Advanced Portfolio Theory

After completing the course, students will be able to:

• Calculate and understand the basic parameters that characterize a portfolio consisting of many different assets, namely its expected return and its risk.
  • (This section requires basic mathematical tools from statistics and linear algebra, such as calculating the mean, variance, covariance, correlation coefficient, etc.)
• Understand the benefits of portfolio diversification, which we study in detail and examine the ways in which we can achieve it.
• Find among the “good” solutions, the optimal solution for an investor that will maximize his expected return per unit of risk.
• The above will help achieve the ultimate goal of the course, which is to find the “optimal” (or “optimal”) portfolio.
• To evaluate the performance of a portfolio using basic evaluation measures such as the Jensen, Treynor, Sharpe measures, as well as measures such as the CAPM, which take into account the so-called “market portfolio” and excess return.
• Taking into account the subjective criteria of an investor (for example, how much he aversive he is to risk) but also his basic characteristics (such as, for example, what his initial wealth is), they will find the optimal portfolio that maximizes the utility function of the investor’s wealth.
• This part of the material, which is also the last, differs from the rest both in terms of the concepts that will be used and in terms of the methodology that will be followed in order to reach our goal, which is the optimal portfolio, which results from solving a problem of maximizing the utility function that characterizes each investor, which is in turn a function of his wealth. Also, in this specific part, students will gain knowledge about the completeness or incompleteness of the market, which plays a decisive role in the problem of maximizing the utility function.