CFMV Q4 13 Revised

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Q4-13 (Using S&P Earnings as of 13 Mar 14)

Combined Fair Market Value

(CFMV)

S&P 500 Fair Value

A Comparison of Professor Robert Shiller’s

Cyclically Adjusted Price to Earnings (CAPE 10),

Nominal Price to Earnings,

Monthly Price to Earnings,

And Year – Over –Year Earnings Growth

By Chris Turner

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I. CFMV Q4-13:

The estimates earnings for 4th Quarter CY-13 earnings (Oct-Dec) 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 earnings – Calculated using Shiller’s 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 Shiller’s CAPE.

S&P Index = Average of daily closes for month end.

http://www.standardandpoors.com/

http://www.econ.yale.edu/~shiller/data.htm

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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 rates – shown below:

NOTE: Shiller Chart as of March 2043 (25.16 does not reflect latest earnings for Q4-his chart is not updated)

B. CAPE METHOD – Professor Shiller uses the long term average for price to earnings for 10 years

(currently 16.53) to arrive at an over or under valued metric based on those earnings. The value 24.86

(correct data) minus 16.53 provides an overvalued metric of 31.95%. With the S&P Sep Index at 1780

(average of daily closes for September 13), a 33% percent correction would result in the S&P being

1200 as fair value.

C. PURPOSE – Financial pundits, economists, and TV persona seem to relish Shiller’s 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 80’s and inflation has been underreported by as much as 7% at present.

Wouldn’t this change the picture? To answer that question – I downloaded Shiller’s 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.

http://www.econ.yale.edu/~shiller/bio.htm

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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 Shiller’s data, some interesting points about the

data surfaced. First, Shiller’s 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 Shiller’s 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 Shiller’s 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 Shiller’s 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 Shiller’s data to make the information

relevant. (Considerable improvement)…

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Since Shiller desires to smooth data – which is understandable – the second question that came to mind

was “Why 10 years?” Isn’t 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 Shiller’s

CPI 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 Shiller’s 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.

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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

Tobin’s Q ratio (Q Ratio Explained) and Shiller’s 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 Shiller’s original chart and the logarithmic chart shows the 1929 vs 2000

bubbles in much better context.

IV. Charts:

A. CFMV – 1950 to Present

http://www.smithers.co.uk/page.php?id=34

http://en.wikipedia.org/wiki/Tobin%27s_q

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B. Original Shiller CAPE – 1871 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 year

11. 5 year Monthly Price divided by Earnings Average

12. 10 Year Monthly Price divided by Earnings Average




16. 5 Year Earnings Yield





21. CFMV 1871 to present

22. 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

12

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

Documents

CFMV Q4 13 Revised