Thursday, May 17, 2012

Bill Bengen’s “How Much is Enough?”


Bill Bengen has written another thought-provoking and important article. This one is “How Much is Enough?” appearing in the May 2012 issue of Financial Advisor.

With sequence of returns risk, what happens in the early part of retirement matters much more than what happens later. If there is any retiree in U.S. history most at risk of witnessing the failure of the 4% rule, it is those retiring at the start of 2000.

But now we have 12 years of data about the progress of 2000 retirees, and so we can begin to see more clearly about how things are working out.
Bill Bengen’s new article provides such a progress report. I explored similar themes in my article, "Will 2000-Era Retirees Experience the Worst Retirement Outcomes in U.S. History? A Progress Report after 10 Years" from the Winter 2011 issue of Journal of Investing. A lot of my thoughts on this matter can be found in that article.

What I want to look at today, though, is the very nice idea Bill Bengen had for grafting the first part of the worst-case retirement scenario onto the end of the 2000-2011 period to see what might still be in store for the 2000 retiree. As it turns out, things may work out for the 2000 retiree after all. That is not to say that 2000 retirees using the 4% rule were doing something reasonably safe with market valuations so high at the time, but in hindsight things might just end up working out for them.

First a couple of preliminary points. In Bill Bengen’s initial work, he used the S&P 500 and intermediate-term government bonds. Later, he added small-capitalization stocks to the mix and this increased the historical SAFEMAX. Today he speaks about 4.5% as the safe withdrawal rate.


I have replicated his results and get the same findings as him. My only different assumption is that I think it is more realistic to have retirees withdraw from their accounts at the beginning of the year, whereas he has them wait until the end. I use the beginning of period assumption here, but I did double-check with end of period withdrawals and confirmed that I get the same result he describes in his article. When markets are dropping, the SAFEMAX actually is lower with end of period withdrawals. It is better to get your money out sooner! 

We have constant inflation-adjusted withdrawals, no account fees, and a 30 year retirement. I will show results for two different asset allocations. First, a simple allocation of 40% large-cap stocks and 60% intermediate-term government bonds, which I think is a pretty viable asset allocation for retirees. Second, I use the asset allocation from Bill Bengen’s article, which is 35% for large-cap stocks, 18% for small-cap stocks, and 47% for intermediate-term government bonds.

When small-cap stocks are left out, the worst retirement period began in 1966. A 40/60 allocation resulted in a maximum sustainable withdrawal rate of 4.04% with beginning of period withdrawals. Using an allocation of 35/18/47, a withdrawal rate of 4.68% could have been supported.
With small-cap stocks included, 1969 becomes the worst-case year to retire, supporting a 4.32% withdrawal rate.

Now comes the interesting insight from Bengen’s article. What happens if we consider the results for 2000-2011, and then to get a 30-year retirement we add to the end the data for 1969-1986. This is some bad news, as we are adding on the first 18 years of the worst-case scenario in history to the already somewhat miserable 2000-2011 period. Will the 4% rule survive?
With Bengen’s preferred allocation, the answer is yes. A 4.68% withdrawal rate could have been supported (as Bengen notes, this was 4.32% with end of period withdrawals, and coincidentally some of the same numbers re-appear in this table – I checked to make sure there are not mistakes). For the 40/60 allocation, essentially things will work out almost right on target. A 3.98% withdrawal rate can be supported.

And just one final note, for those out there predicting very serious doom and gloom and catastrophe still awaiting the U.S. economy. What happens if we make one more change to an already extremely bad luck case of 2000-2011 plus 1969-1986?  What will happen if economic catastrophe begins this summer (coming to a theater near you) resulting in a 65% stock market drop for both large-cap and small-cap stocks in the year 2012, and otherwise keeping the characteristics of this already quite gloomy scenario? Well, the 4% barrier will be broken, but things would not turn out nearly as bad as you might have expected in such circumstances. Depending on the asset allocation, the sustainable withdrawal rate will turn out to be 3.43% or 3.46%.

Table
Maximum Sustainable Withdrawal Rates
For 30-Year Retirement Duration, Inflation Adjustments, No Fees
Using SBBI Data
Asset Allocation Defined as:
S&P 500 / Small-cap Stocks / Intermediate-Term Government Bonds
Retirement Period
Asset Allocation
40 / 0 / 60
35 / 18 / 47



1966 - 1995
4.04
4.68



1969 - 1998
4.23
4.32



2000 - 2011  plus  1969 - 1986
3.98
4.68



2000 - 2011  plus  1969 - 1986
with a 65% stock market drop in 2012
3.43
3.46


In conclusion, the 4% rule is not safe. It certainly hasn’t worked out well for a number of other developed market countries. I love the U.S.A., but I worry that the country won’t always enjoy the same fantastic financial market returns as it did in the 20th century. Nonetheless, in this particular case, 4% may end up working after all. We won’t know for sure until the end of 2029, but maybe we can relax a bit. Maybe I can make my blog less gloomy and more positive!

The thing about financial markets is that no one can predict the future. The best we can do is to constantly keep learning and test our assumptions and experiment and occasionally change conclusions as new information comes to light. It’s an ongoing process. No one has or will have all of the answers.


It is Optimal for Retirees to Plan for Reduced Spending with Age


Recently, I reviewed the economist’s argument for the existence of an annuity puzzle. Buried inside that post is something rather important, which didn’t receive proper consideration since it was secondary to the annuity issue. I’d like to return to that.

A general assumption in safe withdrawal rate research is that people plan to spend a constant inflation-adjusted amount for as long as they live. That is intuitive and it is connected to the idea of consumption smoothing. People like to spend the same amount over time and don’t want to experience reductions to their standard of living.

However, this spending plan is actually not optimal for any reasonable set of preferences about the tradeoff between spending now and later, even if we assume that future market returns are known in advance.

Before explaining why, I do want to make one point clear: there is an unrelated issue that retirees may gradually wish to reduce spending as they age for other reasons. They just slow down with time and don’t get out as much. I reviewed evidence about that in a recent column at Advisor Perspectives. But please ignore that for now. It is a completely separate matter from what I am about to discuss. (Or maybe it isn’t, perhaps people are just behaving rationally after all with a plan to reduce spending)

The issue today is: since your survival probabilities decline with time, it is rational to spend more earlier on while you are more likely to be alive, and to spend less later on when the probability of still being alive is lower. You should intentionally plan to decrease spending as you age to account for the lower probability of living to each subsequent age.

Financial economists have known this for a long time, but I don’t think the message about it has gotten out very well because the result is usually obscured in a mathematical equation rather than being written out with words. We only see it if we try to graph those old equations.

So it is optimal to reduce spending as you age, but by how much?  The answer to that depends on what financial economists call risk aversion, but which I would like to rename as spending flexibility for the retirement period. How flexible are you about letting your spending decrease?  Are you willing to spend more now with an understanding you may have to cut back later, or would you be willing to spend less now to help ensure you can spend just as much later? Generally people want to smooth their consumption, but again the hangup is that this may not always make sense when the probability of survival declines over time. A larger number for spending flexibility means the retiree is less flexible and wants greater consumption smoothing, as retirees care less about upside and really wish to maintain as high of spending as possible even in the low probability event that they happen to live a very long time.

I will assume retirement date wealth of $100. This amount doesn’t impact the results. I assume a male retiree at 65 and use the Social Security Administration 2007 Period Life Tables to obtain survival rates past this age. At retirement, retirees choose their annual spending amounts for ages 65-100. Financial markets are simplified to one asset which always and forever provides the same fixed return. Since retirees know the future investment returns, making these plans is easy to do. They don’t know how long they will live, but they can decide on how much they will spend each year should they still be alive.

There are now two competing tradeoffs: you want to spend the same amount every year for as long as you live to get the most lifetime value from your spending, but you also want to frontload your spending to early retirement when you have the highest chance for survival.

The following figure shows the optimal spending path for different degrees of spending flexibility when asset returns are 0%.
Someone with flexibility of 1 is quite willing to let their spending decrease over time to reflect the low probability of survival as they age. Spending starts higher but declines to very low levels by one’s 90s. With flexibility of 2, more effort is made toward keeping a smooth level of spending. But again, it is still optimal to frontload spending. You can also see for coefficients of 5 and 10 how we obtain greater smoothing even in the face of the decreasing survival probabilities. How much lower would you let your spending fall in your 90s to allow more spending in your 60s?  It’s an important and highly personal question. But if you want something even flatter than the spending flexibility=10 case, it means you are quite risk averse about spending reductions. The constant inflation-adjusted spending assumption creates very extreme inflexibilities and risk aversion on the part of the retiree, and it may not be what retirees really want! Do you want it? 

As the market return increases, you know that your remaining portfolio will grow at a faster rate, allowing you to spend more earlier in retirement. At the same time, you have some incentive to delay spending a bit so that you leave more wealth in your portfolio to grow at the higher rate and support even more spending later. Here we can see the spending pattern when asset returns are 4%:
Naturally as well, the less flexible you are about letting your spending fall, the more valuable a fixed income annuity becomes. As I discussed in the previous blog post, some with flexibility=10 case would require 90% more wealth to be just as happy with not annuitizing as if they had just annuitized in the first place (under the basic assumptions I used). For those with more flexibility, the value of annuities is less than this.

A key point here is: The assumptions of constant inflation-adjusted spending used in safe withdrawal rate studies, though intuitively appealing, is not optimal even in the case that there is no uncertainty about future market returns.

It will be great to move more and more toward combining the theoretical insights and rigorous methods used by finance academics with the real world practicalities and understandings of people and financial planners developing retirement solutions. I think this is a good example of where there is some ample ground for the cross-fertilization of ideas.