Detta arbete syftar till att undersöka relationen mellan företagsstorlek och dess aktieavkastning,annars känt som storlekseffekten, inom halvledarsektorn. Vi använder oss av två portföljer bestående av de tio största och tio minsta halvledarbolagen och görutfallstestet under perioden 2004–2015. Tre olika allokeringsstrategier tillämpas: equal weight, meanvariance och equal risk contribution samt tre olika ombalanseringsperioder. Vårt resultat visar på ett negativt samband mellan företagsstorlek och riskjusterad avkastning oavsettallokeringsstrategi. Resultaten tyder på att effekten inte är en proxy för fundamentala skillnader ellerberor på en felspecificering av β. / This thesis aims to examine the relationship between firm size and stock return, otherwise known asthe size effect, within the semiconductor industry. We construct two portfolios each comprising the ten largest and smallest semiconductor companiesand conduct a back test between 2004-2015. We examine three allocation strategies: equal weight,mean variance, and equal risk contribution along three difference rebalancing periods. Our results show a negative relationship between firm size and risk adjusted return regardless ofallocation strategy. The results also show that size effect is not a proxy for fundamental differencesnor a misspecification of β.

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.

Student Number : 8804388Y - MSc Dissertation - School of Computational and Applied Mathematics - Faculty of Science / This dissertation considers the pricing and hedging of contingent claims in a general semimartingale market. Initially the focus is on a complete market, where it is possible to price uniquely and hedge perfectly. In this context the two fundamental theorems of asset pricing are explored. The market is then extended to incorporate risk that cannot be hedged fully, thereby making it incomplete. Using quadratic cost criteria, optimal hedging approaches are investigated, leading to the derivations of the minimal martingale measure and the variance-optimal martingale measure. These quadratic approaches are then applied to the problem of minimizing the basis risk that arises when an option on a non-traded asset is hedged with a correlated asset. Closed-form solutions based on the Black-Scholes equation are derived and numerical results are compared with those resulting from a utility maximization approach, with encouraging results.

Inicialmente neste trabalho são apresentados os conceitos básicos de média e variância e como estes se aplicam na caracterização de um ativo ou carteira de investimento. Posteriormente são apresentadas as estratégias ótimas de investimento para o modelo de Markowitz sem posições a descoberto em ativos de risco, e sem tal restrição. Ainda neste trabalho é apresentada uma breve revisão do modelo de tempo contínuo para o problema de média-variância sem posições a descoberto em ativos de risco, e como objetivo principal do mesmo é proposto um modelo em tempo discreto multiperíodo a partir do modelo de tempo contínuo, o qual é implementado computacionalmente para o mercado de capitais brasileiro. O resultado obtido é comparado com a estratégia de período único do modelo de Markowitz sem posições a descoberto em ativos de risco, sendo este modelo aplicado sequencialmente no horizonte de tempo considerado para o modelo multiperíodo. / Initially in this work are presented the basics concepts of mean and variance and how they are applied to quantify an asset or a portfolio. After this we present the optimal investment strategy of the Markowitz no-shorting constraints mean-variance portfolio selection in single period and the Markowitz optimal investment strategy without such constrain. Following this, we present a short review of the continuous-time dynamic model for the mean-variance portfolio selection with no-shorting constraints in risky assets problem. As the main objective of this work we propose a discrete time multiperiod model based on the continuous-time portfolio selection with no-shorting constraints in risky assets, that is applied to the Brazilian financial market. This result is compared with the investment strategy of the Markowitz no-shorting constraints mean-variance portfolio selection in single period applied sequentially in the multiperiod case.

This thesis consists of one stock return predictability study and two international risk exposure studies. The first study shows that the statistical significance of out-of-sample predictability of market returns given by Kelly and Pruitt (2013), using a partial least squares methodology, constructed from the valuation ratios of portfolios, is overstated for two reasons. Firstly, the analysis is conducted on gross returns rather than excess returns, and this raises the apparent predictability of the equity premium due to the inclusion of predictable movements of interest rates. Secondly, the bootstrap statistics used to assess out-of-sample significance do not account for small-sample bias in the estimated coefficients. This bias is well known to affect in-sample tests of significance and I show that it is also important for out-of-sample tests of significance. Accounting for both these effects can radically change the conclusions; for example, the recursive out-of-sample R2 values for the sample period 1965-2010 are insignificant for the prediction of one-year excess returns, and one-month returns, except in the case of the book-to-market ratios of six size- and value-sorted portfolios which are significant at the 10% level. The second study examines whether U.S. common stocks are exposed to international risks, which I define as shocks to foreign markets that are orthogonal to U.S. market returns. By sorting stocks on past exposure to this risk factor I show that it is possible to create portfolios with an ex-post spread in exposure to international risk. I examine whether the international risk is priced in the cross-section of U.S. stocks, and find that for small stocks an increase in exposure to international risk results in lower returns relative to the Fama-French three-factor model. I conduct similar analysis on a measure of the international value premium and find little evidence of this risk being priced in U.S. stocks. The third study examines whether a portfolios of U.S. stocks can mimic foreign index returns, thereby providing investors with the benefits of international diversification without the need to invest directly in assets that trade abroad. I test this proposition using index data from seven developed markets and eight emerging markets over the period 1975-2013. Portfolios of U.S. stocks are constructed out-of-sample to mimic these international indices using a step-wise procedure that selects from a variety of industry portfolios, stocks of multinational corporations, country funds and American depositary receipts. I also use a partial least squares approach to form mimicking portfolios. I show that investors are able to gain considerable exposure to emerging market indices using domestically traded stocks. However, for developed market indices it is difficult to obtain home-made exposure beyond the simple exposure of foreign indices to the U.S. market factor. Using mean-variance spanning tests I find that, with few exceptions, international indices do not improve over the investment frontier provided by the domestically constructed alternative of investing in the U.S. market index and portfolios of industries and multinational corporations.

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.

<p>In this thesis, portfolio optimisation is used to evaluate if a specific sample of portfolios have</p><p>a higher risk level or lower expected return, compared to what may be obtained through</p><p>optimisation. It also compares the return of optimised portfolios with the return of the original</p><p>portfolios. The risk analysis software Aegis Portfolio Manager developed by Barra is used for</p><p>the optimisations. With the expected return and risk level used in this thesis, all portfolios can</p><p>obtain a higher expected return and a lower risk. Over a six-month period, the optimised</p><p>portfolios do not consistently outperform the original portfolios and therefore it seems as</p><p>though the optimisation do not improve the return of the portfolios. This might be due to the</p><p>uncertainty of the expected returns used in this thesis.</p>

In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal wealth, subject to a terminal wealth constraint and convex portfolio constraints. The regime-switching is modeled using a finite state space, continuous-time Markov chain and the market parameters are allowed to be random processes. The solution to this problem is of interest to investors in financial markets, such as pension funds, insurance companies and individuals. We establish the existence and characterization of the solution to the given problem using a convex duality method. We encode the constraints on the given problem as static penalty functions in order to derive the primal problem. Next, we synthesize the dual problem from the primal problem using convex conjugate functions. We show that the solution to the dual problem exists. From the construction of the dual problem, we find a set of necessary and sufficient conditions for the primal and dual problems to each have a solution. Using these conditions, we can show the existence of the solution to the given problem and characterize it in terms of the market parameters and the solution to the dual problem. The results of the thesis lay the foundation to find an actual solution to the given problem, by looking at specific examples. If we can find the solution to the dual problem for a specific example, then, using the characterization of the solution to the given problem, we may be able to find the actual solution to the specific example. In order to use the convex duality method, we have to prove a martingale representation theorem for processes which are locally square-integrable martingales with respect to the filtration generated by a Brownian motion and a finite state space, continuous-time Markov chain. This result may be of interest in problems involving regime-switching models which require a martingale representation theorem.

In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal wealth, subject to a terminal wealth constraint and convex portfolio constraints. The regime-switching is modeled using a finite state space, continuous-time Markov chain and the market parameters are allowed to be random processes. The solution to this problem is of interest to investors in financial markets, such as pension funds, insurance companies and individuals. We establish the existence and characterization of the solution to the given problem using a convex duality method. We encode the constraints on the given problem as static penalty functions in order to derive the primal problem. Next, we synthesize the dual problem from the primal problem using convex conjugate functions. We show that the solution to the dual problem exists. From the construction of the dual problem, we find a set of necessary and sufficient conditions for the primal and dual problems to each have a solution. Using these conditions, we can show the existence of the solution to the given problem and characterize it in terms of the market parameters and the solution to the dual problem. The results of the thesis lay the foundation to find an actual solution to the given problem, by looking at specific examples. If we can find the solution to the dual problem for a specific example, then, using the characterization of the solution to the given problem, we may be able to find the actual solution to the specific example. In order to use the convex duality method, we have to prove a martingale representation theorem for processes which are locally square-integrable martingales with respect to the filtration generated by a Brownian motion and a finite state space, continuous-time Markov chain. This result may be of interest in problems involving regime-switching models which require a martingale representation theorem.

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.