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Portfolio Diversification
Francois-Serge Lhabitant
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eBook - ePub
Portfolio Diversification
Francois-Serge Lhabitant
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Portfolio Diversification provides an update on the practice of combining several risky investments in a portfolio with the goal of reducing the portfolio's overall risk. In this book, readers will find a comprehensive introduction and analysis of various dimensions of portfolio diversification (assets, maturities, industries, countries, etc.), along with time diversification strategies (long term vs. short term diversification) and diversification using other risk measures than variance. Several tools to quantify and implement optimal diversification are discussed and illustrated.
- Focuses on portfolio diversification across all its dimensions
- Includes recent empirical material that was created and developed specifically for this book
- Provides several tools to quantify and implement optimal diversification
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Sujet
MatemĂĄticasSous-sujet
TeorĂa de juegos1
Portfolio Size, Weights and Entropy-based Diversification
Abstract
Investors willing to diversify their portfolio will typically spread it amongst various assets. Their implicit assumption is that diversification increases as a function of the number of assets they hold. In financial literature, the latter is often referred to as âportfolio sizeâ or ânumber of linesâ, and is commonly used as a quick indicator of how well or poorly diversified a portfolio is. Intuitively, we would expect a portfolio made of N2 assets to be more diversified than a portfolio made of N1 assets, if N2 is larger than N1. For instance, Markowitz reports that âthe adequacy of diversification is not thought by investors to depend solely on the number of different securities heldâ. Sharpe also affirms that âthe number of securities in a portfolio provides a fairly crude measure of diversificationâ. However, in practice, there are several cases where these statements happen to be wrong. For instance, a 50-stock portfolio can have all its positions equally weighted at 2%, or be 99% invested in one stock and share the remaining 1% between the other 49 stocks. Both portfolios would have an identical size, but their diversification level would obviously be very different. To be meaningful, a measure of portfolio diversification should therefore consider the distribution of asset weights in its calculation.
Keywords
Cross entropy; Entropy-based Diversification; Entropy-based portfolio optimization; HerfindahlâHirschman index; Lorenz curve and the Gini index; Mathematical notations; Portfolio concentration measure; Portfolio Size; Pure weights; Shannon entropy
Investors willing to diversify their portfolio will typically spread it amongst various assets. Their implicit assumption is that diversification increases as a function of the number of assets they hold. In financial literature, the latter is often referred to as âportfolio sizeâ or ânumber of linesâ, and is commonly used as a quick indicator of how well or poorly diversified a portfolio is. Intuitively, we would expect a portfolio made of N2 assets to be more diversified than a portfolio made of N1 assets, if N2 is larger than N1. For instance, Markowitz [MAR 52] reports that âthe adequacy of diversification is not thought by investors to depend solely on the number of different securities heldâ. Sharpe [SHA 72] also affirms that âthe number of securities in a portfolio provides a fairly crude measure of diversificationâ. However, in practice, there are several cases where these statements happen to be wrong. For instance, a 50-stock portfo...