How does a synthetic CDO work, and why does credit correlation dramatically affect tranche pricing?

A synthetic CDO creates tranched credit exposure using a portfolio of credit default swaps (CDS) rather than physical bonds. No actual bonds are bought or sold — the entire structure is derivatives-based.

Structure

Consider Oakbridge Capital structuring a synthetic CDO on 125 investment-grade CDS names, each equally weighted. Total notional is $1.25 billion ($10M per name). The equity tranche absorbs the first $37.5M (3%) of losses; the mezzanine takes the next $50M (3-7%), and so on.

Why Correlation Matters

Credit correlation determines how defaults cluster. This has opposite effects on different tranches:

Low correlation (e.g., 10%): Defaults are largely independent. You expect a steady trickle of 2-4 defaults, which the equity tranche absorbs. The senior tranche is extremely safe because it's virtually impossible for enough independent defaults to reach it.

High correlation (e.g., 50%): Defaults are clustered — either very few names default or a large number default together. This means:

• The equity tranche is less risky (higher chance of zero or very few defaults)
• The senior tranche is more risky (when defaults do occur, they come in waves that penetrate higher attachment points)

The Correlation Smile

In practice, the market-implied correlation that correctly prices each tranche differs:

• Equity tranches imply higher correlation
• Mezzanine tranches imply lower correlation
• Senior tranches imply higher correlation again

This U-shaped pattern is the "correlation smile" — analogous to the volatility smile in options. It reflects the market's recognition that a single Gaussian copula correlation cannot capture the true default dependence structure.

FRM exam tip: Know that increasing correlation helps equity tranche investors (lower spread) and hurts senior tranche investors (higher spread). Mezzanine tranches have ambiguous correlation sensitivity. Questions often present a correlation change and ask which tranche benefits — equity is the answer for correlation increases.

Practice synthetic CDO questions in our FRM Part II question bank.