THE PORTFOLIO OF FINANCIAL ASSETS OPTIMIZATION. DIFFERENT APPROACHES TO ASSESS RISK

Modern research has led to the rejection of the hypothesis of a normal distribution for financial asset returns. Under these conditions, the portfolio variance loses part of its informativity and can not serve as a good risk measure. The central aim of this work is the development and justification of a new technique of portfolio risk measure. We analyzed weekly stock returns of four largest German concerns: Deutsche Telekom, Siemens AG, Bayer AG and BMW. It is shown that asset returns are not normally distributed, but with good precision follow Laplace distribution (double exponential distribution). Using Laplace distribution function, we obtained the analytical expressions for VaR and CVaR risk measures and made calculations of risk measure using these approaches. Using modified Markowitz model the efficient frontiers of portfolios were constructed.