In economic or finance field, one of the most studied issues is to get the best possible return with the minimum risk. The objective of the paper is to select the optimal investment portfolio from SP500 stock market and CBOE Interest Rate 10-Year Bond to obtain the minimum risk in the financial market. For this purpose, the paper consists of the following three points: (1) The marginal density distribution of the two financial assets is described with kernel density estimation to get the �high-picky and fat-tail� shape; From it, it is obvious to tell the advantage of this method compared with the assumption that return rate submits to normal distribution, (2) After the marginal distribution of variables is confirmed, the unknown parameter of Copula function could be evaluated with maximum likelihood estimation. Therefore, the relation structure of assets could be studied with the chosen copula function to describe the correlation of financial assets form a nonlinear perspective. And (3) value at Risk (VaR) is computed through the combination of the optimal Copula function, which is judged by minimum variance test and Monte Carlo simulation to measure the possible maximum loss better of the portfolio. At the same time, it shows the advantage through contrast with the traditional analytical methods based on Gaussian distribution. © Springer Nature Switzerland AG 2020.