Gradually Increasing Bond Allocations: HSWR

The traditional advice to investors is to increase bond allocations as they age.

I examine this using one of the TIPS Ladder Calculators that I developed for Current Research A.

I have collected 30-year Historical Surviving Withdrawal Rates (HSWR). I have determined their regression equations and (made eyeball estimates of their) confidence limits with respect to valuations.

Valuations

I use Professor Robert Shiller’s P/E10 as my measure of valuation. P/E10 is the current value of the S&P500 index (price) divided by the average of its previous 10 years of earnings. Actually, I use the reciprocal, the percentage earnings yield 100% / [P/E10]. This is the best measure of valuation that I have found so far. What is more, the S&P500 P/E10 measure works well with the Large and Small Capitalization, Growth and Value segments individually as well as with the market as a whole.
Professor Shiller’s Web Site
Why P/E10?

Data Collection

Deluxe Calculator V1dot1A08P05

Deluxe Calculator V1dot1A08P05 is a modified version of the standard Deluxe Calculator V1.1A08.

All changes were made to calculations without rebalancing.

The algorithm subtracts increments from the stock total and adds them to the bond total whenever P/E10 exceeds a specified threshold. I set the threshold at 2, which P/E10 always exceeds.

The increment equals the initial BOND principal plus inflation divided by the length of the ladder. When the initial stock allocation is 50%, the initial bond allocation is 50%. With a 30-year ladder, the increment is 3.33% of the initial BOND balance (plus inflation). This works out to 1.67% of the initial balance of the overall portfolio. With a 60-year ladder, the increment is 1.67% of the initial BOND balance, which is 0.83% of the initial balance of the overall portfolio.

When the initial stock balance is 80%, the initial bond allocation is only 20%. With a 30-year ladder, the increment is 3.33% of the initial BOND allocation or 0.67% of the overall portfolio. With a 60-year ladder, the increment is 1.67% of the initial BOND balance, which is 0.33% of the overall portfolio.

The amount of the increment never changes (other than an adjustment for inflation).

I do not subtract the increment unless there are enough funds. That is, I subtract the increment only if the 12/31 stock balance is greater than the increment.

Historical Surviving Withdrawal Rate Procedures

I determined 30-year Historical Surviving Withdrawal Rates for the historical sequences beginning in 1921-1980. [The calculator has dummy data for 2003-2010.] I increased the withdrawal rate in increments of 0.1%. I determined the lowest withdrawal rate that caused a failure for each start year. I subtracted 0.1% from this rate. This value is the Historical Surviving Withdrawal Rate for that sequence.

I set the expense ratio to 0.20% of the initial balance. I used the CPI for inflation.

I set the calculator for NO rebalancing.

I used the S&P500 index for stocks. I used 2.00% I-Bonds for the component other than stocks.

Special Explanation Regarding Data Collection

I have standardized on using I-Bonds with my TIPS Ladder Calculators.

This version does OK with TIPS. The other versions do not.

The other versions transfer dollar increments from bonds to stocks. This produces misleading results when using TIPS because they cannot distinguish between the inflation adjustment to principal and the interest coupon payment.

The difficulty occurs during times of deflation. The calculators interpret a reduction in the TIPS principal in NOMINAL dollars to be a loss of income, even though we are interested in the income in terms of REAL dollars.

Historical Surviving Withdrawal Rates Equations

I determined the regression equations using 30-year Historical Surviving Withdrawal Rates versus the percentage earnings yield 100E10/P (or 100/[P/E10]). I used 1923-1980 data.

This includes the S&P500 stocks and 2.00% I-Bonds.

Withdrawal amounts match inflation. The withdrawal rate is determined relative to the initial balance.

The Calculated Rate is determined directly from the regression equation. The odds are (roughly) 50%-50% that a retirement survives for the full 30 years at the Calculated Rate.

The Safe Withdrawal Rate is the lower confidence limit. The High Risk Rate is the higher confidence limit.

The odds are (roughly) 95% that a portfolio will survive at the Safe Withdrawal Rate. The odds are (roughly) 95% that a portfolio will fail at the High Risk Rate.

80% Stocks with a growing 30-year bond ladder.

The regression equation is y = 0.7146x + 1.3736, where y is the Calculated Rate and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 1.5% and minus 1.1%. R-squared is 0.6769.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Rate is 3.87%. Today’s Safe Withdrawal Rate is 2.8%. Today’s High Risk Rate is 5.4%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Rate was 3.01%. The January 2000 Safe Withdrawal Rate was 1.9%. The January 2000 High Risk Rate was 4.5%.

80% Stocks with a growing 60-year bond ladder.

The regression equation is y = 0.7167x + 1.4341, where y is the Calculated Rate and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 1.9% and minus 1.1%. R-squared is 0.6756.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Rate is 3.94%. Today’s Safe Withdrawal Rate is 2.8%. Today’s High Risk Rate is 5.8%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Rate was 3.07%. The January 2000 Safe Withdrawal Rate was 2.0%. The January 2000 High Risk Rate was 5.0%.

50% Stocks with a growing 30-year bond ladder.

The regression equation is y = 0.4735x + 2.113, where y is the Calculated Rate and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 1.4% and minus 1.0%. R-squared is 0.6491.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Rate is 3.77%. Today’s Safe Withdrawal Rate is 2.8%. Today’s High Risk Rate is 5.2%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Rate was 3.19%. The January 2000 Safe Withdrawal Rate was 2.2%. The January 2000 High Risk Rate was 4.6%.

50% Stocks with a growing 60-year bond ladder.

The regression equation is y = 0.4851x + 2.275, where y is the Calculated Rate and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 1.6% and minus 0.8%. R-squared is 0.6734.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Rate is 3.97%. Today’s Safe Withdrawal Rate is 3.2%. Today’s High Risk Rate is 5.6%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Rate was 3.38%. The January 2000 Safe Withdrawal Rate was 2.6%. The January 2000 High Risk Rate was 5.0%.

Tables

Today’s Rates

Today’s earnings yield is 3.5%.

Safe Withdrawal Rate, Calculated Rate, High Risk Rate.

80% Stocks/30 year ladder: 2.8%  3.87%  5.4% 
80% Stocks/60 year ladder: 2.8%  3.94%  5.8% 
50% Stocks/30 year ladder: 2.8%  3.77%  5.2% 
50% Stocks/60 year ladder: 3.2%  3.97%  5.6%  

Year 2000 Rates

January 2000 P/E10 was 43.77.

Safe Withdrawal Rate, Calculated Rate, High Risk Rate.

80% Stocks/30 year ladder: 1.9%  3.01%  4.5% 
80% Stocks/60 year ladder: 2.0%  3.07%  5.0% 
80% Stocks/30 year ladder: 2.2%  3.19%  4.6% 
50% Stocks/60 year ladder: 2.6%  3.38%  5.0%  

Observations

With all comparisons: the data favor longer ladders (60-year ladders as opposed to 30-year ladders).

Several, but not all, comparisons favor a 50% initial stock allocation (as opposed to 80%).

Calculated Rates at the same valuation are very close.

Calculated Rates at different valuations differ considerably.

Have fun.

John Walter Russell
October 1, 2005