Supplement to my "playing a feasibility game against the 1970s"

This is a follow-up to "Playing a feasibility game against the 1970s." I can't spoon feed the set-up and background here so you might have to go read the previous post. In this post I just wanted to augment the last one with some context that included showing some forward looking dynamic sustainability and feasibility estimates for each year for each player.


Some notes:

1. By feasibility I mean an actuarial estimate of whether a portfolio spending plan stacks up in some present moment by comparing currently observable monitizable wealth to the present value of future spending (or the price of an equivalent SPIA that would defease the spending). This can be at t=0 or t="some other time." See prev post for the math. Note that the chart's blue line is W/F which is wealth at some time t divided by an actuarial estimate for future spending (or an annuity proxy in income terms). The goal is W/F > 1 but that is not 100% required all the time.

2. By sustainability I mean a forward-looking analysis of how a spending program might play out in the future by using some type of analysis or simulation to gauge the expected likely success of the plan. Typically this kind of thing is measured in "fail" or "ruin" or "shortfall" rates at some horizon.  Here I am doing something similar. I am estimating at any given time t of a plan, the "lifetime probability of ruin" (LPR) for the then-future-age and the then-future-conditional-survival-probabilities and the then-future-expected-spend-rate. The advantage here is that LPR takes into consideration the full term structure of future conditional mortality expectations as well as the full constellation of asset exhaustion possibilities in the same projection (this is done at each future age, if I haven't mentioned it yet). LPR will give roughly the same answer as a Monte Carlo sim, I just trust it more because it is more robust in its conception. Ignore for now any pros and cons of using "ruin rates"... The math form is like this
             
where g is a representation of a mini-sim for the probability of portfolio longevity (fail) at some time t from t=0 to infinity and tPx is the conditional survival probability for weighting g using Gompertz math (mode 90, dispersion 8.5). tPx is tuned to the SOA IAM table. g uses a real return expectation of 4% and a vol expectation of 12% and a spend tied to the spend rate expectation of the player at time t given the spend program and the then-current endowment. The return assumptions are arbitrary and illustrative only. None of this is remotely supportable but it does make a post work for a moment.

3. The charts happen to have an illustration where there is a threshold related to a 30% fail rate. This is totally arbitrary. There is no research that I know of (yet) that has a good case for one threshold vs another. I personally get uncomfortable over 10%. A Twitter troll once suggested to me that 40% is better or maybe 50%. But who trusts twitter trolls. 30% is there in the chart just to catch the eye.  Btw, remember that anyone that recommends using high fail rate thresholds is like that friend that tells you to skate really close to that hole in the lake because the ice is really cool and smooth there...but then you notice when you look back that they are not skating along with you. Risk is not linear from shore to hole's edge...

4. Recall that feasibility is defined in the previous post as W/F where W is wealth at time t and F is the valuation of a spend liability at time t for someone aged x, which can also be conceived of as the price of an SPIA at time t for someone aged x that needs income close to F to support the consumption plan.  W/F should be, but doesn't have to be, >= 1.

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Left Axis - Feasibility ratio W/F where W/F likes to be > 1 but doesn't have to be.
Right Axis - LPR is lifetime probability of ruin. Lower is better but we use 30% as a guideline here.



Player A

Player B

Player C

Player D

Comments

I'll leave most of the comments to the previous post. The same evaluation criteria apply (portfolio longevity, lifetime utility, likelihood of having a little money left at 100). The only additional points I'll make here are:

• Imagine that one has a threshold for forward-looking fail rates of 30%. How many years are over 30% and how many of those years are contiguous? How many years are over 50%!?
• Given that a couple of these players are well below their preferred 4% lifestyle in the years when fail rates go sky-high, do they really have any room to cut spending? Do they really have the opportunity to go back to work at the age that shortfalls happen? My guess is "not really."
• How would the sequence have "felt" for each player? How much real stress would there have been at home?
• Player D did not "win" the formal economic utility game but you might see why I could start to have some affection for his or her approach. 
• Contrary to what I believed as recently as 5 days ago, sustainability is not feasibility and vice-versa. One can prove by stochastic calculus that they look the same but it feels like they aren't. Here. 
• I'd love to see various back-fit ad-hoc spend rules out there in the world stacked up against the 70s' (or random simulation or Venezuela or 1990s Japan or...) with a similar eval framework using actuarial feasibility and a rigorous sustainability calc. Without that I frankly don't trust people.  That's a personal problem.