Essays on Financial Risk Management and Asset Allocation

143 Pages·2017·3.46 MB·English

2017-5
Jesper Bo Pedersen
PhD Dissertation
Essays on Financial Risk Management
and Asset Allocation
DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS
AARHUS BSS (cid:2) AARHUS UNIVERSITY (cid:2) DENMARK
E F R
S S A Y S O N I N A N C I A L I S K
M A
A N A G E M E N T A N D S S E T
A
L L O C A T I O N
PHD DISSERTATION
JESPER BO PEDERSEN
AARHUS BSS, AARHUS UNIVERSITY
DEPARTMENT OF ECONOMICS AND BUSINESS ECONOMICS
2017
Copyright (cid:13)c 2017
Preface
This thesis was written in the period from October 2013 to September 2016 during my
graduate studies at the Department of Economics and Business at Aarhus University,
the Department of Econometrics, Statistics, and Applied Economics at University of
Barcelona, and the Rotman School of Management at University of Toronto. I would
like to thank all three institutions for providing me with excellent research facilities.
My studies have been funded through the Danish Government’s Industrial PhD Pro-
grammeandIamverygratefulforthefinancialsupportIhavereceivedfromtheInnovation
Fund Denmark and my host company, Formuepleje. I extend my sincerest gratitude to
Niels B. Thuesen, CEO, and Leif Hasager, CIO, at Formuepleje for giving me the oppor-
tunity to pursue the PhD degree.
I wish to thank my main university supervisor Peter Løchte Jørgensen and my co-
supervisor Tom Engsted for valuable guidance, insightful comments, and helpful contri-
butions. I thank Peter for his continued support through the years and for establishing
the contact with Formuepleje. Without his help I would not have been where I am today.
At Formuepleje I am especially grateful to my company supervisor Leif Hasager for
sharing his extensive knowledge on all matters related to finance, investments, and risk
management. I have learned a lot about the practical aspects of investing by working
with competent colleagues at Formuepleje and I have benefitted greatly from the many
discussions on financial and macroeconomic developments with particularly René Rømer,
Erik Bech, and Otto Friedrichsen.
During my studies I have had the great pleasure of visiting University of Barcelona in
the Spring of 2015 and the University of Toronto in the Spring of 2016. I am very grateful
to Montserrat Guillén and Peter F. Christoffersen for graciously hosting me, giving me
valuablefeedbackonmypapers,providingmewiththeopportunitytopresentmyresearch,
and generally making my stay as delightful as possible.
Karen Vinding has provided excellent proofreading assistance and for that I am very
grateful.
IwouldalsoliketothankmyfellowPhDstudentsformanyacademicandnon-academic
discussions, the many coffee breaks, and for making the student life so enjoyable. In
particular I thank Søren K. Slipsager, Jakob G. Mikkelsen, and Bo Laursen for the many
fun and challenging hours spent together during our eight years of studying economics.
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Lastly, I would like to deeply thank my family and friends for their unconditional
love and support throughout the years. A special heartfelt thank you is reserved for my
girlfriend Rikke for her never-ending support, love, and encouragement. I could not have
made it without you and I am forever grateful.
Jesper Bo Pedersen
Aarhus, September 2016
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Updated Preface
The predefence meeting with an assessment committee consisting of Christian Wagner,
Copenhagen Business School, Monserrat Guillén, University of Barcelona, and Kim Chris-
tensen (chair), Aarhus University was held on November 28, 2016. I am thankful to the
members of the committee for carefully reading the dissertation and for their many con-
structive and insightful suggestions, which have clearly improved the thesis. Many of the
suggestions have been incorporated into this final version while others remain for future
research.
Jesper Bo Pedersen
Aarhus, February 2017
v
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Contents
Preface iii
Summary xiii
Danish Summary xvii
1 Backtesting Historical Simulation with Fully Flexible Probabilities 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Flexible Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Benchmark models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Backtesting procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.4.1 Model confidence set . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4.2 Coverage tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.5 Backtesting results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.5.1 Flexible Probabilities models . . . . . . . . . . . . . . . . . . . . . . 20
1.5.2 Model confidence sets . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.5.3 Coverage tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.5.4 Best state variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2 Forecasting and Controlling Drawdowns using Multivariate Volatility
Models 33
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.1 Drawdown risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.2 Forecasting models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.3 Backtesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.4 Backtesting results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
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2.4.1 Scoring rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.4.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.5 Controlling drawdown risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.5.1 Drawdown control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.5.2 Case study: 2008 Financial Crisis . . . . . . . . . . . . . . . . . . . . 60
2.5.3 Risk-adjusted performance . . . . . . . . . . . . . . . . . . . . . . . 60
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3 Tactical Asset Allocation with Fully Flexible Probabilities 79
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.2 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2.1 Flexible Probabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2.2 Combining state variables . . . . . . . . . . . . . . . . . . . . . . . . 84
3.2.3 Portfolio optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.1 Macroeconomic indicators . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.2 Risk-based indicators . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.3.3 Trend-based indicators . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4.1 Individual state variables . . . . . . . . . . . . . . . . . . . . . . . . 96
3.4.2 Combined state variables . . . . . . . . . . . . . . . . . . . . . . . . 97
3.4.3 Robustness checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Bibliography 115
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List of Figures
1.1 One day 99% Value at Risk for the S&P 500 index over the period from
2001 to 2014 using standard Historical Simulation with a window of 250
observations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Probability vectors stemming from time conditioning by rolling window
and exponential smoothing along with state conditioning based on crisp
and kernel conditioning using a 25% range. z is the VIX and z∗ denotes its
current level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Combining time and state conditioning via Entropy Pooling. . . . . . . . . 9
1.4 Plots of the standardized values of the state variables used in the empirical
exercise. The shaded bars show NBER recessions. . . . . . . . . . . . . . . 15
1.5 Plot of the asymmetric linear loss function. . . . . . . . . . . . . . . . . . . 17
1.6 Mean sample loss for the different state variables across the different con-
ditioning variables, confidence levels, and risk horizons.. . . . . . . . . . . . 24
2.1 Illustratingtheriskofaforcedliquidationthroughthe2008FinancialCrisis.
The figure is inspired by Goldberg & Mahmoud (2014). . . . . . . . . . . . 35
2.2 Maximum drawdown distribution along with 95% Drawdown Threshold
(DT) and 95% Conditional Expected Drawdown (CED). . . . . . . . . . . . 37
2.3 Prices and scaled returns of the different asset classes. Shaded bars mark
NBER recessions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4 Autocorrelations of the asset class returns. . . . . . . . . . . . . . . . . . . 51
2.5 Realized 10 day forward drawdowns along with 10 day predicted 95% Con-
ditional Expected Drawdown for the different models. . . . . . . . . . . . . 53
2.6 Histograms and CDF plots of the probability integral transforms for the
Cop-GJR-EVT model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.7 Sample autocorrelation plots for various powers of the probability integral
transforms from the forecasts of the Cop-GJR-EVT model. . . . . . . . . . 57
2.8 Drawdown control using the Cop-GJR-EVT model. The top panel of each
of the subfigures shows the drawdown controlled portfolio (a) and the lower
panel shows the uncontrolled portfolio (b). . . . . . . . . . . . . . . . . . . 59
2.9 Drawdown control during the 2008 Financial Crisis. . . . . . . . . . . . . . 61
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