Capital Allocation

Overview

One of the common frameworks that banks use to measure performance is capital allocation. That is, once ecoonomic capital has been calculated for the bank as a whole, the banks managers allocate the capital to the various bank divisions or products. Once a division has been allocated capital, the bank can then measure a risk performace measure for the division, such as RAROC by dividing the divisions profits by the capital allocated to it.

Methodologies

Capital allocation is in some sense a form of attribution and suffers from its problems. In particular, the amount of VAR of the bank as a whole is not the sum of the VAR's of the individual divisions, there are interactions between divisions that creates diversification. This creates a complexity that is often ignored. For example, the Basel formulas (see above) are linear in the sense that the total risk is the sum of the individual risks.

Because of the complexities of capital allocation, there is no single agreed upon method. The simplest method of allocation would be to the allocate total capital proportional to the individual VARs of each division.

Most risk measures are homongenous of degree 1, and therefore can be decomposed using Eulers Theorem. See risk attribution.