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A Sanity Check using S&P500 Data

 
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JWR1945
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Joined: 26 Nov 2002
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Location: Crestview, Florida

PostPosted: Mon Jan 31, 2005 6:02 am    Post subject: A Sanity Check using S&P500 Data Reply with quote

A Sanity Check using S&P500 Data

My investigations of switching stock allocations with Large Cap Value and Small Cap Value have produced results that seem to be too good to be true. Both of these investigations use the total return data found in Gummy's database.

I used my Gummy 03 version of the Deluxe Calculator V1.1A08 Revised: January 28, 2005. I weighted the stock allocation entirely to the S&P500. I collected data in the same manner as I did earlier with Large Cap Value and Small Cap Value stocks.

These new data allow us to make comparisons of results based upon this new source of data with our earlier results.

It turns out that we can trust our recent 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 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 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.]

In any event, I centered my original surveys at a P/E10 thresholds of 12 and 21 and I made sure to include an intermediate allocation level of 30%.

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, 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, 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: 3.5
First failure: 3.6
Five failures: 4.2
Ten failures: 4.8

P/E10 threshold = 9 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 4.4
First failure: 4.5
Five failures: 5.3
Ten failures: 5.6

P/E10 threshold = 9 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.3
Ten failures: 5.5

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

P/E10 threshold = 15 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 4.6
First failure: 4.7
Five failures: 4.8
Ten failures: 4.9

P/E10 threshold = 15 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 4.7
First failure: 4.8
Five failures: 4.8
Ten failures: 5.0

P/E10 threshold = 15 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.7
First failure: 4.8
Five failures: 4.9
Ten failures: 5.1

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.

P/E10 threshold = 11 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.4
Ten failures: 5.5

P/E10 threshold = 11 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.2
First failure: 5.3
Five failures: 5.5
Ten failures: 5.7

P/E10 threshold = 11 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.3
Ten failures: 5.5

P/E10 threshold = 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

P/E10 threshold = 13 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 = 13 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.3
Ten failures: 5.6

P/E10 threshold = 14 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 4.6
First failure: 4.7
Five failures: 4.8
Ten failures: 4.9

P/E10 threshold = 14 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 4.7
First failure: 4.8
Five failures: 4.8
Ten failures: 5.0

P/E10 threshold = 14 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.7
First failure: 4.8
Five failures: 4.9
Ten failures: 5.1

The best results are with P/E10 thresholds of 11, 12 and 13. Here they are, presented in a different order.

P/E10 threshold = 11 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.4
Ten failures: 5.5

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 = 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

P/E10 threshold = 11 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.2
First failure: 5.3
Five failures: 5.5
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 = 13 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 = 11 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.3
Ten failures: 5.5

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

P/E10 threshold = 13 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 5.3
Ten failures: 5.6

Presented in this order, we notice that P/E10 thresholds of 12 and 13 are best. The results are identical whether the threshold is 12 or 13 for the allocations examined.

We return to the original presentation for 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 lowest rate with the first failure favors 30%.

Our final selection is a 30% stock allocation with a P/R10 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. There needs to be more thought.

Have fun.

John R.


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