Monday, October 8, 2012

“Optimal Withdrawal Strategy for Retirement-Income Portfolios”

I wrote this on the flight from Boston to Tokyo. It’s the new 787 plane for Japan Airlines and it’s pretty nice.  I’ve just re-read an article which I had read earlier in the year (when it was not publicly available and I couldn’t write about it) and is now published. It’s a pretty impressive article which may effectively make obsolete a large chunk of past safe withdrawal rate research about variable withdrawal rates. However, at the end, I will discuss a critique I have about this type of research which makes me think that while this is a good step forward, it is not the end of the story. In Boston, it became a co-winner of RIIA and Allianz Global Investor’s Academic Thought Leadership Award, along with some past work of mine.

This article is “Optimal Withdrawal Strategy for Retirement-Income Portfolios,” by the Morningstar team David Blanchett, Maciej Kowara, and Peng Chen. The published version from the Retirement Management Journal is not available online, but a working paper version can be found here.


The article is important because it may be the best available approach for the sub-class of safe withdrawal rate research about variable withdrawal rates. It provides a framework for choosing a withdrawal strategy, initial withdrawal rate, and asset allocation.


The article creates a measure called “Withdrawal Efficiency Rate” (WER). The article is based on Monte Carlo simulations for asset returns and ages of death for a 65-year old couple. For each simulation, the authors first calculate the highest sustainable withdrawal rate for constant inflation-adjusted spending for someone with perfect foresight about the sequence of asset returns and the age of death that will be realized.
 

Then, for a variety of withdrawal strategies, the authors calculate the percentage of potential withdrawals the strategy allows with respect to the maximum sustainable withdrawal rate under perfect foresight. The higher the percentage, the more efficient is the withdrawal strategy. No importance is placed on leaving a bequest.
 

An important point is that the different withdrawal strategies these authors consider do not have constant inflation-adjusted withdrawal amounts. One of the strategies they consider is the classic inflation-adjusted constant spending strategy, but even with it, spending will fall to zero if financial assets are depleted. With variable spending from all strategies, they need to make some sort of adjustment to summarize a variable path of withdrawals.
For that, they rely on a utility function which accounts for diminishing enjoyment from increased spending and penalizes the pain in lower spending years more heavily than the extra enjoyment in higher spending years. Their choice of a parameter for the utility function explains how much importance a retiree would place on avoiding low spending years and how much the retiree values a smooth inflation-adjusted spending path. With some math, they calculate the “Certainty Equivalent Withdrawal” (CEW), which is a constant inflation-adjusted withdrawal amount that would provide the same lifetime utility as the fluctuating and variable withdrawal path created by the strategy for that simulation. It would be smaller than the average spending amount, since it accounts for the extra importance the retiree places on enjoying a smooth consumption path.
 

I recognize that the last paragraph may be a bit unclear for some readers. That’s the mathematical intuition for what is going on, but you can keep reading even if you don’t follow all of those details. The point is that you want to be able to withdraw as much as possible and you do need to incorporate some sort of adjustment for the fact that withdrawal amounts may vary over the retirement period, and with some strategies these variations may be bigger than with others, and that needs to be accounted for in some way. Another article which uses this same utility and certainty equivalence approach is one I wrote with Michael Finke and Duncan Williams called “Spending Flexibility and Safe Withdrawal Rates.”
 

In a manner related to my co-winning article, they consider five different withdrawal strategies, though I did not consider the strategy which they found to be optimal. Like me, they determined that the classic constant inflation-adjusted spending until wealth depletes is the worst possible strategy. Playing a game of chicken with constant withdrawals until the portfolio empties and then experiencing a significant drop in spending just isn’t a good idea. It’s important to adjust spending in some degree to changes in the portfolio value and the realized sequence of portfolio returns. The question is about how to best go about doing this. 

Four alternatives they consider are withdrawing a constant percentage of remaining assets, withdrawing a percentage each year that maintains the same failure rate over a fixed total retirement duration like 30 years, using the IRS Required Minimum Distribution percentages for IRAs, and using a withdrawal rate which maintains a constant failure rate percentage after incorporating the updated remaining life expectancy based on the fact that one has lived another year. For this last strategy, let me explain a bit more. The traditional 4% rule is based on a 30-year retirement, with the idea being that a 65 year old might plan to live to 95. The point about updating mortality is that if the person is still alive at age 90, then she (more often than he) better start planning more seriously to live past age 95. Conditional on surviving to age 90, for instance, their life expectancy age is bigger than it was back when they were age 65. They’ve survived all of those intervening years. 


And it is this strategy which the authors find to be optimal. Again, this strategy is to choose a withdrawal rate from remaining assets for each year of retirement which maintains a constant failure rate percentage based on the newly updated remaining life expectancy for each year of retirement.
 

Figuring out what this withdrawal rate is cannot be easily done with an Excel spreadsheet, but it is something which I could calculate given some assumptions about portfolio returns and mortality rates, and probably also a few days set aside for my computer to run the simulations. Then tables could be made and provided for retirees to figure out what will work for their situation. Basically, the table would show you what withdrawal rate from remaining assets you could feasibly use for each year of your retirement. The authors also suggest that using the IRS RMD distribution percentages is a viable sort of second-best alternative for those who do not have access to the more sophisticated version.

Another nice feature of their approach which they do not discuss is the common concern I’ve seen from real people (as opposed to the hypothetical folks I usually deal with) when discussing the traditional 4% rule. What happens if you have a year where you need a bigger expenditure for a home repair or health expense? How does that alter the 4% rule? This methodology would let you see how a bigger expenditure in a particular year would directly impact the subsequent sustainable withdrawal path. That’s valuable.
 

Critiques 
Ultimately, I don’t think I’m convinced that the Withdrawal Efficiency Rate they develop will serve as the best tool for choosing the withdrawal rate and asset allocation strategy, but it is definitely a good start.
 

The paper suffers from the same problem I see in all of the variable withdrawal rate / safe withdrawal rate research. It tells you to spend as much as possible on a utility-adjusted basis. That’s great, but it isn’t otherwise connected to any sort of lifestyle spending goals or minimum needs. Though the utility function would discourage it to some extent, this approach would have you keep spending amounts well beyond your lifestyle goals. The utility function also does not incorporate a flooring level, which makes it unclear about where the punishing aspects of the utility function really start to kick in with respect to the minimum needs and desired lifestyle. I just mean that the spending paths coming from this will be somewhat arbitrary and not connected to a retiree’s needs. That is a potential problem.

As well, it doesn’t present a complete retirement income strategy. Spending decisions are based only on financial assets (rather than a retiree’s complete balance sheet of assets including annuitized income sources). This aspect of the paper could be broadened though.


A less fundamental critique is that in their tables, the WER percentages for different strategies can be rather small, reflecting only minor differences between optimal and sub-optimal strategies. It may make sense to deviate from what is “optimal” to better account for someone’s spending needs and tolerance about the stock allocation. Related to an issue I discussed in "Capital Market Expectations, Asset Allocation, and Safe Withdrawal Rates," the difference between optimal and nearly optimal strategies here can be rather small and so non-optimal alternatives that a retiree may feel more comfortable with are worth taking into greater account. 


I don’t think it is necessary to discuss the specific optimal results from the paper, as it is based on a variation of historical market averages, which do not reflect the situation facing today’s retirees. You can see the paper (linked above) if you are interested in that.


Nonetheless, this is an important paper which is well worth reading for anyone interested in safe withdrawal rates. The constant percentage of failure with updating mortality that they use is, for all practical purposes, surely the best way to think about a withdrawal strategy within the limited safe withdrawal rate research field which consistently ignores the retiree’s entire collection of assets. What they did is a great insight and is common sense. I think the reason it took so long to appear in the research is that it is trickier to calculate.
 

This article is a big step forward. It provides a framework for informing you of an appropriate withdrawal rate based on your assumptions about portfolio characteristics, mortality rates, and flexibility with regard to experiencing spending fluctuations throughout retirement. As it is based on utility, it tells you the appropriate failure rate to use, along with a corresponding initial withdrawal rate and asset allocation. Good stuff.
 

We still need to worry about how to incorporate annuities, a retiree’s entire balance sheet of assets, the possibility for dynamic asset allocation over retirement, Social Security, health expenses, taxes, and other concerns, but this article is a big help. Within another 3-4 years, researchers may have retirement incomes strategies mostly figured out. Lots of progress is being made. Long gone are the days of the simple 4% rule. Stay tuned.