Switching Allocations with Large Cap Value

I started by collecting a baseline with fixed stock allocations of 0%, 30%, 50%, 70% and 100%.

Later, I took a brief survey. I varied the stock allocation depending upon P/E10.

The Calculator

This uses the Gummy 02B revision 1 version of my Deluxe Calculator V1.1A08. I made the revision on January 27, 2005. My Gummy series of calculators use Gummy’s (Peter Ponzo’s) Database instead of Professor Robert Shiller’s S&P500 data. [The commercial paper data is from Professor Shiller’s web site.]

I copied the 1928-2000 Large Cap Value data from the Gummy’s database.
Gummy’s (Peter Ponzo’s) Database

It is necessary to shift Gummy’s data by one column to the right for the calculations to line up correctly. This does not affect calculations that used earlier data sets.

I made a copy of an existing calculator. (I used my latest, my Gummy 02 version of the Deluxe Calculator 1.1A08.) I froze the S&P500 prices at the 1928 level of 17.53. That is, I pasted 17.53 (the value in cell BG184) into all of the cells from BH184 through EK184. I made a set of artificial entries for the dividends in cells BH185 through EB185. I multiplied all of the LV data from Gummy’s database by 17.53 and divided by 100. [I did this indirectly. I do not know whether I would have had to divide by 100 if I had copied his data directly.] I pasted that into cells BH185 through EB185. These cells are listed as the dividend amounts in 1929-2001. Notice that I shifted the entries by one year to the right. I took the value in cell EB185, which is for the year 2001, and pasted it into cells EC185-EK185.

The net effects are that all price changes are zero and all dividend yields equal total returns for Large Cap Value stocks for the years 1928-2000.

The calculations that take place during any particular year appear in the column of the year that follows. That is because the existing data are for January 1st, which tells us what has happened during the last 12 months.

I call my new calculator the Gummy 02B revision 1 version of the Deluxe Calculator V1.1A08 revised on January 27, 2005.

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 Large Cap Value. The non-stock allocation consisted of commercial paper. I left the beginning and end of year withdrawal allocations at 50%, the default setting.

I started by collecting a baseline with fixed stock allocations of 0%, 30%, 50%, 70% and 100%.

Later, 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.

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.

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%. That is, 100% commercial paper.
30-year Failures in 1928-1980:
HSWR: 2.3
First failure: 2.4
Five failures: 2.5
Ten failures: 2.6

Stock Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 4.0
First failure: 4.1 in year 1936
Five failures: 4.5 in years 1930, 1934, 1936-1937, 1939
Ten failures: 4.9

Stock Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 4.6
First failure: 4.7 in year 1930
Five failures: 5.3 in years 1928-1930, 1937, 1969
Ten failures: 5.9

Stock Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.2
First failure: 4.4 in year 1929-1930
Five failures: 5.6 in years 1928-1930, 1937, 1969
Ten failures: 6.7

Stock Allocation = 100%
30-year Failures in 1928-1980:
HSWR: 2.9
First failure: 3.0 in year 1929-1930
Five failures: 5.6 in years 1928-1931, 1969
Ten failures: 7.3

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: 4.3
First failure: 4.4 in year 1939
Five failures: 5.0
Ten failures: 5.6

P/E10 threshold = 9 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.7
First failure: 5.8 in year 1939
Five failures: 6.6
Ten failures: 6.8

P/E10 threshold = 9 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.6
First failure: 6.7
Five failures: 7.2
Ten failures: 7.4

P/E10 threshold = 12 and Allocation =30%
30-year Failures in 1928-1980:
HSWR: 6.1
First failure: 6.2 in year 1956
Five failures: 6.5
Ten failures: 6.9

P/E10 threshold = 12 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 6.7
First failure: 6.8
Five failures: 7.1
Ten failures: 7.5

P/E10 threshold = 12 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.8
First failure: 6.9
Five failures: 7.5
Ten failures: 7.8

P/E10 threshold = 15 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 5.8
First failure: 5.9
Five failures: 6.1
Ten failures: 6.6

P/E10 threshold = 15 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 6.1
First failure: 6.2
Five failures: 6.6
Ten failures: 7.0

P/E10 threshold = 15 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.5
First failure: 6.6
Five failures: 7.1
Ten failures: 7.3

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: 6.6
First failure: 6.7
Five failures: 7.2
Ten failures: 7.4

P/E10 threshold = 12 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.8
First failure: 6.9
Five failures: 7.5
Ten failures: 7.8

P/E10 threshold = 15 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.5
First failure: 6.6
Five failures: 7.1
Ten failures: 7.3

Additional conditions with an intermediate stock allocation of 70%.

P/E10 threshold = 10 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.6
First failure: 6.7
Five failures: 7.2
Ten failures: 7.5

P/E10 threshold = 11 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.6
First failure: 6.7
Five failures: 7.3
Ten failures: 7.5

P/E10 threshold = 13 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.8
First failure: 6.9
Five failures: 7.5
Ten failures: 7.8

P/E10 threshold = 14 and Allocation = 70%
30-year Failures in 1928-1980:HSWR: 6.5
First failure: 6.6
Five failures: 7.1
Ten failures: 7.3

P/E10 threshold = 16 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.5
First failure: 6.6
Five failures: 7.1
Ten failures: 7.3

Comparisons

These are the best results with a fixed allocation.

Stock Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 4.6
First failure: 4.7 in year 1930
Five failures: 5.3 in years 1928-1930, 1937, 1969
Ten failures: 5.9

These are the best results with switching.

P/E10 threshold = 12 or 13 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 6.8
First failure: 6.9
Five failures: 7.5
Ten failures: 7.8

Summary

Large Cap Value stocks have much higher Historical Survival Withdrawal Rates than the S&P500 index.

P/E10 is a useful indicator for portfolios with Large Cap Value as well as for those that have the S&P500 index.

Switching stock allocations in accordance with the P/E10 of the S&P500 index benefits Large Cap Value portfolios.

With an allocation of 70% stocks, a withdrawal rate of 6.5% produced zero failures for all conditions tested. That is, when the lower P/E10 threshold was 9, 10, 11, 12, 13, 14, 15 or 16.

Caution: I have not made any adjustments for today’s valuations. The actual improvement starting with today’s valuations are likely to be less. You can still estimate relative performance when compared to the S&P500 index.

Have fun.

John Walter Russell
From February 1, 2005