Growth-Value Switching with Algorithm D (Treasury Bond Interest Rates)

This continues Current Research D: Expanded Switching Algorithms.

I started with these general conditions:

Algorithm D (Treasury Bond Interest Rates)
Start years: 1928-1980
30-Year Historical Surviving Withdrawal Rates
0.00% expenses

Stock allocations: 100%-50%-0%-0%-0% (the programmed part is 50%-0%-0%).
Thresholds: varies-varies-79-80.

Initial Survey

Entry for Stocks: 80% Large Capitalization Value and 20% T-Bills.
Entry for Commercial Paper: 80% Large Capitalization Growth and 20% T-Bills.

4% WITHDRAWAL RATE:

With a lower threshold of 0% and an upper threshold of 16%, there were zero failures.
With a lower threshold of 0% and an upper threshold of 12%, there were zero failures.
With a lower threshold of 0% and an upper threshold of 8%, there were zero failures.
With a lower threshold of 0% and an upper threshold of 4%, there were 5 failures.

With a lower threshold of 2% and an upper threshold of 16%, there were zero failures.
With a lower threshold of 2% and an upper threshold of 12%, there were zero failures.
With a lower threshold of 2% and an upper threshold of 8%, there were zero failures.
With a lower threshold of 2% and an upper threshold of 4%, there were 5 failures.

With a lower threshold of 4% and an upper threshold of 16%, there were 2 failures.
With a lower threshold of 4% and an upper threshold of 12%, there were 2 failures.
With a lower threshold of 4% and an upper threshold of 8%, there were 2 failures.
With a lower threshold of 4% and an upper threshold of 4%, there were 7 failures.

5% WITHDRAWAL RATE:

With a lower threshold of 0% and an upper threshold of 16%, there were 5 failures.
With a lower threshold of 0% and an upper threshold of 12%, there were 7 failures.
With a lower threshold of 0% and an upper threshold of 8%, there were 7 failures.
With a lower threshold of 0% and an upper threshold of 4%, there were 15 failures.

With a lower threshold of 2% and an upper threshold of 16%, there were 5 failures.
With a lower threshold of 2% and an upper threshold of 12%, there were 7 failures.
With a lower threshold of 2% and an upper threshold of 8%, there were 7 failures.
With a lower threshold of 2% and an upper threshold of 4%, there were 14 failures.

With a lower threshold of 4% and an upper threshold of 16%, there were 2 failures.
With a lower threshold of 4% and an upper threshold of 12%, there were 2 failures.
With a lower threshold of 4% and an upper threshold of 8%, there were 2 failures.
With a lower threshold of 4% and an upper threshold of 4%, there were 7 failures.

Second Survey

I swapped my choices of what to treat as stocks and what to treat as commercial paper.

Entry for Stocks: 80% Large Capitalization Growth and 20% T-Bills.
Entry for Commercial Paper: 80% Large Capitalization Value and 20% T-Bills.

4% WITHDRAWAL RATE:

With a lower threshold of 0% and an upper threshold of 16%, there were zero failures.
With a lower threshold of 0% and an upper threshold of 12%, there were zero failures.
With a lower threshold of 0% and an upper threshold of 8%, there were zero failures.
With a lower threshold of 0% and an upper threshold of 4%, there were zero failures.

With a lower threshold of 2% and an upper threshold of 16%, there were zero failures.
With a lower threshold of 2% and an upper threshold of 12%, there were zero failures.
With a lower threshold of 2% and an upper threshold of 8%, there were zero failures.
With a lower threshold of 2% and an upper threshold of 4%, there were zero failures.

With a lower threshold of 4% and an upper threshold of 16%, there was 1 failure.
With a lower threshold of 4% and an upper threshold of 12%, there was 1 failure.
With a lower threshold of 4% and an upper threshold of 8%, there wase 1 failure.
With a lower threshold of 4% and an upper threshold of 4%, there was 1 failure.

5% WITHDRAWAL RATE:

With a lower threshold of 0% and an upper threshold of 16%, there were 5 failures.
With a lower threshold of 0% and an upper threshold of 12%, there were 3 failures.
With a lower threshold of 0% and an upper threshold of 8%, there were 5 failures.
With a lower threshold of 0% and an upper threshold of 4%, there were 2 failures.

With a lower threshold of 2% and an upper threshold of 16%, there were 5 failures.
With a lower threshold of 2% and an upper threshold of 12%, there were 3 failures.
With a lower threshold of 2% and an upper threshold of 8%, there were 5 failures.
With a lower threshold of 2% and an upper threshold of 4%, there were 2 failures.

With a lower threshold of 4% and an upper threshold of 16%, there were 6 failures.
With a lower threshold of 4% and an upper threshold of 12%, there were 4 failures.
With a lower threshold of 4% and an upper threshold of 8%, there were 6 failures.
With a lower threshold of 4% and an upper threshold of 4%, there were 3 failures.

Second Survey Results

Except for the 5% withdrawal rate and 4% lower threshold condition, the data consistently favor allocating the Large Capitalization Growth portfolio to stocks and using the Large Capitalization Value portfolio as the replacement for commercial paper.

The data consistently speak against selecting 4% as a lower threshold as opposed to zero or 2%. Even with the 5% withdrawal rate, there are fewer failures with zero and 2% lower thresholds than with a 4% lower threshold under comparable conditions.

I decided to stick with the new portfolios:

Entry for Stocks: 80% Large Capitalization Growth and 20% T-Bills.
Entry for Commercial Paper: 80% Large Capitalization Value and 20% T-Bills.

Third Survey

I set the withdrawal rate equal to 5%.

I looked at lower thresholds of 0%, 1%, 2%, 3% and 4%.

I looked at upper thresholds of 16%, 15%, 14%, 13%, 12%, 11%, 10%, 9%, 8%, 7%, 6%, 5% and 4%.

All results with lower thresholds of 0%, 1% and 2% were identical.

All results with an upper threshold of 13%, 14%, 15% and 16% were identical.

All results with a lower threshold of 4%, 5% and 6% were identical.

With a lower threshold of 0%, 1% or 2% and an upper threshold of 13%, there were 5 failures.
With a lower threshold of 0%, 1% or 2% and an upper threshold of 12%, there were 3 failures.
With a lower threshold of 0%, 1% or 2% and an upper threshold of 11%, there were 3 failures.
With a lower threshold of 0%, 1% or 2% and an upper threshold of 10%, there were 2 failures.
With a lower threshold of 0%, 1% or 2% and an upper threshold of 9%, there were 4 failures.
With a lower threshold of 0%, 1% or 2% and an upper threshold of 8%, there were 5 failures.
With a lower threshold of 0%, 1% or 2% and an upper threshold of 7%, there were 4 failures.
With a lower threshold of 0%, 1% or 2% and an upper threshold of 6%, there were 2 failures.

With a lower threshold of 3% and an upper threshold of 13%, there were 7 failures.
With a lower threshold of 3% and an upper threshold of 12%, there were 5 failures.
With a lower threshold of 3% and an upper threshold of 11%, there were 5 failures.
With a lower threshold of 3% and an upper threshold of 10%, there were 4 failures.
With a lower threshold of 3% and an upper threshold of 9%, there were 6 failures.
With a lower threshold of 3% and an upper threshold of 8%, there were 7 failures.
With a lower threshold of 3% and an upper threshold of 7%, there were 6 failures.
With a lower threshold of 3% and an upper threshold of 6%, there were 4 failures.

With a lower threshold of 4% and an upper threshold of 13%, there were 6 failures.
With a lower threshold of 4% and an upper threshold of 12%, there were 4 failures.
With a lower threshold of 4% and an upper threshold of 11%, there were 4 failures.
With a lower threshold of 4% and an upper threshold of 10%, there were 3 failures.
With a lower threshold of 4% and an upper threshold of 9%, there were 5 failures.
With a lower threshold of 4% and an upper threshold of 8%, there were 6 failures.
With a lower threshold of 4% and an upper threshold of 7%, there were 5 failures.
With a lower threshold of 4% and an upper threshold of 6%, there were 3 failures.

Third Survey Results

In every case, there were fewer failures with a lower threshold of 0%, 1% or 2% than with a higher threshold.

I extended the investigation to lower thresholds of 5%, 6%, 7% and 8%. The observation remained true. There were fewer failures at any given upper threshold when the lower threshold was 0%, 1% or 2%.

I lowered the withdrawal rate with a lower threshold of 2%. There were 2 failures (1929 and 1930) when the withdrawal rate was 4.5% regardless of the upper threshold (from 6% through 13%). There was 1 failure (1929) when the withdrawal rate was 4.2% regardless of the upper threshold. There were zero failures when the withdrawal rate was 4.1%.

Combining these results with those at a withdrawal rate of 5%, the best condition appeared to be a lower threshold of 2% (or 1% or 0%) and an upper threshold of either 6% or 10%. Failures occurred in 1929 and 1930.

Fourth Survey

I determined the withdrawal rates at the first, fifth and tenth failure with a lower threshold of 2% and an upper threshold of 6% and 10%.

With a lower threshold of 2%, an upper threshold of 6% and a (Growth) stock allocation of 20%:
The first failure occurred at a 4.1% withdrawal rate.
The fifth failure occurred at a 5.7% withdrawal rate.
The tenth failure occurred at a 6.7% withdrawal rate.

With a lower threshold of 2%, an upper threshold of 6% and a (Growth) stock allocation of 50%:
The first failure occurred at a 4.2% withdrawal rate.
The fifth failure occurred at a 5.6% withdrawal rate.
The tenth failure occurred at a 6.4% withdrawal rate.

With a lower threshold of 2%, an upper threshold of 6% and a (Growth) stock allocation of 80%:
The first failure occurred at a 4.1% withdrawal rate.
The fifth failure occurred at a 5.5% withdrawal rate.
The tenth failure occurred at a 5.9% withdrawal rate.

With a lower threshold of 2%, an upper threshold of 10% and a (Growth) stock allocation of 20%:
The first failure occurred at a 4.1% withdrawal rate.
The fifth failure occurred at a 5.5% withdrawal rate.
The tenth failure occurred at a 6.5% withdrawal rate.

With a lower threshold of 2%, an upper threshold of 10% and a (Growth) stock allocation of 50%:
The first failure occurred at a 4.2% withdrawal rate.
The fifth failure occurred at a 5.2% withdrawal rate.
The tenth failure occurred at a 5.8% withdrawal rate.

With a lower threshold of 2%, an upper threshold of 10% and a (Growth) stock allocation of 80%:
The first failure occurred at a 4.1% withdrawal rate.
The fifth failure occurred at a 4.8% withdrawal rate.
The tenth failure occurred at a 5.2% withdrawal rate.

Fourth Survey Results

The first failure results favor a (Growth) stock allocation of 50%. First failures occurred at withdrawal rates of 4.2% with a 50% (Growth) stock allocation and 4.1% with (Growth) stock allocations of 20% and 80%.

The fifth and tenth failure results favor a 6% upper threshold and a 20% (Growth) stock allocation. All individual comparisons favored a 6% upper threshold. All individual comparisons favored a 20% (Growth) stock allocation.

I selected a 20% (Growth) allocation with Treasury Bond interest rate thresholds of 2% and 6%. Under such circumstances, the withdrawal rates are:

The first failure occurred at a 4.1% withdrawal rate.
The fifth failure occurred at a 5.7% withdrawal rate.
The tenth failure occurred at a 6.7% withdrawal rate.

Comparisons with Algorithm F (T.Bond-C.Paper)

These are the best conditions using Algorithm F in terms of the first failure rate.

With a lower threshold of minus 2% and a 20% (Value) stock allocation:
The first failure occurred at 4.6%.
The fifth failure occurred at 4.9%.
The tenth failure occurred at 5.5%.

With a lower threshold of minus 1% and a 20% (Value) stock allocation:
The first failure occurred at 4.6%.
The fifth failure occurred at 4.9%.
The tenth failure occurred at 5.3%.

I prefer a threshold of minus 2% based upon the tenth failure data.

Here are the best condition with Algorithm F in terms of the fifth and tenth failure rates (as opposed to the first failure rate).

With a lower threshold of zero 0% and an 80% (Value) stock allocation:
The first failure occurred at 4.0%.
The fifth failure occurred at 5.6%.
The tenth failure occurred at 6.7%.

Algorithm D is slightly better than this at the first failure rate (4.1% versus 4.0%). It is slightly better at the fifth failure rate (5.7% versus 5.6%). It is identical at the tenth failure rate (both at 6.7%).

It is likely that further optimization of Algorithm F would improve its results enough to match or better those of Algorithm D (unless only the first failures were compared).

Algorithms D and F are strongly at odds.

Algorithm D (Treasury Bond Interest Rates) uses Large Capitalization Growth stocks as its stock component. It increases its Growth stock holdings as Treasury Bond interest rates rise. Algorithm F (T.Bond-C.Paper) uses Large Capitalization Value stocks as its stock component. It increases the Value stock holdings as Treasury Bond interest rates rise.

There is very little reason to prefer one algorithm over the other, except in terms of the first failure.

Conflicting Stories

Algorithm D (Treasury Bond Interest Rates) and Algorithm F (the interest rate of Treasury Bonds minus the interest rate of commercial paper) produce similar results but they tell conflicting stories.

Or, at least, the stories conflict enough to be of concern. Subtracting the commercial paper interest rate had the effect of switching to more Value stocks at higher Treasury Bond interest rates. Not including commercial paper interest rates had the effect of switching to more Growth stocks at higher Treasury Bond interest rates.

Looking at the historical sequence of rates, I prefer Algorithm F. The Treasury Bond interest rate (as with Algorithm D), when taken alone, grows with time. It is difficult to compare earlier interest rates with later interest rates. There needs to be some form of normalization.

Subtracting the interest rate of commercial paper provides a degree of normalization.

Conclusions

The withdrawal rates for Growth-Value Switching with Algorithm D (Treasury Bonds) are similar to Algorithm F (T.Bonds-C.Paper).

Unfortunately, the two approaches tell conflicting stories.

Tentatively, I shall continue with Algorithm F as a baseline.

Our investigation of Algorithm D puts Algorithm F’s suitability in doubt.

Have fun.

John Walter Russell
October 17, 2005