The UK has a commitment to reduce greenhouse gases by at least 80% from 1990 levels by 2050. This will see the proportion of energy generated in the UK from renewable resources such as wind, solar, marine and bio-fuels is increasing and likely to dominate the future energy market over the next few decades. However, it is unclear what effect future physical climate changes could have on the long term average energy output characteristics of individual renewable energy technologies that may dominate the low carbon energy technologies. It is also unclear how these changes to individual technologies will affect a diverse portfolio of electricity generation technologies. This thesis explores the influence of climate change on renewable electricity generation portfolios and energy security in the UK, with the aim of determining if climate change will affect renewable energy resource in such a way that may leave future low carbon generation portfolios sub-optimal. The research allows long term renewable resource variability to be reflected within models of the costs and risks associated with different electricity generation technologies and using Mean Variance Portfolio Theory (MVPT), it explores the influence of climate change on renewable energy portfolios and energy security in the UK. The scope of this study has a considerable range spanning from renewable resources through to the sensitivity of an optimal portfolio mix of generation technologies to climate change. In brief, the objectives were as follows: Characterise the variability of renewable energy resources and electricity generation output from renewable technology in the UK, in particular solar PV, on and offshore wind, for future climate scenarios for the 2050s and 2080s. Characterise the variability of electricity generation costs and explore the effect of climate change scenarios on generation costs and risk by examining the cost-risk balance of current and potential future low carbon electricity generation technology portfolios. The outcome saw distinctive changes in solar, wind, wave and hydro resource. The changes were largely negative, except in the case of solar, which increased. Levelised costs decreased for solar PV but increased for the technologies with negative resource changes. Evident changes in optimal portfolio mixes were observed and explored.

Ever since it was first introduced in an article in the Journal of Finance 1952, Harry Markowitz’ mean - variance model for portfolio selection has become one of the best known models in finance. The model was one of the first in the world to deal with portfolio optimization mathematically and have directly or indirectly inspired the rest of the world to develop new portfolio optimization methods. Although the model is one of the greatest contributions to modern portfolio theory, critics claim that it may have practical difficulties. Partly because the Markowitz model is based on various assumptions which do not necessarily coincide with the reality. The assumptions which are based on the financial markets and investor behavior contain the simplification that there are no transaction costs associated with financial trading. However, in reality, all financial products are subject to transaction costs such as brokerage fees and taxes. To determine whether this simplification leads to inaccurate results or not, we derive an extension of the mean-variance optimization model which includes brokerage fees occurred under the construction of an investment portfolio. We then compare our extension of the Markowitz model, including transaction costs, with the standard model. The results indicate that brokerage fees have a negligible effect on the standard model if the investor's budget is relatively large. Hence the assumption that no brokerage fees occur when trading financial securities seems to be an acceptable simplification if the budget is relatively high. Finally, we suggest that brokerage fees are negligible if the creation of the portfolio and hence the transactions only occurs once. However if an investor is active and rebalances his portfolio often, the brokerage fees could be of great importance. / Harry Markowitz portföljoptimeringsmodell har sedan den publicerades år 1952 i en artikel i the journal of Finance, blivit en av de mest använda modellerna inom finansvärlden. Modellen var en av dem första i världen att hantera portföljoptimering matematiskt och har direkt eller indirekt inspirerat omvärlden att utveckla nya portföljoptimeringsmetoder. Men trots att Markowitz modell är ett av de största bidragen till dagens portföljoptimeringsteori har kritiker hävdat att den kan ha praktiska svårigheter. Detta delvis på grund av att modellen bygger på olika antaganden som inte nödvändigtvis stämmer överens med verkligheten. Antagandena, som är baserad på den finansiella marknaden och individers investeringsbeteende, leder till förenklingen att transaktionskostnader inte förekommer i samband med finansiell handel. Men i verkligheten förekommer transaktions-kostnader som courtageavgifter och skatter nästintill alltid vid handel av finansiella produkter som t.ex. värdepapper. För att avgöra om modellen påvisar felaktiga resultat på grund av bortfallet av courtageavgifter härleds en utvidgning av Markowitz modell som inkluderar courtageavgifter. Utvidgningen av Markowitz modell jämförs sedan med originalmodellen. Resultaten tyder på att courtageavgifter har en försumbar effekt på originalmodellen om investeraren har en stor investeringsbudget. Slutsatsen är därför att, förenklingen att inga courtageavgifter förekommer är en acceptabel förenkling om investeringsbudgeten är stor. Det föreslås slutligen att courtageavgiften är försumbar om transaktionen av aktier endast sker en gång. Men om en investerare är aktiv och ombalanserar sin portfölj flitigt, kan courtageavgifterna vara av stor betydelse.

This paper consolidates and compares the applicability and practicality of Black-Litterman model versus traditional Markowitz Mean-Variance model. Although well-known model such as Mean-Variance is academically sound and popular, it is rarely used among asset managers due to its deficiencies. To put the discussion into context we shed light on the improvement made by Fisher Black and Robert Litterman by putting the performance and practicality of both Black- Litterman and Markowitz Mean-Variance models into test. We will illustrate detailed mathematical derivations of how the models are constructed and bring clarity and profound understanding of the intuition behind the models. We generate two different portfolios, composing data from 10-Swedish equities over the course of 10-year period and respectively select 30-days Swedish Treasury Bill as a risk-free rate. The resulting portfolios orientate our discussion towards the better comparison of the performance and applicability of these two models and we will theoretically and geometrically illustrate the differences. Finally, based on extracted results of the performance of both models we demonstrate the superiority and practicality of Black-Litterman model, which in our particular case outperform traditional Mean- Variance model.

Portfolio selection theory, developed by Markowitz (1952), is one of the best known and widely applied methods for allocating funds among possible investment choices, where investment decision making is a trade-off between the expected return and risk of the portfolio. Many portfolio selection models have been developed on the basis of Markowitz's theory. Most of them assume that complete investment information is available and that it can be accurately extracted from the historical data. However, this complete information never exists in reality. There are many kinds of ambiguity and vagueness which cannot be dealt with in the historical data but still need to be considered in portfolio selection. For example, to address the issue of uncertainty caused by estimation errors, the robust counterpart approach of Ben-Tal and Nemirovski (1998) has been employed frequently in recent years. Robustification, however, often leads to a more conservative solution. As a consequence, one of the most common critiques against the robust counterpart approach is the excessively pessimistic character of the robust asset allocation. This thesis attempts to develop new approaches to improve on the respective performances of the robust counterpart approach by incorporating additional investment information sources, so that the optimal portfolio can be more reliable and, at the same time, achieve a greater return.

Since most financial institutions use the Sharpe Ratio to evaluate the performance of mutual funds, the objective of most fund managers is to select the portfolio that can generate the highest Sharpe Ratio. Traditionally, they can revise the objective function of the Markowitz mean-variance portfolio model and resolve non-linear programming to obtain the maximum Sharpe Ratio portfolio. In the scenario with short sales allowed, this project will propose a closed-form solution for the optimal Sharpe Ratio portfolio by applying Cauchy-Schwarz maximization. This method without using a non-linear programming computer program is easier than traditional method to implement and can save computing time and costs. Furthermore, in the scenarios with short sales disallowed, we will use Kuhn-Tucker conditions to find the optimal Sharpe Ratio portfolio. On the other hand, an efficient frontier generated by Markowitz mean-variance portfolio model normally has higher risk higher return characteristic, which often causes dilemma for decision maker. This research applies generalized loss function to create a family of decision-aid performance measures called IRp which can well tradeoff return with risk. We compare IRp with Sharpe Ratio and utility functions to confirm that IRp measures are approapriate to evaluate portfolio performance on efficient frontier and to improve asset allocation decisions. In addition, empirical data of domestic and international investment instruments will be used to examine the feasibility and fitness of the new proposed method and IRp measures. This study applies the methods of Cauchy-Schwarz maximization in multivariate statistical analysis and loss function in quality engineering to portfolio decisions. We believe these new applications will complete portfolio model theory and will be meaningful for academic and business fields.

Investment-linked insurance in Taiwan has been listed for almost a decade since 2001. In 2002, after the big sales of the investment-linked insurance, the domestic insurance companies also joined the market. For the investment-linked insurance, the policyholders retain the protection of the life insurance as well as share the earnings of the investment. Since the main investment instruments of the investment-linked insurance are mutual funds, it is important to study how to optimally allocate the portfolio. This research consider the returns of the mutual funds under tree models assumption. The objective is to find the optimal portfolio which has minimum variance and attained a given expected return level. The problem is also known as mean-variance portfolio problem. In the empirical work, we study eleven daily mutual fund price data from Sep. 2007 to Nov. 2008. Using the data of the first 12 months, we first establish initial tree price models, then update the parameters of the tree model by the EWMAmethod. The optimal trading strategies of the mean-variance portfolio are investigated under this model setting. We class the mutual funds into three categories: equity funds, balanced funds and bond funds. Different combination of these three kinds of funds are considered to find the optimal trading strategy respectively. The results showed that the realized returns using this optimal trading strategy in practice is close to the pre-specified expected return level.

The most popular and fundamental portfolio optimization problem is Markowitz&#039 / s one period mean-variance portfolio selection problem. However, it is criticized because of its one period static nature. Further, the estimation of the stock price expected return is a particularly hard problem. For this purpose, there are a lot of studies solving the mean-variance portfolio optimization problem in continuous time. To solve the estimation problem of the stock price expected return, in 1992, Black and Litterman proposed the Bayesian asset allocation method in discrete time. Later on, Lindberg has introduced a new way of parameterizing the price dynamics in the standard Black-Scholes and solved the continuous time mean-variance portfolio optimization problem. In this thesis, firstly we take up the Lindberg&#039 / s approach, we generalize the results to a jump-diffusion market setting and we correct the proof of the main result. Further, we demonstrate the implications of the Lindberg parameterization for the stock price drift vector in different market settings, we analyze the dependence of the optimal portfolio from jump and diffusion risk, and we indicate how to use the method. Secondly, we present the Lagrangian function approach of Korn and Trautmann and we derive some new results for this approach, in particular explicit representations for the optimal portfolio process. In addition, we present the L2-projection approach of Schweizer for the continuous time mean-variance portfolio optimization problem and derive the optimal portfolio and the optimal wealth processes for this approach. While, deriving these results as the underlying model, the market parameterization of Lindberg is chosen. Lastly, we compare these three different optimization frameworks in detail and their attractive and not so attractive features are highlighted by numerical examples.

Within the scope of this thesis, the Black-Litterman Asset Allocation Model (as presented in He & Litterman, 1999) is compared to the classical mean-variance framework by simulating past performance of portfolios constructed by both models using identical input data. A quantitative investment strategy which favours stocks with high dividend yield rates is used to generate private views about the expected excess returns for a fraction of the stocks included in the sample. By comparing the ex-post risk-return characteristics of the portfolios and performing ample sensitivity analysis with respect to the numerical values assigned to the input variables, we evaluate the two models’ suitability for different categories of portfolio managers. As a neutral benchmark towards which both portfolios can be measured, a third market-capitalization-weighted portfolio is constructed from the same investment universe. The empirical data used for the purpose of our simulations consists of total return indices for 23 of the 30 stocks included in the OMXS30 index as of the 21st of February 2014 and stretches between January of 2003 and December of 2013.   The results of our simulations show that the Black-Litterman portfolio has delivered risk-adjusted return which is superior not only to that of its market-capitalization-weighted counterpart but also to that of the classical mean-variance portfolio. This result holds true for four out of five simulated strengths of the investment strategy under the assumption of zero transaction costs, a rebalancing frequency of 20 trading days, an estimated risk aversion parameter of 2.5 and a five per cent uncertainty associated with the CAPM prior. Sensitivity analysis performed by examining how the results are affected by variations in these input variables has also shown notable differences in the sensitivity of the results obtained from the two models. While the performance of the Black-Litterman portfolio does undergo material changes as the inputs are varied, these changes are nowhere near as profound as those exhibited by the classical mean-variance portfolio.   In the light of our empirical results, we also conclude that there are mainly two aspects which the portfolio manager ought to consider before committing to one model rather than the other. Firstly, the nature behind the views generated by the investment strategy needs to be taken into account. For the implementation of views which are of an α-driven character, the dynamics of the Black-Litterman model may not be as appropriate as for views which are believed to also influence the expected return on other securities. Secondly, the soundness of using market-capitalization weights as a benchmark towards which the final solution will gravitate needs to be assessed. Managers who strive to achieve performance which is fundamentally uncorrelated to that of the market index may want to either reconsider the benchmark weights or opt for an alternative model.

<p><strong>Syfte: </strong>En komparativ studie och beskriva möjligheterna för att skapa en effektiv portfölj av olika aktieportföljer, där det undersöks om faktorerna som företagens omsättningsstorlek, branschen de är aktiva i och valet att ha utländska aktier, har betydelse eller inte för att skapa en effektiv portfölj med hänsyn till dess korrelation, avkastning och risk. </p><p><strong>Metod: </strong>Uppsatsen utgår från en kvantitativ studie, som sträcker sig från april 2008 till april 2010, då historiska aktiekurspriser används för olika sorters uträkningar, som baseras på uppsatsens huvudteorier; CAPM, Sharpekvot och portföljteori. Utgångspunkten är deduktiv, där slutsatserna har dragits från teorierna.       </p><p><strong>Slutsats: </strong>Utifrån uträkningarna, kunde det inte dras generella slutsatser där de undersökta faktorerna inte utmärkte sig i något mönster. Däremot visade sig att det blev högre avkastning till liknande risk eller lägre risk till liknade avkastning när man väljer aktier som är olika varandra, då korrelationen inte samvarierar. Det bästa resultatet är när utländska aktier blandas in i portföljen.    </p>

Syfte: En komparativ studie och beskriva möjligheterna för att skapa en effektiv portfölj av olika aktieportföljer, där det undersöks om faktorerna som företagens omsättningsstorlek, branschen de är aktiva i och valet att ha utländska aktier, har betydelse eller inte för att skapa en effektiv portfölj med hänsyn till dess korrelation, avkastning och risk.  Metod: Uppsatsen utgår från en kvantitativ studie, som sträcker sig från april 2008 till april 2010, då historiska aktiekurspriser används för olika sorters uträkningar, som baseras på uppsatsens huvudteorier; CAPM, Sharpekvot och portföljteori. Utgångspunkten är deduktiv, där slutsatserna har dragits från teorierna.        Slutsats: Utifrån uträkningarna, kunde det inte dras generella slutsatser där de undersökta faktorerna inte utmärkte sig i något mönster. Däremot visade sig att det blev högre avkastning till liknande risk eller lägre risk till liknade avkastning när man väljer aktier som är olika varandra, då korrelationen inte samvarierar. Det bästa resultatet är när utländska aktier blandas in i portföljen.