Wednesday, June 22, 2011

Retirement Withdrawals and Leftover Wealth

A recent article from Forbes about pioneering withdrawal rate researcher William Bengen has triggered some interesting discussions, first at the Bogleheads Forum and then at Michael Kitces' blog. The issue regards Bill Bengen's statement in Forbes that retirees using a 4.5% withdrawal rate will still have at least their initial wealth at retirement remaining after 30 years in 96% of cases. Dick Purcell tested this with his Portfolio PATHFINDER software for Monte Carlo simulations and found a success rate of 58%, not 96%.

I have great respect for William Bengen's research contributions about retirement planning, and have modeled some of my own studies after his approach.

However, while this statement he makes is technically correct, I find it misleading in two ways:

1. This is referring to nominal wealth remaining after 30 years, not wealth remaining in terms of today's real purchasing power.  Due to inflation (which varies over time), having $1 million in 30 years means something very different from having $1 million today in terms of the amount of goods and services you can purchase.

2. In the research of William Bengen and the Trinity study authors, the assumption used is that retirement withdrawals are made at the end of each year, rather than the beginning of each year (or throughout the year).  I don't find that assumption to be particularly realistic and I assume beginning of year withdrawals in my own work.  I usually don't think this assumption is too important to get too worked up about, but in this case the difference is rather important.

I will use an asset allocation of 40% large-cap stocks, 15% small-cap stocks, and 45% intermediate-term government bonds.  It may not be the exact allocation Mr. Bengen has in mind, but it is as close as I can guess based on the information provided in the Forbes article and his highly recommended 2006 book.

Regarding these assumptions, the amount of "wealth" remaining after 30 years is more than the initial wealth at retirement in:

* Nominal wealth and end of year withdrawals: 96% of cases
* Nominal wealth and beginning of year withdrawals: 89% of cases
* Real wealth and end of year withdrawals: 69% of cases
* Real wealth and beginning of year withdrawals: 55% of cases

Though it is subject to interpretation and people are free to disagree, I find the 55% number to be the best one to reference in the context of this discussion, not the 96% number.

Also, another ongoing discussion at the Bogleheads Forum is whether historical simulation studies or Monte Carlo simulation studies should be used for retirement planning.  I think that usually the two approaches will provide similar results, though there are occasional exceptions, such as Dick Purcell's finding that historical simulations produce a strong bias against bonds [I discuss this point in more detail in this paper]. But generally, the results should be similar.  Dick has noted that success rates usually are a bit less with Monte Carlo simulations, which I think is understandable given that there are not so many rolling historical periods that fall close to the cutoff point between success and failure.  But there is no real discrepancy on this point.  Dick found 58% with Monte Carlo simulations which corresponds (with matching assumptions) to 55% from historical simulations.

Finally, Bongleur at Bogleheads provides a valid concern that 30 years may not be a long enough retirement duration, and he wonders what happens after 30 years.  I went ahead and made a table showing the evolution of remaining real wealth for up to 60 years.  This table is for the 4.5% withdrawal rate, and the "Real wealth and beginning of year withdrawals assumptions combinations".  This table is rather massive, and you can click on the picture to see a bigger version.  The entire 60-year retirement period can only be investigated for retirement periods beginning up to 1950, but here are the results for remaining real wealth:

As for what to do with this information, more generally, I think that the 4% (or 4.5%) rule does not need to be blindly followed for every retirement.  I think that market conditions at retirement (market valuations, dividend yields, bond yields) can provide a pretty good indication about what the sustainable withdrawal rate might be for a retiree.  I've made this general point in two studies.  First, "Safe Savings Rates: A New Approach to Retirement Planning over the Life Cycle" from the May 2011 Journal of Financial Planning.  Second, "Can We Predict the Sustainable Withdrawal Rate for New Retirees?" which will be included in the August 2011 Journal of Financial Planning.