Measuring of Conditional Value at Risk Portfolio Using Copula
Keywords:
Conditional Value-at-Risk, Multivariate Distribution Function, Copula, Tourism & HospitalityAbstract
The uncertainty of return on investment is a major concern for the vast majority of investors. Under normal market conditions, a portfolio's risk exposure over a specific time frame with a predetermined confidence level can be measured. Since a portfolio’s return is rarely characterized by the assumption of a multivariate normal distribution, the use of normality Value-at-Risk (VaR) plays a crucial role in risk mitigation, but can generate an undesirable measure of risk exposure for portfolio investment. With a dynamic tool in modeling multivariate distribution regardless of the assumption of joint normality, applying a copula is a practical alternative choice for extracting a cumulative joint distribution for a portfolio’s return. The applications in this work are illustrated by the portfolios of the four largest and the four smallest market capitalization stocks in the tourism and hospitality sector. It was found that the portfolio returns of the large and small market capitalization portfolios were characterized by logistic and Student’s t distributions respectively. Consequently, the VaR and conditional VaR based on the Gaussian copula, could be used to characterize and estimated the distributions of the respective portfolio returns according to the logistic and Student’s t distributions. The conditional VaR of the large and small market capitalization portfolios calculated from the copula method provides a slightly higher level of risk than the conditional VaR and the VaR with the assumption of a multivariate normal distribution. Moreover, the small market capitalization portfolio provides slightly higher values of VaR and CVaR than the large market capitalization portfolio for all assumptions of VaR. Therefore, the use of conditional VaR based on the Gaussian copula is more reasonable for investors who conservatively manage their investment portfolios. However, managing the investment portfolio based on a conservative level does not completely imply the performance of portfolio management. On the other hand, an accurate value of VaR, directly estimated from the actual distribution of a portfolio’s returns, provides a vital means of assessing better portfolio management. Due to being sensitively volatile to several surrounding factors within the hospitality and tourism sector, implementing a conservative investment strategy is more suitable.
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