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7/31/2019 CFMV-Q1-12 Rev
1/19
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
7/31/2019 CFMV-Q1-12 Rev
2/19
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/7/31/2019 CFMV-Q1-12 Rev
3/19
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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18
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0
5
10
15
20
25
30
35
40
45
50
1860 1880 1900 1920 1940 1960 1980 2000 2020
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.htm7/31/2019 CFMV-Q1-12 Rev
4/19
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)
7/31/2019 CFMV-Q1-12 Rev
5/19
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
0
10
20
30
40
50
60
0
10
20
30
40
50
60
1860 1880 1900 1920 1940 1960 1980 2000 2020
10 Years Average Earnings Divided by Average Monthly PriceCAPE (Shiller Method) vs Nominal
Nominal
CAPE
7/31/2019 CFMV-Q1-12 Rev
6/19
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
10
100
1000
10
100
1000
1940 1950 1960 1970 1980 1990 2000 2010 2020
Combined Fair Market Value
1950 - Present
CFMV
S&P Composite
1389.24
27.92%1001.33
Combined Fair Market Value
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=347/31/2019 CFMV-Q1-12 Rev
7/19
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 =
7/31/2019 CFMV-Q1-12 Rev
8/19
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
7/31/2019 CFMV-Q1-12 Rev
9/19
CAPE 5 year
Nominal 5 year
100
1000
100
1000
1860 1880 1900 1920 1940 1960 1980 2000 2020
CAPE with 5-Year Trailing Earnings
5 Yr Equivalent
S&P 500 Composite
21.8515.6428.43%994.28
5 YR CAPE
Current P/E =
Long Term Average =
Over/ Under Valued =
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 =
Over/ Under Valued =
S&P Equivalent =
7/31/2019 CFMV-Q1-12 Rev
10/191
CAPE 10 year (Shiller Original data)
Nominal 10 year
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 =
1
10
100
1000
1
10
100
1000
1860 1880 1900 1920 1940 1960 1980 2000 2020
P/E with 10-Year Trailing Earnings
10 Yr Equivalent
S&P Composite
27.61%
1005.72
10 YR Nominal
Current P/E =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
25.03
18.12
7/31/2019 CFMV-Q1-12 Rev
11/191
CAPE 15 year
Nominal 15 year
100
1000
100
1000
1860 1880 1900 1920 1940 1960 1980 2000 2020
CAPE with 15-Year Trailing Earnings
15 Yr Equivalent
S&P Composite
22.9317.1425.22%
1038.89
15 YR CAPE
Current P/E =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
1
10
100
1000
1
10
100
1000
1860 1880 1900 1920 1940 1960 1980 2000 2020
P/E with 15-Year Trailing Earnings
15 Yr Equivalent
S&P Composite
26.51%
1020.90
15 YR Nominal
Current P/E =
Long Term Average =
Over / Under Valued =
S&P Equivalent =
27.22
20.00
7/31/2019 CFMV-Q1-12 Rev
12/191
CAPE 20 year
Nominal 20 year
100
1000
100
1000
1860 1880 1900 1920 1940 1960 1980 2000 2020
CAPE with 20-Year Trailing Earnings
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
100
1000
1
10
100
1000
1860 1880 1900 1920 1940 1960 1980 2000 2020
P/E with 20-Year Trailing Earnings
20 Yr Equivalent
S&P Composite
30.87
22.1228.33%
995.66
20 YR Nominal
Current P/E =
Long Term Average =
Over / Under Valued =
S&P Equivalent =
7/31/2019 CFMV-Q1-12 Rev
13/191
CAPE 30 year
Nominal 30 year
100
1000
100
1000
1880 1900 1920 1940 1960 1980 2000 2020
CAPE with 30-Year Trailing Earnings
30 Yr Equivalent
S&P Composite
28.49
19.00
33.31%
926.54
30 YR CAPE
Current P/E =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
1
10
100
1000
1
10
100
1000
1880 1900 1920 1940 1960 1980 2000 2020
P/E with 30-Year Trailing Earnings
30 Yr Equivalent
S&P Composite
38.78
27.2529.74%976.06
30 YR Nominal
Current P/E =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
7/31/2019 CFMV-Q1-12 Rev
14/191
5 year Monthly Price divided by Earnings Average
10 Year Monthly Price divided by Earnings Average
1
10
100
1000
1
10
100
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 =
Over/ Under Valued =
S&P Equivalent =
1
10
100
1000
1
10
100
1000
1860 1880 1900 1920 1940 1960 1980 2000 2020
10 Year Monthly P/E
10 Yr Monthly PE Equivalent
S&P Composite
10 YR Trailing Earnings
Current P/E =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
28.0715.1645.99%750.35
7/31/2019 CFMV-Q1-12 Rev
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15 Year Monthly Price divided by Earnings Average
20 Year Monthly Price divided by Earnings Average
1
10
100
1000
1
10
100
1000
1860 1880 1900 1920 1940 1960 1980 2000 2020
15 Year Monthly P/E
15 Yr Monthly PE Equivalent
S&P Composite
15 YR Trailing Earnings
Current P/E =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
28.0715.1645.99%750.35
1
10
100
1000
1
10
100
1000
1880 1900 1920 1940 1960 1980 2000 2020
20 Year Monthly P/E
20 Yr Monthly PE Equivalent
S&P Composite
20 YR Trailing Earnings
Current P/E =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
26.2214.7543.76%781.31
7/31/2019 CFMV-Q1-12 Rev
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30 Year Monthly Price divided by Earnings Average
5 Year Earnings Yield
1
10
100
1000
1
10
100
1000
1880 1900 1920 1940 1960 1980 2000 2020
30 Year Monthly P/E
30 Yr Monthly PE Equivalent
S&P Composite
30 YR Trailing Earnings
Current P/E =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
22.1614.3835.09%
901.79
1
10
100
1000
10000
1
10
100
1000
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 =
Over/ Under Valued =
S&P Equivalent =
7/31/2019 CFMV-Q1-12 Rev
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10 Year Earnings Yield
15 Year Earnings Yield
1
10
100
1000
10000
1
10
100
1000
10000
1860 1880 1900 1920 1940 1960 1980 2000 2020
Earnings Yield - 10 Yrs Average VS Long Term Average
10 Yr Earnings Yield
S&P Composite
4.01%
6.29%
36.17%
886.76
Earnings Yield - 10 YR Avg
Current Earnings Yield =
Long Term Average =
Over / Under Valued =
S&P Equivalent =
1
10
100
1000
10000
1
10
100
1000
10000
1860 1880 1900 1920 1940 1960 1980 2000 2020
Earnings Yield - 15 Yrs Average VS Long Term Average
15 Yr Earnings Yield
S&P Composite
3.69%
5.81%
36.55%
881.42
Earnings Yield -15 YR Avg
Current Earnings Yield =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
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20 Year Earnings Yield
30 Year Earnings Yield
1
10
100
1000
10000
1
10
100
1000
10000
1860 1880 1900 1920 1940 1960 1980 2000 2020
Earnings Yield - 20 Yrs Average VS Long Term Average
20 Yr Earnings Yield
S&P Composite
3.24%
5.39%
39.85%
835.68
Earnings Yield - 20 YR Avg
Current Earnings Yield =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
1
10
100
1000
10000
1
10
100
1000
10000
1860 1880 1900 1920 1940 1960 1980 2000 2020
Earnings Yield - 30 Yrs Average VS Long Term Average
30 Yr Earnings Yield
S&P Composite
2.59%
4.58%
43.49%
785.03
Earnings Yield - 30 YR Avg
Current Earnings Yield =
Long Term Average =
Over/ Under Valued =
S&P Equivalent =
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CFMV 1871 to present
CFMV 1950 to present