Safe Withdrawal Rates with Switching

When I made my surveys to optimize switching, I failed to follow through by calculating Safe Withdrawal Rates.

I had thought that calculating Safe Withdrawal Rates would be difficult. This turns out not to be the case.

Historical Surviving Withdrawal Rates

I started with the optimized four threshold, five allocation switching algorithm (with three adjustable allocations). The P/E10 thresholds are 9-12-21-24. The allocations are 100%-50%-30%-20%-0%. When P/E10 is below 9, the stock allocation is 100%. When the P/E10 is between 9 and 12, the stock allocation is 50%. And so on.

[P/E10 is the latest index level (or price) of the S&P500 index divided by the average of the previous ten-years of earnings. Professor Robert Shiller developed this indicator and he has shown that P/E10 has predictive power over the intermediate-term (10 years). It has been our most successful measure of valuations for calculating Safe Withdrawal Rates so far. The calculator uses January values for each year.]

I used my Deluxe Calculator V1.1A08. I set expenses equal to 0.20%. I adjusted withdrawals to match inflation in accordance with the CPI. I set the TIPS interest rate at 2.0%. [TIPS interest rates have fallen considerably. This is high compared to today’s interest rates. It was low when I made my original optimization surveys.] I set the desired lifespan of the portfolio at 30 years.

I increased withdrawal rates in increments of 0.1%. I recorded Historical Surviving Withdrawal Rates. They are the highest rates with a positive balance at year 30. When the withdrawal rate is increased by 0.1%, the balance at year 30 is zero or negative.

I collected a complete set of Historical Surviving Withdrawal Rates from 1871-1980.

Data Analysis

I plotted Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P (or 100% / [P/E10] ). I used Excel’s curve fitting capability to fit straight lines to the data and to report the equations (i.e., regression equations) and goodness of fit (R-squared). I used eyeball estimates to set my confidence limits as a matter of convenience. [There are formulas to generate more accurate numbers, but they are time consuming,]

Using the 1923-1980 data, the formula for the Calculated Rate is:y = 0.3276x+3.9729. R-squared is 0.5815. My eyeball estimates of the confidence limits are plus 1.3% and minus 0.7%. [I place my greatest emphasis on data with earnings yields of 10% and lower.]

Today’s earnings yield is close to 3.5%. Using the 1923-1980 data and a 3.5% earnings yield, the Calculated Rate is 5.12%. Today’s Safe Withdrawal Rate, which is the lower confidence limit, is 4.4%. Today’s High Risk Rate, which is the upper confidence limit, is 6.4%.

Using the 1921-1980 data, the formula for the Calculated Rate is:y = 0.3353x+3.9242. R-squared is 0.7022. My eyeball estimates of the confidence limits are plus 1.5% and minus 0.7%. [I place my greatest emphasis on data with earnings yields of 10% and lower.]

Today’s earnings yield is close to 3.5%. Using the 1921-1980 data and a 3.5% earnings yield, the Calculated Rate is 5.10%. Today’s Safe Withdrawal Rate, which is the lower confidence limit, is 4.4%. Today’s High Risk Rate, which is the upper confidence limit, is 6.6%.

Using the 1871-1980 data, the formula for the Calculated Rate is:y = 0.3622x+3.4421. R-squared is 0.7052. My eyeball estimates of the confidence limits are plus 1.7% and minus 1.2%. [I place my greatest emphasis on data with earnings yields of 10% and lower.]

Today’s earnings yield is close to 3.5%. Using the 1871-1980 data and a 3.5% earnings yield, the Calculated Rate is 4.71%. Today’s Safe Withdrawal Rate, which is the lower confidence limit, is 3.5%. Today’s High Risk Rate, which is the upper confidence limit, is 6.4%.

Switching allocations has improved the goodness of fit associated with the 1921-1980. It has not reduced the variance. The years 1921 and 1922 still have an undue amount of influence on the calculations.

The fit associated with the 1871-1980 data is surprisingly good in light of the anomaly associated with P/E10 for fixed allocations.

Calculated Rates of the last decade

We will use the 1923-1980 equations to maintain consistency with previous studies. The Calculated Rate is y = 0.3276x+3.9729. The lower confidence limit, which is the Safe Withdrawal Rate, is minus 0.7%. The upper confidence limit, which is the High Risk Rate, is plus 1.3%.

Here are the January values of P/E10 throughout the last decade.

1995 20.22
1996 24.76
1997 28.33
1998 32.86
1999 40.58
2000 43.77
2001 36.98
2002 30.28
2003 22.89
2004 27.65
Today: use an earnings yield of 3.5%.

Here are the Safe, Calculated and High Risk Rates of the last decade with Switching with 2% TIPS.

Year, Safe Withdrawal Rate, Calculated Rate, High Risk Rate

1995 4.9 5.59 6.9
1996 4.6 5.30 6.6
1997 4.4 5.13 6.4
1998 4.3 4.97 6.3
1999 4.1 4.78 6.1
2000 4.0 4.72 6.0
2001 4.2 4.86 6.2
2002 4.4 5.05 6.4
2003 4.7 5.40 6.7
2004 4.5 5.16 6.5
Today 4.4 5.12 6.4

Comparisons with HSWR50T2 and HSWR80T2

I was able to locate data for portfolios HSWR50T2 and HSWR80T2. HSWR50T2 has a fixed allocation of 50% stocks and 50% TIPS with a 2% real interest rate. HSWR80T2 has a fixed allocation of 80% stocks and 20% TIPS with a 2% real interest rate. In both cases, portfolios are rebalanced annually to maintain their allocations. Expenses are 0.20%.

Using the 1923-1980 data, the formula for the Calculated Rate for HSWR50T2 is: y = 0.4031x+2.9478. R-squared is 0.7048. My eyeball estimates of the confidence limits are plus 1.5% and minus 0.8%. [I place my greatest emphasis on data with earnings yields of 10% and lower.]

Today’s earnings yield is close to 3.5%. Using the 1923-1980 data and a 3.5% earnings yield, the Calculated Rate for HSWR50T2 is 4.36%. Today’s Safe Withdrawal Rate, which is on the lower confidence limit, is 3.6%. Today’s High Risk Rate, which is on the upper confidence limit, is 5.9%.

Here are the Safe, Calculated and High Risk Rates of the last decade with HSWR50T2.

Year, HSWR50T2 Safe Withdrawal Rate, Calculated Rate, High Risk Rate

1995 4.1 4.94 6.4
1996 3.8 4.58 6.1
1997 3.6 4.37 5.9
1998 3.4 4.17 5.7
1999 3.1 3.94 5.4
2000 3.1 3.87 5.4
2001 3.2 4.04 5.5
2002 3.5 4.30 5.8
2003 3.9 4.71 6.2
2004 3.6 4.41 5.9
Today 3.6 4.36 5.9

Using the 1923-1980 data, the formula for the Calculated Rate for HSWR80T2 is: y = 0.6758x+1.7538. R-squared is 0.6916. My eyeball estimates of the confidence limits are plus 2.0% and minus 1.1%. [I place my greatest emphasis on data with earnings yields of 8% and lower.]

Today’s earnings yield is close to 3.5%. Using the 1923-1980 data and a 3.5% earnings yield, the Calculated Rate for HSWR80T2 is 4.12%. Today’s Safe Withdrawal Rate, which is on the lower confidence limit, is 3.0%. Today’s High Risk Rate, which is on the upper confidence limit, is 6.1%.

Here are the Safe, Calculated and High Risk Rates of the last decade with HSWR80T2.

Year, HSWR80T2 Safe Withdrawal Rate, Calculated Rate, High Risk Rate

1995 4.0 5.10 7.1
1996 3.4 4.45 6.5
1997 3.0 4.14 6.1
1998 2.7 3.81 5.8
1999 2.3 3.42 5.4
2000 2.2 3.30 5.3
2001 2.5 3.61 5.6
2002 2.9 3.99 6.0
2003 3.6 4.71 6.7
2004 3.1 4.20 6.2
Today 3.0 4.12 6.1

Summary

The Safe Withdrawal Rates in 2000 were 3.1% for HSWR50T2, 2.2% for HSWR80T2 and 4.0% with switching with 2% TIPS.

The Calculated Rates in 2000 were 3.87% for HSWR50T2, 3.30% for HSWR80T2 and 4.72% with switching with 2% TIPS.

The High Risk Rates in 2000 were 5.4% for HSWR50T2, 2.3% for HSWR80T2 and 6.0% with switching with 2% TIPS.

Today’s Safe Withdrawal Rates are 3.6% for HSWR50T2, 3.0% for HSWR80T2 and 4.4% with switching with 2% TIPS.

Today’s Calculated Rates are 4.36% for HSWR50T2, 4.12% for HSWR80T2 and 5.12% with switching with 2% TIPS.

Today’s High Risk Rates are 5.9% for HSWR50T2, 6.1% for HSWR80T2 and 6.4% with switching with 2% TIPS.

Conclusions

Switching stock allocations according to P/E10 brings today’s Safe Withdrawal Rate up to 4.4%. It brought the 2000 Safe Withdrawal Rate up to 4.0%.

These are dramatic increases compared to a conventional approach of maintaining fixed allocations.

Have fun.

John Walter Russell
I wrote this on May 22, 2005.