Continued Success with Latch and Hold

This extends my early investigations of Latch and Hold.

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).

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 investigation shows that we can relax our requirements on the upper threshold.

Settings

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).

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.

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.

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.

New Surveys

I conducted new surveys to come up with the settings for LHOptB and LHOptC. I was interested in relaxing the requirements on the upper threshold. I started with a 5.3% withdrawal rate.

As my first step, I eliminated the P/E10 switching threshold of 24. I set the stock allocation equal to 0% whenever P/E10 exceeded 21. I set the upper threshold equal to 21.1.

Varying the lower threshold from 4 through 8 years resulted in the minimum number of failures (3). Varying the higher threshold from 0 through 10 years has no effect when the preference is for the lower threshold. When the preference is for the higher threshold, 0 years is best.

I defined LHOptB as having P/E10 thresholds of 9-12-21-x, stock allocations of 100%-50%-30%-0%-0%, an upper threshold of 21.1 (with an extension of 4 years), a lower threshold of 8 (with an extension of 7 years) and a preference for lower threshold data.

I collected data with LHOptB.

Next, I reduced the upper threshold further. The number of 30-Year failures increased. I stopped at a P/E10 threshold of 20 with a corresponding upper threshold of 20.1.

The lower threshold had to be exactly 7 for the minimum number of failures (6). Varying the higher threshold from 0 through 10 years had no effect when the preference was for the lower threshold. When the preference is for the higher threshold, 0 years is best.

Later, I found that there were 3 failures at a 5.2% withdrawal rate. I could vary the lower threshold from 4 through 8 years and still get the minimum number of failures (3).

I defined LHOptC as having P/E10 thresholds of 9-12-20-x, stock allocations of 100%-50%-30%-0%-0%, an upper threshold of 20.1 (with an extension of 4 years), a lower threshold of 8 (with an extension of 7 years) and a preference for lower threshold data.

I collected data with LHOptC.

Regression Equations

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

y = 0.5658x+2.8359 plus 3.5% and minus 1.4%.
R squared = 0.4946.

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 1923-1980 30-Year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P.

y = 0.5648x+2.7831 plus 3.5% and minus 1.4%.
R squared = 0.4857.

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.

Data Analysis

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

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):

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):

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%.

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%.

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

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%.

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%.

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

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%.

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%.

Conclusions

We can relax our demands on setting the upper threshold. We will not experience any undue penalty. This is helpful because we do not expect history to repeat itself exactly.

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

Have fun.

John Walter Russell
June 11, 2006