Sunday, August 14, 2011

Retirement Withdrawal Rates 2.0: A Preview

Sometimes things move very quickly, and when I’ve gotten some spare moments over the past few days, I’ve been doing a lot of programming.

For one thing, I can now incorporate mortality rates and lifespans into my analysis of retirement withdrawals rates.  As I’ve discussed here before, I’ve always just considered fixed retirement durations, and thought that conservative retirees should consider that they will live a long time even though the chances of this happening are rather low.  Well, actually the safe withdrawal rate for a long time horizon combines a double-dose of worst-case scenarios that should be independent from one another.  It is rather unlucky to retire at a time that will experience a really low withdrawal rate.  And while it is great to live a very long life, it is rather expensive and calls for a lower withdrawal rate earlier on, and the chances of it happening are low.  So it may be too conservative to plan for both of these independent low probability events at the same time. I think that is the point of those who use mortality rates in their analysis.

So now, using the Period Life Table 2007 from the Social Security Administration, I can make Monte Carlo simulations for ages of death by randomly drawing numbers to determine how long past retirement each simulated individual will live.  Some will pass on during their first year of retirement, while others will make it past age 100 (in my 10,000 simulations, one guy made it to 109). These random lifespans are then combined with random simulations for asset returns.  In this framework it is still possible to enjoy a very long life while at the same time falling victim to a low sustainable withdrawal rate, but the low probability of this happening will be more adequately reflected in the results.

Below is a figure showing the probabilities of running out of assets prior to death for different withdrawal rates and asset allocations (large-cap stocks and long-term government bonds in this case --- I know, I know, the assets I use are constantly changing but in this case I’m working within the confines of another paper I’ve been studying).  I had a figure like this when I discussed “Guidelines for Withdrawal Rates andPortfolio Safety During Retirement” by Spitzer, Strieter, and Singh. That earlier figure was for a 30-year retirement duration. The figure below actually takes into account about lifespans by using a random age of death in each simulation which fits the distribution of the observed mortality rates.

As I discussed in the earlier blog entry, this type of figure basically provides a very nice representation of “Retirement Withdrawal Rates 1.0.” It extends the ideas of Bill Bengen and the Trinity Study and basically tells you your chances for failure (or success) with various withdrawal rates and asset allocations, using Monte Carlo simulations instead of historical simulations.

But in looking at this figure, a prospective retiree is left with many questions about a reasonable course of action:

1. What is an acceptable failure probability, anyway?  1%?  10%?  …

2. How does the acceptable failure probability relate to one’s tolerance for risk?

3. Wouldn’t having other sources of guaranteed income (such as Social Security or employer defined-benefit pensions) provide one with more flexibility to accept a higher failure rate since running out of wealth would not represent a complete disaster?

3a. Related to this question, what percentage of wealth should people consider annuitizing in order to lock-in some guaranteed lifetime income?

4. Can someone place less importance on spending at later ages either because they want to account for the lower chance have of still being alive at later ages, or because they just happen to have a stronger desire to spend their wealth sooner rather than later?

5. I’ll add another question because it is something I am in the middle of working through right now as well, but for a different paper: Should we be assuming that future asset returns will follow the same patterns as in the past historical record, or might it be better to use a different set of assumptions about this?

A few days ago, I came across a paper that provides a framework to help answer questions 1-4. I should say, the authors emailed the paper to me. Their paper will not be published until October and there is no version circulating on the Internet as of yet. But now I’m working with the authors to develop some follow-up studies.  We already have some results.  Now that I’m working with co-authors, I’m less free to blab about findings as soon as I have them. But I am quite excited about this and hope to be able to share some more in the coming weeks…


In the comments below, Mike Piper asked about whether the figure was for male survival probabilities, or possibly for joint survival probabilities for a couple.  This is a good question, since couples will be more interested in planning for the full lifespan of both members, rather than just for one member. Especially, females tend to live longer than males anyway.  I updated the above figure to indicate it is for males.  Below is the figure for an opposite-sex couple both aged 65.  Though I could adjust the withdrawal amounts to be less when only one member is still alive, this particular figure assumes that withdrawal amounts are the same regardless of whether two or one individuals are still alive. The lifespans of each member are assumed to be independent from one another (no one is dying from a broken heart), and one is derived with male mortality data while the other is with female mortality data. As can be expected, failure probabilities increase since more time will tend to pass until both members have passed away.



  1. This is great reading. :)

    Just to check, the chart uses mortality rates for a single individual? If so, I'd be curious to see how significantly it changes for a married couple age 65.

  2. Mike, thanks!

    Above you can now find a chart with your request.

  3. Wow, thank you! As always, I find your work quite informative.

    Also, those numbers really don't look so bad.

  4. Thanks, and yes, these failure rates don't look so bad compared to a fixed 30-year retirement period. With this data, there is only a 6% chance that a man will live for 30 years past age 65, while there is a 17% chance that at least one member of the couple will make it that long.

    The shorter average retirement durations allow the failure rates to decrease. On average, men who reach 65 will make it another 17 years, and at least one member of a couple will make it at least 24 years.

  5. Great research. Thank you for the information. It's amazing how a "rule of thumb" like the 4% Rule can provide a fair amount of certainty for someone who wants a quick estimate.
    Thank you.
    Ken Faulkenberry

  6. Ken, thank you.

    And Mike, thank you very much for mentioning this on your very popular blog.

    For anyone interested in the issues here, I cover this theme again in more detail in this blog entry:

  7. Any chance you would be willing to run these for single women? Thanks.

  8. Petunia: Sure, I made a new blog post about this now which includes your request and some other information too.