A Parametric Comparison between Markowitz, Value at Risk and Conditional Value at Risk Models Using Simulated Annealing (SA) Algorithm in Tehran Stock Exchange

Mollaei, M; Sheikh, Mj; Khodamoradi, S

A Parametric Comparison between Markowitz, Value at Risk and Conditional Value at Risk Models Using Simulated Annealing (SA) Algorithm in Tehran Stock Exchange

Authors

M Mollaei

Mj Sheikh

S Khodamoradi

Abstract

Nowadays risk management is as vital as gaining the maximum return. Therefore, researches in risk management area and its different models are very useful for the investors. Using a local (fmincon function) and a global optimization (simulated annealing) algorithms based on three risk management models namely Markowitz, Value at Risk (VaR) and Conditional Value at Risk (CVaR), this research seeks to find the portfolio's optimal weights with the aim of minimizing risks in various levels of return and consequently, draw and compare the three mentioned models’ efficient frontiers. The TEDPIX index data from Tehran Stock Exchange from 1997/8 to 2007/8 (11 years), based on parametric approach (normal distribution of loss and profit), is also used. Three nonlinear programming models were built and were optimized by two independent optimization algorithms. Finally it was concluded that with parametric approach, all these three models have the same results and there is no difference in using them. Also it was concluded that for VaR optimization, we should use global optimization algorithms and for CVaR optimization, we should use local optimization algorithms.

Keywords

Markowitz Model (MPT)

Value at Risk (VaR)

Conditional Value at Risk (CVaR)

Efficient Frontiers

Simulated Annealing Algorithm