A forward walk through the 70s using two types of dynamic asset allocation

Walk-forwards are the anecdotes of the financial modeling world. At worst they set you up for a naively imagined future that will never repeat but can certainly get worse. At best I suppose they provoke a type of useful anti-nostalgia for a past that was bad enough to pay attention to lest it sticks its nose too far under the tent-wall again.  Better modeling options may lay in something like boot strapping history or engaging in open-ended and less-constrained simulation or even scenerio-based strategic planning. But even these can be false orbuculums where the expectation extracted over 10,000 iterations can "bury the lead" where the lead can be conceived of as the special case in which all iterations and paths are bad news of a particular shape. In this case the shape in question is the 1970s, a period of poor returns and high inflation that's more fun to play with than the GFC.  Plus I lived through it. I remember.

This time I'm throwing some simplified forms of dynamic allocation against the 70s to see what sticks to the wall. I'd been playing around with some ideas on glide-paths in an ongoing dialogue with David Cantor, a dialogue that will bear bigger fruit later.  This time it's just the 1970s walk-thru.


The 70s game set-up

- Start with $1M in 1964 and end in 2014
- Assume age 50 and assume full foreknowledge of surviving 50 years
- Evaluate each scenario based on lifetime consumption utility
    o utility is not survival weighted since we assert knowledge of 50 years certain
    o the expectation for utiles over 50y is re-rendered as a certainty equivalent (CE) spend
    o consumption, when it crashes has a min 10k real to reflect SS or charity or something
- Use a base case allocation of 50% SnP and 50% .5x10yr+.5x3mo treasury
- Have a scenario for a fast glidepath of 50/50-->90/10 over 10 years
- Have a scenario for a slow glidepath of 50/50-->90/10 over 20 years
- Change the spend rate from 4% to 3.5% in .1 increments
- Have an unrelated outlier scenario where spending and allocation are fully dynamic:
    o use a lifetime consumption utility simulator every 5 years
    o wealth and assumptions reset to what obtains at time t, except prospective inflation I kept at 3%
    o reset spending and allocation based on generalized results year 6, 11...
    o the spend rate is chosen based on the highest spend rate of 10 highest CE spends
    o allocation is chosen based on the optimal 1 CE spend rate
- Spending is constant except for the outlier scenario
- 6 spend rates x 3 allocation styles + 1 outlier scenario = 19 "Series" or scenarios
- One year steps using Stern School data from A. Damodaran
- Beginning of period spend

The game "win" criteria

- The highest CE spend over 50 years given risk aversion parameters of 1 or 3 wins
- Tie-breaker is highest residual real wealth in 1964 dollars and/or fewest years insolvent
- Residual wealth, if any, measured in '64 dollars.

The game output 

The time series over 50 years of the various consumption paths implied by the table would look like this:

Discussion

- One has to buy in to Utility theory to have this make sense, which is not always a given.

- It should be clear, but maybe hard to see, that the reduction of spending helps at least as much as dynamic allocation (depending on the size of step considered), though the dynamic allocation clearly helps quite a bit in the local case of at least a couple lower spend rates.

- Lower spend rates show rising CE spend over the 50 year lifetime but only up to a point. Would be different if 30 years or random longevity. This is an early retiree game if you hadn't noticed.

- The dynamic spend and allocation "outlier" shows well in this because it does not crash and has high late spending. BUT, from a policy perspective, if we say the 4% lifestyle is the most attractive ex-ante, then the dynamic spend that cuts that in half might be unacceptable and benefit from a minimum spend. Also, there is going to be in both modeling world and in real world some impatience preference for near years vs far when the horizon is shorter or uncertain.  That late spend at 90-100 may not be as fun as it is now.

- Observed real-life consumption in real terms tends to decline over time until the 80s and 90s and then rises with health expenditures, a point made by D Blanchett and repeated recently by M Finke in a podcast.

- I declined to do a dynamic feasibility test or fail rate test at the 5 year marks due to laziness. Next time.

- For a risk aversion coefficient of 3 (no idea what these are in real life if even measurable. I often guess mine at 2 for modeling purposes) a 148% increase in the lifetime CE spend in exchange for a little prudence in consumption and some willingness to change an allocation risk profile over time -- given the anecdote of the 1970s -- seems like a big win for a small price.

- The failure of the "outlier" scenario to evaluate as "best" or to provide a stable consumption path notwithstanding, I would still periodically test my situation every few years for things like sustainability (fail rates), expected consumption utility, feasibility, portfolio longevity percentiles, "perfect withdrawal rate" percentiles, etc etc along with any movement or acceleration in any of those.   I would most certainly adapt.

- Why those particular glide paths? Arbitrary. Ad-hoc. To borrow a phrase: not necessarily "mathematically necessary," but suggested by a path selected on another retirement blog.

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- the CRRA function used (without debate, though perhaps we should) to evaluate spending is in this form:

| gamma < > 1

or U(Ct) = ln[C(t)] | gamma = 1

- The inverted form to extract the CE spend, if I can do it like this for consumption (a unit of wealth we can say), is:

 | gamma < > 1

or, CE(t) = e^E[V(c)] | gamma = 1