Allocation Methods for Alternative Risk Premia Strategies - KTH

102 Pages·2014·0.86 MB·English

Allocation Methods for Alternative Risk Premia
Strategies
Daniel Drugge
For
The First Swedish National Pension Fund
January 30, 2014

Abstract
We use regime switching and regression tree methods to evaluate performance
in the risk premia strategies provided by Deutsche Bank and constructed from
U.S.researchdatafromtheFamaFrenchlibrary. Theregimeswitchingmethod
uses the Baum-Welch algorithm at its core and splits return data into a normal
and a turbulent regime. Each regime is independently evaluated for risk and
theestimatesarethenweightedtogetheraccordingtotheexpectedvalueofthe
proceedingregime. Theregressiontreemethodsidentifymacro-economicstates
inwhichtheriskpremiaperformwellorpoorlyandusetheseresultstoallocate
between risk premia strategies.
The regime switching method proves to be mostly unimpressive but has its re-
sultsboostedbyinvestinglessintoriskyassetsastheprobabilityofanupcoming
turbulent regime becomes larger. This proves to be highly effective for all time
periods and for both data sources. The regression tree method proves the most
effective when making the assumption that we know all macro-economic data
the same month as it is valid for. Since this is an unrealistic assumption the
bestmethodseemstobetoevaluatetheperformanceoftheriskpremiastrategy
using macro-economic data from the previous quarter.

Sammanfattning
Vi anv¨ander en metod som delar upp avkastningsdata i en l˚agrisk-regim och en
h¨ogrisk-regim, samt en metod som skapar ett bin¨artr¨ad vars grenar inneh˚aller
avkastningsdata givet olika makroekonomiska tillst˚and, f¨or att allokera mellan
olika riskpremiestrategier. Vi best¨ammer sannolikheten f¨or att v¨axla mellan
regimer genom den s˚a kallade Baum-Welch algoritmen och efter att ha delat
upp avkastningsdata i olika regimer best¨ammer vi den empiriska riskuppskat-
tningen f¨or l˚agrisk- och h¨ogrisk-regimen. Den slutgiltliga riskuppskattningen
skapasgenomattv¨agaihopdetv˚ariskuppskattningarnamedsannolikhetenf¨or
varderaregim. Bin¨artr¨adetsomanv¨ands¨aretts˚akallatregressionstr¨adochde-
laruppavkastningarnap˚aetts˚adants¨attattskillnadeniSharpekvotmaximeras
mellan olika makroekonomiska tillst˚and.
Regimv¨axlingsmetodenvisarsigvaran˚agonineffektivmenresultatenblirb¨attre
n¨arm¨angdenkapitalinvesteratiriskpremiestrategiernaminskasjuh¨ogresanno-
likheten f¨or att n¨asta period ska vara en h¨ogriskregim ¨okar. Regressionstr¨aden
fungerar v¨aldigt v¨al i ett idealt scenario d¨ar vi vet relevant makroekonomisk
data i f¨orv¨ag men ger ¨aven ganska bra resultat i realistiska scenarion.

Acknowledgements
I would like to thank Peter Emmevid at the First National Pension Fund for
giving me the opportunity to write this report and for providing ongoing sup-
port and feedback. Furthermore I want to thank my supervisor at KTH, Filip
Lindskog for invaluable support regarding the writing process. Lastly I thank
Deutsche Bank for lending the data for me to use.

Contents
1 Introduction 5
1.1 Purpose and Format of the Report . . . . . . . . . . . . . . . . . 5
1.2 Risk Premia Strategies . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Correlation Among the Risk Premia Strategies . . . . . . 7
2 Methods 8
2.1 Portfolio Optimization . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Regime Switching. . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1 Risk Parity Portfolio with Regime Shifting . . . . . . . . 21
2.5 Regression Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.1 Cross Validation . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.2 Bagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Statistical Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Data 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Deutsche Bank Data . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Historical Regimes . . . . . . . . . . . . . . . . . . . . . . 34
3.3 Fama French Research Data . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 Historical Regimes . . . . . . . . . . . . . . . . . . . . . . 37
4 Results 39
4.1 Introduction and Structure . . . . . . . . . . . . . . . . . . . . . 39
4.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.1 Regime Switching . . . . . . . . . . . . . . . . . . . . . . 40
4.2.2 Equity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.3 Fama French Data - Regime Switching . . . . . . . . . . . 46
4.2.4 Fama French Data - Regime Switching, 1960-2012 . . . . 50
4.2.5 Regression Trees . . . . . . . . . . . . . . . . . . . . . . . 52
2
4.2.6 A Simple Cost Analysis . . . . . . . . . . . . . . . . . . . 69
5 Conclusions 71
5.1 Regime Switching. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 Regression Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
A Macro-Economic Terms and Data 74
A.1 Macro-Economic Data . . . . . . . . . . . . . . . . . . . . . . . . 76
B Mathematics 79
C Matlab Code 81
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