This paper proposes an approach based on copula families to determine shape and magnitude of non-linear serial and cross-interdependence between returns and volatilities of financial assets. It is evident the predominance of the student’s t copula in returns relationships. Association in tails is generally larger than the absolute. There is a fast decrease in association along time, but even after 5days, there is still dependence between returns. For volatilities, Joe copula predominates in estimated bivariate relationships fit. Clayton copula rotated 180° (survival), Gumbel, BB6 and BB8 copulas also fit some relationships. The magnitude of lagged associations is larger for risks than returns. Persistence in the dependences is very high, and decreases very little after the first lag. The tail dependence has larger values than the absolute in most relationships. We present a practical application of the proposed approach, based on optimal investment allocation and risk prediction.