英文文献：A Comparison of Traditional and Copula based VaR with Agricultural portfolio
英文文献作者：Mandal, Maitreyi,Lagerkvist, Carl Johan
英文文献摘要：
Mean-Variance theory of portfolio construction is still regarded as the main building block of modern portfolio theory. However, many authors have suggested that the mean-variance criterion, conceived by Markowitz (1952), is not optimal for asset allocation, because the investor expected utility function is better proxied by a function that uses higher moments and because returns are distributed in a non-Normal way, being asymmetric and/or leptokurtic, so the mean-variance criterion cannot correctly proxy the expected utility with non-Normal returns. Copulas are a very useful tool to deal with non standard multivariate distribution. Value at Risk (VaR) and Conditional Value at Risk (CVaR) have emerged as a golden measure of risk in recent times. Though almost unutilized so far, as agriculture becomes more industrialized, there will be growing interest in these risk measures. In this paper, we apply a Gaussian copula and Student’s t copula models to create a joint distribution of return of two (Farm Return and S&P 500 Index Return) and three (Farm Return, S&P 500 Index Return and US Treasury Bond Index) asset classes and finally use VaR measures to create the optimal portfolio. The resultant portfolio offers better hedges against losses.