In this project, we implement portfolio theory to construct our portfolio, applying the theory to real practice. There are 3 parts in this project, including portfolio optimization, Capital Asset Pricing Model (CAPM) analysis and Factor Model analysis. We implement portfolio theory in the portfolio optimization part. In the second part, we use the CAPM to analyze and improve our portfolio. In the third part we extend our CAPM to factor models to get a deeper analysis of our portfolio.

Implemented robust regressio technology in portfolio optimization. Constructed optimized portfolio based on robust regression estimations. Compared the portfolio performance with optimized portfolio which is based on ordinary least square estimation.

The classical mean-variance model, proposed by Harry Markowitz in 1952, has been one of the most powerful tools in the field of portfolio optimization. In this model, parameters are estimated by their sample counterparts. However, this leads to estimation risk, which the model completely ignores. In addition, the mean-variance model fails to incorporate behavioral aspects of investment decisions. To remedy the problem, the notion of ambiguity aversion has been addressed by several papers where investors acknowledge uncertainty in the estimation of mean returns. We extend the idea to the variances and correlation coefficient of the portfolio, and study their impact. The performance of the portfolio is measured in terms of its Sharpe ratio. We consider different cases where one parameter is assumed to be perfectly estimated by the sample counterpart whereas the other parameters introduce ambiguity, and vice versa, and investigate which parameter has what impact on the performance of the portfolio.

The classical mean-variance model, proposed by Harry Markowitz in 1952, has been one of the most powerful tools in the field of portfolio optimization. In this model, parameters are estimated by their sample counterparts. However, this leads to estimation risk, which the model completely ignores. In addition, the mean-variance model fails to incorporate behavioral aspects of investment decisions. To remedy the problem, the notion of ambiguity aversion has been addressed by several papers where investors acknowledge uncertainty in the estimation of mean returns. We extend the idea to the variances and correlation coefficient of the portfolio, and study their impact. The performance of the portfolio is measured in terms of its Sharpe ratio. We consider different cases where one parameter is assumed to be perfectly estimated by the sample counterpart whereas the other parameters introduce ambiguity, and vice versa, and investigate which parameter has what impact on the performance of the portfolio.

Portfolio design is one of the central topics in finance. The original attempt dates back to the mean-variance model developed for a single period portfolio selection. To have a more realistic approach, multi-period selections were developed in order to manage uncertainties associated with the financial markets. This thesis presents a multi-period financial model proposed on the basis of the network flow structure with many planning advantages. This approach comprises two main steps, dynamic portfolio selection, and dynamic portfolio monitoring and rebalancing throughout the investment horizon. To build a realistic yet practical model that can capture the real characteristics of a portfolio a set of proper constraints is designed including restrictions on the size of the portfolio as well as the number of transactions, and consequently the management costs. The model is solved for two-stage financial planning problems to demonstrate the main advantages as well as characteristics of the presented approach.

Portfolio design is one of the central topics in finance. The original attempt dates back to the mean-variance model developed for a single period portfolio selection. To have a more realistic approach, multi-period selections were developed in order to manage uncertainties associated with the financial markets. This thesis presents a multi-period financial model proposed on the basis of the network flow structure with many planning advantages. This approach comprises two main steps, dynamic portfolio selection, and dynamic portfolio monitoring and rebalancing throughout the investment horizon. To build a realistic yet practical model that can capture the real characteristics of a portfolio a set of proper constraints is designed including restrictions on the size of the portfolio as well as the number of transactions, and consequently the management costs. The model is solved for two-stage financial planning problems to demonstrate the main advantages as well as characteristics of the presented approach.

This report discusses a multi-stage stochastic programming model that maximizes expected ending time profit assuming investors can forecast a bull or bear market trend. If an investor can always predict the market trend correctly and pick the optimal stochastic strategy that matches the real market trend, intuitively his return will beat the market performance. For investors with different levels of prediction accuracy, our analytical results support their decision of selecting the highest return strategy. Real stock prices of 154 stocks on 73 trading days are collected. The computational results verify that accurate prediction helps to exceed market return while portfolio profit drops if investors partially predict or forecast incorrectly part of the time. A sensitivity analysis shows how risk control requirements affect the investor's decision on selecting stochastic strategies under the same prediction accuracy. / text

The main objective of the thesis is to analyse impact of wavelet covariance estimation in the context of Markowitz mean-variance portfolio selection. We use a rolling window to apply maximum overlap discrete wavelet transform to daily returns of 28 companies from DJIA 30 index. In each step, we compute portfolio weights of global minimum variance portfolio and use those weights in the out-of- sample forecasts of portfolio returns. We let rebalancing period to vary in order to test influence of long-term and short-term traders. Moreover, we test impact of different wavelet filters including Haar, D4 and LA8. Results reveal that only portfolios based on the first scale wavelet covariance produce significantly higher returns than portfolios based on the whole sample covariance. The disadvantage of those portfolios is higher riskiness of returns represented by higher Value at Risk and Expected Shortfall, as well as higher instability of portfolio weights represented by shorter period that is required for portfolio weights to significantly differ. The impact of different wavelet filters is rather minor. The results suggest that all relevant information about the financial market is contained in the first wavelet scale and that the dynamics of this scale is more intense than the dynamics of the whole market.

In this project, we implement portfolio theory to construct our portfolio, applying the theory to real practice. There are 3 parts in this project, including portfolio optimization, Capital Asset Pricing Model (CAPM) analysis and Factor Model analysis. We implement portfolio theory in the portfolio optimization part. In the second part, we use the CAPM to analyze and improve our portfolio. In the third part we extend our CAPM to factor models to get a deeper analysis of our portfolio.

This thesis documents a heavy-tailed analysis of stable portfolios. Stock market crashes occur more often than is predicted by a normal distribution,which provides empirical evidence that asset returns are heavy-tailed. The motivation of this thesis is to study the effects of heavy-tailed distributions of asset returns. It is imperative to know the risk that is incurred for unlikely tail events in order to develop a safer and more accurate portfolio. The heavy-tailed distribution that is used to model asset returns is the stable distribution. The problem of optimally allocating assets between normal and stable distribution portfolios is studied. Furthermore, a heavy-tail sensitivity analysis is performed in order to see how the optimal allocation changes as the heavy-tail coefficient is altered. In order to solve both problems, we use a mean-dispersion risk measure and a probability of loss risk measure. Our analysis is done for two-asset stable portfolios, one of the assets being risk-free, and one risky. The approach used involves changing the heavy-tail parameter of the stable distribution and finding the differences in the optimal asset allocation. The key result is that relatively more wealth is allocated to the risk-free asset when using stable distributions than when using normal distributions. The exception occurs when using a loss probability risk measure with a very high risk tolerance. We conclude that portfolios assuming normal distributions incorrectly calculate the risk in two types of situations. These portfolios do not account for the heavy-tail risk when the risk tolerance is low and they do not account for the higher peak around the mean when the risk tolerance is high.