Walking back my comment on fail magnitude...

In a recent post I played down the concept of fail magnitude. This was said in the context of times when one (me) is strictly looking at lifetime and portfolio longevity probabilities rather than when looking at the difference between a fixed planning date (say "30 years" or maybe "to age 95" or something) and when a simulator says you might go to zero or below some threshold. Without the hard stop of a specific age or a planning duration it seemed like a slippery concept.  I'm now thinking I was misguided.

In reassessing my opinion I decided to surrender and say it probably is important and I just needed to figure out how to measure it in the context/tool I was using.  If I figured this out in my traditional MC simulator, I can figure it out for my ruin estimation tool, too.

In the end it is as simple, I suppose, as just picking a threshold of interest. In the ruin tool I'm working on now, that is more or less arbitrary so I just created a boundary that I can change as needed later. In this case I decided to measure the distance in years between when the cumulative probability of portfolio failure is greater than, say, 5% and the point where the likelihood of still being alive is less than 5%. Arbitrary but it at least tells you something.

In the following chart I used some generalized placeholder assumptions (4% spend, age 60, 4% net real returns, 10% vol, modal life expectation of 90, etc). I set the threshold for magnitude at .05 for each distribution and let it run.  It looks like this. The arrow is drawn not graphed:

The lifetime probability of ruin comes out here to be 12.9% and with the threshold set as described there is a 17 year distance between the selected boundaries.  By itself that is probably not very meaningful. In comparing two strategies it might be more useful. But either way this adds a little more information, I think.  My guess is that the "area" under the green and blue would be more interesting in terms of a magnitude metric but also pretty hard to interpret.  "Years" has a more human meaning so I'll stick with that. I don't do a ton of strategy evaluation anyway so it probably doesn't matter much for now.  I also probably need to figure out a meaningful threshold level.

The other thing I want to add at some point is some type of "free boundary" measurement concept where one gauges, in any future year, the distance between some percentile in the portfolio distribution for that projected year and the cost to annuitize a baseline acceptable lifestyle at that age. The option to step out of a self-annuitization process as things go south but while one still has the capacity to lock in a pooled risk lifestyle probably has a ton of value (assuming one started with capacity, I guess). But that is another post on another day.