The Role of VaR Limits in Risk Budgeting
In market risk management, limit setting is driven by economic capital allocation, and is normally conducted from the top-down. Economic capital is viewed as an internal solvency constraint on a firm’s value-maximization function (Beeck et al.
1999; Schroeck 2002). More specifically, economic capital serves as a probabilistic loss bound over a target time horizon and is typically measured by value at risk (VaR). Within the trading area, economic capital is allocated assuming that market risk is consistently measurable at all levels. Breaching a limit should entail a book closure and a re-allocation of limits set for other trading desks. The frequency of capital allocation and, consequently, a limit re-setting, varies from quarterly to annually (e. g. Johanning 1998; U. S. Bankruptcy Court 2010).
VaR has been used in the industry for setting and managing risk limits since the 1990s. G-10 regulators have required that banks using the internal models approach for calculating capital for market risk (Basel Committee on Banking Supervision 1996, 2006) also employ their VaR models for setting trading limits. Thus, integrating a VaR model used for calculating the regulatory capital into the limit setting process has been considered a necessary requirement of the model use – test in a bank.
Designing a market risk limit system requires a number of problems to be solved along both the spatial and temporal dimensions, as shown in Fig. 1. Most research has been focused on the coherent treatment of risk diversification at all levels of corporate organizational structure (e. g. Kimball 1998; Kuritzkes et al. 2003). Scarce literature exists, however, on the interrelated problems of consistent time scaling of risk limits, adjusting limits for traders’ P&L, and accounting for model risk in limit setting and management. Progress made in these areas is further reviewed in this note.