Wednesday, July 20, 2011

Should Retirees Increase Stock Allocations as they get Older and Older?

Today's post is a follow-up from my last post on July 18. There I was discussing David Blanchett's "Dynamic Allocation Strategies for Distribution Portfolios: Determining the Optimal Distribution Glide Path" from the December 2007 Journal of Financial Planning.

In the study, he considers various glide paths for asset allocations over the course of one's retirement, comparing fixed asset allocation strategies to "target date" or "lifecycle" strategies that continue decreasing stock allocations as one gets older and older. He finds that a fixed asset allocation which balances stocks and bonds at about 60/40 will probably serve as the best compromise, and that there is no need to continue reducing stock allocations as more years pass by in retirement.  This is good news for the results from most retirement withdrawal rate studies, since the usual assumption is to simplify by only considering fixed asset allocations, with the caveat that the results could be different if lifecyle asset allocation strategies are used.  It turns out, Mr. Blanchett finds, that the fixed asset allocation assumption is quite appropriate after all.

One general result from his study is that a 100% stocks usually supports the highest withdrawal rates.  I made a table of my own about this below. The following table shows which fixed asset allocation among the 11 possibilities allows for the highest withdrawal rate out of 1,000 simulations.  Stocks provide the highest withdrawal rate in 69% of the simulated 40-year periods.



However, that doesn't mean that retirees necessarily want to use 100% stocks.  That is because when 100% stocks fails, it can fail spectacularly.  To see that, consider the figure I made as a part of my July 16 post showing the maximum sustainable withdrawal rate for different fixed asset allocations and with different probabilities of failure for a 40-year retirement period:


































For an aggressive investor who accepts a high probability of failure (such as the 35% failure case), 100% stocks can support the highest withdrawal rates.  But for more conservative retirees who wish to find the highest withdrawal rate possible with a low probability of failure, then lower stock allocations support higher withdrawal rates.  Focusing on a 1% probability of failure, 100% stocks supports a lower withdrawal rate than any other allocations.

And so, 100% stocks is risky.  Mr. Blanchett develops the "success to variability ratio" to incorporate this risk.  In my past blog post, I was suggesting that considering expected utility might be a better way to balance the higher average withdrawal rates from high stock allocations with the small chances for extremely low withdrawal rates from high stock allocations.  I discussed my paper, "An Optimizing Framework for the Glide Paths of Lifecyle Asset Allocation Funds," from the first 2011 issue of Applied Economics Letters.  That paper used the idea of expected utility when people are saving for retirement to justify traditional target date funds that reduce stock allocations during the accumulation phase. 

Again, to express it very simply, expected utility analysis provides a way to compare the trade-off that high stock allocations provide more expected wealth but also a larger chance for extremely low wealth accumulations as well.  People who are increasingly risk averse will value lower stock allocations more because they want to avoid those really low wealth accumulations.  They are willing to sacrifice more of the potential upside in good luck scenarios in order to avoid more of the downside in bad luck scenarios. I obtained the results shown below for the "saving for retirement" case. It is hard to say precisely what these "risk aversion" values mean, but generally someone who is a "conservative investor" probably has risk aversion in the neighborhood of 5.  Risk aversion of 1 implies a rather aggressive investor, and risk aversion of 10 is quite conservative in terms of wanting to protect their wealth.
































Now, for today, what I did was to basically re-configure my program in two ways in order to look at the retirement period. First, I changed from looking at a 40-year long working period when one is saving for retirement, to a 40-year long retirement period when one is withdrawing income from their portfolio.  Second, rather than looking at the distribution of wealth accumulations at retirement for each of 2,211 asset allocation strategies, I instead looked at the distribution of maximum sustainable withdrawal rates for each of the 2,211 asset allocations.  I ran 1,000 simulations for asset returns and applied them to each of these strategies [These results do have a few inconsistencies, suggesting that I should try again with more simulations to get more stable results -- but the general story from these results is clear].  The glide paths shown maximize the expected utility of retirees with different amounts of risk aversion as follows:

































What this shows is that conservative retirees can maximize their expected utility by starting retirement with a balanced asset allocation, but then letting their asset allocation grow increasingly aggressive as the years pass. For risk aversion of 5, the optimal glide path is to start at 40% stocks and gradually increase the stock allocation up to 90% over the 40-year retirement horizon.

Does this make any sense?

Well, to start with, it may not be practical.  There are a whole host of behavioral issues involved in implementing it. Asking 100-year olds to shift to 100% stocks may be asking too much.  The purpose of my blog post here is not to make a strong endorsement of the idea, not at all.  I'm just exploring the idea here.  It is by no means my final recommendation or anything.  It is very preliminary.

But beyond this, the results do kind of make sense as being a reversal of the accumulation phase.  Usually, stocks provide the highest returns, but when your wealth is the largest at retirement, you want to protect it from  sudden drops.  Then, as time passes, you can slowly increase your stock allocation as your horizon becomes shorter and your retirement prospects become more clear.  The only way this does worse than a fixed 60/40, say, is if you get continuous doses of bad luck over your whole retirement. More generally, the slightly less bad retirement scenarios involve doses of bad luck right after retirement and then a more average stock market performance (on average, stocks have outperformed bonds) later in retirement.  Such a scenario is exactly what this reverse glide path protects against.  It helps to raise the sustainable withdrawal rate in these bad luck cases, which provides the downside protection against extremely low withdrawal rates as desired by conservative investors.


To conclude, 100% stocks usually supports the highest withdrawal rates.  But not always.  The purpose of "safe withdrawal rates" is to avoid running out of wealth with sufficient confidence.  The more sure you want to be about not running out of wealth, the lower the withdrawal rate you must use, and the lower the accompanying fixed stock allocation must be.

But when you allow the stock allocation to change over time, what I find in these simulations is that retirees are better off by starting with a lower stock allocation but then actually increasing it over time, rather than decreasing it. This provides protection when wealth is the highest, and then allow for more aggressiveness later on in retirement. Bad retirements generally happen because of poor results just after retirement, and that is what the reverse glidepath helps to protect against.