Diversification and the Optimal Construction of Basis Portfolios (original) (raw)
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A factor analysis of international portfolio diversification
Studies in Economics and Finance, 2008
Purpose -The purpose of this paper is to investigate the relationships between stock market returns of 13 countries based upon monthly data spanning December 1987 to April 2007. Design/methodology/approach -Specifically, the principal component (PC) and maximum likelihood (ML) methods are used to examine any discernable patterns of stock market co-movements. Findings -Factor analysis provides evidence that stock returns in a number of Asian countries are highly correlated and, based on the resulting robust factor loadings, they form the first well-defined common factor. The paper also finds consistent results (based on both the PC and ML methods) suggesting that the stock market returns of developed countries are also highly correlated, and constitute our second factor. Practical implications -The paper concludes that, inter alia, geographical proximity and the level of economic development do matter when it comes to co-movements of stock returns and that this has important implications for financial portfolio diversification if the aim is to reduce systematic risks across countries. Originality/value -Very few previous studies have investigated the benefits from portfolio diversification by using the PC and ML methods.
Optimal Portfolio Diversification via Independent Component Analysis
SSRN Electronic Journal, 2018
A natural approach to enhance portfolio diversification is to rely on factor-risk parity, which yields the portfolio whose risk is equally spread among a set of uncorrelated factors. The standard choice is to take the variance as risk measure, and the principal components (PCs) of asset returns as factors. Although PCs are unique and useful for dimension reduction, they are an arbitrary choice: any rotation of the PCs results in uncorrelated factors. This is problematic because we demonstrate that any portfolio is a factor-varianceparity portfolio for some rotation of the PCs. More importantly, choosing the PCs does not account for the higher moments of asset returns. To overcome these issues, we propose to use the independent components (ICs) as factors, which are the rotation of the PCs that are maximally independent, and care about higher moments of asset returns. We demonstrate that using the IC-variance-parity portfolio helps to reduce the return kurtosis. We also show how to exploit the near independence of the ICs to parsimoniously estimate the factor-risk-parity portfolio based on Value-at-Risk. Finally, we empirically demonstrate that portfolios based on ICs outperform those based on PCs, and several state-of-the-art benchmarks.
Diversification of equity investment portfolios. Application to the IBEX 35
Finance, Markets and Valuation, 2021
At present, there is no unanimity on the effects that stock diversification can have on the total risk of an investment portfolio. In this context, this paper studies some issues related to the evolution of risk in an investment portfolio made up of IBEX 35 stocks. In addition, it is tested whether conclusions drawn for other time periods and in other markets are applicable to the Spanish stock market. The methodology used consists of calculating how the two components that make up the total risk of a portfolio (systematic risk and unsystematic risk) behave as portfolios of increasing size are diversified. The study shows how an increase in the number of securities in the investment portfolio decreases the percentage corresponding to the unsystematic risk component and increases the systematic risk component. Furthermore, it also shows that the benefits of diversification become increasingly marginal as portfolio size increases. Additionally, it is shown that an increase in the numb...
Pesquisa Operacional, 2012
Faced with so many risk modeling alternatives in portfolio optimization, several questions arise regarding their legitimacy, utility and applicability. In particular, a question arises involving the adherence of the alternative models with regard to the basic presupposition of Markowitz's classical model, with regard to the concept of diversification as a means of controlling the relationship between risk and return within a process of optimization. In this context, the aim of this article is to explore the riskdifferentiated configurations that entropy can provide, from the point of view of the repercussions that these have on the degree of diversification and on portfolios performance. The reach of this objective requires that a comparative analysis is made between models that include entropy in their formulation and the classic Markowitz model. In order to contribute to this debate, this article proposes that adaptations are made to the models of relative minimum entropy and of maximum entropy, so that these can be applied to investment portfolio optimizations. The comparative analysis was based on performance indicators and on a ratio of the degree of portfolio diversification. The portfolios were formed by considering a sample of fourteen assets that compose the IBOVESPA, which were projected during the period from January 2007 to December 2009, and took into account the matrices of covariance that were formed as from January 1999. When comparing the Markowitz model with two models that were constructed to represent new risk configurations based on entropy optimization, the present study concluded that the first model was far superior to the others. Not only did the Markowitz model present better accumulated nominal yields, it also presented a far greater predictive efficiency and better effective performance, when considering the trade-off between risk and return. However, with regards to diversification, the Markowitz model concentrated its weights in only five of the fourteen sample assets. Contrary to these two models, the maximum entropy model showed a level of diversification that was very close to the maximum level, which would be a situation that is far more in keeping with Markowitz's diversification precepts. However, these models showed the worst results in the comparative analysis of performance.
Optimal Versus Naive Diversification in Factor Models
We compare the performance of alternative diversification strategies under parameter uncertainty. We show analytically and numerically that if return data are generated by a one-factor model, the Sharpe ratio of the optimal and naive (1/N ) portfolio are very close, even if the true parameters are known. Earlier evidence on the outperformance of sophisticated diversification strategies over naive diversification is therefore not very informative if based on a one-factor set-up. In a two-factor set-up, we show that the difference can become substantially larger. The conditions to obtain these large differences, however, are typically not satisfied for real data. Generalizing our results to the multi-factor context, we show that economically significant results can be obtained for three or more factors. These findings are corroborated empirically.
PORTFOLIO DIVERSIFICATION: AN ECONOMETRIC APPROACH
This paper examines the opportunities of diversification across the European (specifically Eurozone’s) stock exchange markets by using three econometric approaches: short-run correlation, long-run correlation and co-integration in 200 securities randomly obtained from several of capital markets. In the last section the interest is shifted from the econometrics to the real market conditions examining a case study, where a moderate investor choose either the constructed portfolios or 10-year of maturity German bonds.
Statistical Analysis on the Advantages of Portfolio Diversification
The classical mean-variance portfolio selection problem (PSP) pioneered by Markowitz is, undoubtedly, one of the most frequently studied areas in finance, and several financial analysts regard it as the foundation of modern portfolio theory (MPT). The model in its basic form deals with making a choice from a universe of assets to form a master asset known as portfolio of assets. The main aim of such a strategy is to achieve a reasonable trade-off given the conflicting objectives related to making a maximum possible return/profit at the most minimum risk possible, provided that the right choice of constituent assets is made and proper weights (fraction of investment funds) are correspondingly allotted. In this paper, we looked at the effects and advantages of constructing a reasonably diversified portfolio from a pool of assets while giving emphasis on the interrelationship existing among the portfolio's constituent assets.
Factor models in portfolio and
2008
The foundation of modern portfolio theory is the mean-variance port-folio selection approach of Markowitz (1952, 1959). We discuss the role of factor models in implementing portfolio selection, defining the nature of systematic risk, and estimating the premium for risk bearing.
Strategy of asset portfolio risk diversification through value drivers
REBRAE, 2015
The risk diversification of an asset portfolio of investments is underlying in the idea that all securities have an idiosyncratic behavior which allows compensating a specific stock loss by the gain achieved by other stock into the portfolio. However, we know that the portfolio selection process should excel for choosing assets capable of creating and generating value on the long term. Thus, the objective of this research was to verify if the portfolios selected through their value drivers present the diversification benefits that were determined in prior researches. We had used the data available at Economatica data base of the following Stock Exchanges: Argentina; Brazil; Chile; and Mexico. To select the portfolios by value drivers we used a model based upon the weighted factors decision matrix where the securities were hierarchized by their grades. The variables used as factors, were the Tobin’s Q, Beta, Leverage, Price/Earning Ratio, and the Price Sales Ratio. All portfolios wer...