Latch and Hold Equations HCTVR

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 advantage of switching versus fixed allocations in times of high valuations.

These are Half Constant Terminal Value Rate HCTVR equations. They assume a balance equal to one half of the initial balance (plus inflation) at year 30. The year 30 balance falls below one half of the original balance (plus inflation) if you increase the withdrawal rate by 0.1%.

Half Constant Terminal Value Rates are useful for those whose retirement is likely to last longer than 30 years. For example, a retiree may choose full safety in terms of a balance of zero at year 30. But he may allow himself a reasonable amount of risk at the Half Constant Terminal Value Rate.

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.

In this case, I looked at 30-Year Half Constant Terminal Value Rates. Withdrawing at the Half Constant Terminal Value Rate leaves a final balance greater than or equal to one half of the original balance (plus inflation) at year 30. Increasing the withdrawal rate by 0.1% causes the balance to fall below one half of the original balance (plus inflation).

This differs from traditional Historical Surviving Withdrawal Rates which have year 30 balances close to zero.

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

All portfolios consist of stocks (S&P500) and TIPS at a 2.0% (real) interest rate. I set expenses equal to 0.20% of the current balance.

I investigated the following conditions:

1) HSwOptT2 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. HSwOptT2 is the best (stock allocation) switching algorithm in the absence of a memory (that is, without latch and hold).

2) HSwAT2 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 HSwAT2. HSwAT2 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%.

3) HLHOptA is HSwOptT2 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. HLHOptA was the best condition from my initial Latched Threshold Survey.

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

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

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

7) HLHOptE is HLHOptA 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.

8) HLHOptF 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.

9) HLHOptG 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.

Regression Equations

Here is the HSwOptT2 regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates HCTVR versus the percentage earnings yield 100E10/P:

y = 0.373x+2.9701 plus and minus 0.8%.
R squared = 0.6365.

Here is the HSwAT2 regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.4437x+2.4023 plus 1.0% and minus 0.7%.
R squared = 0.7673.

Here is the HLHOptA regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.5546x+2.1411 plus 3.0% and minus 1.2%.
R squared = 0.4718.

Here is the HLHOptB regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.5703x+2.1513 plus 3.5% and minus 1.4%.
R squared = 0.4301.

Here is the HLHOptC regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.5772x+2.0241 plus 3.5% and minus 1.4%.
R squared = 0.427.

Here is the HLHOptD regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.544x+2.1606 plus 3.0% and minus 1.4%.
R squared = 0.4636.

Here is the HLHOptE regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.557x+2.1471 plus 2.5% and minus 1.0%.
R squared = 0.5917.

Here is the HLHOptF regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.4663x+2.3191 plus 1.4% and minus 0.8%.
R squared = 0.7193.

Here is the HLHOptG regression equation of 1923-1975 30-Year Half Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.5018x+2.2599 plus 2.0% and minus 0.8%.
R squared = 0.6194.

Data Summary: All Latch and Hold Conditions

Lowest 30-Year Historical Surviving Withdrawal Rates (1923-1975):

HSwOptT2: 4.4% in 1959.
HSwAT2: 3.9% in 1965.
HLHOptA: 4.6% in 1955, 1956 and 1959.
HLHOptB: 4.6% in 1955, 1956 and 1959.
HLHOptC: 4.5% in 1955, 1956, 1959 and 1964.
HLHOptD: 4.5% in 1955, 1956 and 1959.
HLHOptE: 4.7% in 1956, 1959 and 1965.
HLHOptF: 4.3% in 1965.
HLHOptG: 4.2% in 1964.

Highest 30-Year Historical Surviving Withdrawal Rates (1923-1975):

SwOptT2: 8.5% in 1924 and 1933.
SwAT2: 8.0% in 1924.
HLHOptA: 12.4% in 1924.
HLHOptB: 12.9% in 1924.
HLHOptC: 12.9% in 1924.
HLHOptD: 12.2% in 1924.
HLHOptE: 11.7% in 1924.
HLHOptF: 9.2% in 1924.
HLHOptG: 10.0% in 1924.

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

HSwOptT2:
Safe Withdrawal Rate (95% probability of success, one sided): 3.6%.
Coin Toss Rate (50%-50%): 4.35%.
High Risk Rate (5% probability of success, one sided): 5.2%.

HSwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 3.4%.
Coin Toss Rate (50%-50%): 4.05%.
High Risk Rate (5% probability of success, one sided): 5.1%.

HLHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 3.0%.
Coin Toss Rate (50%-50%): 4.20%.
High Risk Rate (5% probability of success, one sided): 7.2%.

HLHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 2.9%.
Coin Toss Rate (50%-50%): 4.26%.
High Risk Rate (5% probability of success, one sided): 7.8%.

HLHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 2.8%.
Coin Toss Rate (50%-50%): 4.16%.
High Risk Rate (5% probability of success, one sided): 7.7%.

HLHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 2.8%.
Coin Toss Rate (50%-50%): 4.18%.
High Risk Rate (5% probability of success, one sided): 7.2%.

HLHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 3.2%.
Coin Toss Rate (50%-50%): 4.21%.
High Risk Rate (5% probability of success, one sided): 6.7%.

HLHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 3.3%.
Coin Toss Rate (50%-50%): 4.05%.
High Risk Rate (5% probability of success, one sided): 5.5%.

HLHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 3.3%.
Coin Toss Rate (50%-50%): 4.12%.
High Risk Rate (5% probability of success, one sided): 6.1%.

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

HSwOptT2:
Safe Withdrawal Rate (95% probability of success, one sided): 4.8%.
Coin Toss Rate (50%-50%): 5.63%.
High Risk Rate (5% probability of success, one sided): 6.4%.

HSwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 4.9%.
Coin Toss Rate (50%-50%): 5.57%.
High Risk Rate (5% probability of success, one sided): 6.6%.

HLHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 4.9%.
Coin Toss Rate (50%-50%): 6.10%.
High Risk Rate (5% probability of success, one sided): 9.1%.

HLHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 4.8%.
Coin Toss Rate (50%-50%): 6.22%.
High Risk Rate (5% probability of success, one sided): 9.7%.

HLHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 4.8%.
Coin Toss Rate (50%-50%): 6.15%.
High Risk Rate (5% probability of success, one sided): 9.7%.

HLHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 4.7%.
Coin Toss Rate (50%-50%): 6.05%.
High Risk Rate (5% probability of success, one sided): 9.1%.

HLHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 5.1%.
Coin Toss Rate (50%-50%): 6.13%.
High Risk Rate (5% probability of success, one sided): 8.6%.

HLHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 4.9%.
Coin Toss Rate (50%-50%): 5.65%.
High Risk Rate (5% probability of success, one sided): 8.2%.

HLHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 5.1%.
Coin Toss Rate (50%-50%): 5.85%.
High Risk Rate (5% probability of success, one sided): 7.9%.

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

HSwOptT2:
Safe Withdrawal Rate (95% probability of success, one sided): 6.8%.
Coin Toss Rate (50%-50%): 7.63%.
High Risk Rate (5% probability of success, one sided): 8.4%.

HSwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 7.3%.
Coin Toss Rate (50%-50%): 7.95%.
High Risk Rate (5% probability of success, one sided): 9.0%.

HLHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 7.9%.
Coin Toss Rate (50%-50%): 9.07%.
High Risk Rate (5% probability of success, one sided): 12.1%.

HLHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 7.9%.
Coin Toss Rate (50%-50%): 9.28%.
High Risk Rate (5% probability of success, one sided): 12.8%.

HLHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 7.9%.
Coin Toss Rate (50%-50%): 9.24%.
High Risk Rate (5% probability of success, one sided): 12.8%.

HLHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 7.6%.
Coin Toss Rate (50%-50%): 8.96%.
High Risk Rate (5% probability of success, one sided): 12.0%.

HLHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 8.1%.
Coin Toss Rate (50%-50%): 9.11%.
High Risk Rate (5% probability of success, one sided): 11.6%.

HLHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 7.4%.
Coin Toss Rate (50%-50%): 8.15%.
High Risk Rate (5% probability of success, one sided): 9.6%.

HLHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 7.7%.
Coin Toss Rate (50%-50%): 8.53%.
High Risk Rate (5% probability of success, one sided): 10.5%.

Final Comments

These data cover a variety of conditions. Taken as a whole, they tell us a lot about the sensitivity of latch and hold to precise details. This lets us know what is reasonable to expect, looking forward.

I will use these results as part of a simple, easy to use spreadsheet calculator.

Have fun.

John Walter Russell
June 19, 2006