Current Research M: Weighted Earnings

Updated: June 1, 2008.

Background

I examine various earnings weights for P/Ex (P/E10 and others).

This is the result of a Letter to the Editor from P/E 10 Wonderer.

April 11, 2008 Letters to the Editor

Introducing Weighted Earnings

This is what I did using Excel.

First, I thinned Professor Robert Shiller’s S&P500 data from monthly data to (January) annual data.

I inserted a column. I put a 1.00 into the last cell in the column. I put the first year’s weighted value in the cell immediately above it. For example, a 6% weight corresponds to an entry of 1.06. I introduced this as a multiplication of the cell below times the weighted value (e.g., =1.06*cell location that has 1.00). I used the fill handle, moving upward, to continue the multiplications on up the column from the bottom to top.

Next I inserted columns with the Weighted Real Price and Weighted Real Earnings. I multiplied the Real Price value in a row by the weight of that row. I multiplied the Real Earnings of a row by the weight of that row.

Finally, I calculated P/Ex. In the case of x=10, P/E10 is the eleventh weighted real price divided by the average of the first ten weighted real earnings. In my spreadsheet, the first entry was =M19/AVERAGE(N9,N18). I used the fill handle to carry this formula to the bottom of the spreadsheet.

Later, I calculate the percentage earnings yield using weighted P/Ex. The formula is =100/cell location with the weighted P/Ex.

Finally, I introduced columns with results summaries such as the real Stock Returns at Year 10. I made Excel scatter charts, used a linear curve fit and recorded equations and R-squared. For this series of examinations, I estimated data ranges (90% outer confidence limits) visually.

This method of weighting is adequate for my purposes because the percentage weight is very small inside of the range x (in P/Ex, where x is typically 5, 10 or 15). A more precise calculation would use logarithms of the weighted values. Also, I did not include the constant scale factors appropriate for the weighting equations since I was not concerned about comparing the actual values of P/Ex and P/Ey. I was only concerned about how well they fit the data.

Stock Return Predictions Using Weighted Earnings

I looked at the effect of different earnings weights on P/E10.

All of these results were close.

The 0.94 weight did best at Years 10 and 20. The 1.06 weight did best at Year 30.

Prediction Equations with Weighted Earnings

More Prediction Equations with Weighted Earnings

This time I sampled weighed 100E5/P instead of the standard 100E10/P.

All of these results were close.

The 0.94 weight did best at Years 10 and 20. The 1.06 weight did best at Year 30.

In these data, 100E5/P is competitive with 100E10/P.

More Prediction Equations with Weighted Earnings

My Interpretation

The overall return of the stock market is the sum of the Investment Return and the Speculative Return.

The 1.06 weight treats all years equally in terms of the long term trend line. It estimates the Investment Return of the stock market.

The 0.94 weight greatly emphasizes recent earnings. It reveals the Speculative Return. The Speculative Return is the effect of multiples expansion and contraction. Multiples include valuation ratios such as price to earnings, price to book, dividend yield and price to sales. The Speculative Return is a measure of investor expectations in the short and intermediate term.

Weighted Earnings and Safe Withdrawal Rates

I made a copy of Deluxe Calculator Version V1.1A08a. I inserted the 1881-2007 values of weighted P/E10 with the 94% weights into row 186, replacing the standard P/E10 values.

I made a rapid optimization of switching. The thresholds were 12-15-25-80 and the allocations were 100%-80%-50%-20%-0%.

I collected a full set of 30-Year Historical Surviving Withdrawal Rates for start years 1881-1980. I made Excel charts of the 1923-1980 and 1881-1980 data. The regression equation for 1923-1980 was y=0.571x+3.687 plus 2.2 and minus 1.2 with an R-squared value of 0.508. The regression equation for 1881-1980 was y=0.553x+3.380 plus 2.5 and minus 1.2 with an R-squared value of 0.569. Here, y=the historical surviving withdrawal rate in percent and x=100/(the weighted values of P/E10)=the weighted earnings yield in percent.

I put a summary of my Excel data into the Weighted Earnings folder at my Yahoo Briefcase. My username is jwr19452000.

Comparing with “Current Research A: Fundamental Breakthroughs associated with TIPS”: these new 1923-1980 data have a Calculated Rate of 5.37% and a Safe Withdrawal Rate of 4.2% for the year 2005. The new 1881-1980 data have a Calculated Rate of 5.01% and a Safe Withdrawal Rate of 3.8% for the year 2005. The standard switching results were “Today’s Safe Withdrawal Rate would be 4.4% if we could buy TIPS with a 2% interest rate. The Calculated Rate would be 5.12%.”

In essence, using weighted earnings is competitive except at the highest levels of safety. However, the difference between the early years 1881-1922 and the later years 1923-1980 is worth noting. It indicates that a fundamental change took place related to weighted earnings.

References:

Current Research A
Safe Withdrawal Rates with Switching
Yahoo Briefcase