Alternatives to the Cyclically Adjusted Price-to-Earnings Ratio
June 29, 2010

Note from dshort: Over the past decade, Professor Robert Shiller's S&P 500 has popularized the Cyclically Adjusted Price-to-Earnings ratio (CAPE) as a technique for establishing fair market value. The metric actually dates from the pioneering work of Benjamin Graham and David Dodd in their classic book, Security Analysis. They noted that short-term volatility in earnings undermined the usefulness of the traditional ratio of price divided by current earnings. Their solution was to divide the price by a multi-year average of earnings, "not less than five years and preferably seven or ten years" (p. 452). In recent years, Yale professor Robert Shiller, the author of Irrational Exuberance, has popularized the use of a 10-year average of real earnings as the denominator in the P/E ratio. Guest contributor Chris Turner has studied the problem of market valuation with P/E ratios and offers an alternative approach for making the calculation.

Removing the Cape from Robert Shiller's CAPE
By Chris Turner

This article confronts one out of many issues taken for fact — Professor Robert Shiller's S&P 500 fair value metric, the Cyclically Adjusted Price to Earnings ratio (CAPE). An examination of Shiller's data produces some questions, conclusions, and leads to alternative measurements, which I illustrate in the Turner Fair Market Value (TFMV) table.

Understanding the Shiller CAPE data

On his Yale website, Professor Shiller maintains an Excel spreadsheet with the data for calculating the Cyclically Adjusted Price to Earnings (CAPE), which he charts together with long-term interest rates.

For the index price, Shiller uses the monthly average of daily closes, and for the earnings he uses the quarterly earnings from Standard & Poor's website. He uses a simple interpolation to supply earnings data for the months between quarters. He adjusts both numbers for inflation using the Consumer Price Index (CPI) from the Bureau of Labor Statistics. Finally, he divides the real (inflation-adjusted) price by an average of 10 years worth of real monthly earnings to arrive at a real price-to -earnings average for 10 years. This defines the term Cyclically Adjusted (CPI adjusted) Price to Earnings (CAPE).

Professor Shiller's data begins in 1871. He splices earlier historic market data with the S&P 500, which was created in March 1957. He refers to the spliced series as the S&P Composite.

At present, the average (arithmetic mean) of CAPE 10 over the nearly 140 year timeframe is 16.36. By comparing the current CAPE ratio to the long-term average, one can gain a sense of the valuation of the S&P 500. Currently, using the latest data from both Shiller and Standard & Poor's, the CAPE 10 shows 19.99. This means that the P/E would need to drop around 18% (16.36/19.99=.8184) to become fair value. Applying that to the S&P 500 as of March earnings and current index roughly equates to 899 as fair value (.8184 X 1098). The March index was 1152.05, and the P/E back then was 21.00 (16.36/21.00=.7790) — equating to a fair value of 897, pretty close to the numbers this week.

The chart also contains a backdrop of long term interest rates (which just happens to average out at 4.49 since 1871 and 3.41 since 1950).

Before going much further, I must also add that I think Professor Shiller is an outstanding economist. This article is not an attack on his accomplishments but rather an alternative approach to solving the problem of market valuation.

ISSUES

Two issues come to mind when reviewing Shiller's charts and calculations. The first involves CPI and the second involves the 10 year timeframe.

THE CPI PROBLEM: The difficulty I have with using CPI to adjust an index since 1871 is that major changes were introduced in the 1980's and 1990's that substantially changed the method for calculating CPI. At his Shadow Government Statistics website, Economist John Williams preserves the older method of CPI, and the difference is substantial — as much as 8%.

Solution: My solution to the problem is simple. What does the nominal data look like and do CPI calculations add any value to the information presented? I used the same CAPE formula as Shiller, but I use the nominal (not inflation-adjusted) numbers. The chart below demonstrates the very slight differences between nominal and CAPE.

Result: After viewing the differences in the charts and the calculations in the TFMV table — the CPI adjustment does not add value. The time spent adjusting the index and earnings for inflation may actually reduce valuable time to spend elsewhere.

THE TIMEFRAME PROBLEM: Shiller uses an arbitrary 10 years worth of earnings. He does this to smooth cycles, a concept with which I completely agree. However, the following occurred in the last 10 years that makes the arbitrary use of a 10-year earnings denominator seem suspect:

  1. Credit expanded feverishly
  2. Record Mortgage Equity Withdrawal
  3. Record Securitization
  4. Negative savings rate
  5. Peak baby boomer earnings
Solution: I compared different sets of times (5, 10, 20, and 30 years) for both nominal and CAPE to answer my own question. I picked arbitrary numbers also and readers can pick their favorite metric.

Result: CAPE 10 equivalent S&P would equal 899.82. The TFMV table shows the greatest difference between nominal and CAPE at 30 years (which makes sense).

Shiller Chart Improvements

In my full report (available in PDF format here), I changed Shiller's use of long term interest rates (red line) to either the Real S&P (for CAPE) or the nominal S&P for the rest. I added over / under valuation information on each chart and equivalent S&P to each chart. The blue lines represent what the S&P should be predicated on "fair value." All charts use a logarithmic vertical axis for consistency and better visualization of relative values over such a long timeframe.

Additional Table Information

Monthly P/E: During the research, I wondered if a monthly price-to-earnings number would offer a competitive view for fair value. I calculated the nominal monthly price divided by monthly earnings and included those in chart and table format. NOTE: The nominal and real monthly P/E's equate.

Historical Year-over-year Earnings Growth: I added a column to calculate the year over year earnings growth and averaged that number from 1871. Then, I calculated an equivalent fair value based on long-term earnings growth.

Turner Fair Market Value: It seems as though everyone assigns a name to a study — why not this as well. In determining a "fair value" — I simply combined the following aspects and averaged them with equal weighting:

A few words about sentiment: when looking at the charts, we can readily see that over- or under-valuation may remain in place for years. Regardless of the metric used to calculate fair value, the market issues sentiment daily when the closing bell rings and buyers = sellers. Price action displays sentiment, real-time, every second and should be included into a valuation metric. This is simply my method.

Where is the Market Headed?

100% of the time, in 140 years of history, the market always returns to fair value and drops below, usually for a sustained period of time. The question is whether earnings will grow or whether the market will move down, or some combination of the two. We could have multi-year periods of absolutely no growth in the S&P and remain above fair value. In other words, there could be many more years of no index price growth until earnings grow faster and create an undervalued metric. Frankly, I question the likelihood of rapid earnings growth. I believe that the market could spend years in an undervalued position, which would equate to below the 900 level based upon this study.