cfmv-q1-12 rev

7/31/2019 CFMV-Q1-12 Rev

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Q1-12(Using S&P Earnings as of 10 May 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. Estimates for CFMV Q1-12:The estimates for 1st Quarter CY-12 earnings (Jan-Apr) 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 CAPE

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

A Nominal 5 yr 10 yr 15 yr 20 yr 30 yr All Periods 130

Current P/E* 23.16 25.03 27.22 30.87 38.78 29.01Long Term Average 16.38 18.12 20.00 22.12 27.25 20.78

Over Valued 29.28% 27.61% 26.51% 28.33% 29.74% 28.29%

Equivalent S&P 982.44 1005.72 1020.90 995.66 976.06 996.16 23.67%

B CPI Adjusted (Shiller Method-CAPE) 5 YR CAPE 10 15 YR 20 YR 30 YR All Periods

Current P/E* 21.85 22.35 22.93 25.02 28.49 24.13

Long Term Average 15.64 16.43 17.14 17.80 19.00 17.20

Over Valued 28.43% 26.48% 25.22% 28.84% 33.31% 28.45%

Equivalent S&P 994.28 1021.37 1038.89 988.65 926.54 993.95 23.84%

C Monthly P/E Averages 5 YR 10 YR 15 YR 20 YR 30 YR All Periods

Current P/E* 31.80 28.07 28.29 26.22 22.16 27.31

Long Term Average 15.32 15.16 14.95 14.75 14.38 14.91

Over Valued 51.82% 45.99% 47.15% 43.76% 35.09% 44.76%

Equivalent S&P 669.31 750.35 734.19 781.31 901.79 767.39 41.20%

D Earnings Yield 5 YR 10 YR 15 YR 20 YR 30 YR All PeriodsCurrent Yield 4.35% 4.01% 3.69% 3.24% 2.59% 3.58%

Long Term Average 6.92% 6.29% 5.81% 5.39% 4.58% 5.80%

Over Valued 37.11% 36.17% 36.55% 39.85% 43.49% 38.63%

Equivalent S&P 873.69 886.76 881.42 835.68 785.03 852.52 34.67%

E Combined Fair Market Value (CFMV) 1001.33 23.27%

S&P Index - Mar 2012 1389.24

Over Valued 27.92%

*The Earnings value for in each column is the average for the cycle (5, 10, 15, 20, 30 and the average of all periods)

1st Quarter 2012 S&P 500 Fair Value

Currently

Overvalued

by

Current

S&P Index

CurrentlyOvervalued

by

Currently

Overvalued

by

Currently

Overvalued

by
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 18 May 2012 (21.15 does not reflect latest earnings for Q1-his chart is not updated)

B. CAPE METHODProfessor Shiller uses the long term average for price to earnings for 10 years(currently 16.43) to arrive at an over or under valued metric based on those earnings. The value 22.35

(correct data) minus 16.43 provides an overvalued metric of 26.48%. With the S&P Sep Index at 1389

(average of daily closes for Mar 12), a 26.48% percent correction would result in the S&P being 1021

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.

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Long-TermI

nterestRates

Price-EarningsRatio(CA

PE)

Year

19011966

2000

Price-Earnings Ratio

Long-Term Interest Rates

1981

1921

1929

21.15
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 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 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 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 justshowing 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 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 on

differing 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

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1860 1880 1900 1920 1940 1960 1980 2000 2020

10 Years Average Earnings Divided by Average Monthly PriceCAPE (Shiller Method) vs Nominal

Nominal

CAPE

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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.

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 arithmetic

averages 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

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100

1000

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100

1000

1940 1950 1960 1970 1980 1990 2000 2010 2020


1950 - Present

CFMV

S&P Composite

1389.24

27.92%1001.33


SP Index Mar 2012 =

(Average of Daily Closes)

Over / Under Valued =

S&P Equivalent =
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: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.TFMV 1871 to present17.TFMV 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.

100

1000

100

1000

1860 1880 1900 1920 1940 1960 1980 2000 2020

CAPE with 10-Year Trailing Earnings

10 Yr Equivalent

S&P Composite

22.3516.4326.48%

1021.37

10 YR CAPE (Shiller Original)

Current P/E =

Long Term Average =

Over/ Under Valued =

S&P Equivalent =

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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 Average

15.30 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

100

1000

100

1000

1860 1880 1900 1920 1940 1960 1980 2000 2020


5 Yr Equivalent

S&P 500 Composite

21.8515.6428.43%994.28

5 YR CAPE

Current P/E =

Long Term Average =


S&P Equivalent =

1

10

100

1000

1

10

100

1000

1860 1880 1900 1920 1940 1960 1980 2000 2020

P/E with 5-Year Trailing Earnings

5 Yr Equivalent

S&P Composite

23.1616.3829.28%982.44

5 YR Nominal

Current P/E =

Long Term Average =


S&P Equivalent =

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CAPE 10 year (Shiller Original data)

Nominal 10 year

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1000

100

1000

1860 1880 1900 1920 1940 1960 1980 2000 2020


10 Yr Equivalent

S&P Composite

22.3516.4326.48%

1021.37

10 YR CAPE (Shiller Original)

Current P/E =

Long Term Average =


S&P Equivalent =

1

10

100

1000

1

10

100

1000

1860 1880 1900 1920 1940 1960 1980 2000 2020


10 Yr Equivalent

S&P Composite

27.61%

1005.72

10 YR Nominal

Current P/E =

Long Term Average =


S&P Equivalent =

25.03

18.12

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CAPE 15 year

Nominal 15 year

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1000

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15 Yr Equivalent

S&P Composite

22.9317.1425.22%

1038.89

15 YR CAPE

Current P/E =

Long Term Average =


S&P Equivalent =

1

10

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1000

1

10

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1000

1860 1880 1900 1920 1940 1960 1980 2000 2020


15 Yr Equivalent

S&P Composite

26.51%

1020.90

15 YR Nominal

Current P/E =

Long Term Average =


S&P Equivalent =

27.22

20.00

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CAPE 20 year

Nominal 20 year

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1000

1860 1880 1900 1920 1940 1960 1980 2000 2020


20 Yr Equivalent

S&P Composite

25.0217.80

28.84%988.65

20 YR CAPE

Current P/E =

Long Term Average =

Over / Under Valued =S&P Equivalent =

1

10

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1000

1

10

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1000

1860 1880 1900 1920 1940 1960 1980 2000 2020


20 Yr Equivalent

S&P Composite

30.87

22.1228.33%

995.66

20 YR Nominal

Current P/E =

Long Term Average =


S&P Equivalent =

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CAPE 30 year

Nominal 30 year

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1000

1880 1900 1920 1940 1960 1980 2000 2020


30 Yr Equivalent

S&P Composite

28.49

19.00

33.31%

926.54

30 YR CAPE

Current P/E =

Long Term Average =


S&P Equivalent =

1

10

100

1000

1

10

100

1000

1880 1900 1920 1940 1960 1980 2000 2020


30 Yr Equivalent

S&P Composite

38.78

27.2529.74%976.06

30 YR Nominal

Current P/E =

Long Term Average =


S&P Equivalent =

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5 year Monthly Price divided by Earnings Average


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1000

1

10

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1000

1860 1880 1900 1920 1940 1960 1980 2000 2020

5 Year Monthly P/E

5 Yr Monthly PE Equivalent

S&P Compos ite

31.80

15.3251.82%

669.31

5 YR Trailing Earnings

Current P/E =

Long Term Average =


S&P Equivalent =

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1000

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1000

1860 1880 1900 1920 1940 1960 1980 2000 2020

10 Year Monthly P/E


S&P Composite


Current P/E =

Long Term Average =


S&P Equivalent =

28.0715.1645.99%750.35

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1000

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1000

1860 1880 1900 1920 1940 1960 1980 2000 2020

15 Year Monthly P/E


S&P Composite


Current P/E =

Long Term Average =


S&P Equivalent =

28.0715.1645.99%750.35

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1000

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10

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1000

1880 1900 1920 1940 1960 1980 2000 2020

20 Year Monthly P/E


S&P Composite


Current P/E =

Long Term Average =


S&P Equivalent =

26.2214.7543.76%781.31

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5 Year Earnings Yield

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30 Year Monthly P/E


S&P Composite


Current P/E =

Long Term Average =


S&P Equivalent =

22.1614.3835.09%

901.79

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10000

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10000

1860 1880 1900 1920 1940 1960 1980 2000 2020

Earnings Yield - 5 Yrs Average VS Long Term Average

5 Yr Earnings Yield

S&P Composite

4.35%

6.92%

37.11%

873.69

Earnings Yield - 5 YR Avg

Current Earnings Yield =

Long Term Average =


S&P Equivalent =

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1

10

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10000

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10000

1860 1880 1900 1920 1940 1960 1980 2000 2020


10 Yr Earnings Yield

S&P Composite

4.01%

6.29%

36.17%

886.76



Long Term Average =


S&P Equivalent =

1

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1000

10000

1

10

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1000

10000

1860 1880 1900 1920 1940 1960 1980 2000 2020



S&P Composite

3.69%

5.81%

36.55%

881.42

Earnings Yield -15 YR Avg


Long Term Average =


S&P Equivalent =

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1

10

100

1000

10000

1

10

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1000

10000

1860 1880 1900 1920 1940 1960 1980 2000 2020



S&P Composite

3.24%

5.39%

39.85%

835.68



Long Term Average =


S&P Equivalent =

1

10

100

1000

10000

1

10

100

1000

10000

1860 1880 1900 1920 1940 1960 1980 2000 2020



S&P Composite

2.59%

4.58%

43.49%

785.03



Long Term Average =


S&P Equivalent =

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CFMV 1871 to present

CFMV 1950 to present

cfmv-q1-12 rev

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