SWR Costs

I have posted this at the NoFeeBoards.com web site along with a complete set of tables.
SWR Costs Thread on the NFB FIRE board

I have calculated several costs in terms of their influence on 30-year Safe Withdrawal Rates.

I used the Deluxe 1.1A08 version of my calculator to calculate 30-year Historical Surviving Withdrawal Rates to a precision of 0.1%. I set expenses equal to 0.20%. I used the CPI for inflation adjustments.

I looked at the following portfolios:

1) HSWR50T2%, which consists of 50% stocks and 50% TIPS at a 2.0% interest rate and which is rebalanced annually at no cost.
2) HSWR50T2n, which starts out with 50% stocks and 50% TIPS at a 2.0% interest rate but which is never rebalanced.
3) HSWR80T2%, which consists of 80% stocks and 20% TIPS at a 2.0% interest rate and which is rebalanced annually at no cost.
4) HSWR80T2n, which starts out with 80% stocks and 20% TIPS at a 2.0% interest rate but which is never rebalanced.
5) SwAT2, which consists of stocks and TIPS at a 2.0% interest rate with allocations varied in accordance with P/E10. The P/E10 thresholds are 11 and 21. The allocations are 75%-40%-25%. That is, the stock allocation is 75% whenever P/E10 is below 11. It is 40% whenever P/E10 is between 11 and 21. The stock allocation is 25% whenever P/E10 is above 21.
6) The (approximately) optimized Standard Switching Portfolio of stocks and TIPS at a 2.0% interest rate. The P/E10 thresholds are 9-12-21-24. The stock allocations, in order, are 100%-50%-30%-20%-0%.

I plotted the 1923-1980 Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P (or 100/[P/E10] ). I had Excel calculate the best linear fit and supply the equation. This is the Calculated Rate as a function of earnings yield. I used eyeball estimates of confidence limits (at lower levels of earnings yield, that is, below 8% or 10%). I refer to the lower confidence limit as the Safe Withdrawal Rate. The upper confidence limit is the High Risk Rate.

[P/E10 is the price of the S&P500 index divided by the average of the previous ten years of earnings. Yale Professor Robert Shiller has shown that it has predictive capabilities in the intermediate-term (roughly, ten years in the future).]

Equations

Here are the equations and confidence limits:

1) HSWR50T2%: y = 0.4031x+2.9478. R-squared is 0.7048. The confidence limits are minus 0.7 and plus 1.4.
2) HSWR50T2n: y = 0.4881x+2.449. R-squared is 0.6578. The confidence limits are minus 0.8 and plus 2.1.
3) HSWR80T2%: y = 0.6758x+1.7538. R-squared is 0.6916. The confidence limits are minus 1.0 and plus 2.0.
4) HSWR80T2n: y = 0.7171x+1.4744. R-squared is 0.6673. The confidence limits are minus 1.1 and plus 2.0.
5) SwAT2: y = 0.3776x+3.5222. R-squared is 0.6466. The confidence limits are minus 0.7 and plus 1.3.
6) The (approximately) optimized switching portfolio of stocks and TIPS at a 2.0% interest rate: y = 0.3276x+3.9729. R-squared is 0.5815. The confidence limits are minus 0.7 and plus 1.3.

Today’s Calculated Rates

Today’s earnings yield is (roughly) 3.5%. That is, P/E10 is 28 to 29. These are the Calculated Rates of the various portfolios at today’s valuations:

1) HSWR50T2%: Calculated Rate = 4.36% with 3.5% earnings yield. Today's SWR is 3.7%.
2) HSWR50T2n: Calculated Rate = 4.16% with 3.5% earnings yield. Today's SWR is 3.4%.
3) HSWR80T2%: Calculated Rate = 4.12% with 3.5% earnings yield. Today's SWR is 3.1%.
4) HSWR80T2n: Calculated Rate = 3.98% with 3.5% earnings yield. Today's SWR is 2.9%.
5) SwAT2: Calculated Rate = 4.84% with 3.5% earnings yield. Today's SWR is 4.1%.
6) The (approximately) optimized Standard Switching Portfolio of stocks and TIPS at a 2.0% interest rate: Calculated Rate = 5.12% with 3.5% earnings yield. Today's SWR is 4.4%.

SWR Costs

These are times of exceedingly high valuations.

In times such as these, rebalancing improves Safe Withdrawal Rates and Calculated Rates.

With 50% stocks and 50% TIPS at 2.0% a interest rate, rebalancing increases the Safe Withdrawal Rate from 3.4% to 3.7%, an improvement of 0.3%. It increases the Calculated Rate from 4.16% to 4.36%, an improvement of 0.20%.

With 80% stocks and 20% TIPS at 2.0% a interest rate, rebalancing increases the Safe Withdrawal Rate from 2.9% to 3.1%, an improvement of 0.2%. It increases the Calculated Rate from 3.98% to 4.12%, an improvement of 0.14%.

The probability of having a retirement portfolio last for the full 30 years is 50% when withdrawing at the Calculated Rate. It is (close to) 95% at the Safe Withdrawal Rate.

SwAT2 varies allocations subject to Benjamin Graham’s recommended constraint: both stock and bond allocations are kept between 25% and 75%. By varying allocations, SwAT2 increases the chances of success from that of a coin toss (i.e., in the neighborhood of 50%) to being highly likely (i.e., 95%) at a withdrawal rate of 4.1%. More precisely, the Safe Withdrawal Rate of SwAT2 is 4.1%. The Calculated Rates with fixed allocations range between 3.98% and 4.36%.

Looked at differently, the Safe Withdrawal Rate with a 50% fixed stock allocation is 3.4% to 3.7% at today’s valuations. The Safe Withdrawal Rate with an 80% fixed stock allocation is 2.9% to 3.1% at today’s valuations. Varying stock allocations between 25% and 75% raises rates to 4.1%.

The Standard Switching Portfolio brings the Safe Withdrawal Rate up another 0.3% to 4.4%. It brings the Calculated Rate to 5.12% as opposed to 4.84% when constrained between 25% to 75% (with SwAT2).

The Standard Switching Portfolio describes what is best based on the historical record, as is. SwAT2 describes a time-tested method of handling the effect of unexpected factors not directly included in the historical record. In this case, it would reduce the penalty if we were to encounter a new, prolonged bubble and/or it would reduce the penalty if the current secular (i.e., long lasting) bear market were to plunge below bargain levels and reach record lows.

Rebalancing Bonus and Penalty

Rebalancing offers an improvement (of 0.2% to 0.3%) when valuations are high. It comes at the expense of an upside potential of 0.6% to 1.1% when valuations are low. The equations for Calculated Rates crossover at an earnings yield of 5.87% (and P/E10 of 17.0) when the stock allocation is 50%. The equations for Calculated Rates crossover at an earnings yield of 6.77% (and a P/E10 of 15.8) when the stock allocation is 80%.

Historically, the typical P/E10 level has been 14 to 15.

Rebalancing hurts whenever valuations are typical or low. The penalty can be severe. Rebalancing helps when valuations are high (16 to 17 and above).

The real-world rebalancing bonus is less than I have calculated. Rebalancing requires buying and selling. Normal withdrawals not enough. Typical year-to-year stock price fluctuations are too high.

Have fun.

John Walter Russell
June 24, 2005.