Chapter 1 - Value at Risk, Capital Management, and Capital Allocation

Abstract

This chapter introduces the value-at-risk concept and its potential applications in capital management and capital allocation. The chapter also aims at clarifying why a bank should be concerned not only with how risks are measured but also with how those measures enter decision-making and performance evaluation processes. Value at risk (VaR) is the maximum potential loss of a given position or business area or business unit within a given time horizon and confidence level. Value-at-risk measures may be helpful to the manager for solving two crucial problems. The first one is capital management, which concerns the definition of the optimal capital structure of the bank. The second problem is capital allocation, which is defined as the set of choices and decision-making processes concerning the optimal allocation of capital across the different business units inside the bank. Capital management is a complex process since the risk manager does not have a perfect measure for all the risks faced the bank. Capital management decisions have to consider many other factors, such as the viewpoint of outsiders, who may be cautious in trusting the numbers of aggregated values at risk derived by internal models they are unable to check. Capital allocation is also different from simple asset allocation among different asset classes in an equity portfolio, as the risk manager may in fact estimate at best with a certain precision past risk-adjusted returns.