Additional Constraints with Latch and Hold

Latch and Hold dramatically improves the upside of (stock allocation) switching when starting in times of typical and bargain level valuations. Latch and Hold retains the substantial advantage of switching over fixed allocations in times of high valuations.

Benjamin Graham recommended stock and bond allocations between 25% and 75%.

I have looked at new conditions with Benjamin Graham’s constraint in mind.

Background

Latch and Hold Calculator LH02 tells us what happens to Historical Surviving Withdrawal Rates if we extend the crossing of a valuation (P/E10) threshold by a fixed number of years.

I looked at 30-Year Historical Surviving Withdrawal Rates. At the Historical Surviving Withdrawal Rate, the balance at year 30 is zero or positive. Increasing the withdrawal rate by 0.1% causes the balance to become negative.

I adjusted all withdrawals to match inflation. The withdrawal rate is a percentage of the initial portfolio balance (plus inflation).

I investigated the following conditions previously:

1) SwOptT2 consists of stocks (S&P500) and TIPS at a 2% (real) interest rate. It sets the P/E10 thresholds at 9-12-21-24 with stock allocations of 100%-50%-30%-20%-0%, respectively. SwOptT2 is the best (stock allocation) switching algorithm in the absence of a memory (that is, without latch and hold).

2) LHOptA is SwOptT2 with an upper threshold of 24.1 with an extension of 4 years and a lower threshold of 8 with an extension of 7 years. It is set with a preference to use lower threshold data. LHOptA was the best condition from my initial Latched Threshold Survey.

3) LHOptB is LHOptA with P/E10 thresholds of 9-12-21-x, stock allocations of 100%-50%-30%-0%-0% and an upper threshold of 21.1.

4) LHOptC is LHOptB with P/E10 thresholds of 9-12-20-x, stock allocations of 100%-50%-30%-0%-0% and an upper threshold of 20.1.

5) LHOptD is LHOptB with P/E10 thresholds of 9-12-21-100, stock allocations of 100%-50%-30%-25%-0% and an upper threshold of 21.1.

6) SwAT2 has P/E10 thresholds of 11-21 with stock allocations of 75%-40%-25%, respectively. I set the upper threshold to 100. I set the lower threshold to 1. These values eliminate the effects of latch and hold on SwAT2. SwAT2 is the best (stock allocation) switching algorithm in the absence of a memory (that is, without latch and hold) under Benjamin Graham’s constraint that both stock and bond (TIPS) allocations be between 25% and 75%.

7) LHOptE is LHOptA with P/E10 thresholds of 9-11-24-100 with stock allocations of 100%-75%-35%-0%-0%. The lower threshold is 8. The upper threshold is 24.1. The preference is set to use lower threshold data.

My Latest Surveys

I conducted two new surveys that produced LHOptF and LHOptG. I was interested in a maximum stock allocation of 75%, similar to SwAT2.

LHOptF has P/E10 thresholds of 2-11-24-100 with stock allocations of 100%-75%-35%-0%-0%. The lower threshold is 8 (with a 7 year extension). The upper threshold is 24.1 (with a 4 year extension). The preference is set to use lower threshold data.

For LHOptF: I used a withdrawal rate of 5.1%. It has 4 failures with a lower threshold from 4, 6 and 7. Varying the higher threshold from 0 through 10 years has no effect when the preference is for the lower threshold. When the preference is for the higher threshold, 0, 1, 2, 3 and 5 years are best.

LHOptG has P/E10 thresholds of 2-11-21-100 with stock allocations of 100%-75%-35%-0%-0%. The lower threshold is 8 (with a 7 year extension). The upper threshold is 21.1 (with a 4 year extension). The preference is set to use lower threshold data.

For LHOptG: I used a withdrawal rate of 5.1%. It has 3 failures with a lower threshold from 4 through 8. Varying the higher threshold from 0 through 10 years has no effect when the preference is for the lower threshold. When the preference is for the higher threshold, 0 years is best.

Regression Equations: New Conditions

Here is the LHOptF regression equation of 1923-1980 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:

y = 0.4509x+3.1199 plus 1.4% and minus 0.8%.
R squared = 0.7363.

Special note: On the upside, there are two distributions. The higher limit is plus 1.4%. As an approximation: the confidence levels start out as plus and minus 0.8%. The upside splits, with some conditions reaching higher rates.

Here is the LHOptG regression equation of 1923-1980 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:

y = 0.459x+3.2254 plus 2.0% and minus 0.8%.
R squared = 0.6296.

Special note: On the upside, there are two distributions. The higher limit is plus 2.0%. As an approximation: the confidence levels start out as plus and minus 0.8%. The upside splits, with some conditions reaching higher rates.

Data Summary: All Latch and Hold Conditions

Lowest 30-Year Historical Surviving Withdrawal Rates (1923-1980):

LHOptG: 4.9% in 1964.
LHOptF: 5.0% in 1962, 1964, 1965 and 1966.
LHOptE: 5.3% in 1959, 1962 and 1965.
SwAT2: 4.7% in 1965.
LHOptD: 5.1% in 1959 and 1962.
LHOptC: 5.1% in 1959, 1962 and 1964.
LHOptB: 5.2% in 1959, 1962 and 1964.
LHOptA: 5.2% in 1959.
SwOptT2: 5.2% in 1959, 1960, 1961, 1962, 1964 and 1965.
Fixed 80% stocks: 3.9% in 1966.
Fixed 50% stocks: 3.9% in 1937.

Highest 30-Year Historical Surviving Withdrawal Rates (1923-1980):

LHOptG: 12.3% in 1924 (and 12.8% in 1922).
LHOptF: 10.6% in 1924 (and 10.8% in 1922).
LHOptE: 12.3% in 1924 (and 12.8% in 1922).
SwAT2: 8.6% in 1924 (and 9.1% in 1922).
LHOptD: 12.8% in 1924 (and 13.2% in 1922).
LHOptC: 13.4% in 1924 (and 13.7% in 1922).
LHOptB: 13.4% in 1924 (and 13.7% in 1922).
LHOptA: 12.9% in 1924 (and 13.3% in 1922).
SwOptT2: 9.2% in 1924 and 1933 (and 10.1% in 1921 and 1922).
Fixed 80% stocks: 10.3% in 1950.
Fixed 50% stocks: 7.8% in 1980 (and 8.1% in 1921).

At today’s valuation level (P/E10 = 27):

LHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 4.1%.
Coin Toss Rate (50%-50%): 4.93%.
High Risk Rate (5% probability of success, one sided): 6.9%.

LHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 4.0%.
Coin Toss Rate (50%-50%): 4.79%.
High Risk Rate (5% probability of success, one sided): 6.2%.

LHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 3.9%.
Coin Toss Rate (50%-50%): 4.86%.
High Risk Rate (5% probability of success, one sided): 7.4%.

SwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 4.1%.
Coin Toss Rate (50%-50%): 4.86%.
High Risk Rate (5% probability of success, one sided): 5.9%.

LHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 3.4%.
Coin Toss Rate (50%-50%): 4.77%.
High Risk Rate (5% probability of success, one sided): 7.8%.

LHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 3.5%.
Coin Toss Rate (50%-50%): 4.87%.
High Risk Rate (5% probability of success, one sided): 8.4%.

LHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 3.5%.
Coin Toss Rate (50%-50%): 4.93%.
High Risk Rate (5% probability of success, one sided): 8.4%.

LHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 3.7%.
Coin Toss Rate (50%-50%): 4.86%.
High Risk Rate (5% probability of success, one sided): 7.9%.

At a typical valuation level (P/E10 = 14):

LHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 5.7%.
Coin Toss Rate (50%-50%): 6.50%.
High Risk Rate (5% probability of success, one sided): 8.5%.

LHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 5.5%.
Coin Toss Rate (50%-50%): 6.34%.
High Risk Rate (5% probability of success, one sided): 7.7%.

LHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 5.8%.
Coin Toss Rate (50%-50%): 6.77%.
High Risk Rate (5% probability of success, one sided): 9.3%.

SwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 5.6%.
Coin Toss Rate (50%-50%): 6.26%.
High Risk Rate (5% probability of success, one sided): 7.3%.

LHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 5.3%.
Coin Toss Rate (50%-50%): 6.73%.
High Risk Rate (5% probability of success, one sided): 9.7%.

LHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 5.4%.
Coin Toss Rate (50%-50%): 6.82%.
High Risk Rate (5% probability of success, one sided): 10.3%.

LHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 5.5%.
Coin Toss Rate (50%-50%): 6.88%.
High Risk Rate (5% probability of success, one sided): 10.4%.

LHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 5.6%.
Coin Toss Rate (50%-50%): 6.78%.
High Risk Rate (5% probability of success, one sided): 9.8%.

At a bargain valuation level (P/E10 = 8):

LHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 8.2%.
Coin Toss Rate (50%-50%): 8.96%.
High Risk Rate (5% probability of success, one sided): 11.0%.

LHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 8.0%.
Coin Toss Rate (50%-50%): 8.76%.
High Risk Rate (5% probability of success, one sided): 10.2%.

LHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 8.8%.
Coin Toss Rate (50%-50%): 9.75%.
High Risk Rate (5% probability of success, one sided): 12.3%.

SwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 7.8%.
Coin Toss Rate (50%-50%): 8.45%.
High Risk Rate (5% probability of success, one sided): 9.5%.

LHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 8.4%.
Coin Toss Rate (50%-50%): 9.78%.
High Risk Rate (5% probability of success, one sided): 12.8%.

LHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 8.4%.
Coin Toss Rate (50%-50%): 9.84%.
High Risk Rate (5% probability of success, one sided): 13.3%.

LHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 8.5%.
Coin Toss Rate (50%-50%): 9.91%.
High Risk Rate (5% probability of success, one sided): 13.4%.

LHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 8.6%.
Coin Toss Rate (50%-50%): 9.77%.
High Risk Rate (5% probability of success, one sided): 12.8%.

Data Analysis: New Conditions

LHOptE, LHOptF and LHOptG are alternatives to SwAT2. They all do better on the upside. All are similar when starting from today’s unusually high valuations. The process of developing LHOptE was overly involved. Alternatives LHOptF and LHOptG give us a better insight as to what we might actually be able to achieve, looking ahead.

These conditions show us the impact of limiting out maximum stock allocation to 75%. Only SwAT2 limits both the maximum and the minimum stock allocations (75% maximum, 25% minimum), consistent with Benjamin Graham’s advice.

These latest results were sensitive to the lower threshold setting (P/E10 = 8). The upside potential is closely related to how well we react after prices have fallen to bargain levels. The lower threshold sensitivity is related to what happened specifically in the 1920s. It wasn’t the lower threshold NUMBER that was magic. Rather, it was recognizing that there was a bubble and knowing when to get out. Our procedures have not solved that problem. Our numbers have clarified the issue. They point us in the right direction. But they are no substitute for judgment. We cannot rely on numbers alone.

We should load up on stocks after they have fallen to bargain levels. We should not cut back immediately as prices rise. We should hold onto them for several years. At some point, prices will rise so much that we should cut back. Exactly when remains a matter of judgment.

Have fun.

John Walter Russell
June 14, 2006