here then is:

1. Use the PWR approach to calculate a spend rate at each age (starting at 60) given an evolving longevity estimate (plan duration) that is based on the SSA life table at the 95th percentile expectation for that age (i.e., really conservative). That expectation moves around each year and extends out the older you get (all else equal). The PWR at the 5th percentile is used as a proxy for 95% success rate which it more or less is if I have all of this right.  This, by the way, is a reminder on the formula for PWR in the Clare article:

Which, if you look closely and think carefully about Ct, is the same as in the ERN link ...

And finally, this is the SSA 95th percentile data I am working off of for plan duration in the PWR analysis. I got this from AAcalc.com but it can be derived directly from SS data. End age vs age is charted below:

age	yrs(rd)	end age
60	37	96.8
65	32	96.7
70	27	96.6
75	22	96.8
80	17	97.3
85	13	98.2
90	10	99.8
95	7	102.3
100	6	105.6
105	4	109.2

2. Arbitrarily set the return expectation low-ish to reflect things like fees, taxes and inflation. In this case I start with 8% return and 10% std dev[2] and then ding the return for about -4% to reflect some of that stuff.  I have not completely convinced myself I can do that with PWR but I think I can so I will. Then I'll do it again for a -3% ding to get another low-ish net real return (5%) just for fun. 

3. Calculate RH40 at each age for comparison. You'll have to go look at past RH40 posts to see what I was trying to do with this rule of thumb.  Remember, though, that it tracked well with both programmatic simulation and analytic simulation when they were set to pretty conservative assumptions.  Generally it keeps fail rate risk on a forward estimated basis around 5% or so. 

4.  Chart the two PWR curves and RH40 and then step back to take a look. 

When I do all that, this is what I get:

Conclusion?

I tried to make the case in a prior post that PWR is Monte Carlo by another name: it just swaps one outcome distribution for another in a high iteration process and the answers that come out the back-end are about the same when you dig into it.  The fact that in this analysis PWR tracks RH40 -- which itself tracks other legit simulation-based retirement analysis[3] -- tells me that this is really all part of the same game (subtle differences but close enough for today).  Different assumptions for return and success rates might move it around a bit but that'd be true of any other analysis.  Note that because everything in this longevity-adaptive approach more or less lines up with a constant risk process, risk will be constant but that means lifestyle will vary.  If you go back and look at some of my "spending game" posts you'll see that lifestyle in PV terms for RH40 (and now PWR) will be suppressed at 60, rise in the 70s and 80s, and decline pretty rapidly in the 90s+ (though not as fast as a constant inflation adjusted spend would).  The answer there is the pooled risk of annuities before you get to the 90s but that is another story.   

Some of the things I do like about PWR, though, are that: a) it makes sequence risk explainable, visible, and analytically explicit, and b) the output, when put in CDF form makes it easy to see, and pick, tradeoffs between spend and success rates (for a given return distribution assumption) without having to rerun anything.  There's more to check out here of course but I just wanted to throw dynamic longevity against PWR to see what happens...which I did. 

I also like that RH40 kicks it again...  

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[1] uses an analytic approach with some lite simulation to come up with a distribution of spend rates each of which would be perfect for its path in retrospect given the sequence of returns within a given iteration.  Check the links provided.  

[2] Vanguard's 60/40 fund is about this level of return distribution but it doesn't really matter. This is just a wing-it type of effort anyway.

[3] one could argue that the assumptions were cherry-picked to make all of this work out but they really weren't.