Can modern portfolio optimization strategies outperform 1/N on the Danish stock market?

Casper Clement Andersen & Michael Murtaz Musajev

Student thesis: Master thesis


The main objective of this thesis is to assess the performance of modern portfolio choice models in comparison with 1/N on the Danish Stock market in the period from 1980 to 2010. We search for a strategy with the ability to consistently outperform the benchmark. By applying Fama-French theory on a large sample of Danish equities, we form 6 Size and Book-To-Market portfolios, as well as 6 Size and Momentum portfolios. These datasets are analyzed separately and jointly where we find strong evidence in support of the sample-based asset allocation models. This is explained by the modest N and the fact that the constructed Fama-French portfolios, by nature, result in both excellent as well as devastating evolvements. We develop the means to assess optimal asset allocation with time dependency in N, and address extreme cases of +100 shares. In general large values of N imply a well-diversified 1/N strategy, as our results also emphasize, i.e. none of the sample-based models presented even a single incident of outperforming the benchmark in any of the two datasets considered with a substantially large N. By simulating various datasets, calibrated to reflect both stocks as well as portfolios, performance is evaluated for extreme values of M and T. We find that the sample-based strategies have a better chance of outperforming 1/N on stocks rather than portfolios. Inspired by Brandt, Santa-Clara and Valkanov (2007), we suggest a fairly simple approach to allocate wealth relying on the firm characteristic Price-Earnings ratio, and assess whether such a model brings anything new into the field of asset allocation. In alignment with DeMiguel et al. 2007, our study suggests a tendency of the cross-sectional firm characteristic model to enhance performance, although it is not consistently statistically superior, than the sample-based asset allocation models. Putting things into perspective we compare our results on the Danish Stock market with a similar study performed on the U.S. market (DeMiguel et al. 2007). Overall our findings on the Danish market are in alignment with the U.S. results, in the sense that none of the considered strategies were proven to be consistently superior to 1/N. Despite our findings, we present empirical evidence of equity funds that have, at least to some extent, implemented similar strategies to the ones examined in this thesis. The Swiss asset management company Unigestion follows a long-only Minimum-Variance strategy, which presents a convincing performance compared to the DJ Europe Stoxx 600, i.e. considerably lower yearly volatility as well as higher returns. As for asset allocation with respect to Price-Earnings ratios, we clarify the performance of the India Tata Equity P/E fund obtained since it was founded, and compare it to the BSE Sensex 30 index. Evolvements in normalized total return indexes as well as yearly volatilities indicate that the P/E fund outperforms the Indian market.

EducationsMSc in Business Administration and Management Science, (Graduate Programme) Final Thesis
Publication date2010
Number of pages145