My new favorite paper...

Here is another paper where, having now read it, I could probably hang up the blog and take off for a while (Sustainable Retirement Income for the Socialite, the Gardener and the Uninsured, Chris Robinson and Nabil Tahani 2007).  This is the first and only (ok "only" is a little dramatic, I have seen some of this before but it sure doesn't feel like it sometimes) paper that has directly addressed the following things I find to be essential points in playing the retirement finance game:

The Things I'm Very Glad to See in a Retirement Paper

1. There are three (almost) separate, independent stochastic retirement processes involved in shortfall probability estimation: a random return generation process, a random consumption process, and random lifetime.  That consumption is treated as a random process is really rare and in this case, quite encouraging. I said "almost separate" above because the authors create a correlation relationship between random spending and random returns, a point I made in a past post.  The only process they missed is that returns and consumption can be combined into a new fourth process called net wealth that can produce a distribution called portfolio longevity in years, which has its own unique and sometimes weird behaviors, though it is implicit in their math.

2. Did I mention that they made spending a stochastic process?

3. They also gave the random spending process a drift. I did this in my first simulator. The point here is that spending can be modeled as a GBM process just like returns...which they did...and should have done.

4. They correlated spending and returns. And in a nice touch that I appreciated...

5. This point really is the only time I've ever seen something like this other than on my own blog -- they actually mentioned (in a footnote where they also said they wouldn't model it) that the spending-return correlation could be negative.  To quote: "We could conceive of negative correlation in a perverse way. If the stock market treats you badly, you go shopping to compensate. In this paper, we only show results for positive correlation." Perverse happens to be the same word I used in a past post identifying this same possibility and describing my own spending in 2008 where markets went down and, for reasons all my own, spending doubled.  Perverse indeed. Good catch.

6. For shortfall analysis they model consumption as a stochastic present value. This is lovely validation of some past work.

7. They found an effect of random spending variability that I saw in my own past work (and didn't understand) and then explained what it means so now I finally get it! When spending is randomized, it has little effect on"ruin" but it does have some. In particular when spending is relatively low, shortfall probability goes up and vice versa.  Their explanation: "[for  high consumption] if the consumption is stochastic, the part of the distribution that reduces spending enough to avoid ruin does matter. Just like an option, the upside may cause a benefit and the downside cannot hurt any more. If the retiree is pretty secure, however, the tail of the distribution that increases the shortfall probability is more likely to occur with stochastic consumption, than the tail of the distribution that will decrease the already low probability of shortfall." [emphasis added]

The Conclusions that Happen to be Parallel with RiversHedge

The authors also came to some of the same conclusions, after running their model through its paces, that I sometimes harp on here. This list below is not all of their conclusions, just the ones that I am highlighting as similar to some points I've made here before:

A. "The most significant effect on probability of shortfall of the innovations in this paper is the different patterns of consumption." [emphasis added]

B. "A person who retires in the normal age range of 60 – 65 cannot generally expect to sustain an initial consumption rate in retirement greater than 4% of initial wealth."

C. "A person who plans to continue a constant rate of consumption, “the socialite,” cannot sustain a rate of more than 3%"

D. "Someone whose health or other needs entail an increasing rate of consumption in retirement cannot sustain an initial rate of more than 2%."

E. "Making consumption stochastic has a relatively small impact on the probability of shortfall. It increases the risk at low rates of consumption and decreases it at higher rates. "

F. "Making stochastic consumption partially correlated with investment return reduces the risk of shortfall, but not by a great deal." This is a subtle but important point that earlyretirementnow compellingly made this summer. This also happens to point to a possible weak underbelly of dynamic systematic or ad-hoc spend rules.

G. "...retirement at age 65, when most pensions start, encounters a shortfall risk of over 10% for a draw greater than 3%, and the risk rises very rapidly." Gordon Irlam made a point like this at aacalc.com in a piece called "the cost of safety."

H. "The problem for the financial planner is how to allow for a disaster in retirement when no insurance exists or is affordable. Most people will not suffer it, and so simply saving enough for any eventuality is not a feasible solution."


...And the Most Interesting Thing of All in the Paper....

The paper and the underlying model are speaking in the language of shortfall and ruin probability.  The shortfall/ruin concept is often referred to as sustainability analysis.  "Sustainability," which is a future- or projection-oriented kind of thing, is typically, but not always, differentiated from "feasibility" which is a balance sheet task in the present time using current observables to see if it's even worth analyzing sustainability in the first place.

The really really neat thing they did here, in my opinion, is to use some "Ito's lemma" analytic ninja tricks that I don't really understand yet to show that a net wealth process SDE (this happens to be the one that underlies all simulation modeling and thus all fail rate and lifetime ruin calcs and that we've seen here on this blog a bazillion times. i.e., this underpins basic idea of sustainability analysis) like this:

becomes this below which is their analytic form for the probability of ruin:

What's neat about it is that if you look closely you can see that the right side of the inequality on the right in (A.5), which is part of their shortfall and sustainability analysis, is really a stochastic present value of consumption complete with random consumption, random discount rates(returns), and random life.  That means that the whole inequality on the right is actually "balance sheet feasibility" in spades.  In other words one could say "One household balance sheet to rule them all"[1] or at least in this paper we can say that feasibility and sustainability become one.  That conclusion was worth the read.  Now, I do think that the two terms can still be defined separately but I can also see that the space of separability between the two can, at some point, be vanishingly small if not closed entirely. This is also why I once referred to SPV in balance sheet analysis as a type of inside out simulation, though I did not go as far as to tie things together like the authors did here. 

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[1] actually I think that the RIIA has the rather generic term HHBS trademarked...