Parametric Optimization of Markowitz, Value at Risk and Conditional Value at Risk Models Using Local and Global Algorithms in Tehran Stock Exchange

Nowadays risk management is as vital as receiving the maximum return. Therefore researches on risk management area and its models are very useful for the investors. This research is relied on finding the portfolio's optimal weights with the aim of minimum risk by using a local (fmincon function) and global optimization (simulated annealing) algorithms based on three risk management models; Markowitz, Value at Risk (VaR) and Conditional Value at Risk (CVaR) in various levels of return, and consequently drawing and comparing of the three mentioned model's efficient frontiers. With this target we used TEDPIX index data from the Tehran Exchange Stock from 1997 to 2008 (11 years) and based on parametric approach (normal distribution of loss and profit); we have built three nonlinear programming models. These models have been optimized by two independent optimization algorithms and finally it was concluded that with parametric assumption all three models have the same results and there is no difference in using them. Also it was concluded that beside the local optimization algorithms, the investors use the global optimization models. Although the local optimization algorithms are recommended for optimizing in a short time.