Switching Thresholds with 80% / 20% Stocks

Research on Safe Withdrawal Rates

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JWR1945
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Switching Thresholds with 80% / 20% Stocks

Post by JWR1945 » Tue Sep 16, 2003 1:57 pm

Description

This is an analysis of switching allocations in a portfolio consisting of stocks (i.e., the S&P 500 index) and TIPS (Treasury Inflation Protected Securities) on the basis of P/E10. When P/E10 is below a specified threshold, the stock allocation is 80%. When P/E10 is greater than or equal to the threshold, the stock allocation is 20%.

I determined Historical Database Rates using a modified version of the Retire Early Safe Withdrawal (Rate) Calculator (i.e., a modified copy of version 1.61 dated November 7, 2002). I modified it so that its switch feature incorporated stocks and TIPS instead of stocks and commercial paper.

Today's stock market is outside of the historical range both in terms of valuations and dividend yields. That is, prices are high and dividend yields (and payout ratios) are low. To make use of the historical database, I have selected test conditions that are somewhat unusual. I have set the interest rate on the TIPS at 4% (above inflation) and I have set the withdrawal rate at 6%. The high interest rate is necessary because long-term TIPS currently yield considerably more than stocks. Yet, stocks have yielded more than today's TIPS until just recently. The high withdrawal rate is needed to ensure enough portfolio failures to permit meaningful data analysis while not being overwhelmed by portfolio failures. If I had not set the interest rate on the TIPS so high, I would have set it at 5% rate. I have left the expense ratio at the 0.20% default level of the Retire Early Safe Withdrawal Calculator. That is realistic for a low-cost stock index fund. It is much too high for TIPS. In essence, I am simulating TIPS with a 3.8% interest rate, which is 1% higher than what is available on the secondary market today.

I have restricted this analysis to the years of 1921-2002 to avoid the effects of a data anomaly associated with earlier years.

The Numbers of Failures versus Thresholds

This table lists the number of failures on or before a specified number of years when there is switching according to P/E10 at various thresholds. The withdrawal rate is 6%, the TIPS interest rate is 4% and the expense ratio is 0.20%.

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Threshold        20      25      30      35      40
10              0        0      12      24      32
11              0        0       8      14      18
12              0        0      13      18      18
13              0        0      13      15      15
14              0       15      15      16      19
15              0       15      15      16      19
16              0       14      15      16      18
17              0       15      17      20      22
18              0       11      15      18      22
19             10       14      15      18      22
20             10       12      15      17      20


When Failures Occur

This table shows which portfolios failed on or before 40 years. The portfolios began in the years that I have listed.

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Threshold = 10 has portfolio failures in the 1930s, 1940s, 1950s and 1960s.
Threshold = 11 has portfolio failures in 1938 and 1953-1969.
Threshold = 12 has portfolio failures in 1953-1970.
Threshold = 13 has portfolio failures in 1956-1970.
Threshold = 14 has portfolio failures in 1956-1974.
Threshold = 15 has portfolio failures in 1956-1974.
Threshold = 16 has portfolio failures in 1957-1974.
Threshold = 17 has portfolio failures in 1929-1932, 1940, 1957-1958 and 1960-1974.
Threshold = 18 has portfolio failures in 1930-1932, 1938, 1940, 1957-1958 and 1960-1974.
Threshold = 19 has portfolio failures in 1930-1932, 1938, 1940, 1957-1958 and 1960-1974.
Threshold = 20 has portfolio failures in 1930-1932, 1957-1958 and 1960-1974.


When Thresholds are Crossed

This table shows when P/E10 is greater than or equal to various thresholds. The total time period is 1921-2002. Stock allocations are reduced whenever a threshold is crossed (i.e., whenever the P/E10 is greater than or equal to the threshold).

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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 and1983-2002.
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 1986-2002.
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.


Data Interpretation

Except at the extremes, lower thresholds mean smaller stock allocations and higher thresholds mean higher stock allocations. Thus, a lower threshold means that a very early failure is unlikely but long-term growth is limited. A higher threshold means that very early failures can occur, but those portfolios that survive will have robust growth.

We see these effects in the data. When the threshold was between 10-13, there were no failures on or before 25 years. When the threshold was between 14-18, there were some failures on or before 25 years, but none for 20 years. When the threshold was 19-20, there were failures as early as 20 years and less.

Interestingly, we see a qualitative change between setting the threshold at 10 and setting it at 11. In essence, a threshold of 10 is so low that the portfolio behaves almost as if it consisted of TIPS alone. At a threshold of 11, portfolios have enough growth to extend the lifetime of many.

For thresholds between 12-16, the influence of the Great Depression has been overcome (in terms of 40-year survival rates).

In terms of earlier failures, a threshold of 17 has failures at 24 and 25 years in 1931 and 1932 respectively. A threshold of 18 has failures at 28 and 29 years in 1931 and 1932 respectfully. Thresholds on either side, above and below, avoid these early failures (i.e., within 30 years) associated with the Great Depression.

In almost all cases of interest, it is sufficient to examine the years from 1953-1974. In fact, almost all of the really bad portfolios (i.e., earliest failures) started between 1960-1974. In quite a few cases portfolios started after 1974 were headed toward failure, but did not because time ran out (i.e., the historical data ended in 2002).

Applications

When applying this information, do not look at the numbers themselves without thinking. The switching algorithm has only two levels. Either the stock allocation is very high (80%) or it is very low (20%). There is no intermediate level available. It makes sense to act in a more gradual manner.

The lower thresholds are attractive. This suggests purchasing stocks at bargain levels and relying upon TIPS to get you through more hazardous times. TIPS, especially with higher interest rates, allow you to avoid the earliest failures. However, you need at least a little bit of growth. If a third stock allocation were available, it is likely that using an intermediate stock allocation between a threshold (in the neighborhood) of 12-18 would provide more growth without increasing risk.

The TIPS interest rate and the withdrawal rate were chosen to match certain characteristics of stocks in the historical record with today's choices. In terms of today's market and roughly speaking, I have added one percent to both numbers. To translate that into an actual portfolio, it suggests that the number of failures are (pessimistic, but) reasonable for 2.8% TIPS and a 5% withdrawal rate.

Have fun.

John R.

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