Volatility and Stochastic Portfolio Longevity

This is an extension of a prior post illustration of Withdrawal Rates vs. Portfolio Longevity.  Without (too much) commentary, this is another heat scatter, this time for "input" standard deviation vs. portfolio longevity, where

- returns are randomized normally with a real return of .04
- standard dev "input" is uniformly distributed between of .05 and .40
- withdrawal rates are either .03 or .07 with an addition for .12
- a mini sim of the number of years a portfolio lasts is run 500,000 times
- "150 years" stands in here for infinity

The dotted boxes are not analytical but rather aesthetic. They are intended to draw the eye to what I'm thinking about. The conclusions, if I can even make them, might include:

- I'm left vaguely wondering if I mis-coded this...
- lower spend rates last longer, obviously
- lower spend rates seem to insist on lower vol strategies
- higher spend rates look more horizon-dependent.
      - short horizons want lower vol
      - immortals, early retirees, and endowments might need the lottery ticket of higher vol.
- I probably need to think about this more...


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Just to extend this, here is a 12% spend which seems to augment the fuzzy point I was trying to make: