Slides of a paper entitled "Portfolio Diversification Dynamics: a New Measure of Investor Sentiment".

1. Portfolio Diversi…cation Dynamics of Individual Investors:
a New Measure of Investor Sentiment
Patrick ROGER
LARGE Research Center, EM Strasbourg Business School, University of Strasbourg
MFA, New Orleans, February 2012
MFA, New Orleans, February 2012 1/
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2. Purpose of the paper
Introduction of a new measure of investor sentiment
(optimism/pessimism beyond usual risk factors)
Prediction of returns of long-short portfolios based on size (small
stocks are more sentiment-prone)
Comparison with other measures of sentiment
Robustness checks
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3. Intuition and facts
Measures of sentiment
- Surveys: INSEE, University of Michigan, AAII
- Macroeconomics (Baker and Wurgler, 2006, 2007): IPOs, Turnover,
share of equity issues, CEFD, NBER recessions
- Buy-Sell imbalances (Disequilibrium between purchases and sales),
Kumar and Lee, 2006
Individual portfolios are underdiversi…ed
Odean (1999), Mitton and Vorkink (2007), Kumar (2007), Goetzman
and Kumar (2008), Calvet et al. (2007), Roger et al. (2011)
Buying a new stock when two stocks are held reveals more optimism
than buying when …fty stocks are already held
Sentiment can change quickly over time
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4. Summary
A new measure of investor sentiment
- Diversi…cation dynamics as a Markov chain
- Steady-state equilibrium of diversi…cation levels
- The market sentiment index (MSI)
Empirical study
- Data and descriptive statistics
- Multi-factor model and predictive regressions
Concluding remarks
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5. Dynamics of diversi…cation levels
K stocks are traded by I investors
Nt = number of di¤erent stocks held by an investor at date t.
Transition matrix
81 k K , 81 m K , Qt (k, m ) = P (Nt = m jNt 1 = k ) (1)
Assumption: the Markov chain is homogeneous, that is Qt does not
depend on t
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6. Steady-state equilibrium and Market Sentiment Index
If the chain is irreducible (two states always communicate) and
aperiodic (the greatest common divisor of return times is 1), there
exists a steady-state distribution given by any line of limn !+∞ Qtn .
The equilibrium distribution is independent of initial diversi…cation
levels
Estimation of Qt (k, m )
∑ i =1 1 f N + =m g f N =k g
I
i i
t 1 t
Qt (k, m ) = (2)
∑ i =1 1 f N =k g
I
i
t
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7. The Market Sentiment Index
De…nition
For a transition matrix Qt between t 1 and t, denote N∞,t the random
variable "number of di¤erent stocks" in the steady-state equilibrium. The
investor sentiment index MSIt is de…ned by:
1 (P (N∞,t k ) + P (N∞,t k + 1))
1 ∑ k =1
K 1
MSIt = 1 (3)
K 2
De…nition
The orthogonalized MSI (denoted MSI ? ) is the residual of the regression
MSIt = α0 + αMkt RMRFt + αS SMBt + αH HMLt + αM MOMt + εt (4)
where RMRFt is the market factor, SMBt is the size factor, HMLt is the
book-to-market factor (Fama-French factors, 1992) and MOMt is the
momentum factor (Carhart, 1997)
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8. The Sentiment Seesaw (Baker-Wurgler, 2007)
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9. Empirical study : data
Individual investors (Cortal Consors)
- 87,373 investors on 1999-2006 (account value > 100e)
- 8,258,809 trades on stocks
- A "photograph" of portfolios is taken every month
Prices and returns
- Euro…dai for French stocks...and some other European stocks
(traded on Euronext)
- Bloomberg for other stocks (especially US stocks)
- Euro…dai for FF factors and size portfolios
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10. Empirical study : descriptive statistics
Me dia n (da she d) a nd Me a n(Bold) Portfolio Va lue a ndNum be r of Stoc ks (Dotte d)
4
x 10
7
6
5
4
3
2
1
0
0 10 20 30 40 50 60 70 80 90 100
Mo n th
Figure: The three curves represent respectively the time-series of the average
number of stocks held by investors, and the mean and median portfolio value.
The period under consideration starts in January 1999 (month 1) and ends in
December 2006 (month 96). The upper dotted curve is the average number of
stocks ( 104 ). The middle bold curve is the average portfolio value and the
lower curve is the median portfolio value.
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11. Empirical study : descriptive statistics (cont.)
4
x 10
12
11
Number of monthly trades (Buys = Solid line, Sales=Dashed line)
10
9
8
7
6
5
4
3
2
0 10 20 30 40 50 60 70 80 90 100
Month
Figure: Time-series of the number of monthly trades. The solid (dashed) line
represents the evolution of purchases (sales) MFA, New Orleans, February 2012 11 /
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12. Multi-factor approach
Baker-Wurgler (2006) methodology
RSc ,t RBc ,t = a + bSENTIMENTt 1 + εt (5)
where SENTIMENTt is the sentiment index for month t and may be
FSI , BW 1,BW 2, MSI ,BSI ,MSI ? or BSI ? .
In the second step, we control for Fama-French and Carhart factors
(except the size factor since the long-short portfolio is based on size). The
regression model is then the following:
RSc ,t RBc ,t = c + dSENTIMENTt 1 + βRMRFt + hHMLt + mMOMt + εt
(6)
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13. Multi-factor approach
Column BW 2 deleted for "reading"!
Panel A: Equation 5 without controls
? ?
FSI BW 1 MSI BSI MSI BSI
b 0.001 0.007 0.054 0.145 0.068 0.154
t-stat 1.324 1.365 2.069 1.95 2.784 2.06
p-val 0.189 0.176 0.041 0.054 0.007 0.041
2
R 0.008 0.006 0.071 0.054 0.102 0.056
Panel B: Equation 6 with controls
d 0.00 0.011 0.035 0.14 0.054 0.145
t-stat 2.09 2.97 1.44 2.29 2.378 2.24
p-val 0.04 0.004 0.153 0.024 0.019 0.027
2
R 0.22 0.225 0.211 0.238 0.246 0.236
Table: Coe¢ cients of sentiment when regressing the returns of a long-short
portfolio based on size, on sentiment measures (with Newey-West consistent
estimates). Panel A gives the coe¢ cient of sentiment inMFA, New Orleans, February 2012
the simple regression: 13 /
PR (EM Strasbourg Business School) Sentiment 16

14. Robustness checks
Eq. 5 without control Eq. 6 with control
K = 10 MSI MSI ? MSI MSI ?
b 0.052 0.073 0.034 0.06
t-stat 1.93 3.02 1.43 2.77
p-value 0.057 0.003 0.157 0.007
2
R 0.061 0.105 0.208 0.253
K = 20 MSI MSI ? MSI MSI ?
d 0.054 0.068 0.035 0.054
t-stat 2.069 2.784 1.442 2.378
p-value 0.041 0.007 0.153 0.019
2
R 0.071 0.102 0.211 0.246
K = 30 MSI MSI ? MSI MSI ?
d 0.054 0.064 0.035 0.049
t-stat 1.99 2.99 1.33 2.018
p-value 0.05 0.014 0.186 0.047
2
PR
R
(EM Strasbourg Business School)
0.068 0.089
Sentiment
0.209 New 0.236February 2012
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16

15. Robustness checks (cont.)
Without control With control
W > 100 MSI MSI ? MSI MSI ?
b 0.054 0.067 0.035 0.054
t-stat 2.06 2.78 1.43 2.38
p-value 0.041 0.006 0.153 0.019
2
R 0.081 0.102 0.211 0.246
W > 1, 000 MSI MSI ? MSI MSI ?
d 0.056 0.070 0.038 0.056
t-stat 2.10 2.88 1.53 2.49
p-value 0.038 0.005 0.13 0.015
2
R 0.072 0.105 0.214 0.249
W > 5, 000 MSI MSI ? MSI MSI ?
d 0.059 0.073 0.043 0.06
t-stat 2.16 2.96 1.74 2.63
p-value 0.033 0.004 0.085 0.01
2
R 0.071
PR (EM Strasbourg Business School)
0.103
Sentiment
0.219 0.252
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16

16. Concluding remarks
All trades are not informationally equivalent to reveal sentiment
Diversi…cation dynamics and the Markov chain technology are good
ways to measure sentiment despite the fact that prices, returns and
trading volumes are not taken into account
Tests on other data are necessary (especially after 2006)
Disposition e¤ect (selling winners, keeping losers) may be taken into
account by a two-regime model
MFA, New Orleans, February 2012 16 /
PR (EM Strasbourg Business School) Sentiment 16