How Default Correlation Changes CDO Junior-Tranche Risk and Spreads

Summary

This note explains why higher default correlation can reduce the spread on a CDO junior tranche even as it raises the tranche’s value. Correlation shifts the distribution of portfolio defaults toward both extremes: more cases with few or no defaults, and more cases with many defaults. For a junior tranche, the increased chance of no defaults can lower expected losses, making the tranche less risky and reducing the spread investors require.

The explanation is qualitative and focuses on intuition rather than a pricing model or numerical evidence. Its conclusion depends on which part of the default distribution matters to the tranche: a junior tranche benefits from the greater probability of broad survival but remains exposed to severe joint defaults. The document also notes that equity-tranche cash flows are residual amounts after more senior claims are paid, but it does not develop a full waterfall or distinguish how tranche attachment points affect the result.

Key ideas

• Higher default correlation shifts probability toward both low-default and high-default outcomes.
• A junior tranche may become less risky if the increased chance of few defaults outweighs its exposure to severe joint defaults.
• Lower expected tranche losses can reduce the spread investors require.
• Equity-tranche cash flows are residual to payments owed to senior tranches.

Tags

# CDO tranche spread


# CDO tranche spread












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 by dnl (score 2)

https://quant.stackexchange.com/a/21761

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 by Nicholas (score 1)

https://quant.stackexchange.com/a/21746

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.