“Financial Portfolio Optimization”
International Financial Markets
MSc. International and European Economic Studies
Athens University of Economics and Business
TABLE OF CONTENTS
FINANCIAL RISKS FACED BY INVESTORS AND FINANCIAL INSTITUTIONS Introduction Risk Categories Types of Risks Liquidity Risk Systematic or non-diversifiable Unsystematic or Diversifiable Credit Risk Interest Rate Risk Inflation Risk Country Risk Operational Risk Currency Risk Basis Risk Chapter
MAJOR RISK MEASURES USED IN PORTFOLIO OPTIMIZATION AND ASSOCIATED MATHEMATICAL FORMULATIONS OF THE OPTIMIZATION MODELS Introduction Coherent Risk Measure Beta Mean Absolute Deviation Mean - Variance Sharp Ratio Treynor Ratio Value at Risk (VaR) Conditional Value at Risk (cVaR) Stressed VaR and Stressed cVaR Expected Shortfall Put - Call Efficient Frontiers Expected Utility Maximization Spectral Risk Measures Chapter
EMPIRICAL APPLICATION Introduction Data Description Portfolio Optimization Empirical Results Efficient Frontier Back Testing Introduction
Purpose of Presentation
To study the most important portfolio optimization models used to mitigate financial risks and construct an optimal portfolio.
The main aim of risk management departments, financial analyst and individual investors is the selection of optimal investments to maximize their returns, but at the same time, they desire to eliminate their risk exposures.
Definition of risk and the measure of it, are issues that financial society is concerned about many years and a variety of interesting research on risk measuring have been published throw the 20th century.
Investors, usually construct portfolios including a variety of asset classes, such as fixed income, cash, real estate, bonds, stocks, and other financial assets each of which will react differently in the event of major systemic changes.
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. Varied mathematical models have emerged leading towards practical risk-based asset allocation strategies.
Financial Risks faced by Investors and Financial Institutions
A. Risk Categories
Risk in finance is defined as the difference between expected outcome of a financial activity and the actual outcome that occurs. As investors expose their capitals in potential losses, they demand a reward for the risk bearing. The bigger the risk they bear the higher will be the demanded return.
Risk is divided in two parts:
“Systematic” or “Non-Diversifiable”
“Unsystematic” or “Diversifiable”
Arises from the market, affect the whole market and not only an individual item or an individual investor.
The risk that each investor is exposed to, as an individual unit. This part of risk arises from the investors’ decisions for the assets that they hold in their portfolios.
B. Risk Types