Health, Preventable Disease and Retirement Finance

Having been on a health kick lately for its own merits, whether for vanity or longevity I won't say, I found myself in an interesting Twitter dialogue recently about a nexus between health and retirement finance.

There appears to be a mounting pile of evidence (not provided here maybe start here with PD Mangan or with a book I read) that implicates diet (e.g., sugar, processed food, protein intake, fasting etc) and fitness choices in preventable chronic disease, insulin resistance, inflammation, longevity etc.  That evidence can be translated into a retirement finance discussion in addition to usual one about personal well-being and quality of life.

I originally viewed my own health choices as a quality of life thing but it's more than that as Alli Covington (@allicovington) reminded me in this [edited] thread on Twitter and about which I should have already been aware:

The cost of healthcare after you’ve poisoned your body with years of bad food will astound your retirement savings. Imagine being crippled, unable to move easily, in pain AND broke. Put down the down the donut and pick up a dumbbell. Don’t be left broke and broken  

The real matrix […is…] the trap of eating processed food labeled as “healthy” that eventually leads to disease, which siphons all your available cash preventing you from being free…

That got my attention.  So I asked her what she meant.  She's still working privately on something yet to be published but the concept as I understand it seems pretty sound as she explained in a follow-up DM...   

I researched the annual cost for specific conditions that are 1) prevalent and 2) preventable and reversible with diet and exercise  

If they start fit, they avoid millions in spent dollars with interest. If they allow themselves to get a chronic disease like diabetes, they will lose out on millions.

Ahhh, she's singing retirement finance lullabies to me there. And we can test this a little bit even without the data.  I'd love to see the research and analysis but the underlying dynamic is super simple at its core: this is just retirement spending.  And we've beaten that to death here before. But lets just re-color things a bit and take in hand a subset of health spending in particular (the part attached to preventable chronic disease that can be influenced by self-care choices), which before might have seemed an inevitable and fixed cost of future retirement, and now we make it discretionary! Willful ignorance of health choices and future spending will no longer be tolerated here at RH.


General Statement on Spending

Other luminaries in Ret-fin have touched on the actual spending behaviors in retirement (think Blanchett or Banerjee[1]) but we can do this kind of thing ourselves.  Let's look at some BLS data on spending. This is from a 2014 consumer expenditure survey.

Figure 1. Spending in Retirement from BLS survey

Which with a little manipulation and a focus on percentages it can be recast like this

Figure 2. BLS retirement exp as a % 

This is an average, btw. While health $ do not dominate the scene in this chart like housing does, it does assertively rise and then, if one were to be predisposed to either chronic preventable disease or be willfully self-destructive, the health component here might be even a bigger deal.   We can try to start to gauge the nature of the impact.

Lifetime Utility of Consumption  

If we think of this in simple consumption terms it's all pretty easy. If our structural spending, now or expected in the future, is high then bringing it down via whatever means -- in this case we are talking about self-care vs preventable disease -- means benefits will accrue to the expected discounted utility of lifetime consumption. On the other hand, if our structural spending is low because we are mentally reserving for future uncertainty related to the wages of no-self-care then spending (and consumption utility) might rise to fill the vacuum left by the departing uncertainty purchased with self-care.  Borrowing from a past post we can visualize it like this where we can view ourselves as perhaps creating more flexibility in our plan to move towards more optimal consumption.

Figure 3. Expected Discounted Utility of Lifetime Consumption vs Spending

This is a visual of 11 different allocations to risk (diff lines) along an efficient frontier (not shown) for different spend rates (x axis) and a parameterization not discussed since this is merely illustrative. The output (y axis) is the expected discounted utility of lifetime consumption using a CRRA utility function on consumption over an additive lifecycle (in decumulation).

The general point I'm trying to make here is that self care, if it reduces future health cost liabilities, probably frees up our capacity to choose where we are going to be on this kind of chart.  The math and model for this kind of thing is here.  The specific application to the health concept I'm broaching is totally absent for now. We just are proposing that we are adding some unknown ability, by way of self-care choices, to be more intentional about consumption utility than we were before intervening. The exact measurement of this would come if I could model it more specifically, which I can't yet.

An Annuity Model for the Incremental Gain/Loss Concept

Ok, that's a little fuzzy and general so let's try to quantify the probability weighted present value of "changes in spend rates" as a proxy for the impact of self care on preventable disease, on the margin.  Let's use a basic annuity model such as this

Eq 1. RH annuity model

where cf is a cash flow, tPx is a conditional survival probability, R is a discount rate and L is a load factor.  In this case we'll use 4% of $1M as a strawman for cf, the probability is extracted from an annuitant mortality table and R is a real discount rate since we'll pretend this is a real annuity model that just happens to be calibrated to a rate I found looking at a real annuity from the Principal Co. for a 61yo male (past post). The load we'll fake at 5%.  We will also, no doubt ignorantly, assume that the impact of health spending is uniform and static over time. Of course that's a bad assumption but we are swagging here and I don't want to get too complex.

If I plug all that in and look at the incremental impact on the model valuation of a 1 basis point move in spending for a 61yo male, I get a delta of ~$2400.  But that depended on my age and longevity expectation, my endowment, the spend rate expectation, etc. We are also totally ignoring any feedback loops related to changes in longevity.  We are also ignoring that reductions in longevity, perversely, can actually help us in retirement finance since the horizon interval of planning would get shorter.  Oh well.

Here is another way to quantify it. Ditch the load factor and use the same model to value a "1% of wealth" cash flow. That's more or less the same thing as above, really.  That 1% of $1M is worth ~ 225k.  Again we'd have to scale this up or down based on age and endowment and the expected incremental spend impact but that's a reasonable placeholder for now for an order of magnitude.

A Look at Portfolio Longevity Effects

If we can hold, for a moment, onto the conceit that the flow of discretionary savings or spending from self-care (or lack of) vis-a-vis preventable illness is constant and unchanging then we can look at the effects independently of dollar valuation or the human longevity implicit in the annuity or lifecycle utility models.  Here, instead of denominating the incremental impact in dollars (or utiles for that matter) we'll denominate it in years -- portfolio longevity in years -- as inter-mediated by spending.

If we ignore mortality and assume we live forever (which perhaps sounds weird in a post about health and preventable disease) then what happens to the portfolio for incremental changes in spending if we are using a net wealth process recursively? Milevsky articulated the process like this where w is the withdrawal V is the stochastic return and M is wealth:

Eq 2. Net Wealth Process

I'd maybe add terms for income and for annuity purchase but whatever.  When this is animated in simulation we can, at the end, extract a distribution of the number of years a portfolio survives.  Recall from past posts that this is a defective distribution and is a two-fold construct, one distribution that represents the portfolios that die in finite time, and another distribution that represents the portfolios that live forever. The distributions combined as one is our interest here.

If we take some provisional and illustrative assumptions for a fake portfolio (say a real return of 4%, std dev of 12%, max horizon of 100 years, 20,000 iterations) then we can extract some summary stats from the resulting distribution of portfolio longevity in years such as the mean or median or the 5th percentile. That last is useful since it represents a very conservative view about how long a portfolio can last and can be considered a type of frontier when contemplating one's own human longevity. Again, remember that we are ignoring any interaction between our "health intervention" and terminal longevity.  We are also not playing with the parameters for return or vol so there's that too.

Table 1. Portfolio Longevity in Years vs Spend for given parameters

The take away, if we were using real data, might be that self-care of preventable disease, in the absence of any terminal longevity changes and to the extent that it beneficially affects our spending over time, contributes to portfolio longevity. It adds years. And it's not exactly linear either.

Discussion

Ok, so this was over simplified and reductive and it is not even using real data which is likely to be more dynamic than I am modeling. But this, if can see the data some day, would be an interesting course of inquiry if done right.  Avoiding something like diabetes or other insulin-sensitivity implicated chronic disease via discretionary food and lifestyle choice has it's own merits in terms of how well or long we live but it also has an impact on things like portfolio longevity, the price we pay to retire, the year we can retire, and, with little doubt, consumption utility over a retirement.  This is worth a look.  TBD.

Fwiw, I'm sure there is a giant pile of research and literature on this kind of thing out there, I just haven't gotten too far into this yet.  The other thing that I'm missing here, while I'm thinking about it, is that I am mostly working with spend rates here. What is missing is the potential for large, unfunded absolute spending on disastrous health outcomes, outcomes that can lead to chaotic financial cascades that lead to bankruptcy. This is something that Dirk Cotton has written on quite a few times.  Once we get into that zone I have no doubt at all on the valuation Alli describes as millions for the cost of bad choices.



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[1]  Banerjee, S. (2014), How does Household Expenditure Change with Age for Older Americans, ERBI.org 

Blanchett, D. (2016), Estimating the True Cost of Retirement, Morningstar.