Institutional performance assessment had always been and will remain as a key challenge to a multitude of stakeholders. Most of the existing indicators including h-type indicators and many others do not reflect expertise of institutions that defines their research portfolio. Recently, a set of expertise measures such as x and x(g) indices were introduced to reflect expertise of institutions with respect to a specific discipline/field considering strengths in different finer level thematic areas. In this work, an adaptation of the x-index, namely the x_d-index is proposed to reflect the overall scholarly expertise of an institution considering its publication pattern and strength in different coarse thematic areas. This indicator is supposed to reflect the core expertise areas and also the diversity of research portfolio of the institution. This indicator and associated framework are demonstrated on a dataset of 135 institutions. The ability to reflect diversity is validated by determining the correlation with a prominent diversity indicator. x_d-index is found to correlate with the major diversity indicator better than institutional h-index and g-index. Further, the possibilities for effective management of research portfolio of an institution by expanding its diversity is discussed in this work, that may aid concerned stakeholders.