Design Calculations
Here are some designs for 40-year and 50-year retirement portfolios. We are still in the early stages of doing this.
I use the word design when I combine different segments of retirement portfolios to extend the total lifetime. In this case, I started with an all-TIPS portfolio for 10 or 20 years. Then I attached one of our standard 30-year portfolios. I was seeking to reach 40 or 50 years total at a withdrawal rate close to 4% (plus inflation).
In each instance, I determined the highest value of P/E10 that was consistent with reaching the full 40 or 50 years. I applied this at 10 or 20 years. In actual practice, we would take advantage of a favorable opportunity when it occurs. We would switch away from our all-TIPS portfolio to one of our standard portfolios when stock prices dropped to compelling levels.
I made excursions to examine lower withdrawal rates and standard portfolios with guaranteed positive ending balances.
Equations for Design
I have grouped the equations for our standard portfolios together.
Equations for Design
SwOptT2 is an optimized switching portfolio using stocks (S&P500) and TIPS at a 2% interest rate. Allocations vary with P/E10. The P/E10 thresholds are 9-12-21-24. The stock allocations are 100%-50%-30%-20%-0%, respectively.
SwAT2 is an optimized switching portfolio subject to Benjamin Graham’s constraint. I restrict both stock (S&P500) and bond (TIPS) allocations to 25% to 75%. The P/E10 thresholds are 11 and 21. The stock allocations are 75%-40%-25%.
HSWR50T2 consists of stocks (S&P500) and TIPS at a 2% interest rate. The stock allocation is 50%. The TIPS allocation is 50%. I rebalance allocations annually.
HSWR80T2 consists of stocks (S&P500) and TIPS at a 2% interest rate. The stock allocation is 80%. The TIPS allocation is 20%. I rebalance allocations annually.
CTVR50 (Constant Terminal Value Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 50%. The commercial paper allocation is 50%. At the Calculated Rate, the final portfolio balance equals the initial balance.
CTVR80 (Constant Terminal Value Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 80%. The commercial paper allocation is 20%. At the Calculated Rate, the final portfolio balance equals the initial balance.
HFWR50 (Half Failure Withdrawal Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 50%. The commercial paper allocation is 50%. At the Calculated Rate, the lowest portfolio balance equals (or exceeds minimally) one-half of the initial balance throughout the entire 30 years.
HFWR80 (Half Failure Withdrawal Rate) consists of stocks (S&P500) and commercial paper. I rebalance allocations annually. The stock allocation is 80%. The commercial paper allocation is 20%. At the Calculated Rate, the lowest portfolio balance equals (or exceeds minimally) one-half of the initial balance throughout the entire 30 years.
Withdrawing 4% for 40 years.
In all cases, expect to find an excellent buying opportunity. These are the Safe and Calculated rates of the TIPS portfolios. If P/E10 falls below the Safe rate, your portfolio is 95% likely to make it to the full 40 years. If P/E10 falls only to the Calculated rate, your portfolio has 50%-50% odds of making it to the full 40 years.
Portfolio Safe Calculated
SwOptT2 17.7 28.5
SwAT2 16.4 23.6
HSWR50T2 13.6 18.6
HSWR80T2 15.1 20.1
All that has to happen is for valuations to fall to typical levels (P/E10 = 14 or 15) or, with HSWR50T2, slightly lower.
Withdrawing 4% for 50 years. The picture is not nearly so good when trying to reach 50 years. All of the levels have occurred in the past. They have a good chance of happening again, but not necessarily within 20 years. P/E10 fell below 7 briefly in 1982, but not since then.
Portfolio Safe Calculated
SwOptT2 7.3 8.6
SwAT2 7.6 8.9
HSWR50T2 7.2 8.3
HSWR80T2 9.5 11.2
Withdrawing 3.8% for 40 years. In all cases, expect to find an excellent buying opportunity.
Portfolio Safe Calculated
SwOptT2 22.4 43.1
SwAT2 19.8 31.2
HSWR50T2 15.6 22.6
HSWR80T2 16.6 22.7
All that has to happen is for valuations to fall close to typical levels (P/E10 = 14 or 15). With SwOptT2 and SwAT2, it is sufficient for P/E10 to return to 20.
Withdrawing 3.8% for 50 years. The picture is not nearly so good when trying to reach 50 years. All of the levels have occurred in the past. They have a good chance of happening again, but not necessarily within 20 years. P/E10 has not been below 14 since 1986.
Portfolio Safe Calculated
SwOptT2 9.4 11.8
SwAT2 9.6 11.7
HSWR50T2 8.8 10.6
HSWR80T2 11.1 13.5
Withdrawing 3.6% for 40 years. In all cases, expect to find an excellent buying opportunity.
Portfolio Safe Calculated
SwOptT2 30.0 83.6
SwAT2 24.5 44.8
HSWR50T2 18.2 28.4
HSWR80T2 18.2 25.9
All that has to happen is for valuations to fall below hazardous levels (P/E10 = 20).
Withdrawing 3.6% for 50 years. The picture has improved when trying to reach 50 years. All of the levels have occurred in the past. They have a good chance of occurring again, but not necessarily within 20 years. P/E10 has not been below 14 since 1986. P/E10 last fell below 16 in January of 1991. You are likely to see a buying opportunity that will offer you a 50%-50% chance of success (i.e., reaching year 50).
Portfolio Safe Calculated
SwOptT2 12.5 17.1
SwAT2 12.3 16.0
HSWR50T2 10.8 13.7
HSWR80T2 12.9 16.3
Inserting a 30-year extension. I looked at what it would take to extend a 4.0% withdrawal rate from 10 years to 40 years using CTVR80 and HFWR80. At year 10, the balance would have fallen to 78.10% of its initial value. To maintain the withdrawal amount (including inflation adjustments) in the second period would require a withdrawal rate of 5.12%.
CTVR80 would maintain the full balance at year 10 (or 78.10% of the initial balance) plus inflation. HFWR80 would keep the minimum balance above one-half of this level throughout the year 10 to year 40 period. Typically, HFWR80 has an ending balance (at year 40) similar to or greater than its initial balance (at year 10).
Here are the results.
Portfolio Safe Calculated
CTVR80 11.7 14.3
HFWR80 10.6 14.9
These results are with a 4.0% withdrawal rate. These P/E10 levels are between the previous 50-year levels at 3.6% and 3.8% withdrawal rates.
There is a fair chance that you could successfully insert a 30-year extension. It would extend the 4.0% withdrawal rate to year 40 without penalty.
Conclusions We were reasonably successful at reaching 40 years at 4.0%. We can expect to see the necessary valuations.
We were not so successful at reaching 50 years at 4.0%. There is still a good chance. We would have 20 years available to wait for bargain level stock prices.
Alternatively, if we were to cut withdrawals down to 3.6%, we would have an excellent chance of finding stock prices low enough (within 20 years) for us to reach our goal of 50 years.
We have a reasonably good chance of being able to extend a 4.0% withdrawal rate at year 10 to year 40 without penalty. Valuations need only to return to typical levels (P/E10 = 14 to 15).
Putting these findings into perspective, a TIPS-only portfolio at a 2% interest rate would allow you to withdraw 4.0% (plus inflation) for 35 years. It would allow you to withdraw 3.66% for 40 years. It would allow you to withdraw 3.18% for 50 years.
It helps to add stocks when prices are favorable. This design process tells you how much. It lets you know early whether you have been successful.
Have fun.
John Walter Russell
July 28, 2005