The concept of emerging markets came to surface in early 1980 and constituted of only eight countries from the two continents of South America and Asia. The globalization of financial markets has since raised the importance of emerging capital markets. We take a quantitative approach to investigate the performance of emerging markets compared to developed markets. The aim of the study is to conclude if emerging markets offers investment value and if logic in portfolio theory can be used to improve the chance of creating a relatively better performing investment. Included markets in our study are Brazil, Russia, India, China, Colombia, Indonesia, Vietnam, Egypt, Turkey and South Africa. S&P 500 is our benchmark for developed market performance. Sample period is 2002-01-01 to 2011-12-31 and monthly return data, creating 120 data points on each index.   The weighting schemes used for the portfolios are min variance optimization, geographical location and high and low correlation. All investments are scored on performances in correlation to S&P 500, inflation adjusted growth, currency effect, Sharpe ratio, skewness and kurtosis. Rankings are done on the separate categories, on the individual overall ranking on only countries and one overall ranking on all investments. A brief overview of the overall ranking for all investments suggest that medium performing investments are overrepresented (12/20) and the low and high is underrepresented (3/20 and 5/20). Of note is that the min variance portfolio outperforms its components, the geographical portfolios have a wide range and the high correlated portfolio outperforms the low. The country to portfolio ratio over each grade suggests only a small skew of the results. There is no low scoring portfolio but the other two ratios are close to 50/50, suggesting that on average the portfolios create diversification benefits. Furthermore normality of returns seem to be violated and then the concept of volatility as a risk measure is significantly impaired also currency risk can be of high importance, currency effects ranged from -48% to 28.7%. Assuming non-normality seems more accurate than assuming normality; therefore we need to improve on volatility as a tool to measure risk. So one direction for further research we see a need is in the concept of volatility. The initial reason for this research came from small investors’ seemingly intuitive knowledge that emerging markets are a suitable investment option. We have concluded that they in fact are, therefore we suggest that a qualitative study is conducted to investigate this seemingly natural intuition.

This thesis concerns the problem of statistical hypothesis testing for mean vector as well as testing for non-normality in a high-dimensional setting which is called the Kolmogorov condition. Since we consider mainly the first and the second moment in testing for mean vector and we utilize the third and the fourth moment in testing for non-normality, this thesis concerns a more general moment testing problem. The research question is related to a data matrix with $p$ rows, which is the number of parameters and $n$ columns which is the sample size, where $p$ can exceed $n$, assuming that the ratio $\frac{p}{n}$ converges when both the number of parameters and the sample size increase.  The first paper reviews the Dempster's non-exact test for mean vector, with a focus on one-sample case. We investigated its size and power properties compared to Hotelling's $\mathit{T}^2$ test as well as Srivastava's test using Monte Carlo simulation.  The second paper concerns the problem of testing for multivariate non-normality in high-dimensional data. We proposed three test statistics which are based on marginal skewness and kurtosis. Simulation studies are carried out for examining the size and power properties of the three test statistics. / Avhandlingen undersöker hypotesprövning i höga dimensioner, under förutsättning att det så kallad Kolmogorovvillkoret (Kolmogorov condition) är uppfyllt. Villkoret innerbär att antalet parametrar ökar tillsammans med storleken på stickprovet med en konstant hastighet. Till kategorin multivariat analys räknas de statistiska metoder som analyserar stickprov från flerdimensionella fördelningar, särskilt multivariat normalfördelning. För högdimensionella data fungerar klassiska skattningar av kovariansmatris inte tillfredställande eftersom komplexiteten med att skatta den inversa kovariansmatrisen ökar när dimensionen ökar. I den första uppsatsen utförs en genomgång av Dempsters (non-exact) test där skattning av den inversa kovariansmatrisen inte behövs. Istället används spåret (trace) av en kovariansmatris. I den andra uppsatsen testas antagandet om normalfördelning med hjälp av tredje och fjärde ordningens moment. Tre olika testvariabler har föreslagits där sumuleringar också presenteras för att jämföra hur väl en icke-normalfördelning identifieras av testet.

股票市場的報酬率相對於金融市埸是非常重要的，因為其背後的真實機率分配對各種資產定價及選擇權的評價模型都有決定性的影響。本文考慮台灣股票市埸具有漲跌停板的限制來驗證實證中股票報酬機率分配的「厚尾」的現象，希望透過我們的研究能對財務理論在國內金融市埸的應用有更進一步的了解。我們選定了常態分配、對數常態分配及一般化第二種貝它分配 (GB2)來當作是台灣股票報酬率的真實機率分配，以動差法比較再以概似比檢定法(LR test)選出一表現最好的機率分配。由選取的25支國內股票中發現一般化第二種貝它分配 (GB2)可以解釋偏態和峰態對報酬率的影響並且也是概似比檢定法所選出的最適報酬率分配，由此可知一般化第二種貝它分配 (GB2)較為適合作為台灣股票報酬的真實機率分配。