SWR as a Funtion of PE10
This SWR vs PE10 analysis uses the data collected and posted by JWR at (JWR NoFeeBoard Study). Basic analysis of SWR as a function PE10 is presented on intercst’s board at
50/50 Portfolio Analysis
and
80/20 Portfolio Analysis

The raw data is the result of computing safe withdrawal rate for a 30 year retirement starting in each year from 1921 to 1980 using FIRECalc (FIRECalc Historical Simulator) along with the standard unit retiree assumptions. The resulting SWR for each year is then associated with the PE10 value of the initial year in retirement.

The plotted results (SWR vs PE10) indicate that using an initial withdrawal rate of approximately 4% and adjusting for inflation would have survived at least 30 years (assuming inflation adjusted spending model and 0.2% expense ratio) for any retiree who started their retirement since 1921 regardless of PE10 value when the retirement started. In addition, the SWR-PE10 analysis indicates that SWR has been essentially independent of PE10 value for high values of PE10. In the case of a 50/50 stock/bond portfolio, the historical SWR is shown to be ~4% and independent of PE10 for values of PE10 greater than 13. In the case of an 80/20 portfolio, the SWR has been ~4% becoming independent of PE10 for values of PE10 greater than 16.

Significance of PE10 <13 and PE10<16
For PE10 values less than 13 and 16 respectively, the historical record appears to exhibit a dependence of SWR on PE10. There are several reasons why one might choose to ignore this dependence and continue to use the guaranteed safe initial withdrawal rate of 4%. Specifically, those reasons include:

1) Shiller’s data shows that PE10 has been above 13 since March 1986 and above 16 since March 1987. So, the historical data of JWR’s study indicate that PE10 values have had no impact on the SWR of anyone retiring during the past two decades or of those due to retire soon.
2) The 4% rate that applies to PE10 values above 16 has clearly been safe historically (very safe) for low PE10 values as well. Rather than start off trying to use a higher initial withdrawal rate based on more detailed but imperfect SWR-PE10 analysis, a retiree would be safer to start off using 4%, and then increase the withdrawal rate if their portfolio grows significantly in the first few years of retirement. There is no compelling reason to take on the extra risk of a high SWR.
3) The historical SWR dependence on PE10 for low PE10 values exhibits a significant amount of variation clearly indicating that factors not captured in PE10 impact the SWR more dramatically when PE10 has been low. This can be seen in any of the applicable plots of the SWR-PE10 data.
a. The plot of all SWR vs PE10 data shows greater dispersion at lower PE10 values.
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b. The plot of maximum SWR vs PE10 is less smooth and not monotonic at lower PE10 values.
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c. The variation of historical SWR vs PE10 increases for lower PE10 values.). This increased variation is indicative of other important parameters having significant impact on the results. An attempt to describe the SWR in terms of only one variable in this region is likely to overlook other important interactions and therefore incorrectly predict future SWR. Notice in the plots below that the variation in historical SWR increases for decreasing PE10 values. The PE10 regions that exhibit zero variation are regions that consist of a single data point.

Curve Fit to the SWR-PE10 Data
All of the data (both low and high PE10 regions) defined from the SWR-PE10 analysis can be approximated using a decaying exponential curve. Exponential relationships are common in the world of finance and nature. Types of problems that are described by exponentials include interest rate problems, mortgage problems, population problems and radioactive decay problems. The general form of a decaying exponential as applied to SWR and PE10 is given by

SWR = A* exp(b*PE10) + SWR0

Where A, b and SWR0 are constants used to fit the curve to the associated data. SWR0 also has the significance of representing the lowest possible SWR that is achieved when PE10 approaches infinity. (Hopefully we never see PE10 go that high. :^)

The resulting curve fit to the 50/50 and 80/20 data is shown below.

The optimization of the exponential parameters to the data used to create these plots was not a least squares fit. This is an inappropriate choice of metric for this problem since the goal is to find the maximum SWR that is 100% safe, not the average SWR. The optimization goal was chosen to find the curve that fell closest to the data without exceeding any SWR point by more than 0.05%.

The following values of the constants apply to the charts above:

50/50 80/20
A 10.93 22.46
b 0.201 0.217
SWR0 3.80% 3.94%

Why You Should Ignore These Curves As Well As Any Other Empirical SWR vs PE10 Relationships

The amount of variation in the raw SWR-PE10 data is a clear indication that important factors not captured by PE10 are very important to the resulting SWR. It becomes even clearer if the entire historical data set is used rather than just the data since 1921. (see http://www.retireearlyhomepage.com/pestudy1.html) Viewing SWR in terms of only PE10 clearly ignores other important factors that are not completely understood or quantified. An attempt to predict future SWR based on PE10 alone is not justified.

There is no more reason to believe that a decaying exponential is an appropriate functional form to predict future SWR-PE10 dependence than there is to believe that a straight line or an inverse function or any other functional form will describe the future. The exponential curves match the worst case historical data fairly well, but they may not align themselves with future data. In the absence of some underlying theory, an empirical curve fits is nothing but a shorthand method of summarizing the existing data. It is never valid to apply empirical curves to extrapolations outside the data’s numerical or temporal range.