Latch and Hold Equations CTVR

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

Constant Terminal Value Rates are useful for those whose retirement is likely to last longer than 30 years. They also allow us to make meaningful comparisons between conventional withdrawal strategies, which include income from capital gains as well as dividends, and a dividends-only approach. Both provide income indefinitely.

Keep in mind that dividends usually grow faster than inflation by 1% per year over long periods of time. Constant Terminal Value Rates match inflation exactly. Dividends occasionally lag inflation over shorter periods of time. This was an issue for retirements beginning in the late 1960s.

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 Constant Terminal Value Rates. Withdrawing at the Constant Terminal Value Rate leaves a final balance greater than or equal to the original balance (plus inflation) at year 30. Increasing the withdrawal rate by 0.1% causes the balance to fall below 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) CSwOptT2 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. CSwOptT2 is the best (stock allocation) switching algorithm in the absence of a memory (that is, without latch and hold).

2) CSwAT2 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 CSwAT2. CSwAT2 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) CLHOptA is CSwOptT2 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. CLHOptA was the best condition from my initial Latched Threshold Survey.

4) CLHOptB is CLHOptA 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) CLHOptC is CLHOptB 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) CLHOptE is CLHOptA 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) CLHOptF 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) CLHOptG 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 CSwOptT2 regression equation of 1923-1975 30-Year Constant Terminal Value Rates CTVR versus the percentage earnings yield 100E10/P:

y = 0.3645x+2.2578 plus 1.2% and minus 0.8%.
R squared = 0.5683.

Here is the CSwAT2 regression equation of 1923-1975 30-Year Constant Terminal Value Rates versus the percentage earnings yield 100E10/P:

y = 0.4379x+1.6886 plus 1.2% and minus 0.8%.
R squared = 0.7122.

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

y = 0.5283x+1.6283 plus 3.0% and minus 1.6%.
R squared = 0.4106.

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

y = 0.5436x+1.6339 plus 4.0% and minus 2.0%.
R squared = 0.3728.

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

y = 0.5531x+1.4915 plus 4.0% and minus 2.0%.
R squared = 0.3758.

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

y = 0.518x+1.6456 plus 3.5% and minus 1.8%.
R squared = 0.4003.

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

y = 0.5355x+1.6179 plus 2.5% and minus 1.6%.
R squared = 0.5375.

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

y = 0.4591x+1.6232 plus 1.6% and minus 1.0%.
R squared = 0.6708.

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

y = 0.4922x+1.5745 plus 2.0% and minus 1.2%.
R squared = 0.5576.

Data Summary: All Latch and Hold Conditions

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

CSwOptT2: 3.7% in 1956, 1959 and 1965.
CSwAT2: 3.2% in 1964 and 1965.
CLHOptA: 3.8% in 1952 and 1955.
CLHOptB: 3.8% in 1952, 1955 and 1956.
CLHOptC: 3.7% in 1952 and 1955.
CLHOptD: 3.7% in 1952 and 1955.
CLHOptE: 4.0% in 1955 and 1956.
CLHOptF: 3.6% in 1956, 1959 and 1965.
CLHOptG: 3.5% in 1964.

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

CSwOptT2: 7.9% in 1924.
CSwAT2: 7.4% in 1924.
CLHOptA: 11.8% in 1924.
CLHOptB: 12.3% in 1924.
CLHOptC: 12.3% in 1924.
CLHOptD: 11.7% in 1924.
CLHOptE: 11.1% in 1924.
CLHOptF: 8.6% in 1924.
CLHOptG: 9.5% in 1924.

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

CSwOptT2:
Safe Withdrawal Rate (95% probability of success, one sided): 2.8%.
Coin Toss Rate (50%-50%): 3.61%.
High Risk Rate (5% probability of success, one sided): 4.8%.

CSwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 2.5%.
Coin Toss Rate (50%-50%): 3.31%.
High Risk Rate (5% probability of success, one sided): 4.5%.

CLHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 2.0%.
Coin Toss Rate (50%-50%): 3.58%.
High Risk Rate (5% probability of success, one sided): 6.6%.

CLHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 1.7%.
Coin Toss Rate (50%-50%): 3.65%.
High Risk Rate (5% probability of success, one sided): 7.7%.

CLHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 1.5%.
Coin Toss Rate (50%-50%): 3.54%.
High Risk Rate (5% probability of success, one sided): 7.5%.

CLHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 1.8%.
Coin Toss Rate (50%-50%): 3.56%.
High Risk Rate (5% probability of success, one sided): 7.1%.

CLHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 2.0%.
Coin Toss Rate (50%-50%): 3.60%.
High Risk Rate (5% probability of success, one sided): 6.1%.

CLHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 2.3%.
Coin Toss Rate (50%-50%): 3.32%.
High Risk Rate (5% probability of success, one sided): 4.9%.

CLHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 2.2%.
Coin Toss Rate (50%-50%): 3.40%.
High Risk Rate (5% probability of success, one sided): 5.4%.

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

CSwOptT2:
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): 6.1%.

CSwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 4.0%.
Coin Toss Rate (50%-50%): 4.82%.
High Risk Rate (5% probability of success, one sided): 6.0%.

CLHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 3.8%.
Coin Toss Rate (50%-50%): 5.40%.
High Risk Rate (5% probability of success, one sided): 8.4%.

CLHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 3.5%.
Coin Toss Rate (50%-50%): 5.52%.
High Risk Rate (5% probability of success, one sided): 9.5%.

CLHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 3.4%.
Coin Toss Rate (50%-50%): 5.44%.
High Risk Rate (5% probability of success, one sided): 9.4%.

CLHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 3.6%.
Coin Toss Rate (50%-50%): 5.35%.
High Risk Rate (5% probability of success, one sided): 8.9%.

CLHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 3.8%.
Coin Toss Rate (50%-50%): 5.44%.
High Risk Rate (5% probability of success, one sided): 7.9%.

CLHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 3.9%.
Coin Toss Rate (50%-50%): 4.90%.
High Risk Rate (5% probability of success, one sided): 6.5%.

CLHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 3.9%.
Coin Toss Rate (50%-50%): 5.09%.
High Risk Rate (5% probability of success, one sided): 7.1%.

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

CSwOptT2:
Safe Withdrawal Rate (95% probability of success, one sided): 6.0%.
Coin Toss Rate (50%-50%): 6.81%.
High Risk Rate (5% probability of success, one sided): 8.0%.

CSwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 6.4%.
Coin Toss Rate (50%-50%): 7.16%.
High Risk Rate (5% probability of success, one sided): 8.4%.

CLHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 6.6%.
Coin Toss Rate (50%-50%): 8.23%.
High Risk Rate (5% probability of success, one sided): 11.2%.

CLHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 6.4%.
Coin Toss Rate (50%-50%): 8.43%.
High Risk Rate (5% probability of success, one sided): 12.4%.

CLHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 6.4%.
Coin Toss Rate (50%-50%): 8.41%.
High Risk Rate (5% probability of success, one sided): 12.4%.

CLHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 6.3%.
Coin Toss Rate (50%-50%): 8.12%.
High Risk Rate (5% probability of success, one sided): 11.6%.

CLHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 6.7%.
Coin Toss Rate (50%-50%): 8.31%.
High Risk Rate (5% probability of success, one sided): 10.8%.

CLHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 6.4%.
Coin Toss Rate (50%-50%): 7.36%.
High Risk Rate (5% probability of success, one sided): 9.0%.

CLHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 6.5%.
Coin Toss Rate (50%-50%): 7.73%.
High Risk Rate (5% probability of success, one sided): 9.7%.

Final Comments

These data cover a variety of conditions. Viewed 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 to generate simple, easy to use spreadsheet calculators.

These results favor dividend-based strategies when starting at today’s valuations. Yields from carefully selected dividend portfolios easily match these Coin Toss Rates (50%-50% odds). They easily beat these Safe Withdrawal Rates.

Have fun.

John Walter Russell
June 19, 2006