# Confirming the Value of Rising Equity Glide Paths, Delorme (2015)

I really like Luke Delorme’s 2015 paper even though it doesn’t have any startling new conclusions; I like the approach taken in the paper. Delorme relies on mortality-weighted certainty equivalence to compare various strategies.

Unlike previous papers, this one is solely focused on glidepaths **during** retirement. It is silent on the question of glidepaths prior to retirement.

No single metric is perfect for determining the best strategy for retirees, but the certainty equivalence measure may offer a more holistic picture of retirement success.

I’ve looked at certainty equivalence before (it is used in Blanchett et al’s “Withdrawal Efficiency Rate”, for instance) but not explicitly tied together with mortality this way. The usual “probability of failure” doesn’t take mortality into account (so a failure at age 94, when most people are actually dead, is given the same weight as a failure at age 66, when almost everyone is still alive). And by using certainty equivalence it is easier to make comparisons to variable withdrawal strategies.

Delorme uses certainty equivalence to compare a number of declining, rising, and static glidepaths. While the best performer is a glidepath from 20% equities up to 70% equities, it is striking that most other combinations are nearly as good (everything within the black box is within 5% of the optimum).

In other words, there appears to be little difference between:

- 0% equities gliding up to 100% equities
- 70% equities gliding down to 0% equities
- 50% equities constant (i.e. no glide path)

Part of the problem may be that, despite its conceptual appeal, mortality-weighted certainty equivalence is not the right metric. After all, notice that the difference between the *best* performer ($35,385) and the *worst* performer ($31,215) is only 12%, or $4,170 a year. That’s not nothing but it also smaller than you would naively assume. After all, we’re saying that the difference between the best possible asset allocation and just putting it all in 100% bonds is only $4,000 a year.

Nevertheless, he offers some tepid support for rising equity glidepaths:

The average certainty equivalence for the 55 increasing equity glide paths ($34,521) is 2.6 percent higher than the average certainty equivalence for 55 declining equity glide paths ($33,655). This difference is not large, but it does confirm that rising equity glide paths improve simulated utility.

What I like about this paper is that Delorme pushes his model and talks about the impacts:

- “The return assumption significantly influences the optimal glide path.” The more conservative your return assumptions the lower the equity allocations in the optimal glide paths.
- “With an increased risk aversion parameter (gamma) of 10, the optimal strategy does not change.”
- “With a reduced risk aversion parameter of 1, the optimal strategy increases the withdrawal rate to 4.5 percent and the equity allocation to 50 percent”
- Finally…he tests it with a pension. Since most Americans will have a pension making up a substantial part of their retirement income, it makes sense to include it.

When you add in a pension like Social Security it makes things more complicated because you have to decide what percentage of the income comes from the pension versus the portfolio. Delorme assumes $40,000 a year from Social Security and $50,000 a year from the portfolio. Which is plausible.

Now the asset allocation is even less meaningful!

Delorme actually goes on to try 4 different levels of pension (from $0 up to $80,000 a year) at 3 different risk aversion levels.

You can see that “optimal” can vary quite a lot, regardless of whether one is using static allocations or glidepaths. (Also note that there is usually very little difference between the optimal static allocation and the optimal glidepath.)

The effect of all these various asset allocations is swamped by the withdrawal rate. That is, a change of plus or minus half a percent is far, far more important than any asset allocation you can pick.

Rising equity glide paths may offer an improvement in retirement finance, but a more important factor may actually be the withdrawal rate.

What this probably means in practice (based on Delorme’s results): unless you have the “optimal” withdrawal rate then it doesn’t matter all that much whether your glidepath is increasing or decreasing…or whether you use one at all. You’re probably losing more money from having a withdrawal rate that is too low or too high.