A Challenge and a Response for Rising Equity Glidepaths in Retirement

Jared Kizer of the BAM ALLIANCE recently wrote an article called, “An Analytical Evaluation of Rising Glidepath Claims” which concludes that there is no value in using a rising equity glidepath during retirement, contrary to the conclusions that we (Wade Pfau and Michael Kitces) reached in research published in the January 2014 Journal of Financial Planning. We welcome feedback and criticism of our research and are willing to make changes when justified (in fact, just this week we released our own follow-up research showing that rising equity glidepaths are only best in a narrow set of specific circumstances, albeit ones that are present today). But in this case, while we both have a lot of respect for the research and books generated by Jared and his colleagues at the BAM ALLIANCE (such that we took his article quite seriously), we don’t think his criticisms hold under scrutiny.

As the BAM ALLIANCE P.R. department has shared Jared’s article with a large number of media outlets, we feel it’s important to explain why we disagree with the conclusions in Jared’s article. The issue, though, is that we think there are some important problems with Jared’s statistical methodology, and so the discussion in his article and here will be hard to follow for readers who haven’t taken or don’t recall much of what they learned in their statistics or econometrics classes. Nonetheless, after the national media blast, Michael and I need to get our side of the story out there as well.

Probability of Failure

The article begins by making a useful point that if one strategy has a success rate of 80 percent while another is 81 percent, then you can’t really say with confidence that the second strategy works better. There will always be a degree of randomness in the results, and even if the difference in success rates is “statistically significant” in the way that statisticians like to use the term, there is still not much real world practical difference between the numbers.

This is why Michael and I generally frame the results as it being possible with a rising equity glidepath to get just as good of outcome, or possibly even better, using a lower average equity allocation. For example, starting retirement at 30% stocks and slowly increasing to 60% stocks can do just as well, and maybe even better, than just sticking with the 60% stock allocation over the whole retirement period (presuming the client had the tolerance to own 60% stocks in the first place and would have done so absent further advice). We did not attempt to test whether this result is “statistically significant” as an improvement, because the mere fact that a portfolio with significantly less equities getting the same result is still meaningful, though we did find indications that there may be some modest improvement in outcomes as well. In the quote Jared used from our article, we said that rising glidepaths have “the potential” to improve outcomes. The safe withdrawal research says that retirees should hold 50-75% stocks over their whole retirement as a way to minimize the risk of depleting their wealth, and we are saying that this isn’t necessarily the case. Those not comfortable with such high stock allocations can have some comfort with our conclusions.

When Jared gets to the first table in his article, he’s approaching this matter from an entirely different perspective. He’s asking a different research question than what we considered. Table 1 is showing whether rising equity glidepaths as a whole (representing the 55 different rising glidepaths we considered) can support a higher average success rate for the 4% rule than declining equity glidepaths as a whole (representing 55 more cases). The answer he finds is that there is not much statistical evidence to suggest that rising glidepaths are superior as a whole. Also, which has the higher average success rate depends on the choice of capital market expectations – which we actually wanted to illustrate, and is why we tested the analysis with a wide range of capital market assumptions.

Are rising equity glidepaths superior as a whole? Perhaps not, but that wasn’t what we were saying in the first place. As Michael explains it by analogy – our study set out to determine if reputable fund manager DFA funds provides better performance than other mutual fund families or traditionally-weighted index funds, so we compared the long-term track record of DFA to the other fund families and index funds, and concluded that DFA funds do in fact provide a benefit. Jared’s analysis is the equivalent of then coming back in, and measuring whether the AVERAGE of DFA funds AND ALL OTHER MUTUAL FUNDS outperform the indexes, with the conclusion that they do not because all the fund managers in the aggregate are underperforming by the average of their fees. He then concludes that DFA cannot possibly provide value, because the average fund manager underperforms the index. Yet the conclusion is not actually logically coherent; even if the average of all mutual funds underperform an index, it’s not proof that a particular fund can’t still be superior. We were looking for whether the best fund (or in this case, the best glidepath strategy) can be superior, not whether the average fund (or average glidepath strategy) is superior, while Jared just measured the average and then used it to make a logically inappropriate conclusion about a particular fund/glidepath strategy.

Furthermore, by including the average of all the glidepaths we tested, Jared’s analysis ends up including scenarios that we presented for the sake of thoroughness, not because we were ever actually advocating them (even after the study was published). We're more interested in whether rising glidepaths will work for situations that real retirees might consider, i.e. we don’t care too much if a 0% to 10% glidepath isn’t as good as a 10% to 0% glidepath, since neither should be very realistic choices in the first place. 

In addition, there is an important problem with what Jared does here, though he doesn’t start to discuss the problem until later in the article. The issue is that our collection of rising equity glidepaths will have a lower average stock allocation than our collection of declining equity glidepaths. Looking just at initial stock allocations, the rising glidepaths have an average value of 30% stocks, and the declining glidepaths have an average value of 70% stocks. With the 2^nd set of capital market expectations, the success rate for the 4% rule with a fixed 30% stock allocation is 51%, and the success rate is 66% for a fixed 70% stock allocation.

So our rising glidepaths have a severe hurdle to overcome, especially in scenarios where the capital market assumptions are assumed to be especially bad for bonds relative to stocks. Just having the rising equity glidepaths remain competitive on these average success rate measures is a good sign, and while some investors are very pessimistic about markets and might use those low capital market assumptions, others are more optimistic about returns and the rising glidepaths hold up even better in those environments.

But the bottom line is that something close to the same basic outcomes is being achieved with a collection of glidepaths using a lower stock allocation. Risk averse retirees can feel much better now. Actually, this really was our point all along. And saying that the rising equity glidepath represents a more conservative strategy is not an indictment of rising equity glidepaths; it was actually our point!

Magnitude of Failure

Next Jared looks at the magnitudes of failure.  His second table actually shows support for rising glidepaths. He shows that the magnitudes of failure (based on our own data and results) are less severe with rising glidepaths in all three cases for capital market expectations, and that all of these results are highly statistically significant. Apparently unsatisfied with this conclusion, though, he now brings up the issue that rising glidepaths have lower average stock allocations, and suggests that perhaps the favorable results of the rising glidepaths are simply being driven by the fact that they have lower average stock allocations. Fine (since we actually made that point as well!). The problem is that his next choice of regression is not an appropriate way to try to conclude that it is only the lower stock allocations that matter, and not the direction of the glidepath as well.

Even though he left Table 1 as is (which shows the probabilities of success across the strategies, as analyzed earlier), despite this issue of average stock allocations being different, he decides that we cannot use Table 2 (which shows the same results as Table 1 but looks at magnitudes of failure instead) because now he is concerned the rising glidepaths have less stocks. To account for this, he creates a regression model to see how the magnitude of failure relates to two variables: the starting equity allocation and a dummy variable equal to “1” if it’s a rising glidepath and “0” for declining glidepaths. Running this regression suggests that it’s the initial stock allocation that matters, and that the fact that one uses a rising equity glidepath provides a net negative contribution to the results for one of the three sets of capital market expectations (results are not significant in the other two cases). In other words, this is where he really concludes that rising glidepaths are bad, and any benefit we showed actually relates (in his view) only to the fact that the retiree starts at a lower stock allocation, and not to what subsequent glidepath is.

This regression is where we have the biggest disagreement with Jared’s methodology. As indicated, his two variables are initial stock allocation and whether it is a rising glidepath path or a declining glidepath. This choice of variables effectively discards the important information about the magnitude of changes in the glidepath. In other words, there is nothing in his regression to distinguish the important difference between starting at 20% stocks and ending at 30% stocks or ending at 100% stocks. There would be 10 rising glidepaths which start at 0% stocks, and there would be 10 declining glidepaths which start at 100% stocks, and they all appear exactly the same in his regression analysis. But they are not the same! He ignores the magnitude of changes in the glidepath, which can be very material (in terms of both risk and outcome).

The reason Jared set up the regression this way is because believes that the initial stock allocation is the best available estimate for what the average stock allocation will be for the whole retirement. While a portfolio that glides from 30% in stock to 60% over 30 years would have an average allocation of 45% over time, Jared emphasizes that if the portfolio is being spent down, the dollar-weighted allocation will be closer to 30% than 60% (or that it’s at least a close enough approximation even though the dollar-weighted average will vary in each particular Monte Carlo simulation). But we think it is a severe mistake to completely ignore information we have about the magnitude of change in the glidepath. A 0% stock allocation which ends at 10% stocks will not create the same experience for a retiree as a 0% stock allocation that ends at 100% stocks. To say that both are equally well represented by the fact that their initial allocation was 0% is insufficient when one ends at 10% and the other ends at 100%. A proper regression model should do something to account for this.

So how do we correct the problem? Well, we're not all that enamored with this regression approach in the first place. The number of datapoints is somewhat artificial based on the fact that we looked at the glidepaths in 10 percentage point increments. There would have been 15 rising glidepaths if we used 20 percentage point increments, and there would have been 5,050 rising glidepaths if we used 1 percentage point increments, creating strange artificial thresholds to finding significance in the first place. That being said, I think it is still fair to overweight the initial equity allocation (as with a portfolio that spends down, the dollar-weighted allocation will be closer to the starting percentage than the ending), but let’s also do something to avoid wasting the information about how quickly the glidepath changes. For example, we could let the regression variable be equal to:

0.7 * starting equity allocation  +  0.3 * ending equity glidepath

This is still reflecting the importance of the initial stock allocation, but it is also letting the changes in glidepath play a role as well. I simply can’t understand why Jared believes that only considering the initial stock allocation is a better way to investigate this. We can re-run the regression with this new variable, and then we can look at the coefficient on the dummy variable and decide about the rising glidepath.  Here is our version of his third table in which we use this new variable better reflecting the average stock allocation over the retirement:

	Dummy Variable Coefficient	t-stat
Capital Market Expectations I	4.2	7.6
Capital Market Expectations II	2.6	4.2
Capital Market Expectations III	5.9	4.3

Again, we're not so excited about this regression approach in the first place, but in the context of how Jared presented his results, this table shows overwhelming evidence in favor of rising equity glidepaths. The coefficients on the rising glidepath dummy are all positive, suggesting that once we control for our approximation of the average stock allocation over retirement, rising glidepaths give substantially better results in terms reducing the magnitude of failure, relative to declining glidepaths. In addition, those t-statistics are quite large, suggesting that the results are all highly statistically significant. This table is very good news for rising glidepaths.

The important difference, and why this regression is better than the one Jared used, is that this regression also allows the degree of change in the glidepath to play a role as well. As we explained before, Jared’s approach threw away too much information because it only used the starting equity allocation. 

Beyond that, it’s also worth noting once again that we can view the fact that the rising equity glidepath is a path to starting with a more conservative portfolio is also a benefit of implementing the glidepath strategy itself. Continuing the earlier example of analyzing the benefits of using DFA funds, a Kizer-style regression analysis on DFA fund holdings might easily find that DFA funds are disproportionately tilted towards small-cap and value stocks (which isn’t surprising, as DFA’s philosophy is to implement the small-cap and value tilts of the Fama/French three-factor model). By Kizer’s methodology, this implies that using DFA funds has no benefit, because the actual benefits are simply a result of the small-cap and value tilts, not recognizing that the whole point of using DFA funds was to implement those exact tilts in the first place. In addition, while DFA’s beneficial results might be dominated by their small-cap and value tilts, they arguably provide some value in their particular implementation of the strategy as well, yet it clearly seems too narrow to suggest that DFA’s only benefit is the way they invest the tilts and not the fact that they decided to apply the tilts in the first place. Similarly, while we’d actually concur that a significant (though not exclusive) factor of the rising equity glidepath is that its initial equity weighting is lower, the path of the glidepath itself over time does matter too, and the overall value of the strategy is not just about the path of the glidepath but also the fact that it creates a framework to make it acceptable to own that lower initial equity allocation in the first place!