Anna Śleszyńska-Połomska

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The article concerns portfolio analysis where risk is measured by value at risk (VaR) assuming that the returns are normally distributed and short-selling of risky securities has no limitations. Two models have been analysed: one with the assumption that no risk-free security exists in the economy, another assuming just one risk-free security. An analysis of Black Model and Modified Tobin Model has been carried out using VaR as the measure of risk. Models with VaR as a measure of risk and standard deviation as measure of risk have been compared. It is shown that, depending on the confidence level used to calculate VaR, an efficient portfolio might not exist. The results for the model with one risk-free asset and VaR as a measure of risk have not been published before and are the original contribution of this paper.


Value at Risk (VaR), portfolio analysis, E-VaR model with no risk-free assets, E-VaR model with risk-free asset


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