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Q3-12

(Using S&P Earnings as of 29 December 2012)

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 YearOverYear Earnings Growth

By Chris Turner

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I. Final for CFMV Q3-12:The final for 3rd Quarter CY-12 earnings (Jul-Sep) 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:

A. Nominal period trailing earningsCalculated using Shillers method of current S&P 500 Indexaverage 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 4quarter 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 Methodthe other periods are

calculated the same method but for differing periods.

C. Monthly P/E AveragesCalculated by dividing monthly price by monthly 4 quarter trailing earningsNOTE: 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 growthyear over year.

E. Combined Fair Market Value - Calculated by averaging Current Price (sentiment), average of allperiods nominal and Monthly P/E, and Y-O-Y earnings growth. This does not include Shillers CAPES&P Index = Average of daily closes for month end.
http://www.standardandpoors.com/http://www.standardandpoors.com/http://www.standardandpoors.com/http://www.econ.yale.edu/~shiller/data.htmhttp://www.econ.yale.edu/~shiller/data.htmhttp://www.econ.yale.edu/~shiller/data.htmhttp://www.econ.yale.edu/~shiller/data.htmhttp://www.standardandpoors.com/

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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 ratesshown below:

NOTE: Shiller Chart as of December 2012 (22.17 does not reflect latest earnings for Q3-his chart is not updated)

B. CAPE METHODProfessor Shiller uses the long term average for price to earnings for 10 years(currently 16.45) to arrive at an over or under valued metric based on those earnings. The value 21.45

(correct data) minus 16.45 provides an overvalued metric of 24.38%. With the S&P Sep Index at 1443

(average of daily closes for Dec 12), a 24.38% percent correction would result in the S&P being 1091

as fair value.

C.

PURPOSEFinancial pundits, economists, and TV persona seem to relish Shillers chart and do notquestion 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 dataand began

to examine the spreadsheet. By analyzing the data, I wanted to determine what impact, if any, a chang

in the CPI vs nominal might exist.
http://www.econ.yale.edu/~shiller/bio.htmhttp://www.econ.yale.edu/~shiller/bio.htmhttp://www.econ.yale.edu/~shiller/bio.htmhttp://www.econ.yale.edu/~shiller/bio.htm

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D. FAIR VALUEEach investor uses some metric to determine a fair value. As indexes work inaggregate, 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 yearsI 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 CalculationAfter 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 quarterlyearnings 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 voilathe 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&PIndex. By doing this, a comparison to the actual index can be made rather than an interpretation

of where the index should beI actually calculated Shillers data to make the information

relevant. (Considerable improvement)

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Since Shiller desires to smooth datawhich is understandablethe second question that came to mind

was Why 10 years? Isnt this the same time that the following occurred:

1) Credit expanded feverishly2) Record Mortgage Equity Withdrawal3) Record Securitization4) Negative savings rate5) 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 ondiffering time periods and smoothing the impact of the previous 10 years.

B. Nominal Period Trailing Earnings CalculationThese calculations are the exact same as ShillersCPI adjusted, except these are unadjusted numbers. Last time I checked, no one really trades a cpi-

adjusted 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 AveragesWhile researching the data, another metric came to mind. What about thehistorical 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 GrowthI also calculated the 1871 to present day average of 1 yearearnings 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.

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E. Combined Fair Market ValueA number predicated on all calculations using an average ofsentiment (current price), nominal (because we trade nominally), Y-O-Y earnings growth, and monthly

P/E values.

F. Geometric VS Arithmetic CalculationsI contacted Andrew Smithers in the UK about usinggeometric 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 arithmeticaverages work. In fact, the differences in calculations from Geometric and arithmetic are in the

decimals (I calculated both ways) and againwhen talking generically of over and undervalued,

whether the S&P fair value is 899.01 or 899.05 becomes irrelevant.

G. Logarithmic vs ActualMost charts are using Logarithmic due to the long time horizon. Once thetime 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. CFMV1950 to Present
http://www.smithers.co.uk/page.php?id=34http://www.smithers.co.uk/page.php?id=34http://www.smithers.co.uk/page.php?id=34http://en.wikipedia.org/wiki/Tobin%27s_qhttp://en.wikipedia.org/wiki/Tobin%27s_qhttp://en.wikipedia.org/wiki/Tobin%27s_qhttp://en.wikipedia.org/wiki/Tobin%27s_qhttp://www.smithers.co.uk/page.php?id=34

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B. Original Shiller CAPE1871 to Present (original Shiller data applied to logarithmic scale)

C. Charts included in Attachment:CAPE 5 year CAPE 10 year

(Shiller Original

data)

CAPE 15 year CAPE 20 year CAPE 30 year

Nominal 5 year Nominal 10 year Nominal 15 year Nominal 20 year Nominal 30

year

5 Year PE 10 Year PE 15 Year PE 20 Year PE 30 Year PE

5 Year Earnings

Yield

10 Year Earnings

Yield

15 Year Earnings

Yield

20 Year Earnings

Yield

30 Year

Earnings Yield

CMFV 1871 to

Present

CMFV 1950 to

Present

V. About the creator: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.

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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 year11. 5 year Monthly Price divided by Earnings Average12.10 Year Monthly Price divided by Earnings Average13.15 Year Monthly Price divided by Earnings Average14.20 Year Monthly Price divided by Earnings Average15.30 Year Monthly Price divided by Earnings Average16.5 Year Earnings Yield17.10 Year Earnings Yield18.15 Year Earnings Yield19.20 Year Earnings Yield20.30 Year Earnings Yield21.CFMV 1871 to present22.CFMV 1950 to present

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CAPE 5 year

Nominal 5 year

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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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5 Year Earnings Yield

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CFMV 1871 to present

CFMV 1950 to present

cfmv q3-12 final

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