Oct 23, 2020

Real option value of spending less over 20 year horizon

The basic premise here is me trying to figure out the "real option value" of different allocation and spend choices over a 20 year horizon (65->85...ie when I might annuitize stuff) where the strike is the then cost of annuitizing $1 of consumption conditional on a longevity estimate at age 85 plus some margin of error (the strike). 

The Framework

The framework is as is articulated in the following paper

                      The Intuition Behind Option Valuation: A Teaching Note

and where the basic formulation is as follows

                      R = ∑ { P(MT) * PV(max[0, MT - k]) }

which is imperfect because there is no real way to hedge or short so we must work with simulation rather than normal option theory.  

The Setup 
  • Wealth is in units = 1/spend so, say 1/.04 = 25 etc
  • Horizon is 20 years which is me going from 65 to 85 
  • Allocation is done in 10% steps using MPT on the following assets...
  • Asset A N(.035,.04) and Asset B N(.10,.18) but adjusted for 3% infl and -.10 corr
  • Strike k is "9" in units, which is an estimate of the annuity
    value of $1 real at age 85 x 1.5 (= margin of error)
  • All assumptions are arbitrary and illustrative only. 
  • Believe none of this except maybe the "movement" or shape of things
The Goal

The goal is to estimate the 20y real option value of wealth in units based on the framework and setup. This is super rudimentary and a spreadsheet operation that is pretty manual.  The real goal is to see what we give up for spending more (or less) over the interval in visual, not quantitative terms. 

The Output


Some Random Thoughts 
  • I had no idea what this would look like. Actually I thought that higher allocations to risk would suck but I guess risk is risk and options "like it" if it pays off in the expectation. 

  • Higher spend rates totally give away optionality at age 85, an age where, frankly, I might not really care. My mother was demented at 82 and I expect something similar for myself though I am trying to put that off. 

  • Lower spend is therefore a transfer, a gift, to my future self of "optionality." This is important. I have been chastised and shamed by ex girlfriends, wives, and advisors for my frugality. "Live a little, bro" "you are under-living, a life-sucking kill-joy." These are not exaggerations but real comments from hangers-on and parasites (ha!).  What this really is is me standing next to my future-self and my kids and saying "I spend less and therefore here is a beautiful gift from me to you, please, please enjoy it as much as you can because I have sacrificed myself for you because I could see all of this in 2020..."

  • The optionality is non-linear for each increment of conservatism: the gift to future me and kids grows at an an increasing rate. This makes sense, right?
     
  • High spend rates lose their optionality almost entirely.  Me? I love optionality. My ex wife, girlfriends and advisors didn't care because they literally have no skin in my game.
     
  • A 0% spend rate would preserve 100% of my optionality but would also be stupid because I have a life to live. This is where the much debated "consumption utility" thing kicks in and tells me that there are spend rates within a zone that make more sense so that this optionality post is kinda dumb but not totally irrational. 




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