Finance Research Letters 2 (2005) 23–29 www.elsevier.com/locate/frl A generalized coherent risk measure: The firm’s perspective Robert A. Jarrow a,b,∗ , Amiyatosh K. Purnanandam c a Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853, USA b Kamakura Corporation, USA c University of Michigan Business School, Ann Arbor, MI 48109, USA Received 21 October 2004; accepted 30 November 2004 Available online 21 December 2004 Abstract This note extends the concept of a coherent risk measure to make it more consistent with a fir- m’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.  2004 Elsevier Inc. All rights reserved. Keywords: Coherent risk measures; Capital budgeting; Capital determination 1. Introduction Risk management is different from the firm’s and the regulator’s perspective. The firm’s goal is to choose the composition of its (assets and liabilities) portfolio so as to maximize its risk/return trade-off, subject to any regulatory capital requirements. In contrast, a regulator takes the firm’s portfolio composition as fixed, and the regulator’s goal is to determine the capital the firm must have in order to limit the consequences of ruin within a given time- * Corresponding author. E-mail addresses: raj15@cornell.edu (R.A. Jarrow), amiyatos@umich.edu (A.K. Purnanandam). 1544-6123/$ – see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.frl.2004.11.001