Modern longevity shifts vs simulated fail rate estimates

In this link to a Kitces.com article, I highlighted their point of view on the current trend in longevity shifts.  I think their analysis is correct and important.  To quote:

One of the most important assumptions in any financial plan is life expectancy. Assuming too short of a lifespan can result in an excessively high withdrawal rate that depletes all of a client’s assets prior to death. However, despite a desire from financial planners to avoid ever seeing clients run out of money, assuming an unrealistically long lifespan is problematic as well. Excessively low withdrawal rates may lead to a lower quality of life in retirement, a larger than desired legacy inheritance (which the heirs probably won’t complain about, but the retiree might regret!), unfulfilled life goals, and—assuming there may be a relationship between life satisfaction and longevity—possibly even a reduction in lifespan itself!

The basic point of the post, if I have it right, is that while terminal age expectation might be pegged around where it's always been, around 115, the modal expectation is shifting upwards. Or rather the point is that the average longevity expectation is moving up but nothing else much is changing.  The chart from Kitces on this that sums it up is here:

So I decided to see what this "shift" might portend for retirement fail rates in simulations.  This is what I came up with.  First I took standard longevity assumptions (like in the SS table) and then shifted them like the Kitces analysis.  Then I took my simulator[1], which uses SS2013 Life table data, and fitted a Gompertz distribution that looked "close" to that SS expectation (and here we have to say that I am embarking not on science but on an impressionistic riff on retirement finance that has little to do with science, but...let's proceed anyway)

Here is what the probability distributions might look like when "shifted" more or less how the Kitces post pushes it but now rendered as probability density functions. So, the modes are later here and the dispersion gets narrower.  If the expectation were to ever be singular, say everyone keels over at 100, then there would be no distribution at all but a vertical line at 100:

• Blue - SS table density function for a 58 year old, 20,000 samples
• Red - Gompertz distrb with 85.5 mode and a dispersion of 10 (looks like a "fit") (20k samples)
• green - Gompertz distrb with 90 mode and a dispersion of 8.5
• purple - Gompertz distrb with 95 mode and a dispersion of 7
• black - Gompertz distrb with 100 mode and a dispersion of 5

Then I ran 20,000 monte carlo simulations at red, green, purple, and black to see what happens.  Actually I knew what would happen if, on average, we would expect to live longer.  But...I ran it anyway to see how big a deal it is and whether it is non-linear.  This is what I came up with: 

These are the fail rates for the the 20,000 data-pairs of terminal wealth and terminal age (separately at each modal shift point) so they include all of the terminal ages from youngest to oldest.   If longevity expectations were to be fixed (and lower) then maybe fail rates might be not as upwardly-drastic as in this graph but that is a different analysis (these are the fail rates for all of the terminal age cohorts in the analysis including the very longest...so this is very conservative).  In the end the conclusion is fairly simple: if we expect to live longer the chances of running out of money get higher.  No rocket science there, eh?...

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[1] Using more or less generic assumptions:

20,000 sim runs done in a sampling-style approach

Start age = 58  

$1M endowment

4% inflation adj spend rate

Spending variance with custom probability density and skew

Spending has a slight 1% downtrend  

There are no spending shocks in these runs

There are no spending inflection points, three are available

Portfolio is 60/28/12 stock/longbond/shortbill

Bonds are modeled as total return using Stern data from Damodaran

Tax advantaged accounts not modeled

I threw in 1k in Soc Sec at age 70

No annuity or pension

Taxes (a factor is in there but it's rudimentary)

Fees = 60 bps

There is a 2% portf return suppression for 1st 10 yrs

Longevity is capped at 115

If needed I use a PV discount rate of .03