Experimental Finance
Behavioral Finance
Week 5
Read Muradoglu, 2001
Muradoglu et.al. 2005
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Why Experimental Methodology?
Limitations of Share Price Data
Controlled Design
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Muradoglu,2001
Motivation
Efficient Markets Hypothesis, Fama
Overreaction Hypothesis, DeBondt and
Thaler
Experimental work by DeBondt, 1993
If investors are positive feedback traders, they will
expect past trends to continue in the future
Anchors used will be determined by past price
changes and past price levels
Confidence interval assessments will not be
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symmetric
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Limitations of DeBondt,1993
DeBondt experiments
conducted by student subjects
“… an acceptable proxy for the typical investor?”
quasi experimental design
“…does not control for other factors than past
price”
forecasts of various stock indexes and FX
real time forecast of specific stocks?
Short term forecast horizons
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Purpose of
Muradoglu,2001
To investigate if return expectations and
risk perceptions of investors are
adoptive?
If so, what is the expectation formation
process and hedging behaviour?
Is it similar for
stock market professionals versus novices
real-time stock price forecasts versus
• real-time stock index forecasts
• unknown calendar time, unnamed stock forecasts
different forecast horizons
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Research Design and Procedure
Subjects
Student subjects, 45
19 MBA, 26 undergraduates
exposed to EMH and financial forecasting
Professionals in stock market, 35
all licensed brokers
working for brokerage houses
15 prepare research reports
20 managing funds and giving advice
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Research Design and Procedure
Folder for response forms
Info about the study
Price series for unnamed stocks
in graphical and tabular form
Response sheets for unnamed stocks
Response sheets for real-time forecasts
stock index
eight stocks of respondents’ choice
Questionnaire
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Research Design and Procedure
Task
Give point and interval forecasts



I estimate the Friday closing price, one week from now as...............................................pence
The probability that the Friday closing price one week from now is greater than..........pence is 10%.
The probability that the Friday closing price one week from now is less than...............pence is 10%.
For forecasting prices of
unnamed stocks, stock index,specific stocks
 For forecast horizons of
one, two, four and twelve weeks (Long Term?)
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Measurement
Expected price change
EPCi is the difference between the subject's (k)
point forecast of a stock (j) for a forecast
horizon of (i=1,2,4,12) weeks (Fijk) and the
last known price level (P0)
EPCi = Fijk- P0
The average EPCi is calculated as EPCi
=jkEPCijk
DeBondt findings indicated
• EPC
• EPC
• EPC
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0
i, bear < 0
i, bull  EPC
i, bull
i, bear
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Measurement
Risk Perceptions
Confidence intervals
UCIijk = Hijk – Fijk
LCIijk = Lijk – Fijk
Mean Skewness
Si = jk (UCIijk - LCIijk)
DeBondt Findings indicated
S
S
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i, bull
i, bull
<0, S i, bear >0
< S i, bear
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Tests for differences
Expected price changes and skewness
coefficients are normalised by dividing to
matching standard deviations
t-statistics used for differences in means
comparisons of
bull versus bear markets
unnamed stocks, versus index, actual
stocks
experts versus novices
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LT versus ST forecast horizons
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Results
Extrapolate the series and hedge forecasts
EPC i, bull  0, EPC i, bear < 0 , EPC i, bull  EPC i, bear
S i, bull <0,
S i, bear >0,
S i, bull < S i, bear
Experts behave like this for
• unnamed stocks and unknown calendar time
– short forecast horizons of 1,2,4 weeks
• real time index forecasts
– short horizons of 1, 2 weeks
Experts are optimistic otherwise!
Novices are optimistic!
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Muradoglu,2001
Bull Market
Bear Market
For unknown stocks and short forecast horizons
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Results
Immaculate Optimism
EPC i, bull  0, EPC i, bear >0 , EPC i, bull  EPC i, bear
S i, bull >0,
S i, bear >0,
S i, bull > S i, bear
Experts are optimistic for
• Long horizons in forecasts of
– unnamed stocks, Index, Specific stocks
Novices are optimistic for
• All forecast horizons for
– real time forecasts of Index and specific stocks
– unknown stocks - insignificant (?)
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Muradoglu, 2001
 Bull Market
Bear Market
Immaculate Optimism!!!
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Results
Hedging Speculations
Trend followers in bull markets have positive but
smaller skewness coefficients than contrarians
• for short horizons of
– 2 weeks for index - experts
– 1 week for specific stocks - novices
Trend followers in bear markets have positive and
larger skewness coefficients than contrarians
• for long horisons of
– 4, 12 weeks for unnamed stocks - experts
– 12 weeks for index - novices
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Muradoglu, 2001
 Bull Market
Bear Market
Trend Followers versus Contrarians
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Results
Experts versus novices
stocks traded at the stock exchange
Bear market EPC of experts < EPC novices
Bull market skewness of experts > skewness novices
• Experts more optimistic in price reversals in bear markets
• and hedge better on the continuation of a bullish trend
May be one reason for high volatility in the market ?
Maybe anchor for adjustment is the last price, NOT
the price change ?
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Muradoglu, 2001
 Bull Market
Bear Market
Novices
Experts
Novices versus Experts
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Results
Different forecast horizons
For unknown stocks
EPC is higher for longer horizons
S is higher for longer horizons
For index
In bull market EPC is lower for longer horizons
In bear market EPC is higher for longer horizons
In bear market S is lower for longer horizons
For stocks traded at the exchange
EPC is higher for longer horizons
S is higher for longer horizons
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Discussions
Results are different from DeBondt mainly
due to
the presence of contextual information
the trends in the stock market
participants level of expertise
forecast horizon
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Discussions
Real-time, real-task forecasting behaviour
is different!
Many factors involved
Task complexity increases exponentially
Sometimes not possible to duplicate in
experimental setting
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Discussions
Immaculate optimism
Subjects extrapolate bullish trends and
expect price reversals in bearish trends
Optimists exaggerate their talents!
Underestimate likelihood of bad outcomes!
Optimism accompanied by overconfidence!
Source of high volatility (?)
Source of various inefficiencies (?)
Due to selection bias? - Optimism again!
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Discussions
Different decision-making processes may
be at work at different occasions!
Actual heuristic might be
price change? Unnamed stocks?
the last observation? Bull markets?
long term mean? Bear markets?
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Discussions
Behavioural assumptions of the EMH must
be treated with caution!
Variations in risk premia should not only
be explained by traditional risk measures!
Risk perceptions might differ across ….
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Discussions
Melding psychological and financial
research is necessary for a better
understanding of financial markets!
Financial Theory must be based on
more realistic assumptions of human
behaviour!
Further research ?
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Muradoglu, et.al. 2005
 Motivation
 Morkowitz, 1959
mean - variance efficient portfolios
estimations of expected risk and return from past
returns
expectation formation process is assumed to be
rational
 We use subjective forecasts of investors to represent
expected prices
and related variance - covariance matrix.
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Muradoglu, et.al. 2005
Purpose:
To investigate the portfolio performance of
subjective forecasts given in different forms
expectation formation process is based on
subjective forecasts rather than past prices
and
human behavior is integrated into financial
modeling.
Performance compared to that of the
standard approach of time series data.
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Muradoglu, et.al. 2005
 Contributions-1
 Literature on forecasting studies focus on
accuracy;
Yates et.al. 1991
 Muradoglu and Onkal, 1994
biases
Muradoglu, 2002
De Bondt, 1993
Andreassen, 1990
 We focus on portfolio performance
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Muradoglu, et.al. 2005
 Contributions-2
 Port folio performance studies focus on
export managed funds
Ippolito, 1989
standard tests of market efficiency
Fama, 1991
 We focus on subjective forecasts of experts
 we investigate expert subjects revealing judgement in
different formats
 findings robust to task format.
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Muradoglu, et.al. 2005
Research Design
31 experts working for bank affiliated brokerage houses.
Reached at company - paid 20 hours training programs.
All licensed as brokers
Managing funds
giving investment advice to corporate and private clients
preparing research reports
 No monetary/non monetary bonuses offered
 An opportunity to forecast stock prices and reveal uncertainty
in different formats.




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Muradoglu, et.al. 2005
Procedure
Participants were given a folder containing
three forms:
Information about purpose of study
Response sheets for real time forecasts
Questionnaire about participants’ experience
in stock market trading,
its duration and
information sources utilized.
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Muradoglu, et.al. 2005
Response forms
Same as you have
Task was defined as giving
point forecasts
interval forecasts
probabilistic forecasts
For
a horizon of one week
25 compromises listed as ISE
highest volume of trade during previous years
easy to follow, reduces task complexity
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Muradoglu, et.al. 2005
Method
We estimate the efficient frontier
using three sets of data
representing three sets of expectation formation
processes.
“Historical Efficient Frontier”
• Historical distribution of stock returns
“Best estimate efficient Frontier”
• point and interval estimates of experts.
“Probabilistic Efficient Frontier”
• probabilistic forecasts of experts
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Historical Efficient Frontier



Min 2(RH)
subject to
E(RH) = K
where
2(RH) the variance
E(RH) mean of the historical
values of the stock portfolios
K different levels of the mean
Rit 
Pit  Pit 1
Pit 1
N
E ( Ri ) 
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R
t 1
N
it
 w1 
w 
E ( RH )  E ( R1 ) E ( R2 )  E ( RN )  2   RW
 
 
 wN 
 2 ( RH )  w1 w2  wN 
 11  12    1N 

  w1 

  w2 

    W  W

  

 w 

  N 
•R' is the (1XN)row vector of expected returns,
•W is (NX1) column vector of weights held in each asset
•sum of weights add up to one
•and negative weights are not allowed,
•  is the (NXN) variance-covariance matrix
•Expected returns and variance-covariance matrix
• calculated using the last 24 weeks Friday closing prices
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Best Estimate Efficient Frontier
Min 2(RB)
subject to E(RB) = K

2(RB) and E(RB) are calculated from point and interval forecasts as:
E ( Ri j ) 
 ii 




PFijt  Pit 1
Pit 1
[(UIFijt  Pit1 ) Pit 1 ]  [( LIFijt  Pit 1 ) Pit 1 ]
2
UIFijt is the price level for which forecaster j assigns a 2.5% probability that the actual price of
stock i will turn out higher,
LIFijt is the price level for which forecaster j assigns a 2.5 % probability that the actual price of
stock i will turn out to be lower than her/his time t price estimate.
The experiment is designed such that the above distance corresponds to the two standard
deviations assuming that the distribution of returns implied by forecasters is normal.
Off-diagonal covariance terms are calculated from historical returns
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Consensus Best Estimate
Efficient Frontier
In the consensus forecast expected return E(Ri) and variances (ii) are
calculated as follows:
 E(R )
ij
E ( Ri ) 
j
J
[ AUIFit  Pit 1 ) Pit 1 ]  [( ALIFit  Pit 1 ) Pit 1 ]
2
where
 ii 
UIF
ijt
AUIFit 
j
J
and
 LIF
ijt
ALIFit 
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j
J
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Probabilistic Efficient Frontier
subject to



Min 2(RP)
E(RP) = K
2(Rp) and E(Rp) are the variance and mean
calculated from the probabilistic forecasts
it is difficult to assume normality of distributions
revealed by each forecaster
therefore we decided to form a consensus
distribution by averaging the probabilities assigned
to each interval by different forecasters for each
N
stock as follows.
CPFI ji   PFI jin
n 1
• Therefore we used intervals correspond to
losses larger than 3% on a weekly basis.
• We formed the implied consensus normal
distribution for each stock using the following
optimization procedure.
Max
E ( RPi )   ii
Subject to F (6)  CPFI1i
F (3)  F (6)  CPFI 2i

CPFIji is the consensus probability forecast for
stock i in interval j.
 PFIjin is the probability forecast for stock i in
interval j of forecaster n.
 Although the consensus distribution is closer to
normal normality cannot be assured.
 At this point we defined the risk based on losses
rather than gains.
 We assumed that forecasters are more
concerned with large losses than with large
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gains.
• E(Rpi) is the expected return for stock i ,
• ii is the variance of returns for stock i,
• obtained from consensus
probabilistic forecasts of
professionals.
•F(.) stands for the normal cumulative
distribution.
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Estimations
 Efficient frontiers are estimated using the Ibbotson Associates
Encorr optimization program.
 Names and weights of stocks at each portfolio recorded for
minimum risk portfolio
maximum risk portfolio
four medium risk portfolios
the portfolio that matches the standard deviation of the actual
market portfolio
 Index tracking portfolio is used on the benchmark portfolio
 Performance measured the week following the forecasts/forecast
horizon of experts.
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Findings
 Comparison of expectations formation process
historical
best estimate
probabilistic efficient portfolio
 Comparison of expected & realized returns
historical
best estimate
probabilistic efficient portfolios
 Investment performance of portfolios based on
expert’s assessments compared to that based on
historical data.
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Expected Efficient Frontiers
Figure 1. Expected Efficient Frontiers
Historical
Best Estimates
Probabilistic
0.16
0.14
0.12
Return
0.1
0.08
0.06
0.04
0.02
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Standard Deviation
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Expected Historical
Efficient Frontier Versus Realized Returns
Figure 2. Expected Historical Efficient Frontier Versus Realised Returns
0.25
0.2
0.15
0.1
Return
0.05
0
-0.003
-0.031
-0.05
-0.064
-0.088
-0.1
-0.107
-0.125
-0.15
-0.188
-0.2
-0.25
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Standard de v iation
Expected Return
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Realised Return
42
Best Estimates Efficient
Frontier Versus Realized Returns
Figure 3. Best Estimates Efficient Frontier Versus Realised Returns
0.16
0.14
0.12
0.10
Return
0.08
0.06
0.04
0.033
0.02
0.020
0.016
0.023
0.029
0.026
0.00
-0.005
-0.02
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Standard de v iation
Expected Return
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Realised Return
43
Probabilistic Efficient Frontier
Versus Realized Returns
Figure 4. Probabilistic Efficient Frontier Versus Realised Returns
0.08
0.06
0.04
0.02
0.012
0.008
0.002
0.00
Return
-0.007
-0.006
-0.003
-0.02
-0.04
-0.06
-0.08
-0.10
-0.109
-0.12
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Standard De v iation
Expected Return
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Realised Return
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Realized Returns of the Portfolios
on the Efficient Frontiers
Figure 5. Realised Returns of the Portfolios on the Efficient Frontiers
Historical
Best Estimates
Probabilistic
0.05
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Return
-0.05
-0.1
-0.15
-0.2
Standard Deviation
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Summary
 Expectations formation process based on historical prices:
loss on all portfolios
minimum loss (.13%) index tracking portfolio
maximum loss (18.8%) on minimum risk portfolio as risk
increases loss detonates.
 Expectations formation process based on probabilistic forecasts
improved portfolio performance at all risk levels
mild losses, modest gains at higher risk levels
(1.2% max risk portfolio)
 Expectation formation process based on point and interval
forecasts.
further improvement in performance at all risk levels.
gains at all risk levels (except min risk portfolio)
weekly returns of 1.4% to 3.3%.
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Conclusion
 We integrate human behavior into financial modeling.
 We report the performance of portfolios based on
real time forecasts
of actual portfolio managers
 Portfolio performance of subjective forecasts much better
than that based on historical data.
 Literature on poor forecast accuracy versus
excellent portfolio performance!
 Better performing financial models that utilize human
judgement.
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