ترکیب تعادل، بازنمونهگیری و نمایش تحلیلگر در بهینه سازی سبد سرمایه گذاری

This paper proposes the use of a portfolio optimization methodology which combines features of equilibrium models and investor’s views as in Black and Litterman (1992), and also deals with estimation risk as in Michaud (1998). In this way, our combined methodology is able to meet the needs of practitioners for stable and diversified portfolio allocations, while it is theoretically grounded on an equilibrium framework. We empirically test the methodology using a comprehensive sample of developed countries fixed income and equity indices, as well as sub-samples stratified by geographical region, time period, asset class and risk level. In general, our proposed combined methodology generates very competitive portfolios when compared to other methodologies, considering three evaluation dimensions: financial efficiency, diversification, and allocation stability. By generating financially efficient, stable, and diversified portfolio allocations, our methodology is suitable for long-term investors such as Central Banks and Sovereign Wealth Funds.

Portfolio optimization methodologies play a central role in strategic asset allocation (SAA) where it is desirable to have portfolios that are efficient, diversified, and stable. Since the development of the traditional mean–variance approach of Markowitz (1952), many improvements have been made to overcome problems, such as lack of diversification and strong sensitivity of optimal portfolio weights to expected returns. The Black and Litterman (1992) model (hereafter BL) is among the most used approaches. The main idea of this model is that expected returns are the result of two important sources of information: market information in the form of equilibrium returns (implicit returns that clear out the outstanding market allocation), and analysts’ views which tilt the market portfolio to another diversified portfolio compatible with investor beliefs. In this fashion, portfolio managers get an intuitive but formal model to generate optimal allocation. However, while the BL model offers a very useful and intuitive approach to deal with asset allocation, the inputs considered for the calculation of equilibrium returns are subject to estimation error. Michaud (1998) proposed the use of resampling to deal with estimation error, which is an important source of lack of diversification in mean–variance portfolio. This technique considers that data come from a stochastic process instead of being a deterministic input as in Markowitz (1952). This paper proposes the use of a portfolio optimization methodology which combines features of both BL and resampling methodologies. This methodology allows a novel combination of equilibrium and investor’s views as in BL, and at same time, deals with estimation risk as in Michaud (1998). Thus, it generates robust and diversified optimal allocations which are desirable properties for long-term investors such as Central Banks and Sovereign Wealth Funds. We empirically test this methodology using a sample of fixed income and equity indices, achieving very supportive results. We find strong evidence supporting the use of resampling techniques to improve standard models like BL and Markowitz. In general, our proposed combined methodologies, both with and without views, generated very competitive portfolios compared to the other methodologies, considering the three evaluation dimensions: financial efficiency, diversification, and allocation stability. The remainder of this paper is as follows. Next section offers a brief literature review over asset allocation methodologies. The third section describes the Black-Litterman-Resampling combined methodology. The fourth section describes the empirical study, including data, implementation and initial results. Section 6 presents the robustness checks and Section 7 concludes the paper.

This paper deals with a well-documented issue in mean–variance optimization, related to the fact that this methodology typically leads to unintuitive portfolios with extreme positions in asset classes. In this article, we proposed the use of an optimization approach that takes advantage of both BL and resampling techniques to incorporate the main positive aspects of both previous powerful techniques. It is a stochastic general equilibrium model, which can be used as a tool for both passive and active strategies. The main idea is to estimate the efficient frontier using the BL model but consider this frontier as just an input to the resampling method. We empirically test this methodology using a comprehensive sample of bond and stock indices. Compared to traditional portfolio optimization methodologies, we reached very supportive results. We found strong evidence supporting the use of resampling techniques to improve standard methodologies. Generally speaking, our proposed methodologies, both with and without views, generated very competitive portfolios compared to the other methodologies, considering the three evaluation dimensions: financial efficiency, diversification, and allocation stability; and several levels of risk. As a suggestion for further research, we would recommend the use of non-normal distributions, instead of the multivariate normal, together with the BL and Resampling methodologies. For instance, we may extend the MAGH (Multivariate Affine Generalized Hyperbolic) portfolio optimization approach of Fajardo and Farias (2009) in a way to include equilibrium returns and resampling. It is important to highlight that recommendation of specific analysts’ views methodologies is out of the scope of the present study. The view considered in this article is just a naive example to show that the proposed methodology may be adapted to the analysts’ views. We argue that the proposal of views methodologies is still an open avenue for future research in portfolio management.