Another Simple Formula for Spending or Ruin Risk Estimation

Here is another "simple formula" [1] that I picked up from a 2005 CFA article by Milevsky and Robinson.  They present there a way of estimating the risk of ruin without simulation.  The advantage here might be that the assumptions become more transparent and simple, it provides "intuition on the financial trade-off between retirement risk and return" (Milevsky), and one is freed a bit from advisors bearing black boxes. The con might be that it might cut some corners and does not match reality very well but then no simulator does that either.  I view these simple formulas and rules of thumb as useful tools when one is trying to triangulate in on retirement issues by using many tools and points of view to come to a broader conclusion about impending risk.  None of them individually has an "answer." All of them together can help a little.

The main formulas from the article that apply here are as follows but don't worry, the spreadsheet implementation is relatively simple. SPV is "stochastic present value" and w is wealth. Equation 8 interprets in simple terms as  "the probability that the SPV (of spending) is greater than the initial wealth or nest egg" but I would defer to the article for where all this comes from and what it really means as explained by someone who actually knows the underlying math and principles.  Me? I'm just along for the ride.

The main point of this post is not to examine the math but to take the math from the article and from Milevsky's sister essay in the book "Retirement Income Redesigned" by Evensky and Katz where the Excel implementation is not immediately and directly clear and help to make it more clear. The following is an Excel interpretation/example based on what was presented in: 

A Sustainable Spending Rate without Simulation

Moshe A. Milevsky and Chris Robinson, 2005

CFA Institute Vol 61 Number 6

https://pdfs.semanticscholar.org/dade/758022b73607894e15f1f0d9b217e09a3388.pdf

I have an older version of excel because I like the older menus and hot keys so for new versions the formulas are more likely to be gamma.dist() and gamma.inv().

I don't know if this succeeds in clearing it up but there it is.

See also: 5 simple formulas for retirement are now 9

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[1] I call it simple. It looks like gnarly stuff depending on one's background but either way the Excel version is pretty easy if you know Excel.