Small Cap Growth and Switching

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

Later, I made a brief survey. I varied the stock allocation in accordance with 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 Growth.
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 Growth. 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 made a 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 40%. The best P/E10 thresholds were 11 and 21. Similar studies using TIPS favored a 30% allocation and P/E10 thresholds of 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 limited survey. This was not a full optimization. This did not include a full sensitivity study.

Baselines

Calculator data:
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: 3.7
First failure: 3.8
Five failures: 4.1 in years 1936-1937, 1939-1940, 1969
Ten failures: 4.5

Stock Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 3.5
First failure: 3.6
Five failures: 4.7
Ten failures: 5.1

Stock Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.0
First failure: 3.1 in 1969
Five failures: 4.6
Ten failures: 5.0

Stock Allocation = 100%
30-year Failures in 1928-1980:
HSWR: 2.0
First failure: 2.1 in year 1969
Five failures: 3.6 in years 1929, 1968-1970, 1972
Ten failures: 4.3

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.

I collected a full set of data with P/E10 thresholds of 9-15.

P/E10 threshold = 9 and [Intermediate stock] Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 3.9
First failure: 4.0
Five failures: 4.5
Ten failures: 5.0

P/E10 threshold = 9 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 5.2
Ten failures: 5.9

P/E10 threshold = 9 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.2
First failure: 4.3
Five failures: 5.3
Ten failures: 5.8

P/E10 threshold = 10 and [Intermediate stock] Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 3.9
First failure: 4.0
Five failures: 4.5
Ten failures: 5.0

P/E10 threshold = 10 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 5.2
Ten failures: 5.9

P/E10 threshold = 10 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.2
First failure: 4.3
Five failures: 5.3
Ten failures: 5.8

P/E10 threshold = 11 and [Intermediate stock] Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 5.8
Ten failures: 6.0

P/E10 threshold = 11 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.9
Ten failures: 6.1

P/E10 threshold = 11 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.2
First failure: 4.3
Five failures: 5.3
Ten failures: 5.8

P/E10 threshold = 12 and Allocation =30%
30-year Failures in 1928-1980:
HSWR: 4.8
First failure: 4.9
Five failures: 6.3
Ten failures: 6.5

P/E10 threshold = 12 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 5.9
Ten failures: 6.5

P/E10 threshold = 12 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.5
First failure: 4.6
Five failures: 5.3
Ten failures: 6.0

P/E10 threshold = 13 and Allocation =30%
30-year Failures in 1928-1980:
HSWR: 4.8
First failure: 4.9 in 1980
Five failures: 6.3
Ten failures: 6.7

P/E10 threshold = 13 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 6.2
Ten failures: 6.5

P/E10 threshold = 13 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.5
First failure: 4.6
Five failures: 5.3
Ten failures: 6.0

P/E10 threshold = 14 and Allocation =30%
30-year Failures in 1928-1980:
HSWR: 4.9
First failure: 5.0 in 1980
Five failures: 5.5
Ten failures: 5.7

P/E10 threshold = 14 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 4.7
First failure: 4.8
Five failures: 5.3
Ten failures: 5.7

P/E10 threshold = 14 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.0
First failure: 4.1
Five failures: 5.0
Ten failures: 5.5

P/E10 threshold = 15 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 4.4
First failure: 4.5
Five failures: 5.5
Ten failures: 5.7

P/E10 threshold = 15 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 4.5
First failure: 4.6
Five failures: 5.2
Ten failures: 5.6

P/E10 threshold = 15 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 3.9
First failure: 4.0
Five failures: 4.9
Ten failures: 5.5

Analysis

The easiest way to analyze these data is to exclude all conditions with an HSWR level below 5.0. This leaves us with the following conditions:
1) a P/E10 threshold of 9 and an allocation of 50%.
2) a P/E10 threshold of 10 and an allocation of 50%.
3) a P/E10 threshold of 11 and an allocation of 30%.
4) a P/E10 threshold of 11 and an allocation of 50%.
5) a P/E10 threshold of 12 and an allocation of 50%.
6) a P/E10 threshold of 13 and an allocation of 50%.

Here are those conditions:

P/E10 threshold = 9 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 5.2
Ten failures: 5.9

P/E10 threshold = 10 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 5.2
Ten failures: 5.9

P/E10 threshold = 11 and [Intermediate stock] Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 5.8
Ten failures: 6.0

P/E10 threshold = 11 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.9
Ten failures: 6.1

P/E10 threshold = 12 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 5.9
Ten failures: 6.5

P/E10 threshold = 13 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 6.2
Ten failures: 6.5

Discussion

My decision to examine only those conditions with HSWR levels of 5.0 and above is arguable. After all, each HSWR value is determined by a single sequence. On the other hand, the results support my decision. Notice the consistency of the selected stock allocations. Notice that there are no gaps among the selected P/E10 thresholds.

Focusing on the results with five failures, we select P/E10 thresholds of 11, 12 and 13. If we were to select our best condition simply on the HSWR and first failure results, we would select a P/E10 threshold of 11 with a stock allocation of 50%. But this ends up being a comparison of 5.0 and 5.1 based upon a single sequence. Looking at the five failure conditions and then the ten failure conditions, I prefer selecting a P/E10 threshold of 13 with a stock allocation of 50%.

Comparisons

These are the best results with a fixed allocation.

Stock Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 3.5
First failure: 3.6
Five failures: 4.7
Ten failures: 5.1

These are the best results with switching.

P/E10 threshold = 13 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.0
First failure: 5.1
Five failures: 6.2
Ten failures: 6.5

S&P500 Results for Comparison

A comparison with comparable S&P500 data from an earlier sanity check is enlightening.

The best S&P500 Historical Surviving Withdrawal Rate with a fixed allocation was higher than with Small Cap Growth at the first failure. But the rates for the S&P500 were lower at five and ten failures.

Stock Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.1
First failure: 4.2
Five failures: 4.4
Ten failures: 4.8

The best S&P500 condition with switching was:

P/E10 threshold = 12 or 13 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 5.3
First failure: 5.4
Five failures: 5.6
Ten failures: 5.7

Summary

The best S&P500 Historical Surviving Withdrawal Rate with switched allocations was higher than with Small Cap Growth at the first failure. But the rates were lower at five and ten failures.

What has happened is that Small Cap Growth typically has one or two sequences that are much worse than the others. The 1969 sequence was an especially bad sequence for Small Cap Growth stocks. According to these results, including Small Cap Growth stocks has helped the overall performance of the S&P500.

The best allocations and thresholds Small Cap Growth are broadly defined.

Small Cap Growth responded well to switching according to the P/E10 of the S&P500. It increased the Historical Surviving Withdrawal Rates at all levels of failure by 1.4% or 1.5%.

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

Have fun.

John Walter Russell
From February 1, 2005