The Intrinsic Value of the Dow:
This Time with Feeling!
P Dunne, J Forker, A Zholos
Seminar: Trinity College Dublin – Nov 2009
Motivation
• The stock market and sentiment?
– Asset pricing theory weak on sentiment…
– Fundamental valuation...Lee et al.(1999)
• ignores sentiment and ambiguity
– Irrational exuberance….Shiller (1981, 1990, 2005)
• Excess volatility puzzle
– Bubbles spill-over…… Prado & Qin (2009)
Mon-policy / asset price debate
Bernanke & Gertler (2001), concluded that;
• Central Banks should set interest rates in response to
forecast inflation and the output gap, but that they
should not react directly to movements in asset prices.
Other views:The Cecchetti report states that;
– (i) Central Banks can achieve superior performance by
adjusting policy instruments in response to asset prices
with the caveat that an understanding as to why asset
prices have changed is required
– (ii) “asset price misalignments may be difficult to
measure, but this is no reason to ignore them.”
Can fundamental analysis help?
• Can we use fundamental analysis along with
measures of sentiment and risk to explain
“why asset prices have changed”?
• Disagreement exists about how to do
fundamental analysis and even about capital
asset pricing
Capital Asset Pricing
• CAPM assumes a single risk factor
• But alternatives in favour today
– APT
– Fama-French 3 Factor model
– Campbell “Good Beta, Bad Beta”
• It would be good if CAPM worked
– Advantage of ‘Single factor’ and ‘single risky
portfolio’ for investment
– Fewer unknown parameters so easier to use it for
fundamental analysis
Sentiment
– Can we separate sentiment effects from
fundamentals?
– Can Sentiment be represented
– A risk Factor?
– A control variable?
– An ECM term?
– An instrument for risk aversion?
What we do!
• Propose and test a method to obtain a risk
premium that is clean of sentiment (or
uncertainty effects).
• To do this we must appeal to;
– a reinstatement of the CAPM,
– the idea of ‘Bellwether stocks’,
– various ex-ante variables that are seldom used in
fundamental analysis.
Estimates of risk premium
Eit
Eit 1
Pit 

 ...
2
1  rf t  it premt 1  rf t 1   it 1 premt 
Eit
Pit 
rf t   it premt  git
If we assume earnings follow random walk
Plus drift g
E = Monthly IBES analysts core earnings expectations
rf = Risk free rate
 = Forward Looking betas for each firm each period from Options see. Christensen et al.
Estimates of risk premium
Market beta=1
Pmkt ,t 
EMkt ,t
rft *  premt  g Mkt ,t
rf *= Risk free rate adjusted for expected dividend yield
Estimates of risk premium
Market beta=1
Pmkt ,t 
EMkt ,t
rft *  premt  g Mkt ,t
Solve for premium given other info
And assuming a random walk Earnings
rf *= Risk free rate adjusted for expected dividend yield
Backed-out premium for the market: Jan 1996 – Mar 2004
0.075
PREMM
0.050
0.025
0.000
-0.025
20
40
60
80
100
120
This premium is not right!
• It becomes negative?
• It is too variable
• It has the wrong relationship with systematic
volatility
• VIX is a measure of risk implied by option on the S&P
index
• It should be a good indicator of the amount of
systematic risk in existence
Backed-out premium for the market: Jan 1996 – Mar 2004
0.075
PREMM
VIX
0.050
0.025
0.000
-0.025
20
40
60
80
100
120
Decline in implied risk premium could simply reflect an over-valued market
Inverse of the VIX index against the implied risk-premium from market index
0.075
0.10
PREMM
VIX
1/
0.09
0.050
0.08
0.07
0.025
0.06
0.05
0.000
0.04
0.03
-0.025
0.02
20
40
60
80
100
120
So the risk-premium associated with market index is
probably missing control variables or the market is
contaminated by sentiment/uncertainty/ambiguity/bubble
• Using Market premium will miss-value most
stocks
• It is also difficult to get a reliable ex-ante beta
for most stocks
• Most stocks are not well described by the
simple CAPM
– Could this just be reflecting the contamination
from sentiment?
Support for alternative…
• Option-implied beta is source of accurate ex-ante
beta for stocks immune to sentiment…
» Lemmon & Ni (2008)
• In certain regimes the simple CAPM works…..
» Chung & Yeh (2009)
• Perhaps there exists an “easy-to-value” assets with
insignificant sensitivity to other factors/sentiment
» Baker & Wurgler (2007) + Epstein & Schneider(2006)
• The stock we found to be best source of a reliable
risk premium is a well known ‘bellwether’ stock
‘CAT’
Conditions required for sentiment free
implied premium
•
•
•
•
“Easy-to-value” asset…..‘Bellwether’
Unaffected by market sentiment & other factors
For which a CAPM single-factor model fits
One for which an accurate ex-ante, forward
looking beta can be estimated from options
• One for which the permanent-transitory
decomposition of earnings is reliable
“Asset-specific” implied premium
Eit
Pit 
rft  it premit  git
Solve, given Earnings Forecast
“Asset-specific” implied premium
We have monthly IBES ‘core’ earnings forecasts (2 year ahead)
Eit
Pit 
rft  it premit  git
“Asset-specific” implied premium
Eit
Pit 
rft  it premit  git
We obtained ‘option implied’ betas for the stocks in the DJ 30 Index
Source: Christoffersen et al., (2008)
Option implied betas
• Chang, Chrisstoffersen, Jacob & Vainberg (2009)

Option Implied
i,t
 SKEW

 SKEW

OI
i ,t
OI
m ,t
1/ 3



 VAR

VAR

These may suffer from slight bias due to the fact that they are
derived under the assumption of risk-neutrality….
OI
i ,t
OI
m ,t
1/ 2



Example of “option-implied beta”
Option Implied Beta for Caterpillar
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
40
50
60
70
80
90
100
110
120
130
“Asset-specific” implied premium
But earnings forecasts are not just a random walk!
Eit
Pit 
rft  it premit  git
“Asset-specific” implied premium
And dividend policy matters!
Eit
Pit 
rft  it premit  git
Assume growth = an estimated drift?
Decomposition of earnings forecast
Random walk + noise + measurement error
– UC “trend-cycle” model
– Method: Kalman Filter
The decomposition is important for what comes out as the implied premium!
Transitory doesn’t contribute as much to value as permanent
High persistence of shocks to transitory will give them greater role
Decomposition of earnings forecast
IBES
it
E

 Eit  E  measurement error
c
it
Eit    Eit 1  t
t ...iid  0,   
 ( L) E   ( L) t
 t ... iid  0,  


c
it
2
2

Cov t ,  t  s     for s  0 and 0 otherwise
Decomposition of monthly earnings
• We apply a Kalman Filter to this unobserved
components model
• The decomposition is sensitive to assumptions
about Cov t ,  t  s 
• We applied this to a stock that gave promising
results using a more simple ARIMA modelling
• We end-up selecting a UC-ARMA(1,12)
The Earnings Data - Caterpillar
3.0
IBES_CAT
EARN_REPORTED_CA
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
20
40
60
80
100
120
E  E
c
it
c
it 1
Drift terms

i
 2
 2
  t  1 t 1  ....  12 t 12
Log “Trend component” and log forecast earnings
0.96
ADJTRENDD
ADJLEF2
0.80
0.64
0.48
0.32
0.16
0.00
-0.16
-0.32
20
40
60
80
100
Persistent transitory deviations from stochastic trend
120
Valuing the 2 Earnings components

Eit
Pit  .
rf t   it premit  g it

c
it  j
E
1  rft  it premit 
j
The stationary part must be projected forward at each valuation time
The backed-out “CAT” premium
0.14
PREMCAT
0.12
0.10
0.08
0.06
0.04
0.02
0.00
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
PremCAT Vs PremMKT
0.150
PREMCAT
PREMMKT
0.125
0.100
0.075
0.050
0.025
0.000
-0.025
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
PremCAT Vs inverse-VIX
R²=0.13
0.144
45
PREMCAT
VIX
0.128
40
0.112
35
0.096
30
0.080
25
0.064
20
0.048
15
0.032
10
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
PremCAT on sent-index (various)
• R²=0.000
• Tried various non-linear transformations of
sentiment
Recall
• These are both timely “ex-ante” premia!
• So they would be sensitive to change in
forecasts of fundamentals, changes from
option implied betas and changes in the price
of the bellwether equity pricing.
• Variables that can be monitored “real-time”
Back to accounting valuations
• Using a fundamental valuation approach with
1.
2.
3.
4.
Premium based on CATERPILLAR
Premium based on MKT
What does sentiment variable add?
Does it matter if we use other controls?
Fama-French?
Simple empirical model
• Step 1: Cointegration
ln Pit  coni  trendi (t )   ln eit  ln  rft  betait premt    vit
Monthly IBES core FY2 earnings
Risk free rate – expected div yield
FL betas for each firm each period
Backed out for CAT
Simple empirical model
• Step 1: Cointegration with sentiment
ln Pit  coni  trendi (t )   ln eit  ln  rf t  betait premt  
 i Sentat  vit
CAT
R²=0.842,
with sentim ent R²=0.844
45
Price
Valuation
40
Valuation with sentiment
35
30
25
20
15
10
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
BA
R²=0.292,
with sentim ent R²=0.603
70
Price
Valuation
Valuation with sentiment
60
50
40
30
20
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
45
40
AA
AIG
R²=0.575, with sentiment R²=0.711
R²=0.607, with sentiment R²=0.726
P rice
V aluation
V aluation w ith sentiment
120
100
P rice
V aluation
V aluation w ith sentiment
35
80
30
60
25
20
40
15
20
10
0
5
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
64
56
AXP
JPM
R²=0.472, with sentiment R²=0.586
R²=0.180, with sentiment R²=0.326
60
P rice
V aluation
V aluation w ith sentiment
P rice
V aluation
V aluation w ith sentiment
50
48
40
40
32
30
24
20
16
10
8
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
70
60
C
DIS
R²=0.655, with sentiment R²=0.750
R²=0.088, with sentiment R²=0.264
45
P rice
V aluation
V aluation w ith sentiment
40
50
35
40
30
30
25
20
20
10
15
0
10
1994
1995
90
80
P rice
V aluation
V aluation w ith sentiment
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
KO
DD
R²=0.155, with sentiment R²=0.148
R²=0.253, with sentiment R²=0.245
80
P rice
V aluation
V aluation w ith sentiment
70
2001
2002
2003
2001
2002
2003
P rice
V aluation
V aluation w ith sentiment
70
60
60
50
50
40
40
30
30
20
20
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
45
40
XOM
GM
R²=0.528, with sentiment R²=0.594
R²=0.344, with sentiment R²=0.420
100
P rice
V aluation
V aluation w ith sentiment
90
35
80
30
70
25
60
20
50
15
40
10
30
1994
1995
70
60
P rice
V aluation
V aluation w ith sentiment
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
GE
HPQ
R²=0.399, with sentiment R²=0.549
R²=0.137, with sentiment R²=0.380
72
P rice
V aluation
V aluation w ith sentiment
64
2001
2002
2003
2001
2002
2003
P rice
V aluation
V aluation w ith sentiment
56
50
48
40
40
30
32
20
24
10
16
0
8
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
JNJ
R²=0.819, with sentiment R²=0.817
72
64
MRK
R²=0.183, with sentiment R²=0.301
100
P rice
V aluation
V aluation w ith sentiment
90
P rice
V aluation
V aluation w ith sentiment
80
56
70
48
60
40
50
32
40
24
30
16
20
8
10
1994
1995
50
45
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
MCD
MSFT
R²=0.093, with sentiment R²=0.268
R²=0.549, with sentiment R²=0.646
64
P rice
V aluation
V aluation w ith sentiment
56
40
48
35
40
30
32
25
24
20
16
15
8
10
2001
2002
2003
2001
2002
2003
P rice
V aluation
V aluation w ith sentiment
0
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
90
80
MMM
MO
R²=0.824, with sentiment R²=0.830
R²=0.219, with sentiment R²=0.222
60
P rice
V aluation
V aluation w ith sentiment
55
P rice
V aluation
V aluation w ith sentiment
50
70
45
60
40
50
35
30
40
25
30
20
20
15
1994
1995
50
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
PFE
PG
R²=0.521, with sentiment R²=0.530
R²=0.352, with sentiment R²=0.380
55
P rice
V aluation
V aluation w ith sentiment
50
40
2001
2002
2003
2001
2002
2003
P rice
V aluation
V aluation w ith sentiment
45
40
30
35
30
20
25
20
10
15
0
10
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
60
55
SBC
VZ
R²=0.048, with sentiment R²=0.320
R²=0.161, with sentiment R²=0.357
70
P rice
V aluation
V aluation w ith sentiment
P rice
V aluation
V aluation w ith sentiment
60
50
45
50
40
40
35
30
30
25
20
20
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
UTX
45
1999
2000
2001
2002
2003
2001
2002
2003
WMT
R²=0.747, with sentiment R²=0.818
50
1998
R²=0.786, with sentiment R²=0.805
80
P rice
V aluation
V aluation w ith sentiment
70
P rice
V aluation
V aluation w ith sentiment
40
60
35
30
50
25
40
20
30
15
20
10
5
10
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
1994
1995
1996
1997
1998
1999
2000
Step 2: ECM
• Using the ECM terms from step 1
– Assuming that contemporaneous earnings shocks
can be included –i.e., weak exogeneity
– including dummy for end-year effects
– ECM terms are negative and significant
– Explanatory power good
– Sentiment seems to be another driver of returns
in path to equilibrium
ECM
ln Pit  coni  i1 ln Pit 1  i 2 ln Pit 2  ....
i1 ln 1  eit /  rft  betait premt  
i 2 ln 1  eit 1 /  rft 1  betait 1 premt 1    .....
 i ECM it 1
i sentat 1
 it
ECM R²
•
•
•
•
•
•
•
Without sentiment
AXP
0.043
HPQ
0.113
HD
0.081
IBM
0.015
MCD
-0.008
MSFT 0.683
With sentiment
0.116
0.166
0.100
0.033
0.032
0.886
RIM
• Present value of discounted income flows in
excess of the required return on capital (BV).
• Lee (1999) considers the cointegration relation
between this V and the Stock Market Value.
• The deviation (V-P) is an ecm term that drives
future returns.
• For individual stocks we can perform analysis
of the role of sentiment dissequilibrium
More for the future
• Earnings-Decomposition approach
– Robustness check regarding correlated
trend/stationary components
• How does sentiment disequilibrium relate to
future earnings?
– Perhaps sentiment predicts long-run fundamentals
• Proper analysis of causality
• Characteristics of stocks give “sentiment sensitivity”?
• Ambiguity/complexity/uncertainty
Other ECM representations…
• Threshold error-correction-terms?
– It could be that sentiment effects are like a trend
with occasional breaks
– Updating the work of Campbell et al…and of Lee
et al.
• Proper instrumenting for endogeneity of sent
So what?
• We argue the sentiment component can be identified.
• The bellwether premium is very stable
– Risk-aversion quite stable and close to typical assumed 8%
• This could be a valuable input into investment decisions
– Would help to stabilize or “ground” valuations and make the
market less prone to sentiment related bubbles.
• Could be helpful for policy makers trying to spot
when the market is over-valued due to
sentiment
Company list
AA
AXP
AIG
BA
CAT
JPM
C
KO
DIS
DD
XOM
GE
GM
HPQ
ALCOA INC
AMERICAN EXPRESS CO
AMERICAN INTL
BOEING CO
CATERPILLAR
J P MORGAN
CITIGROUP INC
COCA COLA CO
DISNEY WALT CO
DU PONT
EXXON MOBIL
GENERAL ELEC CO
GENERAL MTRS CORP
HEWLETT PACKARD CO
HD
HON
INTC
IBM
JNJ
MCD
MRK
MSFT
MMM
PFE
MO
PG
SBC
UTX
VZ
WMT
HOME DEPOT INC
HONEYWELL
INTEL CORP
IBM
JOHNSON & JOHNSON
MCDONALDS
MERCK & CO
MICROSOFT
3M CO
PFIZER INC
ALTRIA GROUP INC
PROCTER & GAMBLE
SBC COMM INC
UNITED TECH
VERIZON
WAL MART