This paper examines the problem of hedging portfolio returns. Many practitioners and academicians endeavor to solve the problem of how to calculate the optimal hedge ratio accurately. In this paper we compare estimates of the hedge ratio from a classical approach of a linear quantile regression, based on selected quantiles as medians, with that of a non-linear quantile regression. To estimate the hedge ratios, we have used a calibrated Student t distribution for the marginal densities and a Student t copula of the portfolio returns using a maximum likelihood estimation. We created two portfolios of the assets, one for equal weight and another for optimal weight in respect of minimal risk. Our findings show that an assumption of Student t marginal leads to a better estimation of the hedge ratio.