One More Thought on RH40 - Dynamic Longevity

I was thinking about one more thing in evaluating my formula [ Age / (40 - Age/3)].  Longevity estimates are dynamic in real life but I have not been comparing RH40 to retirement calcs where Longevity changes with age. In other words, what would happen if I put RH40 up against a really simple model with dynamic longevity. Right now, using Blanchett's simple formula, I hew to a fixed "to-95" assumption.  But median terminal for someone my age is somewhere around 81-83 depending on the life-table used. Joe Tomlinson once told me maybe 88 is better.  Many retirement writers say use 95 just to be conservative.  But it's not just about setting a single assumption that is conservative. The median expectation for longevity extends out for each year survived while the survival probabilities still continue to go down. For example, using the SS 2013 life table the average expectancy at 95 is ~98, not 82 anymore, even though there are fewer and fewer survivors each year.


So let's do this.  I'll run two dynamic Blanchetts (60/40, 90%PoS, -.01 alpha). In the first one I'll set terminal age to 95 from age 50 to 80 and then from age 81 I'll scale it up to 100 by 100, In the second one I will set terminal age to 88 starting at 50 and then scale it to 100 by 100.  This linear hack is not perfect but it'll do.  The goal here is to compare RH40 to a set of "reasonable" assumptions in Blanchett's formula while trying to make longevity estimates a little more realistic using a dynamic approach that is conservative but not too unrealistic. In Figure 1 it looks like this:


Figure 1. Blanchett's formula with terminal age set to 95 from 50-80 and then scaled up to 100 at 100

Red is RH40

Blue is Blanchett 

Figure 2. Blanchett's formula with terminal age set to 88 at 50 and then scaled up to 100 by age 100

Red is RH40

Blue is Blanchett

Then, just for fun and because I wanted to throw in some legit simulation in addition to Blanchett's formula, I decided to turn on the stochastic longevity in my simulator rather than use a fixed age 95.  I ran it at 50, 60, 70, 80 and 90 with the following assumptions and then interpolated in between:

• 1M endowment
• Gompertz model for longevity with mode = 85 and dispersion = 10
• 60/40
• Constant inflation adj spend
• No return suppression, spending var, spend trends, or spend shocks
• No SS
• 1% fees and some tax effects
• Return distrb based on historical returns
• Spending tuned to generate ~95% success rate

You'll note that this is a little bit of a cheat because the spend rates are those that generate a 5% fail (not 10% as in the Blanchett formula) but what the heck, it makes the lines line up and it makes me a little corrupt in my data analysis.  But I thought the shape of the curve was interesting anyway. That and the implication is that RH40 is conservative rather than risky...

Figure 3. RH40 vs. RiversHedge Longevity Varying Simulator.

red is RH40

black is RH longevity-varying simulation

I thought I'd try to be more consistent in Figure 4.  Here is the RH40 rule again where I've compared it to several different styles of retirement calcs where dynamic longevity is in play but now, where possible, everything is tuned to the same assumption of a 95% success rate, which is about how conservative the RH40 seems to be.

Figure 4. RH40 vs some big guns.

Green - Blanchett's "simple formula," but varying terminal age
Grey - Monte Carlo Simulator with stochastic Gompertz mortality
Blue - Kolmogorov equations from Milevsky's book 7 Equations
Dotted - Gordon Irlam's Merton-based annual portfolio consumption equation
Red - The humble RH40 rule of thumb

Any Conclusions?

Actually I gotta say "not too shabby for a made up rule of thumb" especially when using the hyper-conservative to-95 assumption for most of the way in Blanchett.  Obviously there will be poor fit when moving away from the one Blanchett example I was using.  Throwing it against my simulator, though, was icing on the cake when it comes to visual confirmation. Seems like it's pretty good for a quick and dirty "pocket formula."