"Practical usage of optimal portfolio diversification using maximum entropy principle" by Ostap Chopyk Abstract This thesis enhances the investigation of the principle of maximum entropy, implied in the portfolio diversification problem, when portfolio consists of stocks. Entropy, as a measure of diversity, is used as the objective function in the optimization problem with given side constraints. The principle of maximum entropy, by the nature itself, suggests the solution for two problems; it reduces the estimation error of inputs, as it has a shrinkage interpretation and it leads to more diversified portfolio. Furthermore, improvement to the portfolio optimization is made by using design-free estimation of variance-covariance matrices of stock returns. Design-free estimation is proven to provide superior estimate of large variance-covariance matrices and for data with heavy-tailed densities. To asses and compare the performance of the portfolios, their out-of-sample Sharpe ratios are used. In nominal terms, the out-of- sample Sharpe ratios are almost always lower for the portfolios, created using maximum entropy principle, than for 'classical' Markowitz's efficient portfolio. However, this out-of-sample Sharpe ratios are not statistically different, as it was tested by constructing studentized time-series...

Författarens syfte med studien är att undersöka om optionsstrategin covered call, kan generera bättre riskjusterad avkastning än jämförelseindex. Författaren bygger den kvantitativa undersökningen på sekundärdata som inhämtats från flera leverantörer av finansiell datahistorik. Ekonomisk teori som tillämpas är teorin om effektiva marknader, finansiell beteendevetenskap samt prospektteorin. Resultatet påvisar en riskjusterad högre avkastning för covered call-strategin. Adderas uppskattade transaktionskostnader visar resultatet att covered call har lägre standardavvikelse medan avkastningen är densamma som index.

Based on the assumption that returns in Commercial Real Estate are normally distributed, the Sharpe Ratio has been the standard risk-adjusted performance measure for the past several years. Research has questioned whether this assumption can be reasonably made. The Upside Potential Ratio as a risk-adjusted performance measure is an alternative to measure performance on a risk-adjusted basis but its values differ from the Sharpe Ratio's only in the assumption of skewed returns. We will provide reasonable evidence that CRE returns should not be fitted with a normal distribution and present the Gaussian Mixture Model as our choice of distribution to fit skewness. We will then use a GMM distribution to measure performance of CRE domestic markets via UPR. Additional insights will be presented by introducing an alternative risk-adjusted perfomance measure that we will call D-ratio. We will show how the UPR and the D-ratio can provide a tool-box that can be added to any existing investment strategy when identifying markets' past performance and timing of entrance. The intent of this thesis is not to provide a comprehensive framework for CRE investment decisions but to introduce statistical and mathematical tools that can serve any portfolio manager in augmenting any investment strategy already in place.

The cryptocurrency market is continuously growing but is still a relatively unexplored field within academic research. The ambition with this thesis is to increase existing research on market efficiency of cryptocurrencies, by studying the risk exposure of identical investments between different cryptocurrency exchanges. The study includes four cryptocurrencies and nine different exchanges, the data is tested on a full sample period and two subsample periods. The results reveal significant Sharpe ratio differences for identical investments on selected exchanges, but also improved efficiency between the first and second subsample periods. The study concludes that there are significant market inefficiencies on the cryptocurrency market, but the results also suggests that the market is becoming more efficient over time.

<p>This paper is an empirical study on Harry Markowitz work on Modern Portfolio Theory. The model introduced by him assumes the normality of assets’ return. We examined the OMX Large Cap List1 by mathematical and statistical methods for normality of assets’ returns. We studied the effect of the parameters, Skewness and Kurtosis for different time series data. We tried to figure it out which data series is better to construct a portfolio and how these extra parameters can make us better informed in our investments.</p>

<p><strong>Purpose:</strong> The main purpose of this study is to study the 45 funds, divided into three differentdivisions, then the result will provide a greater understanding of how returns change with ahigher risk.</p><p><strong>Methodology:</strong> The study is based on a quantitative approach. The survey was conducted bygathering raw data from databases and secondary data from literature, printed and electronicsources.</p><p><strong>Theoretical perspectives:</strong> The study is based on the theory: the efficient markethypothesis, which argues that future returns can not be calculated as the market is fullyinformed. The study is therefore studying historical yields.</p><p><strong>Empirical foundation:</strong> Empirical data are acquired from www.morningstar.se, andtherefore also treated on this page. The material is then divided into documents and time axes.</p><p><strong>Conclusions:</strong> The study has shown that high-risk funds give a higher percentage returns thanmedium-and low-risk funds. However, does not imply a higher risk automatically earn ahigher return when the low-risk funds have shown a higher yield than medium-risk funds. Animportant factor to study when you are looking for the fund which generated the highest ROIis the Sharpe ratio. Although this study demonstrates that high-risk funds have a higherSharpe ratio than competing risk groups.</p>

<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>

<p>This paper discusses the indicators of financial success for Swedish companies from 1995 until 2005. Quarterly data on 42 Swedish companies were collected from the Datastream data base and analysed by using both portfolio analyses and parametric analysis. In this study, financial success is measured by using the acclaimed concepts of the Sharpe ratio and the Jensen’s Alpha. The Sharpe ratios of the companies are studied between 1995-2005 and this discussion is complemented by analysis of the Jensen’s Alpha in the second half of that time period i.e. 2000-2005. The relationship between these performance metrics and certain company-characteristics such as the book-to-market ratio, the ROA measure and capital structure is studied. The conclusion is that companies that have a high degree of profitability and maintain high book-to-market ratios outperform other companies in terms of generating excess returns to shareholders. Another interesting observation is the fact that company size does not have any significant relationship to company performance.</p>

This paper is an empirical study on Harry Markowitz work on Modern Portfolio Theory. The model introduced by him assumes the normality of assets’ return. We examined the OMX Large Cap List1 by mathematical and statistical methods for normality of assets’ returns. We studied the effect of the parameters, Skewness and Kurtosis for different time series data. We tried to figure it out which data series is better to construct a portfolio and how these extra parameters can make us better informed in our investments.

This paper discusses the indicators of financial success for Swedish companies from 1995 until 2005. Quarterly data on 42 Swedish companies were collected from the Datastream data base and analysed by using both portfolio analyses and parametric analysis. In this study, financial success is measured by using the acclaimed concepts of the Sharpe ratio and the Jensen’s Alpha. The Sharpe ratios of the companies are studied between 1995-2005 and this discussion is complemented by analysis of the Jensen’s Alpha in the second half of that time period i.e. 2000-2005. The relationship between these performance metrics and certain company-characteristics such as the book-to-market ratio, the ROA measure and capital structure is studied. The conclusion is that companies that have a high degree of profitability and maintain high book-to-market ratios outperform other companies in terms of generating excess returns to shareholders. Another interesting observation is the fact that company size does not have any significant relationship to company performance.