Edited: Sanity Check with the S&P500

My investigations of switching stock allocations with Large Cap Value and Small Cap Value have produced spectacular results. Both of these investigations use the total return data found in Gummy’s database.
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These new data allow us to make comparisons based upon Gummy’s database with our earlier investigations, which used Professor Robert Shiller’s S&P500 data.

It turns out that we can trust our new results.

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. I restricted my stock allocations to Gummy’s S&P500 data. 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 brief survey. I varied stock allocations in accordance with 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 Professor Shiller’s S&P500 data and commercial paper was 40%. [I have recently reported this incorrectly as being 30% with commercial paper. It is 30% with TIPS.] The best P/E10 thresholds were 11 and 21. [With TIPS and with a different number of P/E10 thresholds, sometimes 12 and 13 turned out better than 11.]

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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: 3.4
First failure: 3.5
Five failures: 3.9
Ten failures: 4.2

Stock Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 4.0
First failure: 4.1
Five failures: 4.5
Ten failures: 4.7

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

Stock Allocation = 100%
30-year Failures in 1928-1980:
HSWR: 3.7
First failure: 3.8
Five failures: 4.1
Ten failures: 4.6

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.
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The best intermediate stock allocation is poorly defined. There is an interaction. The best allocation is 70% when the (lower) P/E10 threshold is 9 and 15. It is 30% or 50% when the P/E10 threshold is 12. However, a P/E10 threshold of 12 is clearly better than 9 or 15.

Here are more conditions with a threshold close to 12.

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The best results are with P/E10 thresholds of 11, 12 and 13. I present them here in a different order.

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We return to the original presentation using a P/E10 threshold of 12:

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

P/E10 threshold = 12 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.2
First failure: 5.3
Five failures: 5.6
Ten failures: 5.8

P/E10 threshold = 12 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.3
Ten failures: 5.6

These results favor allocations of 30% and 50%. It is arguable as to which is better. Looking simply at the rate with the first failure favors 30%.

Our final selection is a 30% stock allocation with a P/E10 of 12 or 13.

Comparisons

These are the best results with a fixed allocation.

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

These are the best results with switching.

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

These results have Historical Surviving Withdrawal Rates that are 0.2% higher than those using Professor Shiller’s data. They agree reasonably well.

This survey is very reassuring. We can rely on achieving spectacular results with Large Cap Value and Small Cap Value. We do not need to be overly concerned about our data source. Both selections improve results by much more than 0.2%.

An Additional Implication

Since Large Cap Value and Small Cap Value respond favorably to the P/E10 of the S&P500 and since both have higher Historical Surviving Withdrawal Rates than the S&P500, I question the merit of increasing diversification just for the sake of it. It seems to me that, in both cases, the S&P500 is the result of increased diversification. We need to think more when we diversify.

Caution about Small Capitalization stocks.

In Contrarian Investment Strategies: The Next Generation, David Dreman points out several artifacts associated with Small Cap data. Liquidity is a major issue, especially with so many of today’s mutual funds being set up to invest in Small Cap stocks. The Small Cap sector can be overwhelmed with cash, similar to what happened with emerging markets. Historically, Small Cap data sources have not distinguished between bid and asked prices. They have reported the mid-point. This can cause a major distortion. The lack of liquidity often makes the bid-ask spread very large. In addition, even small volumes of purchases and/or sales can move prices dramatically.

Moreover, the S&P500 index is capitalization weighted. Large Cap stocks dominate its performance.

Have fun.

John Walter Russell
From January 31, 2005