Approximating the numeraire portfolio by naive diversification

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dc.contributor.author Platen, E
dc.contributor.author Rendek, RJ
dc.date.accessioned 2012-10-12T03:35:04Z
dc.date.issued 2012-01
dc.identifier.citation Journal of Asset Management, 2012, 13 (1), pp. 34 - 50
dc.identifier.issn 1470-8272
dc.identifier.other C1 en_US
dc.identifier.uri http://hdl.handle.net/10453/18876
dc.description.abstract Estimation theory has shown, owing to the limited estimation window available for real asset data, that the sample-based Markowitz mean-variance approach produces unreliable weights that fluctuate substantially over time. This article proposes an alternate approach to portfolio optimization, being the use of naive diversification to approximate the numéraire portfolio (NP). The NP is the strictly positive portfolio that, when used as benchmark, makes all benchmarked non-negative portfolios either mean decreasing or trendless. Furthermore, it maximizes expected logarithmic utility and outperforms any other strictly positive portfolio in the long run. The article proves for a well-securitized market that the naive equal value-weighted portfolio converges to the NP when the number of constituents tends to infinity. This result is model independent and, therefore, very robust. The systematic construction of diversified stock indices by naive diversification from real data is demonstrated. Even when taking transaction costs into account, these indices significantly outperform the corresponding market capitalization- weighted indices in the long run, indicating empirically their asymptotic proximity to the NP. Finally, in the time of financial crisis, a large equi-weighted fund carrying the investments of major pension funds and insurance companies would provide important liquidity. It would not only dampen the drawdown of a crisis, but would also moderate the excesses of an asset price bubble.
dc.publisher Palgrave Macmillan Ltd
dc.relation.hasversion Accepted manuscript version en_US
dc.relation.isbasedon 10.1057/jam.2011.36
dc.rights This is a post-peer-review, pre-copyedit version of an article published in Journal of Asset Management (2012). The definitive publisher-authenticated version Journal of Asset Management (2012)13, 34–50 is available online at: http://dx.doi.org/10.1057/jam.2011.36
dc.subject equi-weighted index, growth optimal portfolio, Kelly portfolio, market capitalization-weighted index (MCI), naive diversification, numéraire portfolio
dc.subject equi-weighted index; growth optimal portfolio; Kelly portfolio; market capitalization-weighted index (MCI); naive diversification; numéraire portfolio
dc.title Approximating the numeraire portfolio by naive diversification
dc.type Journal Article
dc.parent Journal of Asset Management
dc.journal.volume 1
dc.journal.volume 13
dc.journal.number 1 en_US
dc.publocation London, UK en_US
dc.identifier.startpage 34 en_US
dc.identifier.endpage 50 en_US
dc.cauo.name BUS.School of Finance and Economics en_US
dc.conference Verified OK en_US
dc.for 1502 Banking, Finance and Investment
dc.personcode 970685 en_US
dc.personcode 996174 en_US
dc.percentage 100 en_US
dc.classification.name Banking, Finance and Investment en_US
dc.classification.type FOR-08 en_US
dc.edition en_US
dc.custom en_US
dc.date.activity en_US
dc.location.activity en_US
dc.description.keywords equi-weighted index; growth optimal portfolio; Kelly portfolio; market capitalization-weighted index (MCI); naive diversification; numeraire portfolio en_US
dc.description.keywords equi-weighted index
dc.description.keywords growth optimal portfolio
dc.description.keywords Kelly portfolio
dc.description.keywords market capitalization-weighted index (MCI)
dc.description.keywords naive diversification
dc.description.keywords numéraire portfolio
dc.staffid en_US
dc.staffid 996174 en_US
pubs.embargo.period Not known
pubs.organisational-group /University of Technology Sydney
pubs.organisational-group /University of Technology Sydney/Faculty of Business
pubs.organisational-group /University of Technology Sydney/Faculty of Business/Finance
pubs.organisational-group /University of Technology Sydney/Faculty of Science
pubs.organisational-group /University of Technology Sydney/Faculty of Science/School of Mathematical Sciences
pubs.organisational-group /University of Technology Sydney/Strength - Quantitative Finance


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