# Retirement Income Planning Is As Easy As PAY

As an alternative to failure rates, I suggest calibrating the downside risk across strategies in order to match them for a level of risk the retiree is comfortable taking. This calibration is done with a customized “PAY Rule™” (previously known as the XYZ Formula) that I first outlined in my article, “Making Sense Out of Variable Strategies for Retirees” in the *Journal of Financial Planning*.

The original XYZ Formula as stated in that article was: Retiree accepts an **X% **probability that *spending* falls below a threshold of **$Y** (in inflation-adjusted terms) by **year Z** of retirement. Where a failure rate might simply say retirees accept a 10% chance of failure within the first 30 years of retirement, an XYZ formula would instead say that the retiree accepts a 10% chance that their spending level will fall below an inflation-adjusted $60,000 by the 30th year of retirement.

Click here to download Dr. Pfau’s fact sheet “The Relationship Between Spending and Aging.”

This can incorporate Social Security and other income sources as well, and it provides a way to compare strategies while otherwise dealing with the reality that higher initial spending rates can be justified if spending is subsequently allowed to drop more steeply.

The formula provides a controlled anchor for those spending drops. When combined with consistent market assumptions and a view of the entire distribution of outcomes, we can compare different variable strategies on an equal footing.

Since publishing that article, I have come to realize that calibrating $Y to *wealth* instead of *spending* will work better. Attempting to calibrate downside spending can easily create a situation in which no spending rule works, which was an issue in my published article.

Higher spending rates caused spending to fall too far, while lower spending rates impeded spending from rising enough. A happy medium was not always available, but defining $Y as wealth instead of spending also corrects for this. Hence the birth of the PAY Rule™. Now, $Y becomes $A.

If the initial spending rate is too high, spending will plummet too quickly without recovery on the downside, and the $A spending threshold cannot be reached. At the same time, if spending is too low initially, it may never rise sufficiently in the bad luck scenarios to meet the needed threshold.

There may not be any level of initial spending that can work. In the bad luck scenarios, no spending strategy worked to keep spending above the desired threshold.

But if we calibrate the $A threshold (previously the $Y threshold) to wealth instead of spending, we do not have this problem. The PAY Rule™ works very well when defined as follows:

Retiree Accepts a |

A number of spending rules include sudden and large discrete changes to spending throughout retirement. With an approach like the traditional 4% rule, when the portfolio is depleted, someone starting with $1 million may spend $40,000 one year and $0 the next.

This can make it harder to compare different spending strategies since the PAY Rule™ may calibrate to a spending strategy that changes dramatically in the year following Y. By shifting the focus to remaining wealth, we reduce the incidence of these discrete shifts to spending.

The PAY Rule™ acts as a behind the scenes constraint to calibrate shortfalls between the strategies, allowing for a better overall understanding of the distribution of potential spending afforded by the strategies.

An important remaining issue, though, is how individuals decide on the parameters for the PAY Rule™. These three parameters should be considered:

- Length of the planning horizon,
- Allowed failure probability by the horizon, and
- The safety margin for remaining wealth at the planning horizon.

A more conservative retiree would choose:

- A lower probability for
**P%**in order to better avoid the bad outcome, - A higher threshold for
**$A**in order to preserve more wealth as a safety margin to cover contingencies, including the possibility of outliving the planning horizon, and - A longer retirement horizon for
**Y**in order to plan for a time period with a smaller chance to outlive.

These three variables are chosen jointly, leading to an overall level of risk for the spending plan. If each parameter is chosen to be extra cautious, the overall degree of plan conservativeness will be high, with the implication that retirement spending must be less in order to meet the requirements of the downside risk threshold.

Not all variables need to be overly conservative. For instance, a higher value for $A means that there is still a larger safety margin for wealth to cover unexpected longevity, which in turn could justify a smaller value for Y. Alternatively, if P% is already quite low then perhaps there is more discretion to justify a lower value for $A or a lower value of Y years.

Ultimately, individuals must find a formulation that creates an acceptable level of downside risk—making each plan comparable—so that the focus can then be shifted to evaluating the overall distribution of spending, the direction of spending over retirement, and the degree of spending volatility.

Factors to consider in choosing parameters for the PAY Rule™ include flexibility to reduce spending, fear of outliving the planning horizon, legacy goals, and the availability of other contingency assets or insurance to protect from spending shocks.