Switching Thresholds with 80% / 50% Stocks

Research on Safe Withdrawal Rates

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Switching Thresholds with 80% / 50% Stocks

Post by JWR1945 » Sat Sep 20, 2003 1:08 pm

Switching Thresholds with 80% / 50% Stocks


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 50%.

This extends my earlier studies: Switching Thresholds with 80% / 20% Stocks dated Tuesday, Sep 16, 2003 at 5:57 pm CDT.
and Switching Thresholds with 50% / 20% Stocks dated Friday, Sep 19, 2003 at 6:03 pm CDT.

One of the results of the first study was that there were a large number of very early failures unless the switching threshold was kept very low, no more than 13. That is the result of the high volatility associated with an 80% stock allocation. Above that threshold, there were many failures that occurred on or before year 25. That was because the allocation above the threshold was only 20% stocks, which generated very little growth.

Then I examined a 50%-20% combination. Having a 50% allocation with thresholds between 14 and 16 improved things up to 25 years. But it started to degrade performance on or before 30 years at higher thresholds. That was associated with lower growth whenever the comparison was between a 50% allocation and an 80% allocation. High stock allocations when the P/E10 is above 17 or 18 are dangerous in today's market because dividend yields are lower than alternative investments (long-term TIPS). In previous years stock dividends were sufficient to make stocks attractive even at high valuations. That is no longer true.

All of this is leading us toward a gradual shift in allocations using three levels (80%-50%-20%). We are limited by the calculator, which only allows us to choose two allocations. By looking at an 80%-50% allocation now along with our previous results with 80%-20% and 50%-20% allocations, we can fill in some gaps. We can get an idea of what might happen with an 80%-50%-20% approach.

Standard Conditions

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%. 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       10      17      22      25
11              0        7      17      19      22
12              1        7      13      17      22
13              1        8      15      17      20
14              6       14      15      19      20
15              6       14      15      20      20
16              6       14      17      19      20
17              5       17      19      22      23
18              5       15      19      21      21
19             10       15      19      21      22
20             10       14      19      20      22

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 1930-1932, 1937-1941 and 1957-1973.
Threshold = 11 has portfolio failures in 1930-1932, 1938 and 1956-1973.
Threshold = 12 has portfolio failures in 1930-1931, 1938 and 1956-1974.
Threshold = 13 has portfolio failures in 1938 and 1956-1974.
Threshold = 14 has portfolio failures in 1930-1931, 1938, 1957-1958 and 1960-1974.
Threshold = 15 has portfolio failures in 1930-1931, 1938, 1957-1958 and 1960-1974.
Threshold = 16 has portfolio failures in 1930-1931, 1938, 1957-1958 and 1960-1974.
Threshold = 17 has portfolio failures in 1929-1932, 1938, 1940, 1957-1958 and 1960-1974.
Threshold = 18 has portfolio failures in 1930-1932, 1938, 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, 1938, 1940, 1957-1958 and 1960-1974.


When compared to an 80%-20% allocation, these conditions consistently under-performed except at a threshold of 10. It limited the degradation at 35 and 40 years. It had failures on or before 25 years, but they could be eliminated if there were a third allocation level.

Compared to a 50%-20% allocation, these conditions proved consistently advantageous only at thresholds of 10-11 and 17-20 at 35 and 40 years. This advantage is offset by a very large number of early failures at the higher thresholds. Using a third level eliminates that problem at the lower thresholds.


All improvements are minor. Introducing a third level would improve one's tolerance for errors when compared to an 80%-20% allocation. That has merit in itself, especially to the extent that cause and effect relationships are uncertain.

The important story that is emerging from these studies has to do with dividend yields. When alternative investments produce higher yields than stocks, it is not necessary to maintain a high stock allocation. In fact, the evidence points strongly in the opposite direction. When dividend yields are extremely low, a high stock allocation is justified only if prices (as measured by P/E10) are below average.

Notice that these conclusions are dependent on the fact that stock dividend yields are well outside of their historical range. The underlying cause has to do with volatility. Historically, prices are highly volatile but dividends are stable. Dividends have isolated retirement withdrawals from price volatility. In fact, the historical database rates are barely above dividend yields under worst case conditions.

It is likely that dividend yields will return to their historical range as P/E10 returns to its historical range. That would justify higher stock allocations.

Have fun.

John R.

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