Switching Thresholds

Research on Safe Withdrawal Rates

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JWR1945
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Switching Thresholds

Post by JWR1945 » Thu Sep 11, 2003 9:27 am

Switching Thresholds

This is an early investigation of thresholds for switching stock allocations according to P/E10. I have looked at thresholds of 12, 15 and 18. I expect to add more in the future. Because of the 1881-1920 anomaly, I have had to analyze everything manually. I have tried looking at the entire 1871-2002 period, but the early years mask much of the information seen in the later years. That slows down the analysis.

I used the modified Retire Early Safe Withdrawal Rate calculator (i.e., modified from version 1.61). In its original form, the portfolio consisted of stocks and commercial paper. In my modified form, the portfolio consists of stocks and TIPS (Treasury Inflation Protected Securities). In both forms, the stock allocation is switched between two levels depending upon whether P/E10 is less than a threshold. The Retire Early Safe Withdrawal Rate calculator is not as easy to use as the FIRECalc, but it presents all of the data, which make analysis easier. The biggest thing that has helped me to collect detailed data is writing down column numbers and years together. For example, column AZ is for 1921. Years are not visible when looking at balances but column numbers (actually, letters) are always visible. That helps me identify when a failure has occurred.

To help interpret cause and effect, these are the years from 1921-2002 in which P/E10 equaled or exceeded the threshold. For a threshold of 12.0, the years were 1927-1931, 1934, 1936-1941, 1945-1946, 1952-1974 and 1987-2002. For a threshold of 15.0, the years were 1928-1931, 1936-1937, 1939-1940, 1946, 1955-1957, 1959-1973 and 1989-2002. For a threshold of 18.0, the years were 1928-1930, 1937, 1956, 1959-1969, 1973 and 1992-2002. [The threshold of 18.0 data have been corrected.]

Compensating for Today's Market

In this analysis I have set the withdrawal rate at 6%, the TIPS interest rate at 4% and expenses at 0.20%. Expenses apply equally to all securities inside of the calculator. The 0.20% expense ratio is realistic for a low cost index fund, but it is much too high for TIPS. In effect, I have modeled TIPS with an interest rate of 3.8%.

Although these values may seem strange, I have selected them to compensate for the realities of today's stock market. Stock valuations are outside of the historical range and so are their dividend yields. Today's TIPS have a higher interest rate (around 2.8%) than today's dividend yields. In the past, dividend yields were 3% or more. To simulate something using the stocks of the past, it is necessary to increase the interest rate of the TIPS. I added 1% to the interest rate of the TIPS and 1% to the withdrawal rate. Normally, I would have chosen a withdrawal rate of 5% in order to have enough failures for analysis but not too many.

It is very important to understand that we are in uncharted territory today. The stocks of the past no longer exist. Prices are higher and dividend yields are lower than we have seen in the historical database. It is exceedingly important to identify cause and effect relationships whenever possible and not to rely upon numbers alone. My emphasis in this analysis is to learn about switching thresholds. These are early results and neither the data set nor the analysis is complete.

These are the results for a stock allocation that switches between 80% stocks (when below threshold) and 20%

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Threshold 20    25     30     35     40
12        0      0     13     18     18
15        0     15     15     16     19
18        0     11     15     18     22


There were no failures that occurred at 25 years or earlier when the threshold was set to 12. With a threshold of 15, such early failures occurred in 1960-1974. With a threshold of 18, such early failures occurred in 1961-1970 and 1974.

These are the results for a stock allocation that switches between 80% stocks (when below threshold) and 50%.

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Threshold 20     25     30     35      40
12         1      7     13     17     22
15         6     14     15     20     20
18         5     15     19     21     21


With a threshold of 12, failures at 25 years or less occurred in 1963, 1966-1970 and 1973. With a threshold of 15, such early failures occurred in 1961-1974. With a threshold of 18, such early failures occurred in 1930-1931 and 1962-1974.

These are the results for a stock allocation that switches between 50% (when below threshold) and 20%.

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Threshold    20    25     30      35      40
12           0      1     16     20     21
15           0     11     16     19     20
18           0      6     17     22     27


With a threshold of 12, there was a failure at 25 years or less in 1966. With a threshold of 15, such early failures occurred in 1962-1970 and 1972-1973. With a threshold of 18 such early failures occurred in 1963 and 1965-1969.

These are the baseline results. The threshold was set at 50, which means that there was no switching. These are the stock allocations when below threshold. (The stock allocation at or above threshold was set to 20%).

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Allocation  20      25     30     35     40
20%          0       9     28     38     49
50%          1      15     18     24     28
80%         14      17     19     23     24



Analysis

TIPS with an interest rate of 3.8% have a Safe Withdrawal Rate of 7.228% over 20 years and 4.903% over 30 years. This means that the balance will be zero exactly at 20 or 30 years, respectively. Thus, TIPS alone would have zero failures within 20 years. This is reflected in the baseline for 20% stocks. As the stock allocation increases, especially at 80% stocks, the odds of a very early failure grow substantially. Notice that there are no failures at 20 years (or earlier) when the stock allocation is 20% when above threshold. Using a 50% stock allocation when above threshold results in a few failures early on.

The data support using a low threshold (i.e., 12) and using a low stock allocation when above threshold (i.e., use 20% as opposed to 50%).

The dangerous years occurred in 1960-1974. Only with a high stock allocation and a high threshold (80% / 50% stocks and a threshold of 18 ) did the depression years of 1930 and 1931 show up as dangerous years. (In the absence of switching, there were many dangerous years and they included some in the 1930s.)

In general, switching improved results.

I expect that looking at additional thresholds will allow us to draw additional conclusions.

Have fun.

John R.

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