This project describes the underlying principles of Modern Portfolio Theory (MPT), the Capital Asset Pricing Model (CAPM), and multi-factor models in detail. It also explores the process of constructing optimal portfolios using Modern Portfolio Theory, as well as estimates the expected return and covariance matrix of assets using the CAPM and multi-factor models. Finally, the project applies these models in real markets to analyze our portfolios and compare their performances.

In this Portfolio Optimization Project, we used Markowitz¡¯s modern portfolio theory for portfolio optimization. We selected fifteen stocks traded on the New York Stock Exchange and gathered these stocks¡¯ historical data from Yahoo Finance [1]. Then we used Markowitz¡¯s theory to analyze this data in order to obtain the optimal weights of our initial portfolio. To maintain our investment in a current tangency portfolio, we recalculated the optimal weights and rebalanced the positions every week. In the CAPM project, we used the security characteristic line to calculate the stocks¡¯ daily returns. We also computed the risk of each asset, portfolio beta, and portfolio epsilons. In the Factor Modeling project, we computed estimates of each asset¡¯s expected returns and return variances of fifteen stocks for each of our factor models. Also we computed estimates of the covariances among our asset returns. In order to find which model performs best, we compared each portfolio¡¯s actual return with its corresponding estimated portfolio return.

This project describes the underlying principles of Modern Portfolio Theory, the Capital Asset Pricing Model (CAPM), and multi-factor models in detail, explores the process of constructing optimal portfolios using the Modern Portfolio Theory, estimates the expected return and covariance matrix of assets using CAPM and multi-factor models, and finally, applies these models in real markets to analyze our portfolios and compare their performances.

This paper analyzes theperformance of five commercial real estate property types (office, retail, industrial, apartment, and hotel) between 2000 and 2012 to determine the U.S. housing crisis'simpact on Real Estate investing. Under the concept of Modern Portfolio Theory, the data was analyzed using investment analysis programs to determine correlation, risk/return characteristics, and trade-offs (Sharpe ratio) as well as the optimal allocation among the individual property types. In light of the results, each property type plays a different role in investment strategies in various economic cycles. Some assets are attractive solely based onpotential return, or risk for return tradeoffs; however, through diversification, other property types play valuable roles in hedging risk on investors' target returns.

Agricultural economists have long studied crop yields and risk to help farm-level risk management. Producers face difficult decisions every year regarding market prices, management practices, and the uncertainty of weather. In our research, we use crop yield records while incorporating the modern portfolio theory to find the optimal planting portfolios giving a specific risk level. Our assets are on corn, cotton, and soybeans yields from the Mississippi Delta region. This study is unique because there are not any previous studies using crop histories linked to the modern portfolio theory. The main idea is to realize how much of each asset or what percentage to invest in out of the specific portfolio. By having these portfolios readily available for farmers, we aim to diminish the risk to help producers with springtime decision-making. Armed with these findings, we can better understand the economic implications of how crop rotations factor into farm-level risk management.

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>

<p>Why do people invest? People are insecure about their future welfare and aim for future guaranteed cash flows. To give ourselves a more thorough introduction to investments we decided to write our bachelor-thesis within the area of finance. This thesis will combine financial institutions and investments. It is a topic repeatedly discussed in the media and a study carried out in Sweden showed that in 2003, 80% of the population were shareholders.</p><p>When trading with stocks and shares there is risk involved that can be defined as the volatility in the cash flow of an investment. A portfolio is a collection of securities that an investor has placed capital in. In order to minimise the risk of the portfolio, the investor can diversify his or her portfolio, which involves investing in different securities in order to minimise risk. Institutional Theory will help us to see how these financial institutions interact with each other and what internal and external factors may influence their behaviour. Institutional investors; such as banks, are seen as large actors on the financial markets as they gain more and more control over the management of equities. It is necessary that intermediaries take care of their customers and inform them thoroughly about the rules of the investment game. With this as a background we felt it would be interesting to investigate the following problem.</p><p>On what basis do financial institutions create their customers’ portfolios and is the process the same across the branch as a whole?</p><p>In order to find an answer to this question; we have done a qualitative study with an overall positivistic influence. The study is based upon an analysis of the empirical material; collected through interviews with three financial institutions, grounded in theory in order to answer our specific question.</p><p>From the information gathered we understood that the first information financial institutions gather is personal information about the investors, which is needed to get a picture and an understanding about their client. We have also learned how important it is to understand risk, as it is the risk that will determine the composition of the portfolio for the investor. We could see with the help of the institutional theory that there is little space for differentiation and can therefore say that the financial institutions work in the same way in the advising of their clients and for the composition of their client’s portfolio.</p><p>Our results show that the basis for the creation of portfolios is more or less the same across the branches as a whole. The service given may differ, due to the competence and knowledge level of employees, between institutions but the end product is similar in all aspects.</p>

<p><strong>Title: </strong>Measuring and handling risk - How different financial institutions face the same problem</p><p><strong>Seminar date: </strong>4^th of June, 2010</p><p><strong> </strong></p><p><strong>Level: </strong>Bachelor thesis in Business Administration, Basic level 300, 15 ECTS</p><p><strong>Authors: </strong>Sarah Rörden and Kristofer Wille</p><p><strong>Supervisor</strong>: Angelina Sundström</p><p><strong>Subject</strong> <strong>terms:</strong> Risk variables, Risk measurement, Risk management, Modern Portfolio Theory, Diversification, Beta</p><p><strong>Target group: </strong>Everyone who has basic knowledge of financial theories and risk principles but lacks the understanding of how they can be used in risk management.</p><p><strong> </strong></p><p><strong>Purpose: </strong>To understand the different Swedish financial institutions’ way of handling and reducing risk in portfolio investing using financial theories.</p><p><strong>Theoretical framework: </strong>The theoretical framework is based on relevant literature about financial theories and risk management, including critical articles.</p><p><strong> </strong></p><p><strong>Method: </strong>A multi-case study has been conducted, built upon empirical data collected through semi-structured interviews at three different financial institutions.</p><p><strong> </strong></p><p><strong>Empiricism: </strong>The study is based on interviews with Per Lundqvist, private banker at Carnegie Investment Bank AB; Erik Dagne, head of risk management department and Joachim Spetz, head of asset management at Erik Penser Bankaktiebolag; and David Lindström, asset manager at Strand Kapitalförvaltning AB.</p><p><strong> </strong></p><p><strong>Conclusion:</strong> There is a practical implementation of the theoretical models chosen for this research. The numbers the financial models generate do not tell one the entire truth about the total risk, therefore the models are used differently at each study object. For a model to hold it has to be transparent, and take each model’s assumptions into account. It all comes down to interpreting the models in an appropriate way.</p>

<p>There is evidence that globalization, economic assimilation and integration among countries and their financial markets have increased correlation among stock markets and the correlation may in turn impact investors’ allocation of their assets and economic policies. We have conducted a quantitative study with daily stock index quotes for the period January 2000 and December 2009 in order to measure the eventual correlation between the markets of ASEAN+3. This economic integration consists of; Indonesia, Malaysia, Philippines, Singapore, Thailand, China, Japan and South Korea. Our problem formulation is:Are the stock markets of ASEAN+3 correlated?Does the eventual correlation change under turbulent market conditions?In terms of the eventual correlation, discuss: is it possible to diversify an investment portfolio within this area?The purpose of the study is to conduct a research that will provide investors with information about stock market correlation within the chosen market. We have conducted the study with a positivistic view and a deductive approach with some theories as our starting point. The main theories discussed are; market efficiency, risk and return, Modern Portfolio Theory, correlation and international investments. By using the financial datatbase, DataStream, we have been able to collect the necessary data for our study. The data has been processed in the statistical program SPSS by using Pearson correlation.From the empirical findings and our analysis we were able to draw some main conclusions about our study. We found that most of the ASEAN+3 countries were strongly correlated with each other. Japan showed lower correlation with all of the other countries. Based on this we concluded that economic integration seems to increase correlation between stock markets. When looking at the economic downturn in 2007-2009, we found that the correlation between ASEAN+3 became stronger and positive for all of the countries. The results also showed that the correlation varies over time. We concluded that it is, to a small extent, possible to diversify an investment portfolio across these markets.</p>

Title: Measuring and handling risk - How different financial institutions face the same problem Seminar date: 4th of June, 2010   Level: Bachelor thesis in Business Administration, Basic level 300, 15 ECTS Authors: Sarah Rörden and Kristofer Wille Supervisor: Angelina Sundström Subject terms: Risk variables, Risk measurement, Risk management, Modern Portfolio Theory, Diversification, Beta Target group: Everyone who has basic knowledge of financial theories and risk principles but lacks the understanding of how they can be used in risk management.   Purpose: To understand the different Swedish financial institutions’ way of handling and reducing risk in portfolio investing using financial theories. Theoretical framework: The theoretical framework is based on relevant literature about financial theories and risk management, including critical articles.   Method: A multi-case study has been conducted, built upon empirical data collected through semi-structured interviews at three different financial institutions.   Empiricism: The study is based on interviews with Per Lundqvist, private banker at Carnegie Investment Bank AB; Erik Dagne, head of risk management department and Joachim Spetz, head of asset management at Erik Penser Bankaktiebolag; and David Lindström, asset manager at Strand Kapitalförvaltning AB.   Conclusion: There is a practical implementation of the theoretical models chosen for this research. The numbers the financial models generate do not tell one the entire truth about the total risk, therefore the models are used differently at each study object. For a model to hold it has to be transparent, and take each model’s assumptions into account. It all comes down to interpreting the models in an appropriate way.