CDO tranche spread

Question

An increase in default correlation ceteris paribus increases the value of the equity tranche of a CDO. This I get.

How then, do I make sense of the statement that as default correlation in the underlying credits increases, the spread decreases?

Isn't the value of the tranche the spread it earns over LIBOR when there is enough funds to pass to the equity tranche?

Answer 1

The intuition behind the statement "if correlation increases, the spread of a CDO junior tranche decreases" is as follows:

• If correlation increases, more probability mass of the default distribution is moving to the tails.
• The risk of joint default increases, but at the same time the chance of joint survivals increases.
• So the higher correlation, the higher the likelihood that there are no defaults.
• The junior tranche becomes less risky and the spread decreases.

Answer 2

for synthetic cdo you could have a look at this paper - http://home.gwu.edu/~sagca/JAI.pdf.

as for equity tranche, i understand that it receives residual cashflow i.e. remainings after paying all senior tranches.