Wednesday, July 13, 2011

"Making Retirement Income Last a Lifetime"

I'm now in the process of re-reading some of the classic studies on retirement planning.  As I am more involved in the research side of it now, doing this allows me to see points that I missed before or otherwise had just forgotten about.  Yesterday I discussed the Terry (2003) article and found that it contained a computation error that works to invalidate the whole premise of the article.  I was reading that one yesterday, because it is critical of John Ameriks, Robert Veres, and Mark J. Warshawsky's December 2001 article from the Journal of Financial Planning, "Making Retirement Income Last a Lifetime".  Actually, this is a really excellent article that deserves lots of accolades.  It is quite innovative. At the end of my review process, I might like to try to put together a top 10 list of the most important articles about sustainable withdrawal rates, and this one is certainly going to be a contender.

Let me highlight a few things about the article:

Contributions of the Article

1. I hadn't realized it, but this article makes a comparison between Monte Carlo simulations and historical simulations.  It considers the results with both cases. I thought Cooley, Hubbard, and Walz (2003) was the first to do it, but I should change my past citations to this article instead.

2. This paper also investigates how partial annuitization can affect safe withdrawal rates.  This is really important.  Annuities don't have to be an all-or-nothing proposition. The authors don't try to find an optimal annuity amount, but they do show about annuitizing 25% or 50% of one's savings can help improve the success rates for a 4.5% withdrawal rate.  The chances for success increase, and the tradeoff is a reduced amount of leftover remaining wealth in many cases.

3. The article incorporates a 1% fee.

4. The article also addresses retirement durations of 35 and 40 years, in addition to the usual 30 years (and also, there are 20 and 25 years too).

Findings of the article

1. The authors consider 4 portfolios with different combinations of stocks, bonds and bills, and they find that over rolling periods and with Monte Carlo simulations that the most aggressive portfolio provides higher withdrawal rates on average, with very little downside risk.  In the rare case that the aggressive portfolio provides a lower maximum sustainable withdrawal rate than a less aggressive portfolio, the difference is very small.  Actually, I am well aware of this type of finding.  As this is a 2001 article, it is quite possible that they were one of the first to note it. With US historical data, it is very hard to beat a 100% stocks portfolio.  The authors do suggest caution about using this result in a forward-looking manner.

2. The annuities part is very important.  Partial annuitization, even with fixed annuities that do not adjust for inflation, can help improve the sustainable withdrawal rate.  They can also allow the remaining portfolio to be invested more aggressively, as the annuities can substitute for bonds in the portfolio.

3. The authors find that less aggressive portfolios work better for shorter retirement durations, but that more aggressive portfolios perform better for the longer retirement durations.

Concerns / Suggestions for Improvement

 1. This article is based on data between 1946 and 1999, which may portray bonds in too negative of a light.  In other words, this time period may be too much "pro-stocks". I discuss this type of issue more extensively in the section "Bias Against Bonds in Historical Simulations" of my paper, "Retirement Withdrawal Rates and Portfolio Success Rates: What Can the Historical Record Teach Us?"

2. As the authors note, the historical simulations are really hampered by the short data period.  For the 35 year case, the simulations will be cut off at 1965, which happens just before some of the worst withdrawal rates in history.

3. The authors include Treasury bills in their less aggressive portfolios, but this may just serve to drag down the performance of the bonds component.  Just including intermediate-term government bonds may be the best way to represent bonds in the portfolio.

4. This is a more minor quibble, but the authors track negative wealth as a way to consider how far into debt people may go with a 4.5% withdrawal rate.  But in this case, depending on their programs, any negative portfolio returns might have actual served to bring their wealth closer to zero rather than farther away from zero.  If they stopped incorporating asset returns once the portfolio ran out of wealth, then there is no problem.  But they don't clarify how they treated this, and I suspect the problem may be there.

The Highest Sustainable Withdrawal Rate Comes From 100% Bonds?

I'm now in the process of reading through some of the classic studies about retirement withdrawal rates. 

One of the papers I read again tonight is Rory Terry's article from the May 2003 issue of Journal of Financial Planning, "The Relationship Between Portfolio Composition and Sustainable Withdrawal Rates."  

Recently in investigating about retirement withdrawal rates I have been growing sympathetic to the idea that retirees should not feel obliged to maintain a high stock allocation of 50-75% as seemingly suggested by the Trinity study and others.  I've been finding that the sweet spot is actually somewhere around 40%. [Update: My July 16 post updates my reviews about asset allocation]

So I am sympathetic to the message in Prof. Terry's article, and his article is cited frequently for providing a loud voice against the notion of using high stock allocations in retirement.  In fact, he concludes that retirees will be best served with 100% bonds.

However, in re-reading the article this evening, I am concerned that his main conclusions are based on a mistake.

He sets up a simple scenario.  An investor will be retired for 30 years and wants to withdraw inflation-adjusted amounts from the portfolio for this length of time.  Bonds provide a nominal return of 6% and no volatility.  In real terms, this means bonds provide a return of about 3%.  Of course investors must deal with reinvestment risk and interest rate risk with bonds, but I will give him the benefit of the doubt that retirees could set up a portfolio with zero-coupon bonds that will provide precisely the necessary spending power with no risk.  Since inflation is constant, there is no inflation risk either.  If the investor lives longer than 30 years, wealth is guaranteed to be gone.  But okay, this is not my main concern.

Next, consider stocks.  Prof. Terry assumes that stocks will have an expected nominal return of 12 percent [or about a 9% real return] and a standard deviation of 10%.  Actually, this is remarkably optimistic!  High returns and a relatively low standard deviation. 

The problem comes with the next calculation, in which Prof. Terry uses Monte Carlo simulations with a normal distribution to find that with this stock portfolio, a retiree can only use a withdrawal rate of 1.85% and still face a 10% chance for retirement failure.  Leaving a 1% chance for failure, the maximum sustainable withdrawal rate is only 0.19%.  With such low withdrawal rates, and since bonds are assumed to have no volatility, it is natural that 100% bonds provides the best outcome for retirees, a withdrawal rate of 4.9%.

The problem is... these Monte Carlo simulation results for the stock portfolio must simply just be wrong.  A standard deviation of 10% really isn't so high to get such terrible results.

When I replicate such a calculation assuming a lognormal distribution with a 9% real return and 10% standard deviation, I find that a withdrawal rate of 6.63% (not 1.85%) is successful with a 10% chance of failure.  For a 1% chance of failure, I get a withdrawal rate of 5.32% (not 0.19%).

To have a withdrawal rate of around 1.85% with a 10% chance of failure, I'm looking at something more like a real return of 2% with a standard deviation of 16%.  I'm using a table which I made a few weeks ago, and it doesn't provide me with any way to get to the 0.19% number.  The worst case scenario I had considered was a 0% real return with a 20% standard deviation and that still gives a 0.45% withdrawal rate with a 1% chance for failure.

I'm sure that I can find some others to also investigate these results and make sure that I am not the one making a mistake.  Pending any further notice, it does seem that there is a serious problem with the results of this article.  Really, the whole basis of the article is centered around that 1.85% withdrawal rate for 100% stocks and how it is lower than the 4.9% withdrawal rate for bonds.  If that 1.85% number is wrong, then it is back to the drawing board.


Update, I made this post at the Bogleheads Forum:

The issue of normal vs. lognormal distribution isn't going to matter. As Dick Purcell wrote, his results are based on the normal distribution, but at multiple points in this thread I confirmed getting very similar results as him with my simulations based on the lognormal distribution.

The two distributions are quite similar and won't make much difference when discussing the US. I used to use the normal distribution, but ran into some problems when doing simulations for more volatile emerging market countries. With a high enough standard deviation, it can become common to see returns from the normal distribution of less than -100%. I had people saving for retirement and not using any leverage who were ending up with negative wealth. But that is impossible. The worst that can happen is that your wealth is wiped out. It can't go negative. The lognormal distribution corrects for this, and I've never looked back.

The Terry (2003) article mentions the importance of using 100,000 simulations. So I just tried that. My results above were based on only 1,000 simulations.

With a 9% real return and a 10% standard deviation, for 100,000 simulations I get the following withdrawal rates:

Worst-case scenario out of 100,000 tries: 3.09%
1% failure rate: 5.16%
5% failure rate: 6.02%
10% failure rate: 6.52%

My earlier calculations were for 1,000 simulations.

Again, Prof. Terry calculated a 1.85% withdrawal rate with a 10% failure rate. This invalidates the whole premise of his article.


Thank you to Mike Piper for linking to this post from his Oblivious Investor blog.