Latch and Hold Equations HSWR
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.
I have calculated equations for 30-Year Historical Surviving Withdrawal Rates. They assume a balance of zero at year 30. The year 30 balance becomes negative if you increase the withdrawal rate by 0.1%.
These formulas include start years of 1923-1975. The shortened time period (versus 1923-1980) corresponds to completed 30-year sequences. This is necessary because my calculator will include Constant Terminal Value Rates and Half Constant Terminal Value Rates. Both require completed sequences.
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).
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) 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) 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%.
3) 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.
4) 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.
5) 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.
6) 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.
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.
8) 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.
9) 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.
Regression Equations
Here is the SwOptT2 regression equation of 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.3874x+3.6363 plus and minus 0.8%.
R squared = 0.6987.
Special note: Unlike conditions with latch and hold, SwOptT2 has only one distribution.
Here is the SwAT2 regression equation of 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.45x+3.1172 plus 1.0% and minus 0.7%.
R squared = 0.7905.
Special note: Unlike conditions with latch and hold, SwAT2 has only one distribution.
Here is the LHOptA regression equation of 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.5763x+2.6968 plus 3.0% and minus 1.2%.
R squared = 0.5276.
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 1.2%. The upside splits, with some conditions reaching considerably higher rates. The improvement on the upside, when the results are on the upside, is dramatic whenever the earnings yield is more than 7.5%.
Here is the LHOptB regression equation of 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.5927x+2.6938 plus 3.5% and minus 1.4%.
R squared = 0.484.
Special note: On the upside, there are two distributions. The higher limit is plus 3.5%. 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 LHOptC regression equation of 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.6009x+2.5881 plus 3.5% and minus 1.4%.
R squared = 0.485.
Special note: On the upside, there are two distributions. The higher limit is plus 3.5%. 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 LHOptD regression equation of 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.5776x+2.6213 plus 3.0% and minus 1.4%.
R squared = 0.5317.
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 LHOptE regression equation of 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.5795x+2.6739 plus 2.5% and minus 1.0%.
R squared = 0.6438.
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.
Here is the LHOptF regression equation of 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.4854x+2.9325 plus 1.4% and minus 0.8%.
R squared = 0.7582.
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 1923-1975 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P:
y = 0.508x+2.9588 plus 2.0% and minus 0.8%.
R squared = 0.6734.
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 (1923-1975):
SwOptT2: 5.2% in 1959, 1960, 1961, 1962, 1964 and 1965.
SwAT2: 4.7% in 1965.
LHOptA: 5.2% in 1959.
LHOptB: 5.2% in 1959, 1962 and 1964.
LHOptC: 5.1% in 1959, 1962 and 1964.
LHOptD: 5.1% in 1959 and 1962.
LHOptE: 5.3% in 1959, 1962 and 1965.
LHOptF: 5.0% in 1962, 1964, 1965 and 1966.
LHOptG: 4.9% in 1964.
Fixed 50% stocks: 3.9% in 1937.
Fixed 80% stocks: 3.9% in 1966.
Highest 30-Year Historical Surviving Withdrawal Rates (1923-1975):
SwOptT2: 9.2% in 1924.
SwAT2: 8.6% in 1924.
LHOptA: 12.9% in 1924.
LHOptB: 13.4% in 1924.
LHOptC: 13.4% in 1924.
LHOptD: 12.8% in 1924.
LHOptE: 12.3% in 1924.
LHOptF: 9.9% in 1924.
LHOptG: 10.6% in 1924.
Fixed 50% stocks: 7.6% in 1924 and 1950.
Fixed 80% stocks: 10.3% in 1950.
At today’s valuation level (P/E10 = 27):
SwOptT2:
Safe Withdrawal Rate (95% probability of success, one sided): 4.3%.
Coin Toss Rate (50%-50%): 5.07%.
High Risk Rate (5% probability of success, one sided): 5.9%.
SwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 4.1%.
Coin Toss Rate (50%-50%): 4.78%.
High Risk Rate (5% probability of success, one sided): 5.8%.
LHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 3.6%.
Coin Toss Rate (50%-50%): 4.83%.
High Risk Rate (5% probability of success, one sided): 7.8%.
LHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 3.5%.
Coin Toss Rate (50%-50%): 4.89%.
High Risk Rate (5% probability of success, one sided): 8.4%.
LHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 3.4%.
Coin Toss Rate (50%-50%): 4.81%.
High Risk Rate (5% probability of success, one sided): 8.3%.
LHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 3.4%.
Coin Toss Rate (50%-50%): 4.76%.
High Risk Rate (5% probability of success, one sided): 7.8%.
LHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 3.8%.
Coin Toss Rate (50%-50%): 4.82%.
High Risk Rate (5% probability of success, one sided): 7.3%.
LHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 3.9%.
Coin Toss Rate (50%-50%): 4.73%.
High Risk Rate (5% probability of success, one sided): 6.1%.
LHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 4.0%.
Coin Toss Rate (50%-50%): 4.84%.
High Risk Rate (5% probability of success, one sided): 6.8%.
At a typical valuation level (P/E10 = 14):
SwOptT2:
Safe Withdrawal Rate (95% probability of success, one sided): 5.6%.
Coin Toss Rate (50%-50%): 6.40%.
High Risk Rate (5% probability of success, one sided): 7.2%.
SwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 5.6%.
Coin Toss Rate (50%-50%): 6.33%.
High Risk Rate (5% probability of success, one sided): 7.3%.
LHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 5.6%.
Coin Toss Rate (50%-50%): 6.81%.
High Risk Rate (5% probability of success, one sided): 9.8%.
LHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 5.5%.
Coin Toss Rate (50%-50%): 6.93%.
High Risk Rate (5% probability of success, one sided): 10.4%.
LHOptC:
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%.
LHOptD:
Safe Withdrawal Rate (95% probability of success, one sided): 5.4%.
Coin Toss Rate (50%-50%): 6.75%.
High Risk Rate (5% probability of success, one sided): 9.8%.
LHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 5.8%.
Coin Toss Rate (50%-50%): 6.81%.
High Risk Rate (5% probability of success, one sided): 9.3%.
LHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 5.0%.
Coin Toss Rate (50%-50%): 6.40%.
High Risk Rate (5% probability of success, one sided): 7.8%.
LHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 5.8%.
Coin Toss Rate (50%-50%): 6.59%.
High Risk Rate (5% probability of success, one sided): 8.6%.
At a bargain valuation level (P/E10 = 8):
SwOptT2:
Safe Withdrawal Rate (95% probability of success, one sided): 7.7%.
Coin Toss Rate (50%-50%): 8.48%.
High Risk Rate (5% probability of success, one sided): 9.3%.
SwAT2:
Safe Withdrawal Rate (95% probability of success, one sided): 8.0%.
Coin Toss Rate (50%-50%): 8.74%.
High Risk Rate (5% probability of success, one sided): 9.7%.
LHOptA:
Safe Withdrawal Rate (95% probability of success, one sided): 8.7%.
Coin Toss Rate (50%-50%): 9.90%.
High Risk Rate (5% probability of success, one sided): 12.9%.
LHOptB:
Safe Withdrawal Rate (95% probability of success, one sided): 8.7%.
Coin Toss Rate (50%-50%): 10.10%.
High Risk Rate (5% probability of success, one sided): 13.6%.
LHOptC:
Safe Withdrawal Rate (95% probability of success, one sided): 8.7%.
Coin Toss Rate (50%-50%): 10.10%.
High Risk Rate (5% probability of success, one sided): 13.6%.
LHOptD:
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): 12.8%.
LHOptE:
Safe Withdrawal Rate (95% probability of success, one sided): 8.9%.
Coin Toss Rate (50%-50%): 9.92%.
High Risk Rate (5% probability of success, one sided): 12.4%.
LHOptF:
Safe Withdrawal Rate (95% probability of success, one sided): 8.2%.
Coin Toss Rate (50%-50%): 9.00%.
High Risk Rate (5% probability of success, one sided): 10.4%.
LHOptG:
Safe Withdrawal Rate (95% probability of success, one sided): 8.5%.
Coin Toss Rate (50%-50%): 9.31%.
High Risk Rate (5% probability of success, one sided): 11.3%.
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 to generate simple, easy to use spreadsheet calculators.
Have fun.
John Walter Russell
June 18, 2006