E10 or D10?

Professor Robert Shiller’s P/E10 does a great job when calculating Safe Withdrawal Rates. Sometimes, using dividends (P/D10) is even better.

Background

The percentage earnings yield 100E10/P (or 100/[P/E10]) and Historical Surviving Withdrawal Rates are tightly related. So are dividends. Regression equations show a good fit.

P/E10 (actually, 100E10/P) does better than the initial dividend yield because of dividend cuts, especially before the 1950s.

Until now, I had not thought of averaging dividend amounts. It turns out that smoothed dividends work well. At times, they do better.

New Data

I collected regression equations using 100E5/P, 100E10/P, 100D5/P and 100D10/P. E5 is with average of the most recent five years of (real) earnings. E10 is with average of the most recent ten years of (real) earnings. D5 is with average of the most recent five years of (real) dividend amounts. D10 is with average of the most recent ten years of (real) dividend amounts. P is the (real) price (or index value) of the S&P500.

Because dividend cuts played such a prominent role in the past, I looked at 1923-1975 and 1941-1980 timeframes for the regression equations. Dividend cuts were commonplace during earlier periods. In recent times, dividend cuts have been punished severely.

1923-1975 30-Year Historical Surviving Withdrawal Rates

1923-1975 Comparisons: D5 versus E5.

Compare spreads and R-squared. The results are mixed. 100E5/P is better than 100D5/P with fixed allocations, but not as good with SWAT2 and SwOptT2.

1923-1975 Equations, x=100D5/P.

y=HSWR50T2=0.5231x+3.5178 plus 2% and minus 1%.
R-squared=0.571.

y=HSWR80T2=0.8757x+2.7565 plus 2.5% and minus 1.5%.
R-squared=0.5579.

y=SWAT2=0.5428x+3.8907 plus 1.5% and minus 1%.
R-squared=0.6306.

y=SwOptT2=0.4441x+4.4054 plus 2% and minus 1%.
R-squared=0.5056.

1923-1975 Equations, x=100E5/P.

y=HSWR50T2=0.4241x+2.8017 plus 1.8% and minus 1%.
R-squared=0.6223.

y=HSWR80T2=0.7272x+1.4335 plus 2.5% and minus 1.5%.
R-squared=0.6377.

y=SWAT2=0.376x+3.6144 plus 2% and minus 1%.
R-squared=0.5015.

y=SwOptT2=0.2878x+4.3237 plus 2.5% and minus 1.5%.
R-squared=0.3519.

1923-1975 Comparisons: D10 versus E10.

Compare spreads and R-squared. Results are mixed. 100E10/P and 100D10/P are similar.

1923-1975 Equations, x=100D10/P.

y=HSWR50T2=0.6037x+3.1974 plus 1.5% and minus 1%.
R-squared=0.7357.

y=HSWR80T2=1.0058x+2.2419 plus 2% and minus 1%.
R-squared=0.712.

y=SWAT2=0.6393x+3.5009 plus 1% and minus 1%.
R-squared=0.8462.

y=SwOptT2=0.5122x+4.1353 plus 1% and minus 1%.
R-squared=0.6504.

1923-1975 Equations, x=100E10/P.

y=HSWR50T2=0.4394x+2.7309 plus 1.5% and minus 1%.
R-squared=0.735.

y=HSWR80T2=0.7425x+1.3902 plus 2% and minus 1%.
R-squared=0.7316.

y=SWAT2=0.45x+3.1172 plus 1% and minus 0.6%.
R-squared=0.7905.

y=SwOptT2=0.3859x+3.6453 plus 1.5% and minus 1%.
R-squared=0.6963.

1941-1980 30-Year Historical Surviving Withdrawal Rates

1941-1980 Comparisons: D5 versus E5.

Compare spreads and R-squared. 100E5/P not as good as 100D5/P.

1941-1980 Equations, x=100D5/P.

y=HSWR50T2=0.7919x+2.5849 plus 1.5% and minus 0.5%.
R-squared=0.7666.

y=HSWR80T2=1.3247x+1.203 plus 2% and minus 1.2%.
R-squared=0.7457.

y=SWAT2=0.7298x+3.0801 plus 1.5% and minus 0.8%.
R-squared=0.8011.

y=SwOptT2=0.4731x+4.1605 plus 1% and minus 1%.
R-squared=0.6369.

1941-1980 Equations, x=100E5/P.

y=HSWR50T2=0.458x+2.3981 plus 2% and minus 0.6%.
R-squared=0.7235.

y=HSWR80T2=0.7679x+0.8774 plus 2.5% and minus 1.2%.
R-squared=0.7068.

y=SWAT2=0.3908x+3.1515 plus 2% and minus 0.8%.
R-squared=0.6481.

y=SwOptT2=0.2834x+3.9731 plus 1% and minus 0.6%.
R-squared=0.6446.

1941-1980 Comparisons: D10 versus E10.

Compare spreads and R-squared. 100E10/P is not as good as 100D10/P.

1941-1980 Equations, x=100D10/P.

y=HSWR50T2=0.7917x+2.6508 plus 1.2% and minus 0.5%.
R-squared=0.8615.

y=HSWR80T2=1.3188x+1.3367 plus 1.8% and minus 1%.
R-squared=0.8308.

y=SWAT2=0.7395x+3.0993 plus 1% and minus 0.5%.
R-squared=0.9248.

y=SwOptT2=0.4923x+4.1192 plus 1% and minus 0.5%.
R-squared=0.7752.

1941-1980 Equations, x=100E10/P.

y=HSWR50T2=0.5048x+2.2869 plus 1.5% and minus 1%.
R-squared=0.7643.

y=HSWR80T2=0.8424x+0.7199 plus 2% and minus 1.5%.
R-squared=0.7396.

y=SWAT2=0.4461x+2.9445 plus 1.5% and minus 0.6%.
R-squared=0.7344.

y=SwOptT2=0.3309x+3.7691 plus 1% and minus 0.8%.
R-squared=0.7642.

1923-1975 15-Year Historical Surviving Withdrawal Rates

1923-1975 Comparisons: D5 versus E5.

Compare spreads and R-squared. 100E5/P is better than 100D5/P.

1923-1975 Equations, x=100D5/P.

y=HSWR50T2=0.5806x+6.4421 plus 3% and minus 2%.
R-squared=0.3435.

y=HSWR80T2=0.9327x+5.5908 plus 4% and minus 3%.
R-squared=0.3347.

y=SWAT2=0.6423x+6.5889 plus 2% and minus 2%.
R-squared=0.4887.

y=SwOptT2=0.6076x+6.8234 plus 2% and minus 1.5%.
R-squared=0.5399.

1923-1975 Equations, x=100E5/P.

y=HSWR50T2=0.5553x+5.0325 plus 2% and minus 2%.
R-squared=0.5209.

y=HSWR80T2=0.9149x+3.1602 plus 3% and minus 3%.
R-squared=0.5339.

y=SWAT2=0.5283x+5.6554 plus 2% and minus 1%.
R-squared=0.548.

y=SwOptT2=0.4577x+6.2466 plus 3% and minus 1%.
R-squared=0.5077.

1923-1975 Comparisons: D10 versus E10.

Compare spreads and R-squared. 100E10/P is better than 100D10/P.

1923-1975 Equations, x=100D10/P.

y=HSWR50T2=0.6772x+6.0546 plus 2.5% and minus 2%.
R-squared=0.4521.

y=HSWR80T2=1.0725x+5.0371 plus 4% and minus 3%.
R-squared=0.4282.

y=SWAT2=0.7603x+6.1112 plus 2% and minus 1.2%.
R-squared=0.6622.

y=SwOptT2=0.6843x+6.5269 plus 1.4% and minus 2%.
R-squared=0.6623.

1923-1975 Equations, x=100E10/P.

y=HSWR50T2=0.5744x+4.9461 plus 2% and minus 1.5%.
R-squared=0.6133.

y=HSWR80T2=0.9249x+3.1724 plus 3% and minus 2%.
R-squared=0.6004.

y=SWAT2=0.6013x+5.1799 plus 2% and minus 1.2%.
R-squared=0.781.

y=SwOptT2=0.5494x+5.6295 plus 1.2% and minus 1.2%.
R-squared=0.8051.

1941-1980 15-Year Historical Surviving Withdrawal Rates

1941-1980 Comparisons: D5 versus E5.

Compare spreads and R-squared. 100E5/P is better than 100D5/P.

1941-1980 Equations, x=100D5/P.

y=HSWR50T2=0.8644x+5.5227 plus 2% and minus 1.5%.
R-squared=0.5069.

y=HSWR80T2=1.368x+4.2009 plus 3% and minus 2.5%.
R-squared=0.475.

y=SWAT2=0.8975x+5.6317 plus 1.5% and minus 1.2%.
R-squared=0.678.

y=SwOptT2=0.712x+6.4011 plus 2% and minus 0.8%.
R-squared=0.6347.

1941-1980 Equations, x=100E5/P.

y=HSWR50T2=0.5347x+5.0488 plus 2% and minus 1.5%.
R-squared=0.547.

y=HSWR80T2=0.8512x+3.4116 plus 3% and minus 2%.
R-squared=0.5187.

y=SWAT2=0.52x+5.4131 plus 2% and minus 1%.
R-squared=0.642.

y=SwOptT2=0.4699x+5.7806 plus 1% and minus 0.8%.
R-squared=0.78.

1941-1980 Comparisons: D10 versus E10.

Compare spreads and R-squared. Results are mixed. 100E10/P and 100D10/P are similar.

1941-1980 Equations, x=100D10/P.

y=HSWR50T2=0.8347x+5.7182 plus 2% and minus 1.5%.
R-squared=0.5313.

y=HSWR80T2=1.3031x+4.5849 plus 3% and minus 2.2%.
R-squared=0.4845.

y=SWAT2=0.8973x+5.7062 plus 1.2% and minus 1%.
R-squared=0.7619.

y=SwOptT2=0.7323x+6.3743 plus 2% and minus 1%.
R-squared=0.755.

1941-1980 Equations, x=100E10/P.

y=HSWR50T2=0.5601x+5.1313 plus 2% and minus 1.5%.
R-squared=0.5221.

y=HSWR80T2=0.8818x+3.6153 plus 3% and minus 2.5%.
R-squared=0.4841.

y=SWAT2=0.5778x+5.253 plus 2% and minus 1%.
R-squared=0.6892.

y=SwOptT2=0.5328x+5.5582 plus 0.8% and minus 1%.
R-squared=0.8719.

Data Summary

At 30 Years: Using dividends is as good as or better than using earnings.

1923-1975 30-Year Historical Surviving Withdrawal Rates
Results are mixed. 100E5/P and 100D5/P are similar.
Results are mixed. 100E10/P and 100D10/P are similar.

1941-1980 30-Year Historical Surviving Withdrawal Rates
100E5/P is not as good as 100D5/P.
100E10/P is not as good as 100D10/P.

At 15 Years: Using earnings is better.

1923-1975 15-Year Historical Surviving Withdrawal Rates
100E5/P is better than 100D5/P.
100E10/P is better than 100D10/P.

1941-1980 15-Year Historical Surviving Withdrawal Rates
100E5/P is better than 100D5/P.
Results are mixed. 100E10/P and 100D10/P are similar.

Analysis

Smoothed dividends do at least as well as smoothed earnings when calculating 30-Year Safe Withdrawal Rates. They do even better when using the latter period because there were fewer dividend cuts.

Smoothed earnings do better when calculating 15-Year Safe Withdrawal Rates.

NOTE: Safe Withdrawal Rates are the lower confidence limits associated with the Historical Surviving Withdrawal Rate regression equations.

Averaging over ten years does better than averaging over five years.

Conclusions

Smoothed dividends and earnings complement each other. Dividend amounts provide a floor to withdrawal rates. Smoothed earnings tell us about the quality of dividends. They protect us against unpleasant dividend surprises, such as happened during the Great Depression.

Have fun.

John Walter Russell
September 10, 2006