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A Multi-Level Extension of the Hierarchical PCA Framework with Applications to Portfolio Construction with Futures Contracts
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2023 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
En flernivåsutbyggnad av ramverket för Hierarkisk PCA med tillämpningar på portföljallokering med terminskontrakt (Swedish)
Abstract [en]

With an increasingly globalised market and growing asset universe, estimating the market covariance matrix becomes even more challenging. In recent years, there has been an extensive development of methods aimed at mitigating these issues. This thesis takes its starting point in the recently developed Hierarchical Principal Component Analysis, in which a priori known information is taken into account when modelling the market correlation matrix. However, while showing promising results, the current framework only allows for fairly simple hierarchies with a depth of one. In this thesis, we introduce a generalisation of the framework that allows for an arbitrary hierarchical depth. We also evaluate the method in a risk-based portfolio allocation setting with Futures contracts. 

Furthermore, we introduce a shrinkage method called Hierarchical Shrinkage, which uses the hierarchical structure to further regularise the matrix. The proposed models are evaluated with respect to how well-conditioned they are, how well they predict eigenportfolio risk and portfolio performance when they are used to form the Minimum Variance Portfolio. We show that the proposed models result in sparse and easy-to-interpret eigenvector structures, improved risk prediction, lower condition numbers and longer holding periods while achieving Sharpe ratios that are at par with our benchmarks.

Abstract [sv]

Med en allt mer globaliserad marknad och växande tillgångsuniversum blir det alltmer utmanande att uppskatta marknadskovariansmatrisen. Under senare år har det skett en omfattande utveckling av metoder som syftar till att mildra dessa problem. Detta examensarbete tar sin utgångspunkt i det nyligen utvecklade ramverket Hierarkisk Principalkomponentanalys, där kunskap känd sedan innan används för att modellera marknadskorrelationerna. Även om det visar lovande resultat så tillåter det nuvarande ramverket endast enkla hierarkier med ett djup på ett. I detta examensarbete introduceras en generalisering av detta ramverk, som tillåter ett godtyckligt hierarkiskt djup. Vi utvärderar också metoden i en riskbaserad portföljallokeringsmiljö med terminskontrakt. 

Vidare introducerar vi en krympningsmetod som vi kallar Hierarkisk Krympning. Hierarkisk krympning använder den hierarkiska strukturen för att ytterligare regularisera matrisen. De föreslagna modellerna av korrelationsmatrisen utvärderas med avseende på hur välkonditionerade de är, hur väl de förutsäger egenportföljrisk samt hur de presterar i portföljallokeringssyfte i en Minimum Variance portfölj. Vi visar att de introducerade modellerna resulterar i en gles och lätttolkad egenvektorstruktur, förbättrad riskprediktion, lägre konditionstal och längre hållperiod, samtidigt som portföljerna uppnår Sharpe-kvoter i linje med benchmarkmodellerna.

Place, publisher, year, edition, pages
2023. , p. 62
Series
TRITA-SCI-GRU ; 2023:059
Keywords [en]
Portfolio construction, asset allocation, principal component analysis, hierarchical principal component analysis, hierarchical shrinkage, eigenportfolio risk
Keywords [sv]
Portföljkonstruktion, tillgångsallokering, principalkomponentanalys, hierarkisk principalkomponentanalys, hierarkisk krympning, egenportföljrisk
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-335737OAI: oai:DiVA.org:kth-335737DiVA, id: diva2:1795170
External cooperation
Lynx Asset Management AB
Subject / course
Financial Mathematics
Educational program
Master of Science - Industrial Engineering and Management
Supervisors
Examiners
Available from: 2023-09-07 Created: 2023-09-07 Last updated: 2023-09-07Bibliographically approved

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