Sunday, April 26, 2015

Revisiting the Guyton Decision Rules

To err is human, and I am very human.  In this post I will issue not one but two corrections of errors made in prior posts.

In our post of April 18, 2015, we showed a graph that compared the expected pattern of future spending budgets for a hypothetical age 65 male retiree who buys a fixed income annuity (Single Premium Income Annuity, or SPIA) under the Actuarial Approach (assuming desired increases in the annual budget equal to the assumed future annual rate of inflation) with budgets produced using the Guyton Decision Rules.  Budget amounts shown were total budgets, including Social Security, payments from the annuity and withdrawals from accumulated savings. 

Subsequent to the April 18th post, I received a nice note from Dr. Wade Pfau indicating that I appeared to have incorrectly applied the Guyton Decision Rules in the example.  Instead of increasing the prior year’s budget with inflation (the preliminary withdrawal amount for the year), the Guyton Decision Rules impose a 10% reduction in the withdrawal amount for a year in which the preliminary withdrawal amount divided by accumulated savings at the beginning of the relevant year exceeds 120% of the initial withdrawal rate.  Mr. Guyton refers to this decision rule as the “capital preservation rule.”  I correctly applied this reduction, but I was unaware, however, that this capital preservation rule is not applied if the retiree is “within 15 years of the maximum planning age.”

Graph #1 below corrects the graph provided in the April 18th post by ceasing application of Mr. Guyton’s capital preservation rule at age 80.   I will also add a warning to my post of July 3, 2014 cautioning those who may visit that post that the graph shown is not based on a correct interpretation of the Guyton Decision Rules.

Graph 1 (click to enlarge)
Dr. Pfau also indicated that since many retirees like higher real dollar spending early in retirement, it wasn’t so obvious to him that the constant spending budget produced under the Actuarial Approach was more desirable.  I’m was actually a little surprised to hear this from Dr. Pfau, as most withdrawal strategies appear to have constant real dollar spending as an objective, and I was somewhat curious as what there was about buying a fixed income annuity that would significantly change someone’s spending objective.  But, be that as it may, as indicated in my previous post, it is easy to change the shape of expected future real dollar budgets under the Actuarial Approach to satisfy a retiree’s objectives.  For example, Graph #2 shows expected future real dollar spending budgets if the same hypothetical retiree makes the conscious decision to front-load his spending budget by inputting 0% desired increases in the portion of his total spending budget attributable to accumulated savings and annuity payments (the Social Security component of his spending budget would still be expected to increase by the inflation assumption of 2.5% per annum).
Graph 2 (click to enlarge)
While the spending budgets shown in Graph 2 for the two approaches are close, the important distinction between the two approaches is that the decision to front-load under the Actuarial Approach is a conscious one where the retiree is fully aware of the out-year implications if future experience is close to assumed experience on average (and the retiree is aware that he has made a commitment not to give himself inflation increases in future years, at least with respect to the portion of his spending budget attributable to the annuity and withdrawals).  The same cannot be said if he uses the Guyton Decision Rules because the retiree doesn’t know what the assumptions for future experience are under that approach.

Even though ceasing application of Guyton’s capital preservation rule when the retiree is within 15 years of the maximum planning age may improve the Guyton’s Decision Rules, I am still not a fan of them.  They are unresponsive to changes in expected future investment returns (nominal or real), changes in expected future levels of inflation (as inflation may affect fixed dollar income components of a retiree’s portfolio), or changes in expected life expectancy.   As previously mentioned, the Guyton Decision Rules do not coordinate with fixed income annuity/pensions and they do not directly consider a bequest motive.  If experience is unfavorable, the retiree can run out of accumulated savings if the rules are blindly followed.   For example, under the Actuarial Approach, a 5.5% withdrawal rate for a retiree with a 30-year expected retirement period with no other sources of retirement income is consistent with an investment return assumption of 6% per annum and an inflation assumption of 2% annum (assuming the retiree desires constant real dollar spending in retirement).  If actual experience is less favorable than these assumptions, real dollar withdrawals under the Guyton Rules will be reduced frequently prior to reaching the 15-year cut-off mark (real dollar withdrawals are expected to be reduced in the 9th year even if experience exactly follows these assumptions).  After the 15th year, there are no cut backs, but there is a risk of running out of money.  Alternatively, if experience is more favorable than these assumptions, it is unlikely that withdrawal rates under the Guyton Rules in later years will fall as low as 4.6%, the approximate threshold for increasing withdrawals under Guyton’s “prosperity rule.”  Therefore, a retiree who experiences favorable experience will likely underspend relative to his objectives.  Finally, my actuarial training causes me to seriously question any approach that doesn’t periodically match assets with liabilities (the present value of the future expected/desired withdrawals and annuity payments) under a reasonable set of assumptions about the future.

As a further illustration of how the Guyton Rules fail to coordinate with other fixed income sources of retirement income, Graph #3 shows expected future real dollar spending budgets for our hypothetical retiree under the assumption that instead of buying the immediate annuity at 65 (SPIA), he spends $150,000 of his accumulated savings on a deferred income annuity (DIA) with benefits commencing at age 80.  According to today’s website, he would be eligible to receive payments of $40,776 for life starting at age 80 (and nothing if he dies prior to age 80) for a premium of $150,000.  Using the Excluding Social Security spreadsheet on this site and inputting the recommended assumptions, $850,000 in accumulated assets ($1,000,000 minus the $150,000 used to purchase the DIA), $40,776 in deferred annuity payments and 16 years as the deferred annuity commencement year [Note, since the retiree in this instance is age 65 in year 1, he is assumed to reach age 80 in year 16, 15 years later.  This is correction #2 of this post as I myself haGraph 1 (click to enlarge)ve made the mistake of inputting 15 years for a deferred annuity starting at age 80 or twenty years for a deferred annuity starting at age 85 for a 65 year old retiree in prior posts discussing deferred annuities/QLACs].  Finally, this graph also assumes that the retiree makes the decision to front-load spending in the same manner as for Graph #2 by inputting 0% desired increases in future spending budgets attributable to the annuity and withdrawals from accumulated savings.  

Graph #3 (click to enlarge)
Graph #3 shows that the Actuarial Approach produces an expected total spending budget pattern that is comparable to the pattern it produced in Graph #2, while the expected spending budget pattern produced by the Guyton Spending Rules under these assumptions doesn’t appear to be consistent with the retiree’s front loaded spending objectives.