I had an error below where I inadvertently goosed the historical inflation with the extra 1.3% period standard dev. This makes the historical inflation exaggerate a bit. Rather than fix it here I'm moving on and will correct it in the next post (Playing around with inflation, part 2). In that post we see a more reasonable historical inflation effect but when I add on an autoregressive model AR(1) we get back all the multi-period-time-driven vol and then some.
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The Point
I just finished 12 posts on lifetime consumption utility and full and partial annuitization. That month-long effort involved, by my estimate, over 100 million iterations of some software I wrote. That's a lot. It also put the issue of nominal annuities front and center. While there are many proxies for inflation protected income out there in the market there is evidently only one insurer that writes a true inflation protected annuity. Nominal annuities, and even the pseudo-protected ones, are an explicit bet on inflation; effectively one is partially or completely short inflation where in extreme inflation it might be better to be long...or employed...or living someplace else.
Most of the models I build factor in inflation a bit but mostly I ignore it or gloss over it. I wanted to think about it some more. I do not have a sophisticated view. I am, as in my other posts, capable with a spreadsheet or R-script but more or less I am naive most of the time. Nothing has changed in that area yet. But let's take a preliminary look-see.
The Data for this Post
There are plenty of ways to look at it: historically, via averages, the experience of other countries (Germany, Zimbabwe, Venezuela, etc), via simple models, via auto-correlated models...whatever. I'm not sure where to start. The only two points of reference I have in hand right now are: (1) a model suggested in an article by Joe Tomlinson (Which Annuities Offer the Best Inflation Protection? (AP, 6/17/19)), and (2) the US historical data at inflationdata.com.
1. Joe T
Joe models it like this
"For inflation modeling, there are strong indications pointing to a 2% future average. The current Treasury/TIPS spread is just under 2% and we also know that the Fed is targeting 2% inflation. However, my purely subjective view is that there is a somewhat greater risk of higher inflation, and I’ve modeled future average inflation based on the following probability distribution:
[he has a table but in R, like this:]
infl.values <- c(.01,.02,.03,.04) infl.prob <- c(.10,.60,.20,.10)
The modeling involves generating 10,000 25-year inflation scenarios. Each of the 10,000 scenarios involves random selection of average future inflation based on the above probability distribution. Then, based on inflation volatility since the early 1980s, I generate random year-by-year inflation assuming a 1.3% standard deviation."
2. Inflationdata.com
This is no more and no less than the historical record. You can check the site but the latest several years are like this where I'll be using the last column between 1914 and 2018:
The Set-up
I'll keep this simple. Most people talk about a 4% constant spend rate and a $1M initial portfolio. Let's stick with that. that means 40k in spending. Assume one buys a 40k nominal annuity to sort-of defease that. What happens in an inflationary scenario? Obviously one's buying power and lifestyle degrade, a lot. But I want to see it for myself. Certainly I saw it first hand in the 1970s. It sucked the life out of a consumption portfolio my mother was living on. That made 2008 look like a walk in the park. So few remember this, especially younger advisors so watch out for them.
Let's see what happens to 40k with the two models/data that we have above. I'll use 10k iterations of sim.
The First Look
If we: (a) run Joe's model in a single period mode, and then (b) do a random draw on inflationdata.com this is the distribution of inflation rates we might see this where black is Joe and blue (the wider distrib if color is hard to see) is inflationdata.com:
 |
| Figure 1 |
| mean | median | min | max | |
| ID.com | 0.032499 | 0.0268 | -0.1085 | 0.178 |
| Joe | 0.022909 | 0.022753 | -0.03495 | 0.081401 |
The Second Look
Let's take 40k and run it out for 30 years using the two models.
yikes.
The Third Look
Now let's look at the distribution of spending at year 30 where Joe is red and ID.com is black....
and some summary stats
Not sure what to say. Using the non-auto-correlated historical data draw we have an 87% chance of losing ground with a nominal annuity. Not sure I trust that model. We also have a good chance that future spending will dwarf our nominal annuity using the median or max stats. This is nothing more than what I said it was, un-hedged spending is an explicit short on inflation at some level. I was just corresponding with Dirk Cotton on this topic and the only hedges we could come up with are TIPS, iBonds (purchase caps!), real annuities (imperfect market), and CPI swaps, to which I'd add what was above plus some other stuff: a secure job that can adapt, living elsewhere on the planet, and maybe gold but I don't really want to go down the gold path right now. Any other ideas readers?
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