Oberseminar Finanz- und Versicherungsmathematik
In this paper, we propose a new approach for quantifying portfolio diversification. The proposed framework defines diversification with respect to a risk measure, and benefits can be interpreted as arising from risk diversification. When satisfying the axioms of coherency, the derived functional is called a coherent risk diversification measure, and it quantifies the percentage of idiosyncratic risk diversified in a portfolio. We also show that under the assumption of elliptically distributed returns, all coherent risk measures depend only on the first two moments of asset returns and portfolio distributions. Finally, we test the proposed risk diversification measures in empirical applications, taking into account various levels of risk aversion.
We discuss the concept of mean-risk-diversification efficient frontiers and illustrate how risk-diversified portfolios perform during periods of financial distress. We further examine the ability of portfolio strategies based on risk
diversification to outperform given tangent portfolios.