Why does default correlation matter so much for credit portfolio losses?

Default correlation is arguably the most important and most difficult parameter in credit portfolio risk management. It measures the tendency for multiple obligors to default together.

Why It Matters: A Simple Example

Consider a portfolio of 100 loans, each with a 2% individual PD and $1M exposure. If defaults are independent (zero correlation), the expected loss is $2M and the standard deviation is only about $1.4M — diversification works perfectly.

But if defaults are positively correlated (say, ρ = 0.10), the probability of seeing 10+ simultaneous defaults jumps dramatically. The tail of the loss distribution fattens:

Notice that expected loss doesn't change — correlation only affects the shape of the distribution. This is why VaR and economic capital are so sensitive to correlation assumptions.

What Drives Default Correlation?

1. Systematic risk factors — All firms are exposed to the macroeconomy. During a recession, PDs rise together. The Basel IRB formula captures this through a single systematic factor.
2. Industry concentration — Banks heavily exposed to one sector (e.g., commercial real estate) face higher correlation.
3. Geographic concentration — Regional banks with local portfolios see correlated defaults when the local economy weakens.
4. Contagion — One firm's default can trigger defaults in its supply chain (e.g., Lehman Brothers' collapse affecting money market funds).

The Gaussian Copula Approach

CreditMetrics and many Basel models use a Gaussian copula to model joint defaults. Each firm's asset return is driven by a common factor plus an idiosyncratic factor:

Rᵢ = √ρ × Z + √(1-ρ) × εᵢ

where Z is the systematic factor and εᵢ is firm-specific. Default occurs when Rᵢ falls below a threshold tied to PD.

For the FRM exam, remember that underestimating default correlation was a key failure in the 2007-2008 crisis — CDO models assumed low correlation and suffered massive unexpected losses. Explore our FRM credit risk materials for deeper analysis.