Dollar Cost Averaging at Year 15
Dollar Cost Averaging reduces the effects of fluctuating prices during accumulation. It does not eliminate them entirely. Valuations matter.
Portfolios
I determined the real (inflation adjusted) balances at Year 15 for the following portfolios when dollar cost averaging:
1) 100% TIPS.
2) 50% stocks and 50% TIPS.
3) 100% stocks.
I used the S&P500 and TIPS at 2.0% interest. I rebalanced annually. I set costs equal to zero.
I invested $1000 at day 1 and an additional $1000 (plus inflation) at the end of each year. My total investment at the end of Year 15 was $16000 (after adjusting for inflation).
I determined regression equations for portfolios begun in 1923-1990. I used Excel’s LINEST to determine the equations and standard statistics. I used Excel’s charting capability to assist in making visual estimates for confidence limits.
Results
Here is the regression equation with 100% TIPS.
Estimates derived from 15 year historical sequences beginning 1923-1990.
Equation:
y = -7600/[P/E10] + 19188
1.64 standard deviations = 1158
Confidence limits = plus and minus $1158 by formula.
Confidence limits = plus and minus $1000 by eyeball.
When P/E10=28 (as it does today):
y = $18917 plus and minus $1158 by formula.
[I prefer to use the visual confidence limits.]
R-squared = 0.0645.
Starting from today’s valuations, you should plan for the following real balances:
95% chance of doing better than $17900.
80% chance of doing better than $18400.
50% chance of doing better than $18900.
20% chance of doing better than $19400.
5% chance of doing better than $19900.
The spread is caused by the slight mismatch between when inflation occurs and when it shows up as an adjustment to the TIPS principal.
Here is the regression equation with 50% stocks and 50% TIPS.
Estimates derived from 15 year historical sequences beginning 1923-1990.
Equation:
y = 106600/[P/E10] + 15981
1.64 standard deviations = 5845
Confidence limits = plus and minus $5845 by formula.
Confidence limits = plus and minus $6000 by eyeball.
Confidence limits at high valuations: plus and minus $5000 from visual inspection.
When P/E10=28 (as it does today):
y = $19788 plus and minus $5845 by formula.
[I prefer to use the visual confidence limits.]
R-squared = 0.3464.
Starting from today’s valuations, you should plan for the following real balances:
95% chance of doing better than $14800.
80% chance of doing better than $17300.
50% chance of doing better than $19800.
20% chance of doing better than $22300.
5% chance of doing better than $24800.
Here is the regression equation with 100% stocks.
Estimates derived from 15 year historical sequences beginning 1923-1990.
Equation:
y = 278900/[P/E10] + 9957
1.64 standard deviations = 15878
Confidence limits = plus and minus $15878 by formula.
Confidence limits = plus $20000 and minus $15000 by eyeball.
Confidence limits at high valuations: plus $20000 and minus $10000 from visual inspection.
When P/E10=28 (as it does today):
y = $19918 plus and minus $15878 by formula.
[I prefer to use the visual confidence limits.]
R-squared = 0.3296.
Starting from today’s valuations, you should plan for the following real balances:
95% chance of doing better than $9900.
80% chance of doing better than $14900.
50% chance of doing better than $19900.
20% chance of doing better than $29900.
5% chance of doing better than $39900.
Historical Minimums
Here are the worst case (real) balances at the end of Year 15:
With 100% TIPS:
1946 $16407
1979 $17102
1980 $17332
1947 $17382
1941 $17407
With 50% stocks and 50% TIPS:
1960 $15892
1967 $16747
1963 $16753
1965 $17150
1964 $17162
With 100% stocks.
1960 $12678
1963 $13989
1967 $14330
1964 $14665
1965 $14827
Analysis
Looking at my charts, an earnings yield 100E10/P of 6% defines when the upside from stocks has consistently overcome the downside risk (when compared to dollar cost averaging into a 100% TIPS portfolio). This corresponds to P/E10=17 and only 60% of today’s S&P500 index level.
The historical minimums are not as bad as indicated by mindless application of the statistical formulas. That is, the dollar distribution is not quite Gaussian (bell shaped, normal) which, in this instance, works in favor of the investor.
Not doing as well as investing into TIPS at Year 15 would be discouraging. The upside potential of a 100% stock portfolio does not balance the downside risk in times of high valuations (P/E10=17 and above). However, a stock allocation of 50% can make sense.
Whenever stocks fall into a more reasonable range of valuations, P/E10 below 17, the downside risk is very small and a high stock allocation is compelling. The upside is high enough to justify a 100% stock allocation as opposed to 50%.
Have fun.
John Walter Russell
October 5, 2006
|