(Stop me if you’ve heard this one.)

My son and I had just shot a round of sporting clays (“catch-and-release hunting”) on a hot summer day and we stopped into City Tap in Pittsboro on the drive home for a couple of ice cold, locally brewed adult beverages and a lunch of disgusting chili dogs, and by “disgusting” I mean “outstanding”.

Here in the South we often have a couple of beers after shooting because several generations of experience have taught most of us that having the beers

*before*shooting is sub-optimal in so many ways.

I soon began complaining about the quality of much of the retirement finance research dealing with portfolio survival, as clay shooters often do (OK, not really). My son is on a “Physician-Scientist” track and spends much of his time researching patient survival. He immediately noticed that portfolio survival research isn’t terribly different than patient survival research and that medical research has better tools to study this than we have in financial research.

[Tweet this]Portfolio survival is a lot like patient survival but medical researchers have better tools to study it.

We had a “you-got-peanut-butter-in-my-chocolate” moment and decided to co-author a paper studying portfolio survival by using two medical research survival study tools, Kaplan-Meier analysis and Competing Risks analysis. Our paper hasn’t been published, yet, but here’s a sneak preview.

In clinical trials, information on some patients will be incomplete. Some patients will drop out of the trial, move away, or the trial will end without discovering the patient’s eventual outcome. Kaplan-Meier analysis is a statistical technique that makes as much use as possible from the incomplete data available for these patients. Kaplan-Meier analysis also removes patients who are no longer at risk from the calculated probabilities.

Kaplan-Meier analysis divides time into intervals and for each interval survival probability is calculated as the number of patients surviving (or portfolios, or whatever is being studied) divided by the number of patients still at risk. In portfolio survival studies, simulated retirees who die or go broke are no longer at risk of going broke before they die. They should be removed from the denominator of the probabilities. (This is referred to as “right-censoring.”)

The probability of a patient or portfolio surviving to any point in time (or age, in our study) is estimated from the cumulative probability of surviving each of the preceding time intervals. This all no doubt sounds very complicated, and it is, but it is easier to see if we look at a Kaplan-Meier curve.

The following graph is the result of a portfolio survival study assuming annual withdrawal rates of 3%, 4% and 5%. The analysis used actuarial tables to generate random lifetimes for a retired couple of the same age retiring at age 65. (Double-clicking any

*Retirement Cafe´*graphic will enlarge it in a separate window.)

To read the curves, for example, a retiree who withdraws 5% annually from her retirement savings portfolio (blue curve) has about an 80% probability of portfolio survival

*if she survives to age 90*. With 4% withdrawals (green curve), she has about a 93% probability of portfolio survival if she lives to age 90.

Reading the curves more generally, retirees don't outlive their savings before about age 80 to 85 assuming any reasonable (say, 5% or less) annual withdrawal rate. Then, the percentage of outlived portfolios heads south, the higher the withdrawal rate, the steeper the fall.

Portfolio survival studies typically calculate a single lifetime probability of survival, commonly quantified around 95%, that doesn’t show how that probability decreases with age, or the effects of random lifetimes. Kaplan-Meier curves do.

Most portfolio survival studies calculate absolute "lifetime" probabilities, or the percentage of all retirees in the study whose portfolios can be expected to fail at some point in their lifetimes. Kaplan-Meier analysis calculates conditional probabilities, meaning the percentage of failed portfolios expected among retirees who are still alive and haven't already depleted their savings.

There is a big difference between losing most or all of your retirement savings, thereby losing some standard of living, and experiencing financial setbacks so dire as to lead to bankruptcy. In my previous post, Why Retirees Go Broke, I suggested that very few retirees will go broke due to sequence of returns risk though there is a possibility of losing standard of living for that reason. Our portfolio survival research, combined with bankruptcy rates by age, is part of that argument.

As the following graph shows, few simulated portfolios are outlived before age 80 to age 85 (blue curve) but most bankruptcies (red curve) are filed before that age – portfolio ruin accelerates about the same time that new bankruptcy filings become negligible. By about age 83, nearly everyone who is going to go bankrupt has, while portfolio ruin has just begun. Thus, the probability that a retiree filed bankruptcy due to sequence of returns risk is quite small – retirees go broke for several reasons, but sequence of returns risk doesn't appear to be a major contributor.

(Note the vastly different scales of the

*y-*axes. Portfolio survival probabilities range from about 80% to 100% in this scenario while bankruptcy probabilities are always less than half a percent. I present the graph this way to emphasize the timing of the two events.)

We applied Kaplan-Meier analysis to a portfolio survival model that included random lifetimes to provide greater insight into the portfolio ruin process. This should help you understand how your risk of outliving your savings –

*as a function of market volatility*– will change as you age. (There are other "non-market" reasons that you might deplete your savings, like devastating medical expenses. Portfolio survival studies typically only look at ruin due to poor market returns.)

We also considered another statistical method from the medical research field, competing risks analysis.

I’ll discuss that in the near future.

Special thanks to my son, Cary, of whom I am obviously ridiculously proud, for collaborating on this research and for helping me explain it in a blog post.