Markowitz approach

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. 

In this chapter we addressed the question of what proportions corporate and government bonds of different credit quality and maturity segments an investor should hold in a fixed-income portfolio. Maximizing the risk/ return relation according to the Markowitz approach is the core issue here. Optimal portfolio weights were established in ex post simulations. 

The first approach adopts the classical Markowitz s MV model to handle randomness in the objective function coefficients of prices, in which the expected profit is maximized while an appended term representing the magnitude of operational risk due to variability or dispersion in price, as measured by variance, is minimized (Eppen, Martin, and Schrage, 1989). The model can be formulated as minimizing risk (i.e., variance) subject to a lower bound constraint on the target profit (i.e., the mean return). 

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. 

Markowitz et al. developed a different approach, again in an attempt to overcome some of the inherent difficulties that arise when imprinted bulk materials are used as catalysts [82], Here, the authors used a template-directed method to imprint an a-chymotrypsin TSA at the surface of silica nanoparticles, prepared with a number of organically modified silanes as functional monomers. Silica particle formation was performed in a microemulsion, where a mixture of a non-ionic surfactant and... 

Markowitz [66] also notes that the entropy changes for reactions (2.13) and (2.14) are similar for the majority of metal perchlorates. Hence the differences in AG for reactions (2.13) and (2.14) arise from the differences in A// for these two reactions. As discussed above, this difference will then be determined by the differences in the enthalpies of formation of equivalent amounts of the chloride and the oxide. Such values are often more accessible than values of AG fo .son- The validity of this approach is confirmed [66] by a consideration of available data for the decomposition products of metal perchlorates. 

Figure 3 Surfactant TSA and amphiphilic templates used by Markowitz et al. for imprinting into silica surfaces via a sol-gel approach. ...

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