Allocation of Risk Capital in Financial Institutions

Financial Management (Financial Management Association), Autumn, 1999 by Francesco Saita

The attention devoted to risk management in recent years has mostly focused on risk measurement, whereas the use of such measures in actual decision processes has been unaddressed. This paper focuses on the implementation issues involved with using value-at-risk measures in the capital-allocation process. In particular, this paper deals with the process of capital allocation and its consequences on risk-adjusted performance evaluation. When defining a measure of risk-adjusted performance, there is no multipurpose solution: the measure must be chosen based on the characteristics of each business unit and the degree of centralization or decentralization of the allocation process. Greater attention to capital allocation is therefore required so that more sophisticated risk measures can produce the desired results.

Risk management has become a critical issue for commercial and investment banks. In fact, the lack of proper risk management practices (whether related to credit risk or market risk) has generally been a key factor in recent banking crises. In many countries, the process of financial deregulation--by heightening competition--has led to increased pressure on banks' risk-taking practices. These trends have simultaneously increased the perceived need for risk management in financial institutions [1] and forced both regulatory authorities and bankers to improve internal systems devoted to risk evaluation, pricing, and control.

A first step in this effort has been to attain a more precise measurement of the risks faced by financial institutions. With respect to market risks, methodologies such as Bankers Trust's RAROC and J.P. Morgan's [RiskMetrics.sup.TM] have gained widespread acceptance. Other risks being monitored include credit and counterparty, liquidity, operational, legal, and reputational risk (see Santomero, 1995b). Some banks are beginning to model the risk from earnings volatility in fee-based businesses (such as advisory or payment services).

The most widespread methodology used to measure bank-wide risk is the well-known Value-at-Risk (VaR) measure. Broadly speaking, the VaR of a position whose market value at time t is [V.sub.t] can be defined as the amount PL such that

Pr[[V.sub.t] - [V.sub.t+[delta]t] [greater than] PL][less than or equal to] [alpha] (1)

In other words, VaR is the maximum potential loss that may occur in a given time interval of length [delta]t (e.g., one day, one month, or one year) within a probability range of 1-[alpha].

It is difficult to measure exactly the potential loss for each of the different risks experienced by financial institutions. Consequently, a substantial amount of research is currently underway with respect to the methodological issues concerning the appropriate measurement of these risks, both at a single position and at the portfolio level. For instance, as far as market risks are concerned, topics such as the relative effectiveness of variance-covariance VaR estimation methods compared to historical or Monte Carlo simulations, [2] the choice among different estimation techniques for VaR model parameters, and even the degree of consistency of VaR results across different software vendors [3] have received attention. The issue of how to measure the risk inherent in illiquid positions is still open. [4] With respect to credit risk, methodologies based either on maximum changes in credit spreads or on probability of default estimated from bond portfolio history provide a framework, and many key issues (such as the impact of geographic/industry diversification and the economic cycle on portfolio risk) are now being addressed. [5] Nevertheless, the development of internal models to assess and quantify market, credit, and counterparty risks is superior to state-of-the-art practices for other forms of risk. Considering the complexity of the risk measurement issues that still remain to be solved, it is not surprising that another critical aspect of risk management has so far been left almost unaddressed.

In fact, much of the debate about RAROC or earnings-at-risk or value-at-risk methodologies has been centered on the measurement of the amount of shareholders' capital-at-risk. Much less attention has been paid so far to the problem of capital allocation throughout the bank. Santomero (1995b) has clearly stated the problem, observing, "there has been much discussion of the RAROC and EaR methodologies as an approach to capturing total risk management. Yet, frequently, the risk decision is separated from risk analysis. If aggregate risk is to be controlled, these or similar methodologies need to be integrated into actual decision making."

The subject of this paper is the process of capital allocation to effect this integration. Section I describes the two dimensions of risk management systems. Section II deals with the identification of risk-taking centers. Section III discusses the nature of the allocation process and the criteria financial institutions use to allocate capital. Section IV evaluates alternative CaR and risk-adjusted performance (RAP) indicators to support performance evaluation, while the linkages between those measures and the reward/punishment system are addressed in Section V. Section VI concludes the paper.