Friday, July 15, 2011

“Guidelines for Withdrawal Rates and Portfolio Safety During Retirement”



Today’s classic withdrawal rate study is “Guidelines for Withdrawal Rates and Portfolio Safety During Retirement” from the October 2007 Journal of Financial Planning. The authors of this study are John Spitzer, Jeffrey Strieter, and Sandeep Singh.

A lot of retirement withdrawal rate studies are very repetitive and do not really offer anything new.  There are many variations of the Trinity study, which looks at success rates (or the corresponding failure rates in the case of today's article) of various withdrawal rate and asset allocation strategies. At first, I thought it might be the case for this article too. 

However, as I read it again, I realized that this article offers a very nice graphical way of presenting its results. So nice, in fact, that prospective retirees would be better off looking at the figures of this study than at the tables of the Trinity study when doing traditional retirement planning. The graphical presentation of the results do provide some insights about withdrawal rates and asset allocations in a very straightforward and easy to understand way. 

The study does look only at 30 year periods, and it assumes end of year withdrawals.  It uses bootstrapping for annual returns from SBBI since 1926. The two asset classes are the S&P 500 and intermediate-term government bonds.  With any kind of simulations based on past historical data, the study assumes that future market returns will behave with similar patterns as in the past. As a side note, my article "Retirement Withdrawal Rates and Portfolio Success Rates: What Can the Historical Record Teach Us?" summarizes my concerns about that.

The key point of this article is that we can’t just talk about a one-size-fits-all withdrawal rate or asset allocation for all retirees.  The appropriate withdrawal rates (assuming the retiree would like to withdraw at least this much) and asset allocation depend on the probability of failure that a retiree is willing to accept. It also depends on what kind of estate the retiree wishes to leave behind.

Asset Allocation Strategy to Provide the Highest Withdrawal Rate for a Given Probability of Failure

The information about failure probabilities, withdrawal rates, and asset allocation is summarized very nicely in their Figure 1. 

I’ve replicated that figure below using 1000 Monte Carlo simulations for each strategy based on the annual SBBI data (1926-2010) for the same assets and assuming beginning-of-year withdrawals for inflation-adjusted withdrawals over a 30-year period. No taxes or fees are deducted.

What this shows is that if a retiree is only willing to accept a 1% chance of failure, then the most they can hope to withdraw is about 3.8%  with a 35-40% stock allocation.  For a 5% chance of failure, a withdrawal rate of about 4.2% with a stock allocation of around 40-45% works best. Accepting a 10% chance of failure, one can go with a 4.5% withdrawal rate with a stock allocation of around 50%.  And with a 25% chance of failure, a withdrawal rate of around 5.5% with any stock allocation above about 60% works out.  As the probability of failure increases, the withdrawal rate obviously increases, but also the optimal stock allocation increases. Therefore, failure rates, withdrawal rates, and asset allocations are all linked to one another and it is inappropriate to talk about one aspect of these without considering what is needed for the other two as well.  Also, note that including some stocks in the retirement portfolio is justified, as bonds just do not provide high enough returns to support higher withdrawal rates for a given chance of failure. Also 100% stocks do not become uniquely optimal until quite high failure rates (somewhere around 35%) are accepted. Notice the hump-shaped nature of these curves.




Asset Allocation to Provide Lowest Failure Rate for Given Withdrawal Rate

Next, their Figure 2 shows the probabilities of failure for different withdrawal rates and different asset allocations. This is looking at the same underlying information in a different way. For a given withdrawal rate, you can see what asset allocation minimizes the probability of failure. Lower withdrawal rates allow for a more conservative asset allocation, while higher withdrawal rates require a higher stock allocation to minimize their failure rates, though of course these failure rates are still higher than with low withdrawal rates.



Incorporating Bequest Desires

Finally, I’ve modified their Figure 3 to show the median real wealth remaining after 30 years for different withdrawal rates and asset allocations. Their Figure 3 shows mean remaining wealth, but they explain that a few outliers drive the means upward. With the median, there is a 50% chance to end up with more wealth, and a 50% chance to end with less. Initial starting wealth was $100 and these wealth amounts are in real terms. Whenever wealth ran out before the end of 30 years, the amount entered for this calculation is $0. The $100 line thus preserves the real purchasing power of the initial wealth at retirement.

You can see here that if the aim is to preserve initial wealth in real terms for the median case, a variety of strategies allow this with a trend of increasing withdrawal rates require increasing stock allocations.  However, remember from Figure 1 that these strategies have different failure rates.  Higher withdrawal rates and higher stock allocations will also increase the likelihood of running out of wealth before the end of 30 years. You have to consider these factors together.  And if leaving a specific bequest is particularly important for you, you should not be basing the decision on the median case as shown here.





































So there you have it.  Two more points I would like to make are that the results do come out differently when using historical simulations (overlapping periods from the historical data).  I discuss about this in my paper mentioned above, "Retirement Withdrawal Rates and Portfolio Success Rates: What Canthe Historical Record Teach Us?" Here is a figure from that paper which is doing something similar as the second figure above, but uses the Trinity study data to compare the results for a 4% withdrawal rate from the historical simulations with the Trinity study to the results using Monte Carlo simulations based on the same underlying data.  These are success rates now, not failure rates (success rate = 100 - failure rate). My paper explains more about why the historical simulations are too strongly biased against bonds.  People get the idea from the Trinity study that for a 4% withdrawal rate, the best stock allocation is 75%.  That is not really the case.



Second, I think in this day and age, many people may need to be planning for a 40-year retirement instead of 30 years.  For this case, I’ve re-produced below that Figure 1 for a 40-year retirement. I'm just now looking at the figure for the first time, and it does trigger some alarms!  For a 40-year retirement horizon, it is no longer possible to get a 4% withdrawal rate with a less than 10% probability of failure!!



 

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