The aim of the article is to assemble an optimal portfolio of chosen stocks of the Prague Stock Exchange. The Markowitz portfolio model is used. At rst, Pearson correlation coecients and covariance are calculated for the stocks ČEZ, KOMERČNÍ BANKA, TELEFÓNICA, UNIPETROL, NWR and PX Index in order to nd the dependence measure from 2003{ 2012. These values are presented in a correlation matrix and covariance matrix. Yield, risk and yield to risk ratios are calculated for stocks and PX Index. The dependence between yield and risk of stocks as well as yield and risk of portfolios are found. Stocks have di erent weights in a portfolio. A set of possible portfolios and a set of ecient portfolios are assembled for various combinations of ve-component stock portfolios. Based on that, an optimal portfolio is assembled. This article brings a method that can be used by investors and other subjects of the nancial market while deciding to what stocks to invest in.
Financial analysts have recently paid more attention to so-called emerging markets that are slowly reaching the level of developed stock markets. The objective of this paper is to evaluate the level of yields and risk attributed to developed stock markets (USA, United Kingdom and Germany) and to emerging markets (Brazil is South America, Mexico in Central America, Hong Kong in Asia and Australia). These levels are set separately for the periods from 30 September 2004 to 30 September 2008 and from 30 September 2008 to 30 September 2012. The author compares the changes in levels between both periods and also development of the level of yields and risk within whole period of 12 months periodicity. The macroeconomic situation of these countries during selected period is monitored by means of GDP growth. The values of the stock indices are taken from major stock exchanges in these countries and bond yields are also used. Different standard deviations from the yield of the stock index, variation coefficients and Sharpe ratios are calculated. The author investigates to what extent it is true that higher yields can be achieved on emerging markets, but at the expense of a higher risk than on developed stock markets. Based on founded results it is clear that higher yields can be achieved on emerging markets at the expense of higher risk than on developed ones, but not in every case.
The paper focuses on the Value at Risk model, which is nowadays often used for risk analysis mostly in the banking and insurance industries. Following the characteristics of the model principle, the Value at Risk is interpreted in the economic sense. Two sub-methods are mentioned: Monte Carlo method and historical simulation method. Author presents a number of empirical studies focused on the application of these methods in the practice. The aim of the paper is to apply the Value at Risk model to selected stocks from the SPAD segment of the Prague Stock Exchange within the 2011 period using these two sub-methods. The confidence interval, hold period and other important parameters related to the sub-methods are selected. Based on historical stock prices, various statistical indicators are calculated. Non-diversied and diversified Value at Risk, calculated by the sub-methods are compared. The individual dierences among relative, absolute and marginal Value at Risk are described in the paper. Author presents possibility of reducing the Value at Risk.
CS
Článek se zaměřuje na model Value at Risk, který se v současnosti často používá na analýzu rizika, zejména v bankovnictví a pojišťovnictví. Po charakteristice principu modelu je ekonomicky interpretována hodnota Value at Risk. Zmíněny jsou dvě dílčí metody, a to metoda Monte Carlo a metoda historické simulace. Autor uvádí řadu empirických studií zaměřených na aplikaci těchto metod v praxi. Cílem článku je aplikace modelu Value at Risk na vybrané akcie ze segmentu SPAD pražské Burzy cenných papírù v rámci roku 2011, a to s využitím tìchto dvou dílčích metod. Je zvolen interval spolehlivosti, doba držení a další dùležité parametry, které se vztahují k dílčím metodám. S využitím historických kurzù akcií jsou vypočteny různé statistické ukazatele. Jsou srovnány vypočtené nediverzifikované a diverzifikované hodnoty Value at Risk u dílčích metod. V článku jsou dále popsány jednotlivé rozdíly mezi relativní, absolutní a marginální Value at Risk. Autor uvádí možnosti snížení hodnoty Value at Risk.
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