Latched Threshold Survey

I have just built a Latch and Hold Calculator. It 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. For example, if we set the threshold at P/E10 = 20 and if we set the extension at 4 years, the calculator acts as if P/E10 were equal to 20 until four years after it has fallen below 20.

With Latch and Hold Calculator LH02, there is a threshold for low valuations as well.

It is possible for the Latch and Hold result at the higher threshold to conflict with the lower threshold. I allow you to choose which result to prefer (i.e., higher or lower reported value of P/E10).

As a final step, LH02 clips both processed P/E10 results to remain within the upper and lower thresholds. Otherwise, it would have been possible for the internally processed P/E10 level to extend beyond a threshold indirectly.

Except for this pre-processing of P/E10, the calculator is the standard Deluxe V1.1A08a version. Pre-processing affects only what happens with switching (i.e., varying stock allocations in accordance with P/E10).

This is my initial survey with Latch and Hold Calculator LH02.

Baselines

I used the optimized switching algorithm SwOptT2 as my first baseline. 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.

I used SwAT2 as an alternative baseline. It constrains stock and TIPS allocations to 25% to 75%. It sets the P/E10 thresholds at 11-21 with stock allocations of 75%-40%-25%, respectively.

Early Lessons from SwOptT2

Clipping is always on.

I started with SwOptT2. I set the withdrawal rate at 5.2%. I set the upper P/E10 latching threshold equal to 100. I set the lower P/E10 holding threshold equal to 1. I set both holding periods to 4 years.

There were zero failures at year 30 with a withdrawal rate of 5.2%. There were six failures with a withdrawal rate of 5.3%.

I set the withdrawal rate to 5.3% and increased the lower, holding threshold in increments of one. There was no change as I increased it to 9. When I set the holding threshold equal to 10, the number of failures increased dramatically from 6 to 18.

On further analysis, I determined that I had effectively removed the lowest P/E10 threshold and its 100% allocation. Because of clipping, the calculator never sees a processed P/E10 below 10. In effect, the lowest threshold became 12, which has an allocation of 50%.

I found a similar effect with the highest threshold, P/E10 = 24. Increasing the latching threshold to 24 effectively changed the highest threshold. Setting it to 24.1 (with a holding period of zero) effectively removed any effect. The small 0.1 increment from 24 to 24.1 was needed because I use greater than (and less than) comparisons, not greater than or equal (and not less than or equal).

Pay Attention to the Lower Threshold.

I set the higher, latching P/E10 threshold equal to 100. This was high enough to remove it from having any effect.

I set the lower, holding threshold equal to 8. I varied the holding period. When preferring the lower threshold, the number of failures started at 6 with a holding period of 0 and 1 years. It fell to 5 at 2 years. It was 3 at 3 years. It was 2 at 4, 5 and 6 years. It was 1 at 7 years. It was 2 at 8 years. It was 4 at 9 and 10 years.

Then I changed the preference to the upper threshold. That is, I set cell I25 equal to 1. In all instances, as I varied the holding period from 0 to 10 years, the number of failures remained at 6.

Pay Less Attention to the Higher Threshold.

I set the higher, latching threshold equal to 24.1. I set the lower threshold equal to 8 with a holding period of 7 years. With a preference for the lower threshold, there was always 1 failure as I varied the holding period of the higher, latching threshold from 0 to 10 years.

Then I changed the preference to the higher threshold. There were 6 failures with a holding period of 0, 1, 2, 3, 4 and 5 years. At 6 years, there were 10 failures. There were 12 failures at 7 years. There were 10 failures at 8 years. There were 11 failures at 9 years. There were 12 failures at 10 years.

Lessons from SwOptT2.

The higher, latching threshold is less important than the lower, holding threshold. It does not matter much if you take a few years to reinvest after a period of extremely high valuations. The big payoff, however, is to buy and hold stocks for an extended time after their prices have hit bargain levels.

Early Lessons from SwAT2

SwAT2 Results.

I set up SwAT2. I set the withdrawal rate at 5.0%. I set the upper P/E10 latching threshold equal to 100. I set the lower P/E10 holding threshold equal to 1. I set both holding periods to 4 years. There were 4 failures. To bring the number of failures down to zero, I had to reduce the withdrawal rate to 4.7%.

I returned to a withdrawal rate of 5.0%.

I set the lower, holding P/E10 threshold equal to 8. I set the preference to the lower threshold. I varied the holding period. There were 4 failures with periods of 0, 1, 2, 3, 4, 5, 6, 7 and 8 years. There were 6 failures with holding periods of 9 and 10 years.

Then, I set the preference to the higher threshold. The higher, latching threshold was still 100. There were 4 failures as the holding period of the lower threshold varied from 0 to 10.

I lowered the higher threshold to 21.1. I set the preference to the lower threshold. I set the holding period of the lower threshold equal to 0 years. The number of failures remained constant at 4 as I varied the holding period of the upper, latching threshold.

I kept the higher threshold at 21.1. I changed the preference to the higher threshold. I kept the holding period of the lower threshold equal to 0 years. The number of failures varied as I varied the holding period of the upper, latching threshold. At 0 years, there were 4 failures. At 1 year, there were 8 failures. At 2 and 3 years, there were 10 failures. At 4 years, there were 8 failures. At 5 years, there were 5 failures. At 6 and 7 years, there were 14 failures. At 8 years, there were 13 failures. At 9 and 10 years, there were 14 failures.

SwAT2 Lessons.

These results caution us about the higher, latching threshold. Staying out too long can cause problems.

In retrospect, I must point out that I lowered the latching threshold for SwAT2 to 21.1 as opposed to 24.1. This procedure differs from what I did with the lower, holding threshold. I set the holding threshold equal to an absolute bargain level (P/E10=8) as opposed to something relative to the SwAT2 P/E10 threshold of 11.

Initial Survey

This concludes my initial survey. It reinforces the notion of buying heavily when prices are low. It reinforces the idea that you should continue to hold the new shares until much later.

This was a quick survey. I did not collect a set of Historical Surviving Withdrawal Rates. I only looked at extremes. The more interesting story will be later.

My research has shown that switching (stock allocations) is superior when starting from times of high valuations, but not when starting at times of normal and bargain level valuations. One way to improve your results is to wait for attractive valuations. It has the disadvantage that it requires judgment as to when to add stocks. The new latch and hold features may allow us to automate this process somewhat.

Have fun.

John Walter Russell
June 9, 2006