Adding Constraints to Latch and Hold

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

Earlier investigations showed that we can relax our requirements on the upper threshold. This investigation moves toward Benjamin Graham’s constraint on both stock and bond allocations to 25% to 75%.

We lose very little when we make the minimum stock allocation equal to 25%.

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).

Previously, our stock (S&P500) and bond (TIPS) allocations have been allowed to range between 0% and 100%. We had looked at the following conditions:

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.

Now we introduce Benjamin Graham’s constraint on the minimum stock allocation:

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%.

New Surveys

I conducted a new survey for LHOptD. I was interested in relaxing the requirements on the upper threshold. I started with a 5.2% withdrawal rate. There were 2 failures with a lower threshold from 4 through 8. Varying the higher threshold from 0 through 10 years had no effect when the preference is for the lower threshold. When the preference was for the higher threshold, 0 years was best.

LHOptD has P/E10 thresholds of 9-12-21-100 with stock allocations of 100%-50%-30%-25%-0%. The lower threshold is 8. The upper threshold is 21.1. The preference is set to use lower threshold data.

6) SwAT2 has P/E10 thresholds of 11-21 with stock allocations of 75%-40%-25%, respectively. I set its upper threshold to 100. I set its lower threshold to 1. These values eliminated the effects of latch and hold on SwAT2.

Regression Equations: New Conditions

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

y = 0.5701x+2.6562 plus 3.0% and minus 1.4%.
R squared = 0.5618.

Special note: On the upside, there are two distributions. The higher limit is plus 3.0%. The more common, inner condition has a limit of plus 0.8%. As an approximation: the confidence levels start out as plus and minus 1.4%. The upside splits, with some conditions reaching considerably higher rates.

Here is the SwAT2 regression equation of 1923-1980 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P.

y = 0.4091x+3.341 plus 1.0% and minus 0.7%.
R squared = 0.7451.

Special note: Unlike conditions with latch and hold, SwAT2 has only one distribution.

Data Summary: All Latch and Hold Conditions

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

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):

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):

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):

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):

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

We lose very little when we make the minimum stock allocation equal to 25%. We keep most of the upside that we have gained by using latch and hold.

SwAT2 has a very narrow confidence interval. This, combined with a slightly better Coin Toss Rate, results in a substantially higher Safe Withdrawal Rate at today’s valuations than that of LHOptD. This difference is probably real, not simply an artifact of the data.

The minimum Historical Surviving Withdrawal Rates found in the historical record favor LHOptD. But the bulk of the data, taken as a whole, lead to a different conclusion. There are only a few conditions at the extreme (i.e., at the highest valuation levels).

We will be in good shape as long as we take advantage of the bargains when valuations are low.

Have fun.

John Walter Russell
June 11, 2006