The aim of this paper is to determine the Value at Risk (VaR) of the portfolio consisting of several long positions in risky assets. We consider the case when the tail parts of distributions of logarithmic returns of these assets follow the power law of the same degree and the lower tail of associated copula C follows the power law of degree 1. We provide the asymptotic formula for Value at Risk and determine the optimal portfolio. We show that the part of the capital invested in the i-th asset should be equal to the conditional probability that the drop of the value of the i-th asset will be smaller than the others under the condition that the value of the all assets will be smaller than c times their initial value (c << 1).

PACS numbers: 89.65.Gh