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This empirical study has shown that optimal portfolios need approximately 10 securities to diversify away the unsystematic risk. This challenges previous studies of randomly chosen portfolios which states that at least 30 securities are needed. The result of this study sheds light upon the difference in risk diversification between random portfolios and optimal portfolios and is a valuable contribution for investors. The study suggests that a major part of the unsystematic risk in a portfolio can be diversified away with fewer securities by using portfolio optimization. Individual investors especially, who usually have portfolios consisting of few securities, benefit from these results. There are today multiple user-friendly software applications that can perform the computations of portfolio optimization without the user having to know the mathematics behind the program. Microsoft Excel’s solver function is an example of a well-used software for portfolio optimization. In this study however, MATLAB was used to perform all the optimizations. The study was executed on data of 140 stocks on NASDAQ Stockholm during 2000-2014. Multiple optimizations were done with varying input in order to yield a result that only depended on the investigated variable, that is, how many different stocks that are needed in order to diversify away the unsystematic risk in a portfolio. / <p>Osäker på examinatorns namn, tog namnet på den person som skickade mejl om betyg.</p>

This thesis focuses on stochastic dominance in portfolio selection problems. The thesis recalls basic knowledge from the area of portfolio optimization with utility functions and first, second, $N$-th and infinite order of stochastic dominance. It sumarizes Post's, Kuosmanen's and Kopa's criteria for portfolio efficiency and necessary and sufficient conditions of stochastic dominance for discrete and continuous probability distributions. The thesis also contains formulations of optimization problems with second order stochastic dominance constraints derived for discrete and continuous probability distributions. A practical application is also a part of the thesis, where the optimization problems for monthly returns of Czech stocks are solved using optimization software GAMS.

In this thesis we study models, which search for an optimal portfolio from a set of stocks. On the contrary to the classical approach focusing only on expected return and variance, we examine models where an additional crite- rion of skewness is included. Furthermore we formulate a model for measuring performance of a portfolio defined as the distance from the Pareto efficient frontier. In numerical experiments we apply the models on historical prices and stock data from the electronic stock market NASDAQ. We analyze the stock data from companies listed in the index NASDAQ-100. We conclude by comparing of optimal portfolios created using different models among each other, with trivial single-stock portfolios and the with NASDAQ-100 index itself.

Hlavním cílem této práce je poskytnout přehledné a ucelené informace o aplikaci portfolia managementu v projektovém řízení, zprostředkovat zkušenosti a doporučení ze zahraničních aplikací a také seznámit potencionální zájemce s návody, jak v případě zájmu postupovat při aplikaci v praxi. Práce vychází z obecného pohledu klasické teorie portfolia, na tuto část navazuje teoreticky zaměřený úsek věnující se teorii portfolio managementu. Poslední část je věnována aplikaci portfolia managementu a konkrétní ukázce implementace z praxe.

This study constructs a cross-market risk model based upon local multi-factor risk models of Taiwan, China and Singapore equity markets. This model allows each local market to adopt different local factors rather than force all local markets to use one parsimonious set of factors. We employ the world, country, industry, and global risk factors to build a structural model which could explain the relationship between local factors across market by further decomposing local factor returns. Therefore, this model could provide both in-depth and broad coverage analysis of international equity portfolios. Furthermore, we build a simple portfolio and its corresponding benchmark to illustrate the usage of our model. Once the contents of a portfolio are decided, this model could provide not only the risk estimation and decomposition in advance but also the performance attribution compared with the benchmark after the portfolio is realized. The analytical viewpoint could also easily change with different numeraire perspectives. The result demonstrates that this model is practical and flexible for international equity portfolio analysis.

With the advent of globalization and knowledge economic era, organizations have to face an increasingly competitive business environment. With limited resources, it is imperative for organizations to allocate them effectively, to focus on potential projects, to choose high value-added projects, and to find out the proper project portfolio. The purpose of this research is to investigate the decision model and the operational mechanism of project portfolio selection for military investment and to analyze the characteristics of related projects. Finally, this research mainly proposes a decision model for project portfolio selection and the measurement of portfolio performance and develops a portfolio selection decision support system to provide a communicative platform and information for decision makers and project managers. This will improve portfolio performance, reduce the crowding out effect of organizational resources, and enhance the linkage of both project and organizational goals.

The purpose of this study is to analyze the functional requirement of web-based portfolio supporting system and to investigate the relationship between learning portfolio and personal knowledge management. First, this study surveys the literature to explore the architecture of web-based portfolio supporting system. Then, a prototyping system that adopts the system architecture is implemented and finally this study evaluates the system by using the questionnaire and observing learners¡¦ operating conditions. A total of 69 subjects are from Kaohsiung Hospitality College. The main findings show that web-based portfolio supporting system meets learners¡¦ need mostly and has a positive effect on learners¡¦ learning process. Most learners are not familiar with portfolio assessment, and therefore teachers must make learners to understand what is portfolio assessment. A few learners organize and manage their personal learning portfolio according to their learning need. Furthermore, most learners are not used to sharing their files and knowledge. However, teachers can encourage learners to interact by promoting their sharing will. Finally, based on the research findings, this study proposes following suggestions for the follow-up research. 1. Portfolio assessment must be put into practice as soon as possible. 2. Improving teachers¡¦ participation to promote learners¡¦ will of interaction and sharing. 3. Adding teaching assistants to reduce learners¡¦ loading to establish learning portfolio.

<p>The financial portfolio model often referred to as the Black-Litterman model is analyzed using two approaches; a mathematical and a behavioral finance approach. After a detailed description of its framework, the Black-Litterman model is derived mathematically using a sampling theoretical approach. This approach generates a new interpretation of the model and gives an interpretable formula for the mystical parameter<b> τ</b>, the weight-on-views. Secondly, implications are drawn from research results within behavioral finance. One of the most interesting features of the Black-Litterman model is that the benchmark portfolio, against which the performance of the portfolio manager is evaluated, functions as the point of reference. According to behavioral finance, the actual utility function of the investor is reference-based and investors estimate losses and gains in relation to this benchmark. Implications drawn from research results within behavioral finance indicate and explain why the portfolio output given by the Black-Litterman model appears more intuitive to fund managers than portfolios generated by the Markowitz model. Another feature of the Black-Litterman model is that the user assigns levels of confidence to each asset view in the form of confidence intervals. Research results within behavioral finance have, however, shown that people tend to be badly calibrated when estimating their levels of confidence. Research has shown that people are overconfident in financial decision-making, particularly when stating confidence intervals. This is problematic. For a deeper understanding of the use of the Black-Litterman model it seems that we should turn to those financial fields in which social and organizational context and issues are taken into consideration, to generate better knowledge of the use of the Black-Litterman model.</p>

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