Analysis of Switching Data
We are in the early stages of analyzing portfolio switching. Until just recently, it had been thought that switching portfolio allocations (on the basis of P/E10) caused only a minimal improvement when the fixed income component was commercial paper. Very recently, we have looked at switching using TIPS, which showed a substantial improvement. It required a modification of the Retire Early Safe Withdrawal [Rate] Calculator for us to collect that data. Eventually, I ended up looking at switching with commercial paper once again. I found that switching with commercial paper produces a substantial improvement.
What had happened is that the calculator had been designed to accommodate two switching thresholds and three stock allocations. Evidently, it had a bug and its switching capability was cut back to one threshold and two stock allocations. But that change was not publicized and the only data that was collected showed little improvement.
The Calculator and its Input Data
Analyzing data with the Retire Early Safe Withdrawal Calculator requires more effort than using the FIRECalc, which I had used previously. It has the advantage that all of the details related to a calculation can be extracted. The Retire Early Safe Withdrawal Calculator is the only calculator that I know of with a switching capability. I have posted instructions on the Excel thread so that people can modify it to use TIPS with switching and also so that withdrawals can be a percentage of the current balance. That makes a total of four calculators: switching with commercial paper versus TIPS and withdrawing a constant percentage of the portfolio's initial balance versus the current balance.
These results make use of the Retire Early Safe Withdrawal Calculator as-is. It is both powerful and useful. It is version 1.61 dated November 7, 2002. It is available for download for free at http://rehphome.tripod.com/re60.html
The calculator is in a zip file. Noncommercial users can download a Free ZIP wizard from Coffee Cup software: http://www.coffeecup.com/freestuff/ I learned it from one of
Kim Komando's Tip of the Day http://www.komando.com/newsletter.asp
Yale Professor Shiller compiled the data that is used with the Retire Early Safe Withdrawal Calculator (and other historical sequence calculators such as the FIRECalc). He has made it available for downloading for free at http://www.econ.yale.edu/~shiller/data.htm
Setting up the Calculator
I use an initial balance of $100 000 to reduce the effect of round-off errors. I leave most values at their default settings. That includes expenses of 0.20% of a portfolio's current balance, using the CPI, increasing (or decreasing) withdrawal amounts to match inflation (or deflation) and re-balancing the portfolio annually.
I have chosen to use the default values for the month (January) and the split of the withdrawal amount (50%). This means that the withdrawal amount is calculated in terms of January 1 and then split in half (or 50%). The first withdrawal is made on January 1 and the second is made on December 31 in each year. This second withdrawal is just a little bit different from the withdrawal that occurs on the next day, January 1 of the following year, because the inflation index changes from one year to the next.
Data input cells F19, B20 and I20 work. Cells I19 and F20 are not used (with this version). Cell F19 is the Low PE to Mid PE switching threshold. B20 is the Stock Allocation for Low PE Years and I20 is the stock allocation for High PE Years. As indicated in the Stock Switching Model box, put a 6 in the Fixed Income Series and put 0% into the cell for the Stock Allocation. (The wording on line 6 is somewhat confusing. 0% is what you put into cell B6.)
It has not been necessary for me to select a payout period. The summaries that I have used are always calculated. When reading the summaries, notice that they are calculated using complete sequences, not partial sequences. (I have not verified the details beyond observing that they vary.) That is very important. The last complete 40-year sequence starts in 1962. That means that the 40-year summary data excludes many of the most dangerous years in the historical record for starting a retirement. The information can be read from the data, but not from the summary table.
Choosing Inputs
From an earlier survey (using data summary tables), I decided to use a withdrawal rate of 4.5% of the initial balance. That rate was almost always safe for thirty years, but it resulted in enough failures by forty years for analysis to be meaningful. I retained my 80% stock allocation below threshold that I had used when investigating switching with TIPS. At this stage I have investigated P/E10 thresholds of 12, 13, 14, 15, 16 and 17 with stock allocations (above threshold) of 20%, 40% and 60%.
I had initially looked at thresholds of 12, 14 and 16. Then I filled in 13, 15 and 17. Later, when you look at the data, you will see why I had to add more thresholds. You will also see that adding them was a very good decision. From early work I knew that thresholds below 12 were not likely to be better and that very high thresholds were not likely to be better, although there might be something worth learning at P/E10 thresholds of 18, 19 and 20.
The P/E10 threshold is put into cell F19. The stock allocation (above threshold) is put into cell I20. You must always make sure to press enter or click on another cell so that your new input is included in the calculations.
Collecting the Results
I record the start and end of a retirement sequence in terms of the 01/01 row for each year. The first such year is 1872, not 1871, using my method. As such, my dates may not line up with others. For example, my results are offset from those of the FIRECalc by exactly one year. For my method, the row is 199 and the first cell is C199. Notice that there is a 12/31 entry on row 215 in cell B215. Column B corresponds to the year 1871 (row 197 identifies the years corresponding to individual columns).
All historical sequence readouts are for 60 years. After that, no further data are collected for that sequence. By using my method I limit all data output sequences to 59 years (maximum). Again, on row 199, I start with cell C199 (which is year 1872) and end with cell BJ199 (which is 1931). The difference is 1931-1872 = 59, not 60. If you look at BJ215, you will find the final balance (corresponding to year 60).
It is helpful to make a list that matches column letters with the years shown on row 197.
For reducing data, list the column letter at the start of a sequence that fails and the column letter at which failure first occurs. (I.e., the balance becomes negative, which is indicated by parentheses.) I have found it helpful to start by looking at the end of sequences because so many last for an entire sixty years. Do not convert the column letters to years right away. You save a lot of time by delaying that step.
After you have a complete set of data, translate all of the years at the beginning and end of failed portfolios. Then convert them into the start year and the year in which the failure first occurred. For example, on one of my conditions the start year column letter was AP and failure first occurred at CE. Translating from column letters to years, the 1911 portfolio failed first in 1952. It lasted (1952 - 1911 = ) 41 years. Then I write down 1911F41 as the result. I have a complete set of data when I complete that list. It is easy to sort out failures according to portfolio lifetimes.
Making Tables
Put the data into tables to make the data easier to understand. In this case, I ended up putting together all of the tables that were possible until I figured out what was going on.
One very simple lesson is that sequence lengths of 50 and 60 years simply confuses one's analysis. We are most interested in those sequences that fail at lower withdrawal rates. The decade of the 1960s stands out as having many early failures. The last complete 40-year sequence started in 1962. Thus, many of the failures in the 40-year portfolio lifetime data are for only partially completed sequences. There is nothing else from the 1960s that gets into the 50 and 60-year summaries. Any additional failure has to come from the Great Depression or earlier.
We must break out the periods of 1871-1920 and 1921-1980 for separate analysis. We cannot ignore the 1871-1920 anomaly since we know that it exists. Admittedly, it is a burden. It is a necessary burden.
The tables that have the most information show the number of failures for different thresholds and stock allocations (above threshold). I made separate tables for 30-year and 40-year portfolio lifetimes. I made separate tables for 1872-1980, 1872-1920 and 1921-1980. (Refer to my earlier remarks about how I label the historical sequences and why 1872 is the first sequence according to my labeling method.) That totals six tables.
These tables have been corrected (the 1955 results were in error).
Results for 30-Years
1872-1980 results with a 30-year lifetime and a 4.5% withdrawal rate.
Code: Select all
Threshold 20% 40% 60%
12 0 0 2
13 0 0 2
14 2 2 5
15 2 4 6
16 1 2 5
17 1 2 3
Code: Select all
Threshold 20% 40% 60%
12 0 0 0
13 0 0 0
14 0 0 0
15 0 0 0
16 0 0 0
17 1 1 1
Code: Select all
Threshold 20% 40% 60%
12 0 0 2
13 0 0 2
14 2 2 5
15 2 4 6
16 1 2 5
17 0 1 2
1872-1980 results with a 40-year lifetime and a 4.5% withdrawal rate.
Code: Select all
Threshold 20% 40% 60%
12 13 7 10
13 10 6 10
14 13 13 12
15 15 13 13
16 11 12 10
17 11 12 13
Code: Select all
Threshold 20% 40% 60%
12 5 2 3
13 3 2 3
14 3 2 3
15 5 2 3
16 2 2 3
17 3 3 5
Code: Select all
Threshold 20% 40% 60%
12 8 5 7
13 7 4 7
14 10 11 9
15 10 11 10
16 9 10 7
17 8 7 8
Keep in mind that we are looking for clues as to causal relationships. We never depend upon numbers in isolation. We are interested in spotting any sensitivities. We want to develop approaches that tolerate errors in our estimates. We need to report what we find whether or not we understand it completely. Somebody else may be able to interpret what we have missed.
Those tables that we have made allow us to visualize what is going on. Bigger numbers mean more failures, which is bad. Smaller numbers mean success, which is good.
Look at each column individually. This shows us how the results depend upon thresholds by themselves. Notice that the number of failures starts low, increases and then falls again as we vary the threshold from 12 to 17. This tendency is strongest in the 1921-1980 tables. If anything, the 1872-1920 data weakens this relationship.
Then, again, there are only a few failures in the 1872-1920 data. That means that data from the 1871-1920 anomaly influence results minimally, except to give us a sense of well being. In this case we can point to significant periods of deflation as a specific factor since commercial paper has always produced a positive (nominal) interest rate. Significant periods of deflation occurred until 1933 (or so). Subsequent times of deflation have been very mild and isolated.
This may help us understand why we were able to use the Historical Database Rates for the entire 1871-1980 period. The 100% safe level is always determined by the single year that begins the worst case sequence. Almost all of those years came from the post-anomaly period. Thus, the entire period can be used at the 100% safe level, but it may be overly optimistic at lesser degrees of safety. (This is similar to adding a lot of zero to a list of numbers and then claiming that the amount of data has been increased.)
Now look at individual rows.
Both sets of tables show that a 60% stock allocation (when above threshold) is harmful. Both 20% and 40% look good in the 30-year tables. There is a dip that favors 40% in the 40-year table. It is especially noticeable if you limit yourself to thresholds of 12, 13 and 17. These effects are mild, indicating a reasonable amount of tolerance if we make an error.
Once again, we see that the 1872-1920 data adds little, if any, benefit.
It is a good idea to look for diagonals or other features. Those would be interactions. None are immediately obvious.
I had already made a list of switching intervals versus P/E10 threshold settings. I had thought that the intermediate levels of 14, 15 and 16 might have switched more frequently than 12, 13 and 17. That turns out to be untrue. I have copied my original summary for the 1921-1980 period.
Code: Select all
Lower thresholds: Years 1921-2002 (entire period).
Threshold = 5 Years 1921-2002 (entire period).
Threshold = 6 Years 1922-2002.
Threshold = 7 Years 1923-2002.
Threshold = 8 Years 1923-1981 and 1983-2002.
Threshold = 9 Years 1925-1932, 1934-1979, 1981 and 1982-2002.
Threshold = 10 Years 1926-1931, 1934-1977 and 1985-2002.
Threshold = 11 Years 1926-1931, 1934-1941, 1944-1948, 1951-1974, 1976-1977 and 1986-2002.
Threshold = 12 Years 1927-1931, 1934, 1936-1941, 1945-1946, 1952-1974 and 1987-2002.
Threshold = 13 Years 1927-1931, 1934, 1936-1941, 1946, 1953, 1955-1974 and 1987-2002.
Threshold = 14 Years 1928-1931, 1936-1937, 1939-1940, 1946, 1955-1957, 1959-1973, 1987 and 1989-2002.
Threshold = 15 Years 1928-1931, 1936-1937, 1939-1940, 1946, 1955-1957, 1959-1973, 1989-2002.
Threshold = 16 Years 1928-1931, 1936-1937, 1940, 1955-1957, 1959-1973, 1990 and 1992-2002.
Threshold = 17 Years 1928-1930, 1936-1937, 1956, 1959-1970, 1972-1973, 1990 and 1992-2002.
Threshold = 18 Years 1928-1930, 1937, 1956, 1959-1969, 1973 and 1992-2002.
Threshold = 19 Years 1929-1930, 1937, 1962-1969 and 1992-2002.
Threshold = 20 Years 1929-1930, 1937, 1962, 1964-1969 and 1993-2002.
Threshold = 21 Years 1929-1930, 1937, 1962, 1964-1966, 1968-1969, 1994 and 1996-2002.
Threshold = 22 Years 1929-1930, 1965-1966 and 1996-2002.
Threshold = 23 Years 1929, 1965-1966 and 1996-2002.
Threshold = 24 Years 1929, 1966 and 1996-2002.
Threshold = 25 Years 1929 and 1997-2002.
Threshold = 26 Years 1929 and 1997-2002.
Threshold = 27 Years 1929 and 1997-2002.
Threshold = 28 Years 1997-2002.
Threshold = 29 Years 1998-2002.
Threshold = 30 Years 1998-2002.
Threshold = 31 Years 1998-2001.
Threshold = 32 Years 1998-2001.
Threshold = 33 Years 1999-2001.
[From an analysis standpoint, dividend levels influence the probability distribution of return by establishing a floor on losses. The mathematical formula looks as if dividend yields have no effect, but that is only superficially. That is similar to what happens during accumulation when one is depositing money instead of making withdrawals. Superficially, there is only a change in sign (to negative withdrawals). In reality, the difference is dramatic. For example, dollar cost averaging is good during accumulation and bad during distribution.]
Have fun.
John R.