Applications of Physics and Geometry to Finance

203 Pages·2014·1.9 MB·English

by  Jaehyung Choi

Applications of Physics and Geometry
to Finance
A Dissertation Presented
by
Jaehyung Choi
to
The Graduate School
in Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy
in
Physics
Stony Brook University
May 2014
Stony Brook University
The Graduate School
Jaehyung Choi
We, the dissertation committee for the above candidate for the
Doctor of Philosophy degree, hereby recommend
acceptance of this dissertation.
Robert J. Frey - Dissertation Advisor
Research Professor, Dept. of Applied Mathematics and Statistics
Jacobus Verbaarschot - Co-Advisor
Professor, Department of Physics and Astronomy
Alfred S. Goldhaber - Chairperson of Defense
Professor, Department of Physics and Astronomy
Dominik Schneble - Committee Member
Associate Professor, Department of Physics and Astronomy
Noah Smith - External Committee Member
Assistant Professor, College of Business
This dissertation is accepted by the Graduate School.
Charles Taber
Dean of the Graduate School.
ii
Abstract of the Dissertation
Applications of Physics and Geometry to
Finance
by
Jaehyung Choi
Doctor of Philosophy
in
Physics
Stony Brook University
2014
Market anomalies in finance are the most interesting topics to aca-
demics and practitioners. The chances of the systematic arbitrage
are not only the counter-examples to the efficient market hypothe-
sis but also the sources of profitable trading strategies to the prac-
titioners. Approaches to finding, predicting, and explaining the
anomalies by using ideas from physics and geometry had not been
permeated.
Inthefirstpart, Idevelopmonthlymomentumandweeklycontrar-
ian strategies with stock selection rules based on various measures
from risk management and analogy of momentum in physics. The
iii
better performance and risk profile are achieved by the alternative
strategies implemented in diverse asset classes and markets.
The concept of spontaneous symmetry breaking is suggested for
modeling the arbitrage dynamics. In the model, the arbitrage
strategy is considered as being in the symmetry breaking phase
and the phase transition between arbitrage mode and no-arbitrage
mode is triggered by a control parameter. It is also tested with
contrarian strategies in various markets.
In the last part, I prove the correspondence between K¨ahler man-
ifold and information geometry of signal processing models under
conditions on transfer function. The various advantages of intro-
ducing the Ka¨hler manifold are visited. Several implications to
time series models are also given in the K¨ahlerian information ge-
ometry.
iv
Contents
List of Figures ix
List of Tables xi
Acknowledgements xiv
Vita and Publication xvi
1 Introduction 1
2 Fundamentals of momentum and contrarian strategies 12
3 Maximumm drawdown, recovery, and momentum 20
3.1 Construction of stock selection rules . . . . . . . . . . . . . . . 21
3.2 Dataset and methodology . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 South Korea equity market: KOSPI 200 . . . . . . . . 27
3.3.2 U.S. equity market: SPDR sector ETFs . . . . . . . . . 33
v
3.3.3 U. S. equity market: S&P 500 . . . . . . . . . . . . . . 38
3.3.4 Overall results . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Factor analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.4.1 Weekly . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.4.2 Monthly . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . 50
4 Reward-risk momentum strategies using classical tempered
stable distribution 52
4.1 Risk model and reward-risk measures . . . . . . . . . . . . . . 53
4.1.1 Risk model . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1.2 Reward-risk measures . . . . . . . . . . . . . . . . . . . 54
4.2 Dataset and methodology . . . . . . . . . . . . . . . . . . . . 57
4.2.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . 60
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.1 Currency markets . . . . . . . . . . . . . . . . . . . . . 61
4.3.2 Commodity markets . . . . . . . . . . . . . . . . . . . 66
4.3.3 Global stock benchmark indices . . . . . . . . . . . . . 70
4.3.4 South Korea equity market: KOSPI 200 . . . . . . . . 74
4.3.5 U.S. equity market: SPDR sector ETFs . . . . . . . . . 78
4.3.6 U.S. equity market: S&P 500 . . . . . . . . . . . . . . 82
4.3.7 Overall results in various universes . . . . . . . . . . . 87
4.4 Factor analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . 91
vi
5 Physical approach to price momentum and its application to
momentum strategy 94
5.1 Theoretical background . . . . . . . . . . . . . . . . . . . . . . 95
5.2 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2.1 South Korea equity markets: KOSPI 200 . . . . . . . . 103
5.2.2 U.S. equity markets: S&P 500 . . . . . . . . . . . . . . 103
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3.1 South Korea equity market: KOSPI 200 . . . . . . . . 104
5.3.2 U.S. equity market: S&P 500 . . . . . . . . . . . . . . 107
5.4 Factor analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . 112
6 Spontaneous symmetry breaking of arbitrage 114
6.1 Spontaneous symmetry breaking of arbitrage . . . . . . . . . . 115
6.1.1 Arbitrage modeling . . . . . . . . . . . . . . . . . . . . 115
6.1.2 Asymptotic solutions . . . . . . . . . . . . . . . . . . . 117
6.1.3 Exact solutions . . . . . . . . . . . . . . . . . . . . . . 121
6.2 Application to real trading strategy . . . . . . . . . . . . . . . 124
6.2.1 Method and estimation of parameters . . . . . . . . . . 124
6.2.2 Data sets for the strategy . . . . . . . . . . . . . . . . 129
6.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.3 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . 137
7 K¨ahlerian information geometry for signal processing 140
7.1 Information geometry for signal processing . . . . . . . . . . . 141
7.1.1 Spectral density representation in frequency domain . . 141
vii
7.1.2 Transfer function representation in z-domain . . . . . . 145
7.2 Ka¨hler manifold for signal processing . . . . . . . . . . . . . . 154
7.3 Example: AR, MA, and ARMA models . . . . . . . . . . . . . 166
7.3.1 AR(p) and MA(q) models . . . . . . . . . . . . . . . . 167
7.3.2 ARMA(p,q) model . . . . . . . . . . . . . . . . . . . . 171
7.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8 Conclusion 177
Bibliography 179
viii
List of Figures
3.1 For weekly contrarian, cumulative returns for the traditional
contrarian (gray), R (blue), CR (red), and CMR (green). For
monthly momentum, cumulative returns for the traditional mo-
mentum (gray), CM (blue), RM (red), and CMR (green). . . . 45
4.1 Cumulative returns for the traditional momentum (gray), R-
ratio(50%,99%)(blue),R-ratio(50%,95%)(red),andR-ratio(50%,90%)
(green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.1 Cumulativereturnsforthetraditionalcontrarian(gray),p(1)(υ,R)
(blue), p(2)(υ,R) (red), and p(3)(1/σ,R) (green) in South Korea
KOSPI 200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2 Cumulativereturnsforthetraditionalcontrarian(gray),p(1)(υ,R)
(blue), p(2)(υ,R) (red), and p(3)(1/σ,R) (green) in U.S. S&P 500.109
6.1 Return vs. λ/λ . In the left graph, t=5 (blue), t=10 (red),
c
t=25 (black), and t=∞ (gray dashed). In the right graph, t=∞
(black) and λ/λ = 1 (red dotted) . . . . . . . . . . . . . . . . 122
c
6.2 Return vs. time. long-living arbitrage mode (blue), short-living
arbitragemode(reddashed),andasymptoticreturn(graydashed)122
ix
6.3 Flowchartoftheschemebasedonspontaneoussymmetrybreak-
ing concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4 Cumulative excessive weekly returns in S&P 500 and KOSPI
200. Returntimeseriesbycontrarianstrategy(blue), bywinner
(gray), by loser (gray dashed), and by benchmark (red dashed) 131
6.5 S&P 500. SSB-aided weekly contrarian strategy (blue) and
naive weekly contrarian strategy (red dashed). MA window
size ranges from 2 to 100. . . . . . . . . . . . . . . . . . . . . 134
6.6 KOSPI 200. SSB-aided weekly contrarian strategy (blue) and
naive weekly contrarian strategy (red dashed). MA window size
ranges from 2 to 100. . . . . . . . . . . . . . . . . . . . . . . . 135
x