| Περίληψη : | The main purpose of this dissertation is to study the most important optimization models to mitigate financial risks. Especially, we want to construct optimal portfoliosusing the concepts of first-order stochastic dominance, second-order stochastic dominance and third-order stochastic dominance as well as the CVaR approach, including three different investment tactics. The concept of Stochastic Dominance is theoretically appealing: if a return distribution A first-order, second-order, third-order stochastically dominates another distribution B, then all investors with some specific preferences will prefer A to B. Portfolio optimization is a cornerstone of modern finance theory, as it is very attractive in the field of decision making under uncertainty. Financial crises, economic imbalances, algorithmic trading and highly volatile movements of asset prices in the recent times have raised high alarms on the management of financial risks. Inclusion of risk measures towards balancing optimal portfolios has become very crucial and equally critical. Formally, financial portfolio optimization adheres to a formal approach in making investment decisions, (1) for selection of investment portfolios containing the financial instruments, (2) to mitigate financial risks and ensure better preparedness for uncertainties, (3) to establish mathematical and computational methods on realistic constraints and (4) to provide stability across inter and intraday market fluctuations. Risk management has been recognized to play an increasingly important role in financial problems such as the international asset allocation, where widespread deregulation has entailed a substantial increase in asset price and currency volatility. We start with an introduction of the mean-variance approach, as well as with a description of the different kinds of financial risks that are faced by investors and financial institutions. Moreover, we present the major risk measures used in portfolio optimization such as variance, mean-absolute deviation, Value at Risk, Conditional Value at Risk and the associated mathematical formulations of the optimization models. Next we focus on the Utility Theory and on how people make choices when faced with uncertainty, leading up to the development of the first, second and third stochastic dominance rules. Furthermore we define the key concepts and present the appropriate mathematical formulations in order to construct optimal portfolios based on the CVaR optimization model, including three different investment tactics, as well as the FSD, SSD and TSD efficiency algorithms developed by Kuosmanen (2001,2004). More specifically in the empirical tests we consider investments in the US market. We want to construct several optimal portfolios based on alternative strategies. We use data on monthly closing prices of S&P500, including a number of stocks obtained by Datastream covering the period from December 1999 to July 2016. We choose assets from different sectors and thus a total number of 30 assets are concerned in each portfolio. We conduct both static test (efficient frontier), considering the CVaR optimization model, and dynamic tests in order to find the optimal portfolio weights (backtesting experiments over the last 120 months). Finally, we examine the statistical characteristics of the historical data set, we describe briefly the computational tests and we compare the statistical characteristics of the optimal portfolios. Moreover we employ four commonly used parametric performance measures in order to evaluate the performance of all the alternative competing strategies with respect to the market benchmark portfolio: the Sharpe ratio, the Sortino ratio, opportunity cost and portfolio turnover.
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