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Q3-11 Estimate

(Using S&P Earnings as of 10 November 11)

Combined Fair Market Value (CFMV) S&P 500 Fair Value


A Comparison of Professor Robert Shillers Cyclically Adjusted Price to Earnings (CAPE 10), Nominal Price to Earnings, Monthly Price to Earnings, And Year Over Year Earnings Growth

By Chris Turner

I. Revised Earnings for CFMV Q3-11:


The revised earnings for 3rd Quarter CY-11 earnings (Jul-Sep 11) Combined Fair Market Value (CFMV) using data sets from the S&P Website (S&P Website ) and Professor Robert Shiller (Shiller Online Data) are listed below:

** Note: The addition of the right column shows approximate valuation based on the time of publication. The S&P 500 currently at 1250 resulting in how much we are still over (or under) valued.
A. Nominal period trailing earnings Calculated using Shillers method of current S&P 500 Index average price of monthly closes divided by average earnings over column period earnings. B. CPI Adjusted (Shiller Method-CAPE) Professor Shiller adjusts current S&P 500 Index price and 4 quarter trailing earnings at month close by CPI, then divides CPI-adjusted price by CPI-adjusted earnings 10 years. The 10 year calculation is the original Shiller Method the other periods are calculated the same method but for differing periods. C. Monthly P/E Averages Calculated by dividing monthly price by monthly 4 quarter trailing earnings. NOTE: This calculation results in the same number whether using CPI or nominal. D. Historical Y-O-Y Earnings Growth: Calculated by averaging of entire time period earnings growth year over year. E. Combined Fair Market Value - Calculated by averaging Current Price (sentiment), average of all periods nominal and Monthly P/E, and Y-O-Y earnings growth. This does not include Shillers CAPE. S&P Index = Average of daily closes for month end.

II. Background:
A. PROFESSOR SHILLER: Yale Professor of Economics Robert Shiller, (Bio Here), developed a cyclically adjusted price to earnings ratio (CAPE) that simply uses monthly CPI- adjusted S&P 500 Index and divides that by an average of 10 years worth of CPI adjusted trailing monthly earnings. Professor Shiller uses this data and creates a long term chart that compares this ratio over time with a backdrop of long term interest rates shown below:

NOTE: Shiller Chart as of 10 Nov 11 (20.71 does not reflect latest earnings for Q3-his chart is not updated)

B. CAPE METHOD Professor Shiller uses the long term average for price to earnings for 10 years (currently 16.41) to arrive at an over or under valued metric based on those earnings. The value 19.67 (correct data) minus 16.40 provides an overvalued metric of roughly 16%. With the S&P Index at 1183 (average of daily closes for Sep 11), a 16% percent correction would result in the S&P being 979 as fair value. C. PURPOSE Financial pundits, economists, and TV persona seem to relish Shillers chart and do not question the metrics involved in creating the chart. The first question that occurred to me was Why use the BLS CPI? Head over to John Williams Shadowstats website and we see that BLS changed metrics back in the early 80s and inflation has been underreported by as much as 7% at present. Wouldnt this change the picture? To answer that question I downloaded Shillers data and began to examine the spreadsheet. By analyzing the data, I wanted to determine what impact, if any, a change in the CPI vs nominal might exist.
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D. FAIR VALUE Each investor uses some metric to determine a fair value. As indexes work in aggregate, assigning a fair value to the overall S&P 500 index is cumbersome. However, since Shiller went through the process of assigning his fair value to the CAPE for 10 years I went many steps further and compared differing time periods for both nominal (no CPI adjustment) and CAPE (CPI adjusted), then compared the averages for all time periods.

III.

Methodology:

A. Shiller CAPE Calculation After a quick perusal of Shillers data, some interesting points about the data surfaced. First, Shillers calculation is not just using the simple 10 year average of monthly earnings, it is actually 10 years of 1 year of trailing earnings. To clarify: The data on the left from Shillers spreadsheet shows the total earnings (this is GAAP or actual earnings BTW, not operating) under the Earnings column. A quick glance over at the S&P website (right picture line 54) confirms that looking at quarterly earnings of 6/30/2008 reveals earnings of $12.86. However, on Shillers line 1658, the number is 51.37. So I added a column to S&P (shown far right) to calculate 1 year trailing earnings and voila the earnings agree.

Shiller then uses this 1 year of trailing earnings (commonly referred to as trailing twelve months earnings - TTE) and divides price (defined by average of monthly closes) by 10 years average of the trailing earnings. This creates the underlying data set for his chart. So far, all the data makes sense. I went one step further with Shillers data and assigned an over/under value based on the index vs just showing the raw P/E ratio. Then, rather than looking at a chart with a comparison of long term interest rates, I changed the background to either the historical nominal or CPI adjusted S&P Index. By doing this, a comparison to the actual index can be made rather than an interpretation of where the index should be I actually calculated Shillers data to make the information relevant. (Considerable improvement)

Since Shiller desires to smooth data which is understandable the second question that came to mind was Why 10 years? Isnt this the same time that the following occurred: 1) Credit expanded feverishly 2) Record Mortgage Equity Withdrawal 3) Record Securitization 4) Negative savings rate 5) Peak baby boomer earnings (40-50) To compare 5, 10, 15, 20, and 30 years goes further to answer the relevancy of the data based on differing time periods and smoothing the impact of the previous 10 years. B. Nominal Period Trailing Earnings Calculation These calculations are the exact same as Shillers CPI adjusted, except these are unadjusted numbers. Last time I checked, no one really trades a cpiadjusted Index anyway Additionally, the differences between the nominal and CPI adjustment are too small. The chart below shows the actual difference between Shillers CAPE data and simply using the nominal number. Clearly, the differences are subtle and perhaps adjusting for CPI is unnecessary.

C. Monthly P/E Averages While researching the data, another metric came to mind. What about the historical monthly price divided by earnings? What would those charts look like for 1 year (essentially the monthly price divided by the earnings which is the 4 quarter trailing earnings), 5 year, etc

D. Historical Y-O-Y Earnings Growth I also calculated the 1871 to present day average of 1 year earnings growth to arrive at the long term average. This number shows more of a linear representation of where the S&P would be based upon the long term average of earnings growth. E. Combined Fair Market Value A number predicated on all calculations using an average of sentiment (current price), nominal (because we trade nominally), Y-O-Y earnings growth, and monthly P/E values. F. Geometric VS Arithmetic Calculations I contacted Andrew Smithers in the UK about using geometric vs arithmetic calculations. He uses Geometric for his chart (Click Here) that compares Tobins Q ratio (Q Ratio Explained) and Shillers CAPE. Geometric is appropriate for Earnings Per share calculations over time, however Price divided by earnings are snapshots in time and arithmetic averages work. In fact, the differences in calculations from Geometric and arithmetic are in the decimals (I calculated both ways) and again when talking generically of over and undervalued, whether the S&P fair value is 899.01 or 899.05 becomes irrelevant. G. Logarithmic vs Actual Most charts are using Logarithmic due to the long time horizon. Once the time horizon passes 30 years, using actual index numbers (even CPI adjusted) prevents a true representation. Comparing Shillers original chart and the logarithmic chart shows the 1929 vs 2000 bubbles in much better context. IV. Charts: A. CFMV 1950 to Present

B. Original Shiller CAPE 1871 to Present (original Shiller data applied to logarithmic scale)

C. Charts included in Attachment: 1. CAPE 5 year 2. Nominal 5 year 3. CAPE 10 year (Shiller Original data) 4. Nominal 10 year 5. CAPE 15 year 6. Nominal 15 year 7. CAPE 20 year 8. Nominal 20 year 9. CAPE 30 year 10. Nominal 30 year 11. 5 year Monthly Price divided by Earnings Average 12. 10 Year Monthly Price divided by Earnings Average 13. 15 Year Monthly Price divided by Earnings Average 14. 20 Year Monthly Price divided by Earnings Average 15. 30 Year Monthly Price divided by Earnings Average 16. TFMV 1871 to present 17. TFMV 1950 to present V. About the creator:
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Chris Turner, resides in Kansas, full-time pilot for military with a part-time hobby for economic and market research. Independent options trader and managing partner for small Investment LLC.

ATTACHMENT 1
1. CAPE 5 year 2. Nominal 5 year 3. CAPE 10 year (Shiller Original data) 4. Nominal 10 year 5. CAPE 15 year 6. Nominal 15 year 7. CAPE 20 year 8. Nominal 20 year 9. CAPE 30 year 10. Nominal 30 year 11. 5 year Monthly Price divided by Earnings Average 12. 10 Year Monthly Price divided by Earnings Average 13. 15 Year Monthly Price divided by Earnings Average 14. 20 Year Monthly Price divided by Earnings Average 15. 30 Year Monthly Price divided by Earnings Average 16. CFMV 1871 to present 17. CFMV 1950 to present

CAPE 5 year

Nominal 5 year

CAPE 10 year (Shiller Original data)

Nominal 10 year

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CAPE 15 year

Nominal 15 year

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CAPE 20 year

Nominal 20 year

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CAPE 30 year

Nominal 30 year

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5 year Monthly Price divided by Earnings Average

10 Year Monthly Price divided by Earnings Average

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15 Year Monthly Price divided by Earnings Average

20 Year Monthly Price divided by Earnings Average

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30 Year Monthly Price divided by Earnings Average

CFMV 1871 to present

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CFMV 1950 to present

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