These calculations are for 80% stocks and 20% commercial paper and 0.00% in expenses.
I have made a graph for 1923-1972 30-year returns versus the percentage earnings yield 100E10/P. I had Excel fit the graph with a straight line.
With 30-year periods and excluding all sequences with dummy data, results from 1923-1972 are available for making a curve fit if we stay within the modern era. The formula is y = 0.2976x+3.6738 and the variation in the data is very close to and slightly greater than plus and minus 1.5%. R-squared is 0.3112. In terms of P/E10, the equation is y = [29.76 / (P/E10)]+3.6738.
I looked up the values of P/E10 from the post Calculated Rates of the Last Decade dated Wednesday, Jun 23, 2004.
http://nofeeboards.com/boards/viewtopic.php?t=2657
I used the 1923-1972 results to make the following table. The formula is y = [29.76 / (P/E10)]+3.6738 and the confidence limits are plus and minus 1.5%. Recent S&P500 index levels have been close to the referenced level of 1134.11.The last entry in Professor Shiller's list is for November 2003. The S&P500 index was at 1054.87 and P/E10 was 25.898702. [To help with scaling: today's the S&P500 index started at 1134.41. If ten-year earnings were the same as in November 2003, today's P/E10 would be 25.898702*(1134.41/1054.87) = 27.851533.]Code: Select all
1995 20.219819 1996 24.763281 1997 28.333753 1998 32.860928 1999 40.578255 2000 43.774387 2001 36.98056 2002 30.277409 2003 22.894158
Year, 1923-1972 Calculated 30-Year Return, Upper Confidence Limit, Lower Confidence Limit
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1995 5.15 6.65 3.65
1996 4.88 6.38 3.38
1997 4.72 6.22 3.22
1998 4.58 6.08 3.08
1999 4.41 5.91 2.91
2000 4.35 5.85 2.85
2001 4.48 5.98 2.98
2002 4.66 6.16 3.16
2003 4.97 6.47 3.47
Summary
These results apply when a portfolio is left untouched for 30 years assuming that all dividends are reinvested. Expenses have been set at 0.00% in these calculations to make them compatible with previous calculations.
Starting from today's valuations, this portfolio [80% stocks and 20% commercial paper] can be expected to grow at an annualized real rate of 4.7% plus and minus 1.5% in 30 years.
Compare this with a portfolio of 100% stocks. It will grow at 5.3% plus and minus 2%.
With the [80%] high stock portfolio, one can depend upon a real return of 3.2% (minimum). With an all-stock portfolio, one can depend upon a real return of 3.3% (minimum). That is, 30 years is long enough for the upside of a 100% stock portfolio to overcome its downside risk as compared to an 80% stock / 20% commercial paper portfolio.
It turns out that both the high (80%) stock portfolio and the 100% stock portfolio produce almost identical minimum returns at 30 years. Discussions about the penalty [at high levels of safety] for selling stocks early, when based upon a 30-year period, apply equally well to both portfolios.
Have fun.
John R.