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.

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.

A passive investment management model was developed via a critical literature review of portfolio methodologies. This model was developed based on the fundamental models originated by both Markowitz and Sharpe. The passive model was automated via the development of a computer programme that can be used to generate the required outputs as suggested by Markowitz and Sharpe. For this computer programme MATLAB is chosen and the model’s logic is designed and validated. The demonstration of the designed programme using securities traded is performed on Johannesburg Securities Exchange. The selected portfolio has been sub-categorised into six components with a total of twenty- seven shares. The shares were grouped into different components due to the investors’ preferences and investment time horizon. The results demonstrate that a test portfolio outperforms a risk- free money market instrument (the government R194 bond), but not the All Share Index for the period under consideration. This design concludes the reason for this is due in part to the use of the error term from Sharpe’s single index model. An investor following the framework proposed by this design may use this to determine the risk- return relationship for selected portfolios, and hopefully, a real return.

<p>There is a big interest for alternative investment strategies than investing in traditional asset classes. Commodities are having a boom dynamic with increasing prices. This thesis is therefore based on applying Modern Portfolio Theory concept to this alternative asset class.</p><p>In this paper we manage to create optimal portfolios of commodities for investors with known and unknown risk preferences. When comparing expected returns to actual returns we found that for the investor with the known risk preference almost replicated the return of the markets. The other investor with unknown risk preference also profited but not as efficient as the market portfolio.</p>

There is a big interest for alternative investment strategies than investing in traditional asset classes. Commodities are having a boom dynamic with increasing prices. This thesis is therefore based on applying Modern Portfolio Theory concept to this alternative asset class. In this paper we manage to create optimal portfolios of commodities for investors with known and unknown risk preferences. When comparing expected returns to actual returns we found that for the investor with the known risk preference almost replicated the return of the markets. The other investor with unknown risk preference also profited but not as efficient as the market portfolio.

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>