Stepping into simple component analysis

In a recent post (My Retirement-Finance-Model "Topography" Strawman) I laid out what I thought was a reasonable framework for viewing the concept of retirement finance modeling. I am sure it is actually more complex than this but I wanted a simple way to think about it. It looked like this:

Figure 1

Now, since I am bored with covid and home life, I am going to fill my time by learning chess, working out, fixing my house and by diving back into Milevsky's "Retirement Recipes in R," that last for two reasons: ego, since I got acknowledged in the front of the book; and because that book puts us squarely and confidently at point "a" in figure 1. An advantage of being at point "a" is that one can move anywhere in the cube's dimensions... where if we start at "b" we may be stuck with someone else's model that we don't understand and where we can't really move to any other point other than "b." Planting our feet at point "a" is an incipient power move.

My ambition at one point was to go through every formula in the book and play around but: 1) that's a lot of work, and 2) I have personally covered a lot of the same ground over the last 10 years so it feels a little redundant with past work. I'll keep going for a bit, though, and see what happens and continue to try to flesh out, in my own mind, some more thoughts on figure 1. 

Here is the first example. One is barely into the first chapter and the very first formula is the one for valuing an annuity, growing at g, priced at v and over N periods. This is basic finance and the R formula looks like this:

RGOA <- function(g,v,N){

(1-((1+g)^N)*(1+v)^(-N))/((v-g)/(1+g))

}

Pretty simple, right? But, I mean, why price an annuity, though? Because it is fundamental finance. All those programs I built, all the flavors of MC simulators, the 1000 or 5000 lines of code beasts, all get to the same place that something like this takes us in one line. The trick here is that one can, if one were to be interested in these kind of things, back into a spend rate analysis very very quickly by simply using RGOA. To spend down $100, say, over some horizon between 10 to 50 years -- which is a pretty reasonable human horizon -- using some real rate of return, all we have to do is divide 100 by RGOA with some flex assumptions. Doing that with ~9 lines of code, we can produce this:

Figure 2

Where the X axis is the horizon of 10 to 50 years, the Y axis is the spend rate that consumes the $100 over the horizon, blue is a real return of 1%, red is 2%, green is 3% etc, the black dashed line is the 4% rule, and the grey one is the 2% spend level that Ed Thorp hypothesized as a perpetuity or endowment. 

If you have an inkling about longevity expectations, Figure 2 takes us, with 9 lines of code (fewer if I hadn't hit the carriage return so often), pretty far into ret-fin. It's kinda all there in a way. Certainly I can see that when I retired at 50 and might have had a 50y horizon and if I had had realistic expectations about real returns: 1) the 4% rule might seem a little rich, and 2) a sub 3% spend gets a little closer to self-denial. Of course there is no volatility or sequence risk here but that is for another day. The point is the simplicity of point "a" in figure 1 can take us pretty far if all we are doing is having a conversation about retirement. And I didn't even have to simulate anything.