The Lower Latch and Hold Threshold

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.

This time I looked at the lower threshold.

I have included my earlier results in this article.

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%.

Latest Survey

I conducted a new survey that produced LHOptE. This time, I was interested in the lower threshold. I had intended to simplify the requirements on the upper threshold along the lines of SwAT2. I ended up with something quite different.

LHOptE has 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.

I used a withdrawal rate of 5.3%. It has 0 failures with a lower threshold from 4 through 7. Varying the higher threshold from 0 through 10 years has no effect when the preference is set for the lower threshold. When the preference is for the higher threshold, 0 years is best.

Regression Equations: New Conditions

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

y = 0.5554x+2.8031 plus 2.5% and minus 1.0%.
R squared = 0.653.

Special note: On the upside, there are two distributions. The higher limit is plus 2.5%. As an approximation: the confidence levels start out as plus and minus 1.0%. The upside splits, with some conditions reaching considerably higher rates.

Data Summary: All Latch and Hold Conditions

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

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):

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):

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):

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):

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 is an attractive alternative to SwAT2. It has a narrow downward confidence interval. It has an attractive upside. The two approaches are similar when starting from today’s valuations. LHOptE is better when valuations are favorable or typical.

The process of developing LHOptE was overly involved. We cannot expect to replicate its full performance looking forward. What we can rely on is that, once again, the EXACT details associated with the upper threshold are not very important. We should focus on the lower threshold.

Of interest: I was not able to eliminate the 100% stock allocation below the lower threshold (P/E10 = 9). That is, I could not successfully reduce the lowest allocation threshold below 9. Nor could I increase the lower, holding threshold to 9 or higher. We can live with Benjamin Graham’s constraint on stock allocations to 25% when valuations are high, but we must pay a penalty if we limit ourselves to a 75% stock allocation when valuations are especially attractive (i.e., P/E10 below 9).

Have fun.

John Walter Russell
June 13, 2006