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Conditional Value-at-Risk Optimization for Conversion of Convertible Bonds  

Park, Koo-Hyun (홍익대학교 산업공학과)
Shim, Eun-Tak (홍익대학교 산업공학과)
Publication Information
Korean Management Science Review / v.28, no.2, 2011 , pp. 1-16 More about this Journal
Abstract
In this study we suggested two optimization models to answer a question from an investor standpoint : how many convertible bonds should one convert, and how many keep? One model minimizes certain risk to the minimum required expected return, the other maximizes the expected return subject to the maximum acceptable risk. In comparison with Markowitz portfolio models, which use the variance of return, our models used Conditional Value-at-Risk(CVaR) for risk measurement. As a coherent measurement, CVaR overcomes the shortcomings of Value-at-Risk(VaR). But there are still difficulties in solving CVaR including optimization models. For this reason, we adopted Rockafellar and Uryasev's[18, 19] approach. Then we could approximate the models as linear programming problems with scenarios. We also suggested to extend the models with credit risk, and applied examples of our models to Hynix 207CB, a convertible bond issued by the global semiconductor company Hynix.
Keywords
Value-at-Risk(VaR); Conditional Value-at-Risk(CVaR); Convertible Bond; Portfolio Optimization; Scenarios; Coherent Risk Measurement;
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