A Diversification Measure for Portfolios of Risky Assets

Diversification Measures and the Optimal Number of Stocks in a Portfolio: An Information Theoretic Explanation

“…Since the pioneering work of Markowitz (1952), different methods have been proposed, in an attempt to measure diversification across portfolios. Despite these proposals, there has not been consensus on a metric to measure diversification (Frahm & Wiechers 2011;Rudin & Morgan 2006). The lack of consensus is not because of conflicting definitions of the concept, rather it arises out of the problem of how to measure the quantity defined.…”

“…The relationship between the degree of diversification, and variance, is what makes diversification an important concept. According to Frahm & Wiechers (2011), "It is the diversification effect among different assets that seems to contribute to portfolio performance". One interpretation of this is that the more independent sources of variation there are in a portfolio, the less likely it will be heavily vulnerable to individual component shocks.…”

“…An example is the method introduced by Meucci (2010) which uses the principal component analysis approach with information theory in quantifying diversification. The merits and demerits of these approaches are discussed in Frahm & Wiechers (2011). In this paper we make use of the PDI measure to capture the level of diversification in a portfolio.…”

Improving portfolio diversification: Identifying the right baskets for putting your eggs

“…The challenge with the factor‐based approach lies in identifying the underlying risk factors. The standard approach for extracting the orthogonal factors is to use the principal component analysis (PCA; Frahm & Wiechers, ; Lohre, Neugebauer, & Zimmer, ). Meucci et al () note several disadvantages of the PCA‐based diversification measures.…”

Modeling and Forecasting Realized Portfolio Diversification Benefits

“…Recently, the work in Frahm and Memmel (2010) suggested to measure diversification as a ratio of the current portfolio variance and the GMVP variance. The work in Frahm and Wiechers (2013) analyzed the properties of this measure and showed that it possesses a convenient economic interpretation. The availability of intraday returns allows computing daily realized variances and covariances of risky asset returns, which are consistent estimators of the daily covariance matrix (Barndorff-Nielsen and Shephard 2004).…”