Gulnur Muradoglu1 Experimental Finance Behavioral Finance Week 5 Read Muradoglu, 2001 Muradoglu et.al. 2005.
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Gulnur Muradoglu 1
Experimental Finance
Behavioral FinanceWeek 5
Read Muradoglu, 2001
Muradoglu et.al. 2005
Gulnur Muradoglu 2
Why Experimental Methodology?
Limitations of Share Price DataControlled 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
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 FXreal time forecast of specific stocks?
Short term forecast horizons
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Purpose of Muradoglu,2001To 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 novicesreal-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 undergraduatesexposed to EMH and financial forecasting
Professionals in stock market, 35all licensed brokersworking for brokerage houses15 prepare research reports20 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 indexeight 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 ofunnamed stocks, stock index,specific stocks
For forecast horizons ofone, two, four and twelve weeks (Long Term?)
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Measurement
Expected price changeEPCi 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 i, bull 0• EPC i, bear < 0
• EPC i, bull EPC i, bear
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Measurement
Risk Perceptions Confidence intervals
UCIijk = Hijk – FijkLCIijk = Lijk – Fijk
Mean SkewnessSi = jk (UCIijk - LCIijk)
DeBondt Findings indicatedS i, bull <0, S i, bear >0S i, bull < S i, bear
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Tests for differencesExpected price changes and skewness
coefficients are normalised by dividing to matching standard deviations
t-statistics used for differences in meanscomparisons of
bull versus bear markets unnamed stocks, versus index, actual
stocks experts versus novices 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 weeksExperts 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 OptimismEPC 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 SpeculationsTrend 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 novicesBull 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 versus Experts
NovicesExperts
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ResultsDifferent forecast horizons
For unknown stocksEPC is higher for longer horizonsS is higher for longer horizons
For indexIn bull market EPC is lower for longer horizonsIn bear market EPC is higher for longer horizonsIn 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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DiscussionsMelding 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 week25 compromises listed as ISEhighest volume of trade during previous yearseasy to follow, reduces task complexity
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Muradoglu, et.al. 2005
MethodWe 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
WW
WR
N
N
NH
N
NH
w
w
w
wwwR
w
w
w
RERERERE
2
111211
212
2
1
21
)(
)()()()(
N
RRE
P
PPR
N
tit
i
it
ititit
1
1
1
)(
•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
Gulnur Muradoglu 36
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:
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
1
1)(
it
itijtji P
PPFRE
2
])([])([ 1111 ititijtititijt
ii
PPLIFPPUIF
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Consensus Best Estimate Efficient Frontier
In the consensus forecast expected return E(Ri) and variances (ii) are calculated as follows:
J
RE
RE jij
i
)(
)(
J
LIF
ALIF
andJ
UIF
AUIF
where
PPALIFPPUIFA
jijt
it
jijt
it
ititititititii
2
])([])[ 1111
Gulnur Muradoglu 38
Probabilistic Efficient Frontier
Min 2(RP)
subject to 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 stock as follows.
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 gains.
N
njinji PFICPFI
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.
• 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.
i
i
iiPi
CPFIFF
CPFIFtoSubject
REMax
2
1
)6()3(
)6(
)(
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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.
Gulnur Muradoglu 41
Expected Efficient Frontiers
Figure 1. Expected Efficient Frontiers
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Standard Deviation
Retu
rn
Historical Best Estimates Probabilistic
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Expected Historical
Figure 2. Expected Historical Efficient Frontier Versus Realised Returns
-0.188
-0.003
-0.031
-0.064
-0.088
-0.107
-0.125
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
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 deviation
Re
turn
Expected Return Realised Return
Efficient Frontier Versus Realized Returns
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Best Estimates Efficient Frontier Versus Realized Returns
Figure 3. Best Estimates Efficient Frontier Versus Realised Returns
-0.005
0.0160.020
0.0230.026
0.0290.033
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Standard deviation
Re
turn
Expected Return Realised Return
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Probabilistic Efficient Frontier Versus Realized Returns
Figure 4. Probabilistic Efficient Frontier Versus Realised Returns
-0.109
-0.007 -0.006-0.003
0.0020.008
0.012
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Standard Deviation
Re
turn
Expected Return 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
-0.2
-0.15
-0.1
-0.05
0
0.05
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Standard Deviation
Retu
rn
Historical Best Estimates Probabilistic
Gulnur Muradoglu 46
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%.
Gulnur Muradoglu 47
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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