Note: I posted this entry last week and then I subsequently withdrew it and now I have reposted it again. I originally posted it because I think this is an interesting way to look at spend liabilities on a household balance sheet and the stochastic present value idea in particular has some affinities with both balance sheets and probabilities of success. I withdrew it because I found I had made some material errors in the spreadsheets I was using that undermine my point...in addition to the fact that I wasn't all that confident in the idea at the time and had been cavalier about my rigor in looking into this kind of thing. I reposted because I still think the idea is worthwhile for contemplation, I found some validation in a 2009 paper by Dimitry Mindlin (more later), I have since re-written the process in R rather than Excel, and I want the option to refer back to this when exploring this idea some more. I could fix the spreadsheet but at this point, why?
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This post is not legit data science because many of my assumptions and inputs don't line up or are maybe even cherry picked (omg) a little bit. But the outcomes do line up so I am suppressing my gag reflex on my corrupt methods in order to throw it out there just for fun. My guess is that a little bit of honest effort into being serious about lining up and rationalizing my assumptions would make my results diverge more than I want but where is the fun in that.
In this case I used my own future spending assumptions (values not shown for obvious personal reasons) to see how it all looked for my own plan -- I mean as long as I have been perseverating on this spend liability thing lately I thought I might as well. I used the spreadsheet-spending-sim that I did in a couple recent posts but now I did it: with my real spending plan design, inflated at 3%, stepped down in custom steps at 69 and 86, varied randomly year to year, discounted at a rate closer to annuity discounting (2.8%), and, finally, with an age assumption varied between sim iterations that is plucked randomly but also mostly in line with a conservative SOA annuitant mortality curve.
With the distribution of spending-liability NPVs from that effort in hand, I found the median for the distribution and plotted it on a chart. Then I also figured out the spend-level NPV on the distribution that roughly matches the net monetizable assets that I have available to serve my current and future spending risk (before other liabilities like spend shocks and such). I determined the percentile location on the spend distribution for that amt and plotted it as well on my chart. When I plot it it looks like this:
I realize that: a) I am hiding important info (personal) here, b) have an overly simplistic model, and c) it was kinda gratifying to do this exercise because the lines are far apart for me, but this was also interesting to me for two other reasons:
1. It shows me directly the equivalent of a free-boundary distance in dollar terms. If we ignore the fact that I am focusing on a spend liability more than the full scope of liabilities that might show up on a real household balance sheet then this is very close to (if not same as) the free-boundary concept I mentioned before in another post and that has been articulated by others (Collins) better than me. The line on the right is what I have on hand in (at risk) present value terms to discharge future spending liabilities. The line on the left, on the other hand, is a version of a "free boundary." This, in Collins, would be the price of an annuity that defeases spending commitments; here it is more specifically the median of the spend-liability distribution that the annuity would (probably unsuccessfully in the end) try to defease. In a past post I showed that these two things (spend liab and annuity price, ignoring things like Money's worth ratios) could be considered the same value or solved to be the same value (but that one might then have an annuity that might pay too much early and too little late which creates a cash management over time problem). In other words: free boundary ≈ median spend liability ≈ approximate annuity price (??). The closer the two lines are and the closer for longer rather than shorter time frames, the more one would get nervous and the more one might feel inclined to annuitize assets in order to take longevity risk and some spending risk off the table. I have no idea on where the proximity trigger location might be, though (future post), and
2. The point on the spend NPV distribution where the PV of net assets lies is of interest to me and it looks vaguely like Monte Carlo simulation results. In this non-generic case above my net monitizable assets available to discharge spending obligations reside at about the 98th percentile of the (fake) spend-NPV distribution. That's cool because there is a decent gap there but it also reminded me that the ruin estimates and the MC sims I have run recently are also in that range as well in terms of success rates. That is something I wanted to know more about.
So, if we again, as above, ignore that I am not lining up my assumptions very well then this is where it got mildly interesting for me. The 98%tile (.979667) of the spend distribution where my net-assets sit reminded me of ruin calcs so I decided to run them. First I ran my FRET (flexible ruin estimation) tool that is a raw, simple estimate of ruin risk similar to a Kolmogorov equation or a simple sim where the math for lifetime probability of ruin (LPR) looks like this:
These results all, in my mind, cohere. Like I mentioned, this may be lucky or even forced but it seems like the same game is being played[1]. We can ignore the fact that we need to specifically take a hard look at the assumptions around discount rates, return assumptions, longevity, social security, and so forth. We can just marvel that the same answer keeps coming up here in one massively reductive look at some unique-to-me retirement calcs (it might just be that at high percentiles everything looks more or less the same across different methods; that'd be no fun). But then again it is also not all that surprising either. If you look closely you can see that the underlying processes being modeled are the same or similar. It's just that we are working in PV time here rather than FV time give or take some simplification implied by that comment. On the other hand I think there might be some advantages in looking at spending very directly and closely in this way, especially if it can give similar answers to a sim. Spending is the one great lever we retirees have and contrary to an awful lot of retirement lit it is neither constant nor invariable before we even get to inflation or "rules." It might be worth digging into it's nature more than we have to date. This was a new way for me to look at this kind of thing. I'm curious now to see if the results would continue to cohere if I were to add more rigor to the inputs and/or to vary the scenarios more than I have. That, however, my friends, is another post...
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[1] On reflection I'm thinking "not really." Since I can artificially widen or narrow the distribution I don't know how much water this idea holds. Probably none. I'll play with it now anyway.
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