Edited: Switching Allocations with Small Cap Value

I started by collecting a baseline with fixed stock allocations of Small Capitalization Value stocks. The fixed allocations were 0%, 30%, 50%, 70% and 100%.

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

The Calculator

I used my Gummy 03 version of the Deluxe Calculator V1.1A08 Revised: January 28, 2005. I weighted the stock allocation entirely to Small Cap Value.
Gummy’s (Peter Ponzo’s) Database

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 Small Cap Value. I used commercial paper for my non-stock allocation. 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: 4.3
First failure: 4.4 in year 1937
Five failures: 5.3 in years 1929, 1936-1940, 1969
Ten failures: 5.5

Stock Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 6.1
Ten failures: 7.0

Stock Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.4
First failure: 4.5
Five failures: 5.9
Ten failures: 7.7

Stock Allocation = 100%
30-year Failures in 1928-1980:
HSWR: 2.7
First failure: 2.8 in year 1929
Five failures: 5.8 in years 1928-1930, 1937, 1969
Ten failures: 8.1

The Survey of Thresholds and Allocations

Calculator data: 1928-2000.
30-year sequences from 1928-1980, $100000 initial balances, 0.20% expenses.
Calculator settings:
P/E10 thresholds: varies-21-24-80.
Allocations: 100-varies-0-0-0.
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The best intermediate stock allocation was 70%. Here is a summary of those results.

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Additional conditions with an intermediate stock allocation of 70%.

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Comparisons

These are the best results with a fixed allocation.

Stock Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 6.1
Ten failures: 7.0

These are the best results with switching.

P/E10 threshold = 13 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 8.0
First failure: 8.1
Five failures: 8.6
Ten failures: 9.0

Summary

It is easy to understand why Mike [a popular participant at the NoFeeBoards.com discussion boards] has been interested in Small Cap Value stocks. They have much higher Historical Survival Withdrawal Rates than the S&P500 index and Large Cap Value stocks.

Switching stock allocations in accordance with the P/E10 of the S&P500 index is highly beneficial with Small Cap Value stocks. Compare the best results with a fixed allocation to the best results with switching. The improvement is dramatic.

With an allocation of 70% stocks, a withdrawal rate of 7.4% produced zero failures for all conditions tested. That is, when the lower P/E10 threshold was 9, 10, 11, 12, 13, 14, 15, 16, 17 or 18.

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.

It will be interesting to see how Historical Surviving Withdrawal Rates for Small Cap Value stocks vary with the percentage earnings yield 100E10/P of the S&P500 index.

Have fun.

John Walter Russell
From January 30, 2005