A generalized coherent risk measure: The firm's perspective

This note extends the concept of a coherent risk measure to make it more consistent with a firm's capital budgeting perspective. A coherent risk measure defines the risk of a portfolio to be that amount of cash that must be added to the portfolio such that it becomes acceptable to a regulator. As such, a coherent risk measure implicitly assumes that the firm has already made its capital budgeting decision. Except for a cash infusion, the portfolio composition remains unchanged. We propose a generalized version of a coherent risk measure that also allows the portfolio composition to change as well. Once the investment decisions are fixed, our measure collapses to a coherent risk measure.