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