Dynamic Asset Allocation

323 Pages·2017·13.99 MB·English

by  Peter Nystrup

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Dynamic Asset Allocation - Identifying Regime Shifts in Financial Time Series to Build
Robust Portfolios
Nystrup, Peter
Publication date:
2018
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Citation (APA):
Nystrup, P. (2018). Dynamic Asset Allocation - Identifying Regime Shifts in Financial Time Series to Build
Robust Portfolios. DTU Compute. DTU Compute PHD-2017 Vol. 465

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Ph.D.Thesis
DoctorofPhilosophy
Dynamic Asset Allocation
IdentifyingRegimeShiftsinFinancialTimeSeriestoBuild
Robust Portfolios
Peter Nystrup
KongensLyngby
November2017
TechnicalUniversityofDenmark
DepartmentofAppliedMathematicsandComputerScience
RichardPetersensPlads,Building324
2800KongensLyngby,Denmark
Phone[phone]
[email protected]
www.compute.dtu.dk
Short Contents
Short Contents i
Abstract iii
Resumé v
Preface vii
Acknowledgments ix
Publications xi
Acronyms xiii
Contents xv
1 Introduction 1
2 Contribution 9
3 Conclusion 23
References 27
A StylizedfactsoffinancialtimeseriesandhiddenMarkovmod-
els in continuous time 37
B Long memory of financial time series and hidden Markov
models with time-varying parameters 59
C Regime-based versus static asset allocation: Letting the data
speak 85
ii ShortContents
D Dynamic allocation or diversification: A regime-based ap-
proach to multiple assets 99
E Detecting change points in VIX and S&P 500: A new ap-
proach to dynamic asset allocation 119
F Greedy Gaussian segmentation of multivariate time series 141
G Dynamic portfolio optimization across hidden market regimes173
H Multi-period trading via convex optimization 203
I Multi-period portfolio selection with drawdown control 263
Abstract
Long-terminvestorscanoftenbeartheriskofoutsizedmarketmovementsortail
events more easily than the average investor; for bearing this risk, they hope to
earn significant excess returns. Rebalancing periodically to a fixed benchmark
allocation,however,isnotthewaytodothis. Inthepresenceoftime-varyingin-
vestmentopportunities,portfolioweightsshouldbeadjustedasnewinformation
arrives to take advantage of favorable regimes and reduce potential drawdowns.
This thesis contributes to a better understanding of financial markets’ behavior
in the form of a model-based framework for dynamic asset allocation.
Regime-switchingmodelscanmatchfinancialmarkets’tendencytochangetheir
behaviorabruptlyandthephenomenonthatthenewbehavioroftenpersistsfor
several periods after a change. Regime shifts lead to time-varying parameters
and, in addition, the parameters within the regimes and the transition proba-
bilities change over time. Using recursive and adaptive estimation techniques
to capture this, we are able to better reproduce the volatility persistence that
dynamic asset allocation benefits from. With this approach it is sufficient to
distinguish between two regimes in stock returns in order for it to be profitable
to change asset allocation based solely on the inferred regimes, both in a single-
and multi-asset universe.
We advocate the use of model predictive control for translating forecasts into a
dynamicstrategyandcontrollingdrawdownsbysolvingamulti-periodoptimiza-
tionproblem. Weimplementthisbasedonforecastsfromamultivariatehidden
Markov model with time-varying parameters. Our results show that a substan-
tialamountofvaluecanbeaddedbyadjustingtheassetallocationtothecurrent
market conditions, rather than rebalancing periodically to a static benchmark.
By proposing a practical approach to drawdown control, we demonstrate the
theoretical link to dynamic asset allocation and the importance of identifying
and acting on regime shifts in order to limit losses and build robust portfolios.
Keywords: Risk management; Regime switching; Adaptive estimation; Fore-
casting; Model predictive control; Portfolio optimization; Drawdown control.
iv
Resumé
Langsigtede investorer kan ofte bære risikoen for store markedsudsving eller
ekstreme hændelser bedre end den gennemsnitlige investor. Som kompensation
foratpåtagesigdennerisikohåberdeatopnåbetydeligemerafkast. Periodevis
rebalancering til en statisk benchmark-allokering er imidlertid ikke måden at
opnå dette. Ved tilstedeværelse af tidsvarierende investeringsmuligheder bør
porteføljevægtene tilpasses, efterhånden som ny information bliver tilgængelig,
foratdragefordelafgunstigeregimerogreducerepotentielletab. Denneafhand-
ling bidrager til en bedre forståelse af finansielle markeders opførsel i form af et
modelbaseret fundament for dynamisk aktivallokering.
Regimeskiftmodeller kan genskabe finansielle markeders tendens til pludseligt
at skifte opførsel og det fænomen, at den nye opførsel ofte varer ved længe efter
et skift. Regimeskift fører til tidsvarierende parametre, men også parametrene
inden for regimerne og overgangssandsynlighederne ændrer sig over tid. Ved at
bruge rekursive og adaptive estimationsmetoder til at fange dette er vi i stand
til bedre at genskabe den volatilitetspersistens, som dynamisk aktivallokering
udnytter. Med denne tilgang er det tilstrækkeligt at skelne mellem to regimer
i aktieafkast, før end det er profitabelt at ændre aktivallokering udelukkende
baseretpådeudledteregimeriuniverserbeståendeafetenkeltellerflereaktiver.
Viadvokererforbrugenafmodelprædiktivreguleringtilatomsætteforudsigelser
tilendynamiskstrategiogkontrolleretabgennemløsningafetflerperiodeopti-
meringsproblem. Vi implementerer dette baseret på forudsigelser fra en skjult
Markov model med tidsvarierende parametre. Vores resultater viser, at be-
tydelig værdi kan tilføres ved at tilpasse aktivallokeringen til de nuværende
markedsforhold frem for at rebalancere periodevist til et statisk benchmark.
Ved at foreslå en praktisk tilgang til tabskontrol demonstrerer vi den teoretiske
forbindelsetildynamiskaktivallokeringogvigtighedenafatidentificereogagere
på regimeskift for at begrænse tab og bygge robuste porteføljer.
Nøgleord: Risikostyring;Regimeskift;Adaptivestimation;Forudsigelse;Model-
prædiktiv regulering; Porteføljeoptimering; Tabskontrol.
vi
Preface
This thesis was prepared in the Department of Applied Mathematics and Com-
puter Science at Technical University of Denmark in partial fulfillment of the
requirements for the degree of Doctor of Philosophy (Ph.D.) in Engineering. It
consists of a collection of nine papers written during the course of my Ph.D.
study.
The research study was carried out in collaboration with Danish pension fund
SampensionandLundUniversityinSweden,withsupportfromInnovationFund
Denmark under Grant No. 4135-00077B. As part of the study, I spent the sum-
mer of 2016 as a visiting student researcher in the Department of Electrical
Engineering at Stanford University in California.
InadditiontoahandfulofvisitstoStanford,thefinancialsupportfromSampen-
sionandInnovationFundDenmarkhasallowedmetoparticipateinconferences
and seminars in London, Frankfurt, Rennes, Aarhus, Paris, New York, Austin,
Cairns, and Brussels.
Thisthesisdealswithdifferentaspectsofmathematicalmodelingofthestylized
behavior of financial returns using regime-switching models with the aim of
developing a model-based framework for dynamic asset allocation. The idea for
the study emanated from my Master’s thesis (Nystrup 2014), which established
the potential for model-driven, regime-based asset allocation. In continuation
of this work we initially focused on adaptive estimation of regime-switching
models. Before pursuing with a multi-period optimization approach based on
model predictive control, demonstrating the connection between dynamic asset
allocationanddrawdowncontrol,wetestedstrategieswheretheassetallocation
was fully determined by the identified market regime.
Copenhagen, November 2017
Peter Nystrup