Apr 17, 2018

3D utility surface in WDT model: return vs spend rate

This is pretty predictable, I think, but I wanted to see it anyway. Go to "3D "utility surface" in a Wealth Depletion Time model: spend rates vs annuity" for background. This time I wanted to see what happens in terms of different combinations of spend rates and really low real return assumptions in the absence of annuitization.  The outcome made sense before I even did it but it was worth looking at.  The outcome in the chart looks choppy and weird, I presume, because of rounding and threshold effects but could also be due to modeling or data-entry errors. No idea yet and I probably won't go back to figure it out unless I think I made a truly stupid error. I think the overall picture makes sense though.


Assumptions

Age. start = 60, end = 120
Wealth. start = $1M
Spend rate. variable: .03 to .05 in .02 increments, growth at .03., forced to income at WDT
Spend inflections. not used
Returns.
   - .03 inflation factor embedded
   - real return is varied from .025 to 0 in .001 increments
   - .01 penalty for taxes and fees is added.
   - Simple sequence risk modeled to age 95 +/- .005
   - This exercise explores the lower half of an expected distribution over ~35 years if real
      returns were to be .03 static in the forthcoming future (or .025 after we try to acct for some vol)*
Social Security. 12k (fv) starts at 70
Annuities. Ignored in this run (zero)
Annuity Load. 1.10 + x
Risk Aversion. gamma = 1
Subjective utility discount. .005
Lifetime. Probability weighted. If a hard date is used it is = 95. Not stochastic here.
Inflation. .03

Surface


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