Calculating trading book capital: is risk separation appropriate?

Regulatory capital for trading book positions includes two components that cover different risks but apply to the same portfolio, one for market risk and one for credit risk. Similar approaches are common in banks’ internal models for economic capital. Although it is known that joint market and credit risk of certain investments can be larger than the sum of risks, the problematic cases identified so far have been relatively exotic. I show that very common investments – corporate bond holdings or CDS portfolios – are also affected. There are realistic conditions under which credit risk (represented by ratings and default) and spread risk (represented by rating specific spread indices) combine to a total value-at-risk (VaR) 50 percent larger than the sum of spread and credit VaR; this effect is even stronger for the expected shortfall. If migration risk is segregated from default risk and incorporated into spread risk, as recently put forward by the Basel Committee, total risk is no longer underestimated. Furthermore, I improve a theoretic result of Breuer et al. (2010) that defines a sufficient condition under which risk separation is harmless.