Switching with Large Cap Value using Exponential E10/P

Research on Safe Withdrawal Rates

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JWR1945
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Switching with Large Cap Value using Exponential E10/P

Post by JWR1945 » Sun Jan 30, 2005 12:18 pm

Switching with Large Cap Value using Exponential E10/P

I copied the 1928-2000 Large Cap Value data from the Gummy's database.
http://www.gummy-stuff.org/returns.htm

I started with my Gummy 02B revision 1 version of the Deluxe Calculator V1.1A08 revised on January 27, 2005. I upgraded it to the Gummy 02B rev 1 exp E10/P version of the Deluxe Calculator V1.1A08, revised January 30, 2005.

This new calculator uses Gummy's Exponential Weighting of E10/P data. I downloaded the values of E(10ma)/P from his spreadsheet. I used this link:
http://www.gummy-stuff.org/E10-P.htm
I calculated 1/[E(10ma)/P] on a separate worksheet. I pasted these values, which are P/E(10ma), into cells BG186-EA186. I used the fill handle to copy the year 2000 value as dummy data for the remaining years (up to 2010).

I repeated my earlier study, but this time comparing P/E(10ma) to the thresholds.

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/E(10ma). When P/E(10ma) was below the lower threshold (which varied), the stock allocation was 100%. When P/E(10ma) was between the two thresholds, I used an intermediate allocation of 30% or 50% or 70% as indicated. When P/E(10ma) 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, 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: 5.4 in years 1928-1930, 1937, 1969
Ten failures: 5.9
[Previously, I incorrectly reported the five-failure rate as 5.3%.]

Stock Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.2
First failure: 4.3 in year 1929-1930
Five failures: 5.6 in years 1928-1930, 1937, 1969
Ten failures: 6.7
[Previously, I incorrectly reported the first-failure rate as 4.4%.]

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, 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: 5.0
First failure: 5.1 in year 1939
Five failures: 5.4
Ten failures: 5.6

P/E10 threshold = 9 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.5
First failure: 5.6 in year 1930, 1969
Five failures: 5.9
Ten failures: 6.3

P/E10 threshold = 9 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 5.1
First failure: 5.2
Five failures: 6.2
Ten failures: 6.8

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: 6.5
First failure: 6.6
Five failures: 6.8
Ten failures: 7.2

P/E10 threshold = 12 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 5.9
First failure: 6.0
Five failures: 6.8
Ten failures: 7.3

P/E10 threshold = 15 and Allocation = 30%
30-year Failures in 1928-1980:
HSWR: 5.7
First failure: 5.8
Five failures: 6.0
Ten failures: 6.3

P/E10 threshold = 15 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.2
First failure: 5.3
Five failures: 6.2
Ten failures: 6.5

P/E10 threshold = 15 and Allocation = 70%
30-year Failures in 1928-1980:
HSWR: 4.6
First failure: 4.7
Five failures: 6.2
Ten failures: 6.8

Summary of results with the best intermediate stock allocation. Arguably, it was 50%. [There is an interaction at a high P/E10 threshold and a 30% stock allocation. In addition, there seems to be a change in the nature of the underlying distribution.]

P/E10 threshold = 9 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.5
First failure: 5.6 in year 1930, 1969
Five failures: 5.9
Ten failures: 6.3

P/E10 threshold = 12 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 6.5
First failure: 6.6
Five failures: 6.8
Ten failures: 7.2

P/E10 threshold = 15 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.2
First failure: 5.3
Five failures: 6.2
Ten failures: 6.5

Additional conditions with an intermediate stock allocation of 50%.

P/E10 threshold = 9 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.5
First failure: 5.6 in year 1930, 1969
Five failures: 5.9
Ten failures: 6.3
[Repeated here for convenience.]

P/E10 threshold = 10 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 6.1
First failure: 6.2
Five failures: 6.5
Ten failures: 6.9

P/E10 threshold = 11 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 6.2
First failure: 6.3
Five failures: 6.6
Ten failures: 7.0

P/E10 threshold = 12 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 6.5
First failure: 6.6
Five failures: 6.8
Ten failures: 7.2
[Repeated here for convenience.]

P/E10 threshold = 13 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 6.5
First failure: 6.6
Five failures: 6.8
Ten failures: 7.2

P/E10 threshold = 14 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.9
First failure: 6.0
Five failures: 6.3
Ten failures: 6.7

P/E10 threshold = 15 and Allocation = 50%
30-year Failures in 1928-1980:
HSWR: 5.2
First failure: 5.3
Five failures: 6.2
Ten failures: 6.5
[Repeated here for convenience.]

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: 5.4 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 = 50%
30-year Failures in 1928-1980:
HSWR: 6.5
First failure: 6.6
Five failures: 6.8
Ten failures: 7.2

Summary

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

P/E(10ma) is not as good an indicator as P/E10 for portfolios with Large Cap Value.

With an allocation of 50% stocks, a withdrawal rate of 5.2% produced zero failures for all conditions tested. That is, there were zero failures when the lower P/E(10ma) threshold was 9, 10, 11, 12, 13, 14 or 15. This is better than for all of the conditions without switching.

The best thresholds were 12 and 13 for both P/E10 and P/E(10ma). However, the best stock allocations were 70% with P/E10 and 50% with P/E(10ma).

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 R.

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