Gradually Increasing Bond Allocations: Returns Addendum
I have added 15-year bond ladders.
Data Collection
Calculator Settings
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.
Regression Equations
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.]
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 15-year bond ladder.
At year 10
The regression equation is y = 1.2525x – 3.292, 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 0.4311.
Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.09%. 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 = 0.9547x – 1.3543, 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 0.5565.
Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.99%. Today’s lower confidence limit is (0.2%). Today’s upper confidence limit is 5.8%.
P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 0.83%. The January 2000 lower confidence limit was (1.4%). The January 2000 upper confidence limit was 4.6%.
At year 30
The regression equation is y = 0.4768x + 2.2612, 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 0.4748.
Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 3.93%. Today’s lower confidence limit is 2.3%. Today’s upper confidence limit is 5.9%.
P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 3.35%. The January 2000 lower confidence limit was 1.8%. The January 2000 upper confidence limit was 5.4%.
50% Stocks with a growing 15-year bond ladder.
At year 10
The regression equation is y = 0.802x – 1.3997, 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 0.4901.
Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.41%. Today’s lower confidence limit is (1.6%). Today’s upper confidence limit is 4.4%.
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 (2.6%). The January 2000 upper confidence limit was 3.3%.
At year 20
The regression equation is y = 0.667x – 1.0359, 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 1.8%. R-squared is 0.6661.
Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.30%. Today’s lower confidence limit is (0.5%). Today’s upper confidence limit is 3.7%.
P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 0.49%. The January 2000 lower confidence limit was (1.3%). The January 2000 upper confidence limit was 2.9%.
At year 30
The regression equation is y = 0.5305x – 0.51, where y is the Calculated Return and x is the percentage earnings yield 100/[P/E10]. The confidence limits (eyeball estimates) are plus 1.0% and minus 0.8%. R-squared is 0.8645.
Today’s earnings yield is 3.5% (approximately, rounded). Today’s Calculated Return is 1.35%. Today’s lower confidence limit is 0.6%. Today’s upper confidence limit is 2.4%.
P/E10 peaked in December 1999. It was 43.77 in January 2000. The January 2000 Calculated Return was 0.70%. The January 2000 lower confidence limit was (0.1%). The January 2000 upper confidence limit was 1.7%.
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/15 year ladder: (4.5%) 1.09% 6.1%
80% Stocks/30 year ladder: (4.5%) 1.11% 6.1%
80% Stocks/60 year ladder: (4.7%) 1.11% 6.1%
50% Stocks/15 year ladder: (1.6%) 1.41% 4.4%
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/15 year ladder: (6.0%) (0.43%) 4.6%
80% Stocks/30 year ladder: (6.0%) (0.43%) 4.6%
80% Stocks/60 year ladder: (6.2%) (0.44%) 4.6%
50% Stocks/15 year ladder: (2.6%) 0.43% 3.3%
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/15 year ladder: (0.2%) 1.99% 5.8%
80% Stocks/30 year ladder: 0.0% 2.15% 6.0%
80% Stocks/60 year ladder: 0.0% 2.22% 6.0%
50% Stocks/15 year ladder: (0.5%) 1.30% 3.7%
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/15 year ladder: (1.4%) 0.83% 4.6%
80% Stocks/30 year ladder: (1.2%) 0.98% 4.8%
80% Stocks/60 year ladder: (1.1%) 1.06% 4.9%
50% Stocks/15 year ladder: (1.3%) 0.49% 2.9%
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/15 year ladder: 2.3% 3.93% 5.9%
80% Stocks/30 year ladder: 2.8% 4.38% 6.4%
80% Stocks/60 year ladder: 2.6% 4.58% 6.6%
50% Stocks/15 year ladder: 0.6% 1.35% 2.4%
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/15 year ladder: 1.8% 3.35% 5.4%
80% Stocks/30 year ladder: 2.3% 3.86% 5.9%
80% Stocks/60 year ladder: 2.1% 4.09% 6.1%
50% Stocks/15 year ladder: (0.1%) 0.70% 1.7%
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. They clearly disfavor the combination of a short 15-year ladder and a 50% stock allocation.
The Calculated Returns generally favor 80% stocks.
The spread is much greater with 80% stocks than with 50% stocks.
At year 30:
The Calculated Returns strongly favor an 80% initial stock allocation.
The Calculated Returns 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.
Conclusions
These comparisons are at high valuations. Today’s valuations exceed those of 1929 and the 1960s.
All of these comparisons favor longer ladders. This keeps the stock allocation higher, longer as the bond allocation grows gradually.
The short 10-year interval favored an initial 50% stock allocation. Longer intervals favored an initial 80% stock allocation. Keep in mind that longer time intervals reduce the effects of stock volatility.
Use a 2.00% return as a standard of comparison. That was the interest rate of the I-Bonds. [This is larger than today’s TIPS and I-Bonds yield. Ten and twenty year TIPS have yielded 2.00% recently. Today’s TIPS yield less.]
Returns at year 10 fail to meet this standard. Some returns at year 20 are able to meet it, but many fail. Returns at year 30 consistently beat this standard.
Stocks reduced the expected returns (i.e., Calculated Returns) for most of the short intervals. The odds often favored I-Bonds for time intervals less than 30 years.
Have fun.
John Walter Russell
October 3, 2005