"
Arbitrage CDOs" have recorded an explosive growth during the years before the outbreak of the financial crisis. In the present paper we discuss potential sources of such
arbitrage opportunities, in particular
arbitrage gains due to mispricing. For this purpose we examine the risk profiles of Collateralized Debt Obligations (CDOs) in some detail. The analyses reveal significant differences in the risk profile between CDO tranches and corporate bonds, in particular concerning the considerably increased sensitivity to systematic risks. This has farreaching consequences for risk management, pricing and regulatory capital requirements. A simple analytical valuation model based on the CAPM and the single-factor Merton model is used in order to keep the model framework simple. Then, the conditional expected
loss curve (EL profile) is studied in some detail. In the next step, the asset correlation associated with a CDO
tranche is estimated treating the structured instrument as a single-name credit instrument (i.e., a loan equivalent). While tractable, the loan-equivalent approach requires appropriate parameterization to achieve a reasonable approximation of the tranche´s risk profile. We consider the
tranche as a "virtual" borrower or bond for which a single-factor model holds. Then, the correlation parameter is calculated via a non-linear optimization. This "bond representation" allows to approximate the risk profile (expressed by the EL profile) using a single-factor model and to express the dependence on the systematic risk factor via the corresponding asset correlation. It turns out that the resulting asset correlation is many times higher than that of straight bonds. Then, the Merton type valuation model for the corresponding bond representations is applied for valuation of the CDO tranches. Using a sample CDO portfolio, some opportunities for "CDO
arbitrage" are described where it is assumed that investors are guided solely by the tranches’
rating and ignore the increased systematic risk for pricing. In the next section we discuss how tranches with high systematic risk can be generated and how CDO arrangers can exploit this to their advantage. It comes as no surprise that precisely these types of structures featured in many of the CDOs issued prior to the outbreak of the financial crisis.
[Source: Discussion Paper No 13, Series 2: Banking and Financial Studies, 2009, Deutsche Bundesbank, Frankfurt/Main]