Optimization mean-variance portfolio

TABLE 1 Selected Optimal Mean-Variance Portfolios... 

Konno and Yamazaki (1991) proposed a large-scale portfolio optimization model based on mean-absolute deviation (MAD). This serves as an alternative measure of risk to the standard Markowitz s MV approach, which models risk by the variance of the rate of return of a portfolio, leading to a nonlinear convex quadratic programming (QP) problem. Although both measures are almost equivalent from a mathematical point-of-view, they are substantially different computationally in a few perspectives, as highlighted by Konno and Wijayanayake (2002) and Konno and Koshizuka (2005). In practice, MAD is used due to its computationally-attractive linear property. 

The obvious answer to heightened complexity and uncertainty lies in utilizing financial engineering techniques to manage asset portfolios. This chapter reviews the current state of the art from a practitioner s perspective. The prime focus is on mean-variance optimization techniques, which remain the principal application tool. The key message is that while the methods employed by today s specialists are not especially onerous mathematically or computationally, there are major issues in problem formulation and structure. It is in this arena that imagination and inventiveness take center stage. 

COMBINING MEAN-VARIANCE ANALYSIS WITH OTHER TECHNIQUES—CONSTRUCTING OPTIMAL HEDGE FUND PORTFOLIOS... 

In order to answer the question what share should be taken up by corporate bonds in a portfolio, ex post simulations were run. The Markowitz approach of portfolio optimization is based on using expected returns. Since the question of determining the optimal fixed income portfolio is to be answered against the background of historical data, the return and variance/covariance estimators are replaced by their historical return means and variances/covariances respectively. These historical data are computed congruently to the relevant investment horizon. For a 3-year investment horizon, the return means and variances/covariances of assets are computed on the basis of 36 monthly returns. The same is, in analogy, done for a 5-year investment horizon on the basis of 60 monthly returns. Investment horizons of three, five, and 10 years are analyzed here. For the investment horizon of, for example, five years, the monthly data in the time window from February 1980 to January 1985 are used. 

This research uses minimum-variance instead of the mean-variance approach to create a benchmark. There are several reasons for implementing the minimum-variance instead of originally proposed mean-variance approach. One of the disadvantages of mean-variance is the requirement of choosing the expected return, which is hard to estimate. Errors in estimation of that parameter lead to inefficient portfolios. As a consequence, weights become highly unstable. The other pitfall of the mean-variance approach is the sensitivity to small changes in the mean returns of portfolio s assets. Michaud [6] concludes that mean-variance method is the error-maximization method. In order to avoid the problems connected to mean-variance optimization, we concentrate on the minimum-variance portfolio. 

Run mean-variance optimization Obtain efflcient frontier and portfolio weights... 

The last stage of the BL portfolio optimization is application of the mean-variance approach, where we obtain the efficient portfolio weights based on previously calculated adjusted portfolio returns. ... 

Optimization model was built in Excel spreadsheet as proposed. Inputs for the optimization were 30-days average mean return for each share, variance-covariance matrix, and initial investment (at the beginning of each month). Excel add-in Solver was implemented into the macro and used to minimize portfolio s variance at the beginning of the each month. For each optimization. Solver was calibrated as the minimum of... 

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