Enhancing multi-asset portfolios future performance by applying different covariance estimates
Author
Frydkjær, Anker
Term
4. semester
Publication year
2022
Abstract
This thesis tests whether improving covariance estimation within the Markowitz mean-variance framework can enhance the future performance of multi-asset portfolios. Using monthly data for a well-diversified set of 10 assets across five asset classes over 22 years (January 2000 to December 2021) and a 20-year evaluation period, the study backtests mean-variance portfolios built with three covariance estimators: the conventional historical sample covariance, a shrinkage estimator (Ledoit and Wolf, 2004), and the Gerber Statistic. Their performance is also compared with a naive equal-weight (1/N) allocation. Across nearly all scenarios considered, portfolios based on the Gerber Statistic achieve higher returns than those using historical or shrinkage covariances, although the advantage is modest. Overall, the selected covariance methods do not produce markedly different future performance relative to one another. The 1/N portfolio does not outperform the optimized portfolios at similar risk (standard deviation) levels, but delivers very similar results, consistent with the ongoing debate in the literature.
Denne afhandling undersøger, om forbedrede estimater af kovariansmatricen i Markowitz’ mean-variance-ramme kan løfte porteføljers fremtidige performance. Med månedlige data for en veldiversificeret portefølje på 10 aktiver fordelt på fem aktivklasser over 22 år (januar 2000 til december 2021) og en evalueringsperiode på 20 år backtestes mean-variance-optimerede porteføljer baseret på tre kovariansestimater: den traditionelle historiske prøvekovarians, en shrinkage-estimator (Ledoit og Wolf, 2004) og Gerber-statistikken. Resultaterne sammenlignes desuden med en naiv ligevægtet 1/N-allokering. I næsten alle undersøgte scenarier leverer porteføljer baseret på Gerber-statistikken højere afkast end både historisk og shrinkage-kovarians, men fordelen er beskeden. Overordnet set differentierer de valgte kovariansmetoder sig ikke markant i forhold til fremtidig performance. 1/N-porteføljen overgår ikke de optimerede porteføljer ved samme risikoniveau (standardafvigelse), men præsterer meget ens, hvilket stemmer med den fortsatte debat i litteraturen.
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