Gradually Increasing Bond Allocations: Returns

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 10, 20 and 30-year real, annualized total returns. This includes regression equations and (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?

Deluxe Calculator V1dot1A08P05

Deluxe Calculator V1dot1A08P05 is a modified version of the standard Deluxe Calculator V1.1A08, which is also known as the Deluxe Calculator V1dot1A08.

All of the changes were made to the portion without rebalancing. It requires too much effort to include rebalancing (at least, for now).

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.

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.

Data Collection

Real, Annualized Total Returns

I set the withdrawal rate equal to 0.00%.

I set the expense ratio to 0.00% 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.

I collected total return data with 2.00% TIPS as well.

The real, annualized total returns are located in a table starting with cell A3400.

Special Comments 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.

The total return data that I took with TIPS did show differences when there was deflation. However, there were no differences in the maximum and minimum returns.

Real, Annualized Total Returns

I determined the regression equations using 10, 20 and 30-year real annualized total returns versus the percentage earnings yield 100E10/P (or 100/[P/E10]). I used 1923-1972 data. [Dummy data distort 30-year returns too much to include 1973-1980.]

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

There are no withdrawals. There are no expenses.

The Calculated Return is determined directly from the regression equation. The odds are (roughly) 50%-50% that the total return exceeds Calculated Return.

The odds are (roughly) 95% that the return will exceed lower confidence limit. The odds are (roughly) 95% that the return will be lower than the higher confidence limit.

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

At year 10

The regression equation is y = 1.267x – 3.3277, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits eyeball estimates) are plus 5.0% and minus 5.6%. R-squared is 0.4216.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.11%. Today’s lower confidence limit is (4.5%). Today’s upper confidence limit is 6.1%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was (0.43%). The January 2000 lower confidence limit was (6.0%). The January 2000 upper confidence limit was 4.6%.

At year 20

The regression equation is y = 0.9558x – 1.1999, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 3.8% and minus 2.2%. R-squared is 0.5309.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 2.15%. Today’s lower confidence limit is 0.0%. Today’s upper confidence limit is 6.0%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 0.98%. The January 2000 lower confidence limit was (1.2%). The January 2000 upper confidence limit was 4.8%.

At year 30

The regression equation is y = 0.4288x + 2.9786, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 2.0% and minus 1.6%. R-squared is 0.3804.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 4.38%. Today’s lower confidence limit is 2.8%. Today’s upper confidence limit is 6.4%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 3.86%. The January 2000 lower confidence limit was 2.3%. The January 2000 upper confidence limit was 5.9%.

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

At year 10

The regression equation is y = 1.2743x – 3.3465, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 5.0% and minus 5.8%. R-squared is 0.417.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.11%. Today’s lower confidence limit is (4.7%). Today’s upper confidence limit is 6.1%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was (0.44%). The January 2000 lower confidence limit was (6.2%). The January 2000 upper confidence limit was 4.6%.

At year 20

The regression equation is y = 0.9568x – 1.1289, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 3.8% and minus 2.2%. R-squared is 0.5185.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 2.22%. Today’s lower confidence limit is 0.0%. Today’s upper confidence limit is 6.0%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 1.06%. The January 2000 lower confidence limit was (1.1%). The January 2000 upper confidence limit was 4.9%.

At year 30

The regression equation is y = 0.4078x + 3.156, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 2.0% and minus 2.0%. R-squared is 0.3804.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 4.58%. Today’s lower confidence limit is 2.6%. Today’s upper confidence limit is 6.6%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 4.09%. The January 2000 lower confidence limit was 2.1%. The January 2000 upper confidence limit was 6.1%.

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

At year 10

The regression equation is y = 0.8446x – 1.4703, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 3.0% and minus 3.0%. R-squared is 0.4495.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.49%. Today’s lower confidence limit is (1.5%). Today’s upper confidence limit is 4.5%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 0.46%. The January 2000 lower confidence limit was (2.5%). The January 2000 upper confidence limit was 3.5%.

At year 20

The regression equation is y = 0.7056x – 0.7389, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 2.4% and minus 1.4%. R-squared is 0.6035.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.73%. Today’s lower confidence limit is 0.3%. Today’s upper confidence limit is 4.1%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 0.87%. The January 2000 lower confidence limit was (0.5%). The January 2000 upper confidence limit was 3.3%.

At year 30

The regression equation is y = 0.48x + 0.7911, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 1.5% and minus 0.8%. R-squared is 0.678.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 2.47%. Today’s lower confidence limit is 1.7%. Today’s upper confidence limit is 4.0%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 1.89%. The January 2000 lower confidence limit was 1.1%. The January 2000 upper confidence limit was 3.4%.

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

At year 10

The regression equation is y = 0.8656x – 1.5095, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 3.4% and minus 3.5%. R-squared is 0.4301.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.52%. Today’s lower confidence limit is (2.0%). Today’s upper confidence limit is 4.9%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 0.47%. The January 2000 lower confidence limit was (3.0%). The January 2000 upper confidence limit was 3.9%.

At year 20

The regression equation is y = 0.7128x – 0.5161, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 2.5% and minus 1.4%. R-squared is 0.5519.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.98%. Today’s lower confidence limit is 0.6%. Today’s upper confidence limit is 4.5%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 1.11%. The January 2000 lower confidence limit was (0.3%). The January 2000 upper confidence limit was 3.6%.

At year 30

The regression equation is y = 0.3909x + 1.9477, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 1.5% and minus 1.0%. R-squared is 0.472.

Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 3.32%. Today’s lower confidence limit is 2.3%. Today’s upper confidence limit is 4.8%.

P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 2.84%. The January 2000 lower confidence limit was 1.8%. The January 2000 upper confidence limit was 4.3%.

At Year 10 Summary

Today’s Returns

Today’s earnings yield is 3.5%.

Lower Confidence Limit, Calculated Return, Higher Confidence Limit at year 10.

80% Stocks/30 year ladder: (4.5%)  1.11%  6.1% 

80% Stocks/60 year ladder: (4.7%)  1.11%  6.1% 
50% Stocks/30 year ladder: (1.5%)  1.49%  4.5% 
50% Stocks/60 year ladder: (2.0%)  1.52%  4.9% 

Year 2000 Returns

January 2000 P/E10 was 43.77.

Lower Confidence Limit, Calculated Return, Higher Confidence Limit at year 10.

80% Stocks/30 year ladder: (6.0%)  (0.43%)  4.6% 
80% Stocks/60 year ladder: (6.2%)  (0.44%)  4.6% 
50% Stocks/30 year ladder: (2.5%)   0.46%   3.5% 
50% Stocks/60 year ladder: (3.0%)   0.47%   3.9% 

At Year 20 Summary

Today’s Returns

Today’s earnings yield is 3.5%.

Lower Confidence Limit, Calculated Return, Higher Confidence Limit at year 20.

80% Stocks/30 year ladder: 0.0%  2.15%  6.0% 
80% Stocks/60 year ladder: 0.0%  2.22%  6.0% 
50% Stocks/30 year ladder: 0.3%  1.73%  4.1% 
50% Stocks/60 year ladder: 0.6%  1.98%  4.5% 

Year 2000 Returns

January 2000 P/E10 was 43.77.

Lower Confidence Limit, Calculated Return, Higher Confidence Limit at year 20.

80% Stocks/30 year ladder: (1.2%)  0.98%  4.8% 
80% Stocks/60 year ladder: (1.1%)  1.06%  4.9% 
50% Stocks/30 year ladder: (0.5%)  0.87%  3.3% 
50% Stocks/60 year ladder: (0.3%)  1.11%  3.6% 

At Year 30 Summary

Today’s Returns

Today’s earnings yield is 3.5%.

Lower Confidence Limit, Calculated Return, Higher Confidence Limit at year 30.

80% Stocks/30 year ladder: 2.8%  4.38%  6.4% 
80% Stocks/60 year ladder: 2.6%  4.58%  6.6% 
50% Stocks/30 year ladder: 1.7%  2.47%  4.0% 
50% Stocks/60 year ladder: 2.3%  3.32%  4.8% 

Year 2000 Returns

January 2000 P/E10 was 43.77.

Lower Confidence Limit, Calculated Return, Higher Confidence Limit at year 30.

80% Stocks/30 year ladder: 2.3%  3.86%  5.9% 
80% Stocks/60 year ladder: 2.1%  4.09%  6.1% 
50% Stocks/30 year ladder: 1.1%  1.89%  3.4% 
50% Stocks/60 year ladder: 1.8%  2.84%  4.3% 

Observations

At year 10:

The Calculated Returns slightly favor 50% Stocks at today’s valuations.

The Calculated Returns are almost identical at Year 2000 valuations.

The spread is much greater with 80% stocks than with 50% stocks.

At year 20:

The Calculated Returns slightly favor longer ladders.

The Calculated Returns are ambivalent as to the stock allocation.

The spread is much greater with 80% stocks than with 50% stocks.

At year 30:

The Calculated Returns favor an 80% initial stock allocation.

The Calculated Returns slightly favor longer ladders.

The spread is a little bit greater with 80% stocks than with 50% stocks.

Calculated Returns differ significantly at year 30. This is in contrast to shorter time intervals.

Have fun.

John Walter Russell
October 1, 2005