Portfolio optimization with VaR and CVaR: the case of Gold and Euro portfolio

The correlation between the gold price and the USD/EUR exchange rate is often negative with some exceptions in shorter periods. Hence, gold is known to be used as a useful tool to secure dollar deposits. This paper examines the portfolio optimization possibility using VaR and CVaR as risk measures. We use the t-distribution and the Normal Inverse Gaussian (NIG) distribution as well as the normal distribution as a comparative benchmark to approximate the empirical probability distribution. We construct several portfolios with various composition of gold and assets denominated in euro. First, parameters of all candidate distributions are estimated. Then, the risk measures of these portfolios are computed. We also repeat this procedure for those periods with highest positive and negative correlation. The obtained results show that it is possible to determine the optimal structure of these portfolios with VaR and CVaR as a risk measure