Many internal systems rely on the logic of distributing physical units of capital rather than risk. This made sense until about 15 or 20 years ago, when in banking buying a risk generally necessitated relinquishing cash – i.e., making a loan, buying a stock or note, etc. Since that time, the growth of derivatives has made it a commonplace to separate financing and risk. For capital markets risks, it has swiftly become the case that it is risk, not capital that needs to be allocated. Through good pricing, risks are taken to maximize value and capital is there to provide a buffer.

Even though this separation between financing and risk has caught on quickly, is not perfect. Exchange-traded futures, for example, require variation margin so that the exchange does not have to bear the credit risk of every contract holder. Conventions like variation margin, overcollateralization, repo haircuts and the like are evidence that financing and risk are not fully independent. But in many circumstances the dependence can be avoided. Large firms, for example, can easily avoid variation margin by careful structuring (e.g., using a forward instead of a future) and through credit risk transactions. So, for the purposes at hand, the separation between financing and risk taking is a legitimate starting point for capital associated with bank warehouse functions.

Under these circumstances, capital is a risk buffer and shouldn’t be allocated across investments. Nevertheless, this is something that many institutions still do, perhaps because it seems so intuitive, perhaps because they don’t believe in the separation of capital and risk.9 In any case, the diversification effect says that the sum of the standalone risks contributed by individual positions does not equal the total capital required. For example, consider offsetting swap contract positions, which are perfectly negatively correlated. The risk of the combined swaps is zero, so no capital is required to support them. However, the standalone capital requirements for each leg would be positive. Clearly the sum of the standalone capital requirements is larger than the capital required for the hedged position; hence the diversification savings.

In addition, the swap legs have equal negative inframarginal capital contributions. Removing either side of the hedge would lead to an increase in risk. Hence each leg acts as hedge against the other. The sum of these negative inframarginal risks is necessarily less than zero; this is just another way to see the diversification benefit. The inframarginals, like the standalones, fail to add up to total capital and therefore can’t be allocated.10 Some take this to mean that there is no practical way to allocate capital sensibly.

However, the marginal risks of positions do add up. Think of the combined swap portfolio as pre-existing. Then consider adding a marginal amount of risk to one leg, chosen arbitrarily. Then do the same to the other. The first marginal increase will add positive risk, the second will add equal and offsetting negative risk. Summing the covariances with the pre-existing portfolio results in the right answer: that the marginal risks sum to zero. Thus, as long as the pre-existing portfolio doesn’t evolve too quickly, so that we can consider such increments as small, an allocation of capital according to the marginal covariance is internally consistent.11

While the adding up property is helpful, it would nevertheless be a mistake to base capital charges on only marginal capital. The biggest single problem with marginal-capital based charges is that a risk is only costly to the extent it contributes to bank portfolio risk. Systematic risk and intra-corporate agency problems also necessitate capital charges, as discussed below. However, because these do not appear in marginal capital, the resulting allocations cannot alone be used as a basis for pricing.12

9 See, for example, F. Saita, “Allocation of Risk Capital in Financial Institutions,” Financial Management, 28, 95-111, 1999.

10 See R. Merton and A. Perold, “The Theory of Risk Capital in Financial Firms,” Journal of Applied Corporate Finance, 6, 16-32, 1993.