 Approximating the Numeraire Portfolio by Naive DiversificationEckhard Platen () and Renata Rendek No 281, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney Abstract: Estimation theory has shown, due to the limited estimation window available for real asset data, the sample based Markowitz mean-variance approach produces unreliable weights which fluctuate substantially over time. This paper proposes an alternate approach to portfolio optimization, being the use of naive diversification to approximate the numeraire portfolio. The numeraire portfolio is the strictly positive portfolio that, when used as benchmark, makes all benchmarked nonnegative portfolios either mean decreasing or trendless. Furthermore, it maximizes expected logarithmic utility and outperforms any other strictly positive portfolio in the long run. The paper proves for a well-securitized market that the naive equal value weighted portfolio converges to the numeraire portfolio 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 numeraire portfolio. Empirical evidence is presented that the Sharpe ratios of equi-weighted indices surpass significantly those of corresponding market capitalization weighted indices. This empirical stylized fact applies also to the market portfolio of equity markets of countries, which questions the applicability of the intertemporal capital asset pricing model. Finally, in time of financial crisis, a large equi-weighted fund carrying the investments of the major pension funds and insurance companies would provide important liquidity. It would not only dampen the extremes of a crisis but would also moderate the excesses of any asset price bubble. Keywords: Numeraire portfolio; growth optimal portfolio; Kelly portfolio; naive diversification; equi-weighted index; market capitalization weighted index; liquidity; Sharpe ratio; intertemporal capital asset pricing model (search for similar items in EconPapers) Published as: Platen, E. and Rendek, R., 2012, "Approximating the Numeraire Portfolio by Naive Diversification", Journal of Asset Management, 13(1), 34-50. There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:281 Access Statistics for this paper More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC. |
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