Imperfect Allocation Switching
Posted: Mon Oct 25, 2004 6:46 pm
This is a brief survey of what happens when switching allocations between stocks (i.e., the S&P500 index) and TIPS with a 2.0% interest rate depending upon P/E10 (i.e., the current price of the S&P500 index divided by the average of the last ten years of earnings).
This lets you know the penalty of buying high and selling low as well as the rewards of investing properly.
Procedure
I set up my latest Deluxe Calculator V1.1A07 (which is a modified version of the Retire Early Safe Withdrawal Calculator version 1.61 dated November 7, 2002) for switching allocations between stocks and 2.0% TIPS. I set the expense ratio at 0.20%. I rebalanced all portfolios annually. I selected the CPI for making inflation adjustments.
I determined the highest withdrawal rates that would have survived all 30-year sequences from 1921-1980. [Dummy data are used for 2002-2010.] The precision is 0.1%. That is, there always would have been at least one failure if the withdrawal rate were increased by 0.1%.
I set the P/E10 thresholds to 3-12-20-80. The thresholds of 3 and 80 eliminate the effects of allocations other than the three programmable selections. For the three programmable allocations I selected all possible combinations of 30%, 50% and 70%.
Results
Here are the results. The stock allocations are shown in the order of P/E10 below 12, P/E10 between 12 and 20 and P/E10 above 20. They are in percent although the percentage symbol is not included. The percentages shown are the historical surviving withdrawal rates (i.e., the highest withdrawal rates with no failures within 30-years).
30-30-30 4.3%.
30-30-50 4.1%.
30-30-70 3.7%.
30-50-30 4.1%.
30-50-50 3.8%.
30-50-70 3.5%.
30-70-30 3.8%.
30-70-50 3.5%.
30-70-70 3.2%.
50-30-30 4.5%.
50-30-50 4.4%.
50-30-70 4.3%.
50-50-30 4.3%.
50-50-50 4.2%.
50-50-70 4.1%.
50-70-30 4.1%.
50-70-50 3.9%.
50-70-70 3.8%.
70-30-30 4.7%.
70-30-50 4.6%.
70-30-70 4.5%.
70-50-30 4.5%.
70-50-50 4.4%.
70-50-70 4.3%.
70-70-30 4.2%.
70-70-50 4.1%.
70-70-70 4.0%.
Analysis
I made comparisons with allocations of X-Y-30, X-Y-50 and X-Y-70. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were highest for X-Y-30, in the middle for X-Y-50 and lowest for X-Y-70. That is, reducing stock allocations always helped when P/E10 was above 20.
This is as expected.
I made comparisons with allocations of 30-X-Y, 50-X-Y and 70-X-Y. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were lowest for 30-X-Y, in the middle for 50-X-Y and highest for 70-X-Y. That is, increasing stock allocations always helped when P/E10 was below 12.
This is as expected.
I made comparisons with allocations of X-30-Y, X-50-Y and X-70-Y. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were highest for X-30-Y, in the middle for X-50-Y and lowest for X-70-Y. That is, reducing stock allocations always helped when P/E10 was between 12 and 20.
This is new information. It is consistent with previous results that have favored low stock allocations with P/E10 values in the middle range.
[The previously determined optimal stock allocations when including TIPS were 100-50-30-20-0% with P/E10 thresholds of 9-12-21-24.]
Using these results, I checked the results with the 70-30-30 allocation. It is, in fact, a global maximum, which is what we would expect.
I checked the results with the 30-70-70 allocation. It is, in fact, the global minimum, which is what we would expect.
I checked for interactions. Notice that the spread for allocations of 30-X-Y varies by 0.6% as Y varies from 30% to 70%. The spread for allocations of 50-X-Y varies by 0.2% to 0.3% as Y varies from 30% to 70%. The spread for allocations of 70-X-Y varies by 0.2% as Y varies from 30% to 70%.
This is the interaction:
A low stock allocation when P/E10 is low causes a wider than normal scatter in the results (i.e., historical surviving withdrawal rates).
A higher stock allocation when P/E10 is low produces more consistent results.
Comparisons
Here are the relevant buy-and-hold comparisons.
The allocation combination of 70-30-30 produced the best results. The historical surviving withdrawal rate was 4.7%.
A buy-and-hold allocation of 70% (i.e., 70-70-70) produced a historical surviving withdrawal rate of 4.0%.
A buy-and-hold allocation of 50% (i.e., 50-50-50) produced a historical surviving withdrawal rate of 4.2%.
A buy-and-hold allocation of 30% (i.e., 30-30-30) produced a historical surviving withdrawal rate of 4.3%.
The allocation combination of 30-70-70 produced the worst results. The historical surviving withdrawal rate was 3.2%.
Notice that the average of the best and worst switching allocations is 3.95%. [That is, (4.7+3.2) / 2 = 3.95.] This is slightly worse than the historical surviving withdrawal rates of every one of the buy-and-hold choices.
Summary
Increasing allocations when valuations are favorable and reducing them when allocations are unfavorable produces a substantial benefit compared to maintaining a constant allocation. This is buying low and selling high.
Decreasing allocations when valuations are favorable and increasing allocations when allocations are unfavorable results in a substantial penalty compared to maintaining a constant allocation. This is buying high and selling low.
In the absence of other information, a buy-and-hold strategy produces slightly better results than varying allocations. This is more of a statistical observation than a practical result.
These results are in terms of historical surviving withdrawal rates. The general findings apply to Safe Withdrawal Rates as well. Avoid using these numbers by themselves before adjusting for valuations.
Have fun.
John R.
This lets you know the penalty of buying high and selling low as well as the rewards of investing properly.
Procedure
I set up my latest Deluxe Calculator V1.1A07 (which is a modified version of the Retire Early Safe Withdrawal Calculator version 1.61 dated November 7, 2002) for switching allocations between stocks and 2.0% TIPS. I set the expense ratio at 0.20%. I rebalanced all portfolios annually. I selected the CPI for making inflation adjustments.
I determined the highest withdrawal rates that would have survived all 30-year sequences from 1921-1980. [Dummy data are used for 2002-2010.] The precision is 0.1%. That is, there always would have been at least one failure if the withdrawal rate were increased by 0.1%.
I set the P/E10 thresholds to 3-12-20-80. The thresholds of 3 and 80 eliminate the effects of allocations other than the three programmable selections. For the three programmable allocations I selected all possible combinations of 30%, 50% and 70%.
Results
Here are the results. The stock allocations are shown in the order of P/E10 below 12, P/E10 between 12 and 20 and P/E10 above 20. They are in percent although the percentage symbol is not included. The percentages shown are the historical surviving withdrawal rates (i.e., the highest withdrawal rates with no failures within 30-years).
30-30-30 4.3%.
30-30-50 4.1%.
30-30-70 3.7%.
30-50-30 4.1%.
30-50-50 3.8%.
30-50-70 3.5%.
30-70-30 3.8%.
30-70-50 3.5%.
30-70-70 3.2%.
50-30-30 4.5%.
50-30-50 4.4%.
50-30-70 4.3%.
50-50-30 4.3%.
50-50-50 4.2%.
50-50-70 4.1%.
50-70-30 4.1%.
50-70-50 3.9%.
50-70-70 3.8%.
70-30-30 4.7%.
70-30-50 4.6%.
70-30-70 4.5%.
70-50-30 4.5%.
70-50-50 4.4%.
70-50-70 4.3%.
70-70-30 4.2%.
70-70-50 4.1%.
70-70-70 4.0%.
Analysis
I made comparisons with allocations of X-Y-30, X-Y-50 and X-Y-70. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were highest for X-Y-30, in the middle for X-Y-50 and lowest for X-Y-70. That is, reducing stock allocations always helped when P/E10 was above 20.
This is as expected.
I made comparisons with allocations of 30-X-Y, 50-X-Y and 70-X-Y. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were lowest for 30-X-Y, in the middle for 50-X-Y and highest for 70-X-Y. That is, increasing stock allocations always helped when P/E10 was below 12.
This is as expected.
I made comparisons with allocations of X-30-Y, X-50-Y and X-70-Y. In all cases, with X and Y equal to 30% or 50% or 70%, the historical surviving withdrawal rates were highest for X-30-Y, in the middle for X-50-Y and lowest for X-70-Y. That is, reducing stock allocations always helped when P/E10 was between 12 and 20.
This is new information. It is consistent with previous results that have favored low stock allocations with P/E10 values in the middle range.
[The previously determined optimal stock allocations when including TIPS were 100-50-30-20-0% with P/E10 thresholds of 9-12-21-24.]
Using these results, I checked the results with the 70-30-30 allocation. It is, in fact, a global maximum, which is what we would expect.
I checked the results with the 30-70-70 allocation. It is, in fact, the global minimum, which is what we would expect.
I checked for interactions. Notice that the spread for allocations of 30-X-Y varies by 0.6% as Y varies from 30% to 70%. The spread for allocations of 50-X-Y varies by 0.2% to 0.3% as Y varies from 30% to 70%. The spread for allocations of 70-X-Y varies by 0.2% as Y varies from 30% to 70%.
This is the interaction:
A low stock allocation when P/E10 is low causes a wider than normal scatter in the results (i.e., historical surviving withdrawal rates).
A higher stock allocation when P/E10 is low produces more consistent results.
Comparisons
Here are the relevant buy-and-hold comparisons.
The allocation combination of 70-30-30 produced the best results. The historical surviving withdrawal rate was 4.7%.
A buy-and-hold allocation of 70% (i.e., 70-70-70) produced a historical surviving withdrawal rate of 4.0%.
A buy-and-hold allocation of 50% (i.e., 50-50-50) produced a historical surviving withdrawal rate of 4.2%.
A buy-and-hold allocation of 30% (i.e., 30-30-30) produced a historical surviving withdrawal rate of 4.3%.
The allocation combination of 30-70-70 produced the worst results. The historical surviving withdrawal rate was 3.2%.
Notice that the average of the best and worst switching allocations is 3.95%. [That is, (4.7+3.2) / 2 = 3.95.] This is slightly worse than the historical surviving withdrawal rates of every one of the buy-and-hold choices.
Summary
Increasing allocations when valuations are favorable and reducing them when allocations are unfavorable produces a substantial benefit compared to maintaining a constant allocation. This is buying low and selling high.
Decreasing allocations when valuations are favorable and increasing allocations when allocations are unfavorable results in a substantial penalty compared to maintaining a constant allocation. This is buying high and selling low.
In the absence of other information, a buy-and-hold strategy produces slightly better results than varying allocations. This is more of a statistical observation than a practical result.
These results are in terms of historical surviving withdrawal rates. The general findings apply to Safe Withdrawal Rates as well. Avoid using these numbers by themselves before adjusting for valuations.
Have fun.
John R.