In the diploma seminar thesis entitled Conditional Value at Risk and portfolios optimization, a portfolio optimization approach based on the minimization of the portfolio risk measure, called the Conditional Value at Risk, is presented. Although the definition of the above-mentioned risk measure is based on the definition of the risk measure, called the Value at Risk, the technique of the portfolio optimization approach based on minimization of the Conditional Value at Risk of the portfolio does not require the calculation of the Value at Risk of the portfolio beforehand. The optimization of the portfolio, more precisely, the shares of the non-negative positions in individual financial instruments in the portfolio, is transformed to the minimization of a convex and continuously differentiable function, through which the values of the Conditional Value at Risk and the Value at Risk of the portfolio are obtained. The function contains an integral of the joint probability density function of financial instruments returns. To use the approach on concrete data, we use one of the sampling techniques from the values of the portfolio related market variables, approximate the beforementioned integral and transform the optimization problem into the problem of linear programming.
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