is it s o bad that we cannot recognize black swans?
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IS IT SO BAD THAT WE CANNOT RECOGNIZE BLACK
SWANS?
Fuad Aleskerovand Lyudmila Egorova
National Research UniversityHigher School of Economics
Zurich, 2011
INTRODUCTION
A Black Swan:
is an outlier, and nothing in the past can convincingly point to its possibility;
carries an extreme impact; has retrospective (though not prospective)
predictability.
Nassim Nicolas Taleb «The Black Swan. The Impact of The Highly Improbable» 2
INTRODUCTION
«The central idea of this book concerns our blindness with respect to randomness, particularly the large deviations: Why do we, scientists or nonscientists, hotshots or regular Joes, tend to see the pennies instead of the dollars? Why do we keep focusing on the minutiae, not the possible significant large events, in spite of the obvious evidence of their huge influence?»
Nassim Nicolas Taleb «The Black Swan. The Impact of The Highly Improbable»
3
PROBLEM
We will model economic fluctuations representing them as a flows of events of two types:
Q-event reflects the “normal mode” of an economy;
R-event is responsible for a crisis.
The number of events in each time interval has a Poisson distribution with constant intensity.
is the intensity of the flow of regular events Q. is the intensity of the flow of crisis events R. >> holds (that is, Q-type events are far more frequent than the R-type events).
4
PROBLEM
We will model economic fluctuations representing them as a flows of events of two types:
Q-event reflects the “normal mode” of an economy;
R-event is responsible for a crisis.
The number of events in each time interval has a Poisson distribution with constant intensity.
is the intensity of the flow of regular events Q. is the intensity of the flow of crisis events R. >> holds (that is, Q-type events are far more frequent than the R-type events).
5
PROBLEM
6
PROBLEM
X
Q
RThe problem of correct identification (recognition)
Unknown
State of nature
7
PROBLEM
X
Q
R
Q
Q
R
R
Player´s perceived identification of the state of nature
8
PROBLEM
X
Q
R
Q
Q
R
R
aPayoff of correct identification of regular event
9
PROBLEM
X
Q
R
Q
Q
R
R -bIncorrect identification of regular event
10
PROBLEM
X
Q
R
Q
R
Q
R
d>>b-d
cc>>a
11
PROBLEM
right
right
wrong
wrong
12
PROBLEM
How large will be the sum of payoffs received up to time t? 13
SOLUTION
Random value Z=∑X of the total sum of the received payoffs during the time t is a compound Poisson type variable.
We give the expression for the expectation of a random variable payoff:
E (Z) = [λ(p 1a – q 1b ) + μ(p 2c – q 2d )] t
14
APPLICATION TO REAL DATA
We consider a stock exchange and events Q and R which describe a ‘business as usual’ and a ‘crisis’, respectively.
The unknown event X can be interpreted as a signal received, e.g. by an economic analyst or by a broker, about the changes of the economy that helps him to decide whether the economy is in ‘a normal mode’ or in a crisis.
15
PARAMETERS FOR S&P 500
02/08
/1999
22/11
/1999
13/03
/2000
03/07
/2000
23/10
/2000
12/02
/2001
04/06
/2001
24/09
/2001
14/01
/2002
06/05
/2002
26/08
/2002
16/12
/2002
07/04
/2003
28/07
/2003
17/11
/2003
08/03
/2004
28/06
/2004
18/10
/2004
07/02
/2005
30/05
/2005
19/09
/2005
09/01
/2006
01/05
/2006
21/08
/2006
11/12
/2006
02/04
/2007
23/07
/2007
12/11
/2007
03/03
/2008
23/06
/2008
13/10
/2008
02/02
/2009
25/05
/2009
14/09
/2009
0
200
400
600
800
1000
1200
1400
1600
1800
0
2
4
6
8
10
12
14
16
PARAMETERS FOR S&P 500
02/08
/1999
22/11
/1999
13/03
/2000
03/07
/2000
23/10
/2000
12/02
/2001
04/06
/2001
24/09
/2001
14/01
/2002
06/05
/2002
26/08
/2002
16/12
/2002
07/04
/2003
28/07
/2003
17/11
/2003
08/03
/2004
28/06
/2004
18/10
/2004
07/02
/2005
30/05
/2005
19/09
/2005
09/01
/2006
01/05
/2006
21/08
/2006
11/12
/2006
02/04
/2007
23/07
/2007
12/11
/2007
03/03
/2008
23/06
/2008
13/10
/2008
02/02
/2009
25/05
/2009
14/09
/2009
0
200
400
600
800
1000
1200
1400
1600
1800
0
2
4
6
8
10
12
14
21.09.200123.07.2002
25.10.2002 21.01.2008
16.10.2008
09.03.2009
30.07.2009
17
PARAMETERS FOR S&P 500
02/08
/1999
22/11
/1999
13/03
/2000
03/07
/2000
23/10
/2000
12/02
/2001
04/06
/2001
24/09
/2001
14/01
/2002
06/05
/2002
26/08
/2002
16/12
/2002
07/04
/2003
28/07
/2003
17/11
/2003
08/03
/2004
28/06
/2004
18/10
/2004
07/02
/2005
30/05
/2005
19/09
/2005
09/01
/2006
01/05
/2006
21/08
/2006
11/12
/2006
02/04
/2007
23/07
/2007
12/11
/2007
03/03
/2008
23/06
/2008
13/10
/2008
02/02
/2009
25/05
/2009
14/09
/2009
0
200
400
600
800
1000
1200
1400
1600
1800
0
2
4
6
8
10
12
14
21.09.200123.07.2002
25.10.2002 21.01.2008
16.10.2008
09.03.2009
30.07.2009
18
PARAMETERS FOR S&P 500
Estimates for indices with the threshold 6%
Index λ μ a, % -b, % c, % -d, %
S&P 500 246 4 0,6 -0,6 2,8 -2,9
Dow Jones 246 4 0,6 -0,6 1,9 -2,4
CAC 40 243 7 0,8 -0,8 3,0 -2,5
DAX 239 11 0,8 -0,9 2,1 -2,5
Nikkei 225 245 5 0,8 -0,9 2,6 -3,2
Hang Seng 241 9 0,9 -0,9 2,6 -3,0
19
PARAMETERS FOR S&P 500
In fact, it is enough to identify regular Q-events in almost half of the cases to ensure a positive outcome of the game (q1≤0.46).
E(Z)0
Probability of incorrect identification of crisis R-event
Probability of incorrect recognition of regular Q-event
20
PROBLEM
21
k
MODEL WITH STIMULATIONif
if
22
MODEL WITH STIMULATION
23
MODEL WITH LEARNINGif
if
24
CONCLUSION We showed in a very simple model that
with a small reward for the correct (with probability slightly higher than ½) identification of the routine events (and if crisis events are identified with very low probability) the average player's gain will be positive.
In other words, players do not need to play more sophisticated games, trying to identify crises events in advance. 25
THANK YOU FOR YOUR ATTENTION!
26
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