Derivative Portfolio Optimization Model Based On CVaR

With the fast change of the financial system, the investors are not in pursuit of the maximum of the return, but the tradeoff of the maximum of the return and the minimum of the risk, so the management of the risk becomes very important. One crucial aspect of the management is the risk measure, it has many ways, and the risk measure method of CVaR (Conditional Value-at-Risk) which comes forth recently, is developed on basis of the shortcoming of Value-at-Risk, raised by Rockafellar at 1999. The implication of CVaR is the conditional loss over VaR of portfolio, which reflects the average exceed quota. Since CVaR reflects underlying loss better than VaR, it becomes a latest research content in financial risk management.This paper focuses on the applications of CVaR in the portfolio theory. Firstly, the paper introduces modern portfolio theory and all kinds of traditional risk measure methods, then puts forward CVaR risk measure method, introduces the definition, the calculation, and applications and so on. Secondly, this paper introduces and extends the portfolio optimization model, proposes to include transaction cost, and then uses 12 shares from Shanghai and Shenzhen stock market to do the empirical analysis to the portfolio model, and compares the efficient frontier of mean-CVaR under different confidence level and different transaction cost.Derivative contracts have become increasingly important as investment tools for achieving higher return and decreasing funding cost, so this paper extends the portfolio optimization model based on CVaR to the derivative portfolio optimization model, and also introduces cost as an additional preference, the cost is modeled as proportional to the magnitude of the holding positions.The standard method for a CVaR optimization problem is a linear programming approach, but this approach becomes inefficient for large scale CVaR optimization problems. A computationally method based on a smoothing technique is proposed to efficiently solve a simulation based CVaR optimization problem.