We study the relationship between the performance of firms and their technological portfolios using tools borrowed from complexity science. In particular, we ask whether the accumulation of knowledge and capabilities associated with a coherent set of technologies leads firms to experience advantages in terms of productive efficiency. To this end, we analyze both the balance sheets and the patenting activity of about 70 thousand firms that have filed at least one patent over the period 2004-2013. We define a measure of corporate coherent diversification, based on the bipartite network linking companies with the technological fields in which they patent, and relate it to firm performance in terms of labor productivity. Our measure favors technological portfolios that can be decomposed into large blocks of closely related fields over portfolios with the same breadth of scope, but a more scattered diversification structure. We find that the coherent diversification of firms is quantitatively related with their economic performance and captures relevant information about their productive structure. In particular, we prove on a statistical basis that a naive definition of technological diversification can explain labor productivity only as a proxy of size and coherent diversification. This approach can be used to investigate possible synergies within firms and to recommend viable partners for mergers and acquisitions.