S&P500 and Government Long Bonds (Revised)

I made a brief survey. I determined Historical Surviving Withdrawal Rates using S&P500 and Government Long Bond data from Gummy’s database.

First, I varied the stock allocation in accordance with P/E10. Then, I collected baseline data with fixed stock allocations.

The Calculator

I copied the 1928-2000 Government Long Bond data from Gummy’s database.
Gummy’s (Peter Ponzo’s) Database

The fixed income data in Gummy’s database are more realistic than the existing data in the historical sequence calculators. The existing data use single-year returns only from interest. Gummy’s data include single-year capital gains and losses as well as interest payments. Neither set of data includes transaction costs.

I revised my Gummy 02A version of the Deluxe Calculator 1.1A08. I corrected the year-to-year timing with this revision. I pasted 1928-2000 Government Long Bond data on top of the commercial paper cells corresponding to 1929-2001 (in cells BH177 through EB177). This single-year shift is necessary because each column reference date is for January. An investment’s total return that occurs during 1928 shows up as a January entry in the column for 1929. The December balance in the 1929 column shows up only at the very end of the calculations. It is copied to become the top entry in the column for 1930. And so forth.

I pasted over the commercial paper data because I was interested in varying stock and bond allocations according to P/E10. My calculators allow switching with commercial paper, TIPS and I-bonds, but not with 5-year Treasury Notes and not with 30-year Treasury Bonds. [The Retire Early Safe Withdrawal Calculator, Version 1.61 dated November 7, 2002, from which I made my original modifications, allows switching only with commercial paper.]

Although this treatment of fixed income investments is better than before, it is different from what many fixed income investors are likely to do. Our calculators treat fixed income investments as single-year trading vehicles. They do not allow you to lock in favorable interest rates.

Conditions

I set the starting balance at $100000. I set expenses to 0.20%. I varied the withdrawal rate. I used the CPI for inflation. I examined 30-year sequences starting in 1928-1980. There are 53 sequences. Stock allocations consisted of the S&P500 index from Professor Shiller’s database. I set my withdrawals so that 50% would occur at the beginning of the year and the other 50% would occur at the end of the year. These are the default values.

I took a brief survey. I varied the stock allocation depending upon P/E10. When P/E10 was below the lower threshold (which varied), the stock allocation was 100%. When P/E10 was between the two thresholds, I used an intermediate allocation of 30% or 50% or 70% as indicated. When P/E10 exceeded the upper threshold, which I set at 21, the stock allocation was 0%.

The best intermediate stock allocation (when there was only one intermediate allocation) from a previous survey using commercial paper was 30%. The best P/E10 thresholds were 12 and 21.

I collected baseline data with fixed stock allocations of 0%, 30%, 50%, 70% and 100%.

Procedure

I increased the withdrawal rate in increments of 0.1%. I recorded the highest rate at which all portfolios from 30-year sequences beginning in 1928-1980 survived. I have listed those rates as HSWR.

I continued increasing withdrawal rates in increments of 0.1%. I recorded the lowest withdrawal rate at which 1 or more, 5 or more and 10 or more portfolios failed.

This method allows me to survey a large number of conditions rapidly. By including data with 5 and 10 failures, I am able to spot difficulties associated with probability distributions.

Results

This was a brief survey. This was not a full optimization. This did not include a full sensitivity study.

The Survey of Thresholds and Allocations

Calculator data: 1928-2000.
30-year sequences from 1928-1980, $100000 initial balance, 0.20% expenses.
Calculator settings:
P/E10 thresholds: varies-21-24-80.
Allocations: 100-varies-0-0-0.

P/E10 threshold = 9 and [Intermediate stock] Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 3.9
Ten failures: 4.0

P/E10 threshold = 9 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.0
Ten failures: 4.5

P/E10 threshold = 9 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.1 in years 1963-1968 Ten failures: 4.7

P/E10 threshold = 12 and Allocation =30%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.0
Ten failures: 4.2

P/E10 threshold = 12 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.1
Ten failures: 4.5

P/E10 threshold = 12 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.1 in years 1963-1967
Ten failures: 4.7

P/E10 threshold = 15 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 3.3
First failure: 3.4
Five failures: 3.6
Ten failures: 4.0 in years 1959-1968

P/E10 threshold = 15 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 3.4
First failure: 3.5
Five failures: 3.8
Ten failures: 4.3

P/E10 threshold = 15 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.5
First failure: 3.6
Five failures: 3.9
Ten failures: 4.6

Summary of results with the best intermediate stock allocation, which was 70%.

P/E10 threshold = 9 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.1 in years 1963-1968
Ten failures: 4.7

P/E10 threshold = 12 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.1 in years 1963-1967
Ten failures: 4.7

P/E10 threshold = 15 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.5
First failure: 3.6
Five failures: 3.9
Ten failures: 4.6

Additional conditions with an intermediate stock allocation of 70%.

P/E10 threshold = 8 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.4
First failure: 3.5
Five failures: 3.8
Ten failures: 4.4

P/E10 threshold = 9 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.1
Ten failures: 4.7

P/E10 threshold = 10 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.7
First failure: 3.8
Five failures: 4.2
Ten failures: 4.8

P/E10 threshold = 11 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.7
First failure: 3.8
Five failures: 4.2
Ten failures: 4.8

P/E10 threshold = 12 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.1
Ten failures: 4.7

P/E10 threshold = 13 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.6
First failure: 3.7
Five failures: 4.1
Ten failures: 4.7

P/E10 threshold = 14 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.5
First failure: 3.6
Five failures: 3.9
Ten failures: 4.6

P/E10 threshold = 15 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.5
First failure: 3.6
Five failures: 3.9
Ten failures: 4.6

Baselines

Calculator data: 1928-2000.
30-year sequences from 1928-1980, $100000 initial balance, 0.20% expenses.
Calculator settings:
Fixed allocations. No switching, but with annual rebalancing.
Stock Allocations: 0%, 30%, 50%, 70%, 100%.

Stock Allocation = 0%
30-year Failures in 1928-1980:
HSWR: 2.4
First failure: 2.5
Five failures: 2.7
Ten failures: 2.8

Stock Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 3.1
First failure: 3.2
Five failures: 3.4
Ten failures: 3.8

Stock Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 3.4
First failure: 3.5
Five failures: 3.8
Ten failures: 4.2

Stock Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.5
First failure: 3.6
Five failures: 4.0 in years 1964-1968
Ten failures: 4.6

Stock Allocation = 100%
30-year Failures in 1928-1980:
HSWR: 3.7
First failure: 3.8
Five failures: 4.2 in 1929, 1965-1966, 1968-1969
Ten failures: 4.7

Comparisons

Two conditions with switching did better than the 100% stock allocation. They had lower P/E10 thresholds of 10 and 11. The upper P/E10 threshold was 21. The intermediate stock allocation was 70% (making the stock allocations 100-70-0% when P/E10 fell below, between and above the thresholds).

Five conditions with switching did better than all of the fixed allocations (of 0%, 30%, 50% and 70%) that included Government Long Bonds. They had lower P/E10 thresholds of 9, 10, 11, 12 and 13. The upper P/E10 threshold was 21. The intermediate stock allocation was 70% (making the stock allocations 100-70-0% when P/E10 fell below, between and above the thresholds).

Almost all of the failures were for sequences beginning in the 1960s. For the condition that I checked with 10 failures, they occurred in 1959-1968. The only exception among the conditions that I checked was the year 1929. It showed up with 100% stocks.

Summary

These results remind us that the owners of Government Long Bonds were hurt by inflation and rising interest rates associated with the late 1960s and the 1970s.

Switching allocations with stocks did better than abandoning Government Long Bonds entirely.

Keep in mind that an investment that matches inflation exactly has a 30-year Safe Withdrawal Rate of 3.33% (plus inflation).

Keep in mind that our calculators treat fixed income investments as single-year trading vehicles. They do not allow you to lock in favorable interest rates.

Have fun.

John Walter Russell
From January 29, 2005