This is very subjective and depends on both my code correctness and my assumptions/parameters. I am skeptical of everything here but I ran it to see what it looks like anyway.
The goal here was to run a sim to calc the expected discounted utility of lifetime consumption for these main variables:
- different risk aversion coefficients between 1 and 3 [1], and
- two main reductive spending strategies (constant and percent of portfolio)
The assumptions are in digest form:
- 100k iterations
- .04/.12 portfolio
- Spend between 1 and 12% either constant or % of Portfolio
- Age 63 with generic middle of the road longevity expectations
- Risk aversion between 1 and 3 in .2 increments
- Spending is binary: either constant or a percent of Portfolio
- U[c(t)] = either log Utility for RA=1 or CRRA for RA > 1
- I have a subjective non-zero floor for consumption, email me if curious
I spent a little too much time this afternoon running this stuff but for 11 different RA values and for two different spend strategies, it came out like this in Figure 1.
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| Figure 1. Optimal (?) spend rates for diff risk aversion param |
The blue line is constant spend. The orange line is percent of portfolio spend. X is risk aversion coefficients. Y is the simulation-derived "optimal" spend rate using a consumption utility framework. That latter depends on so many design assumptions that one needs to be pretty skeptical. This is not some kind of closed form professional optimal math thing that is easy to explain. It's just some amateur dude in FL kicking out some funky stuff. The red boxes are what I am calling fuzz where in simulation, depending on how one looks at it, there is some discretion on what might be considered "optimal." See Figure 2 right side. Basically what might be considered reasonable to spend at age 63 is either a) not an optimal point, or even b) a line. It is a zone that really doesn't matter too much because we are -- or I am -- going to re-evaluate next year anyway based on what happens this year.
These are the runs with diff parameterizations at RA = 2. The scaling of Y is a little diff in each so it might look weird. Round 1 means rounding to 4.1 instead of 4.11 etc. The red boxes in the right column are my subjective fuzz ranges.
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| Figure 2. Simulation output |
Thoughts?
Idk. At RA = 3 I am skeptical of either a 2% constant spend or a 5% variable spend; not sure what they even mean here. At RA = 1, I am very skeptical of an 8% variable spend and a 5% constant spend might be within a realm of possibility if we accept that RA1 is a fairly big risk taker. Me? I'm conservative at 63 but my monthly (annualized) spend ranges from under 3 to well over 4 depending on the month. That smooths out annually so something somewhere in the middle. That is not so much a choice at it is a necessity given what I have committed to for me and my kids this year. Anyway I already cut my lifestyle in half back in 2012; it has a lower bound. Obviously if that commitment is going to put me under a bridge I'd have to re-evaluate but my point is that the math and the sim convince me of nothing here. Or at least very little. I just watch this stuff very very generally -- not even close to the analytics I do here on the blog -- and then I adapt as needed as things change. These charts and sims are mostly just a hobby. It's like my 75 yo brother that builds and runs N-gauge model train sets on a table in his basement. That hobby does not attach to reality too much. It is just an odd thing he does in his spare time at which some people might laugh. I don't. It's a well run table. Plus he owns an actual railroad in IP terms and was in the line of consideration for CEO of Amtrak once upon a time. Amtrak could have used him given what I know of subsidized money-losing quasi-public institutions.
------- notes ------------------------------------
[1] Frankly I am super skeptical of utility evaluation even though I do it. It is common in the literature and it seems to bend spend evaluations in a constructive way. Think about it this way. What is the optimal spend rate looking at it from an accumulation, or even a decumulation, perspective if we only look at the portfolio at the end. It is probably zero, which is dumb. There a) has to be consumption, and b) it can't be zero and can't be super high. Econ Utility is helpful here even if I am dubious; I perpetuate that of which I am skeptical but whatever. Anyway, I effectively have two readers now: one supportive, one moderately critical in what I assume is a constructive sense. Both are necessary and neither will, I hope, be offended here. The other way to look at it is to strictly look at portfolio longevity, which I like, but even that doesn't always get me all the way to what I want to see. Support or critique away as you wish.
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