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Capital Utilizations

When addressing capital allocations as the measure of capital used up by those transactions, technical issues arise because risks are "sub-additive." Considering an existing portfolio, or an existing portfolio plus some new transactions, the issue is to define the fraction of the global and diversified risk of the portfolio that should be allocated to any existing transaction or sub-portfolio, or to new transactions. Those are capital utilizations.

There is a key difference between regulatory capital and economic capital. Regulatory capital is calculated by transaction and then summed up to make up total regulatory capital. Hence, there is no issue for regulatory capital charged for credit risk which adds up the capital charges for transactions. Regulators defined capital charges for credit risk as embedding some average correlation effect, but not the actual diversification effect that is specific to a portfolio.

When using economic capital, either credit VaR or market VaR, dependencies, or diversification effects, make risks non-additive. The issue is to define some methodology for moving top-down or bottom-up from total capital to individual transactions or sub-portfolios. The capital allocation system provides the top-down and bottom-up links between the global, diversified, risk of the bank's portfolio and individual transactions or sub-portfolios.

Capital utilizations serve as a risk metric. As a measure of risk, they make up a basis for limit management. They also serve for defining risk-adjusted performance, since such measures require a measure of risk.

Such capital allocations are called risk contributions of facilities or sub-portfolios to the overall portfolio risk. The terminology applies to both credit risk and market risk when using economic measures of risk rather than additive regulatory capital charges. The economic risk contributions should also add up arithmetically to obtain the total risk, for reconciling allocated risks with the overall risk. For pricing purposes, they should also be such that pricing based on risk contributions should keep the portfolio risk-adjusted return in line with the overall risk-adjusted target.

There are many types of risk contributions. Risk contributions include those applying to the existing transactions, others are variations of the portfolio risk "before and after" inclusion of new transactions. The convention in this text is that "risk contributions" apply to the existing portfolio, whereas "marginal risk contributions" measure the incremental risk due to new transactions. The modeling of risk contributions necessitates defining risk contributions to the portfolio loss volatility and risk contributions to the portfolio capital. Some also consider the risk contributions to the "fat tail" of the loss distribution as being relevant for some issues, such as reducing the capital given the confidence level, or simply identifying those transactions that contribute more to extreme risk. For common usages, the former two types of risk contributions are sufficient: risk contributions and marginal risk contributions. Risk contributions are defined in such a way that they add up to the existing portfolio capital or loss volatility.

For allocating existing risks, risk contributions apply. They measure the current risk, or capital utilizations, within the existing portfolio. The gap between capital utilizations and normative capital authorizations measures the capability of expanding businesses subject to capital constraints. When considering new transactions, the issue is to determine the additional risk to the existing portfolio. Measuring additional risk requires marginal risk contributions for limit management and for risk-based pricing, which should compensate for the additional risk.

 
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