Credit Risk Fundamentals › Portfolio Credit Risk
Quantitative FinanceAll chapters Credit Risk Fundamentals › Portfolio Credit RiskOne section · Sections in this chapter10 / 15 ↓
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Individual loan metrics tell only part of the story. Portfolio effects, such as diversification and concentration, significantly affect total credit risk. A well-diversified portfolio of many small exposures to borrowers in different industries and regions will have much lower risk than a concentrated portfolio with large exposures to a few correlated borrowers. Understanding these portfolio dynamics is essential for managing credit risk at the enterprise level.
def portfolio_expected_loss(portfolio_df):
"""Calculate total portfolio expected loss (additive)."""
return portfolio_df["Expected_Loss"].sum()
def portfolio_unexpected_loss_independent(portfolio_df):
"""
Calculate portfolio UL assuming independence.
Under independence, variances add, so UL = sqrt(sum of squared ULs).
"""
return np.sqrt((portfolio_df["UL"] ** 2).sum())
def portfolio_unexpected_loss_correlated(portfolio_df, default_correlation):
"""
Calculate portfolio UL with default correlation.
Uses simplified one-factor model approach.
"""
n = len(portfolio_df)
uls = portfolio_df["UL"].values
# Correlation adds covariance terms
# Var(sum) = sum(var) + 2*sum(cov)
variance_sum = (uls**2).sum()
# Add correlation effect
covariance_sum = 0
for i in range(n):
for j in range(i + 1, n):
covariance_sum += 2 * default_correlation * uls[i] * uls[j]
return np.sqrt(variance_sum + covariance_sum)
# Calculate portfolio metrics
port_el = portfolio_expected_loss(portfolio)
port_ul_ind = portfolio_unexpected_loss_independent(portfolio)
port_ul_corr = portfolio_unexpected_loss_correlated(
portfolio, default_correlation=0.20
)Portfolio Credit Risk Summary ======================================================= Total Exposure: $28.0M Portfolio Expected Loss: $86,145 Portfolio UL (independent): $415,977 Portfolio UL (20% correlation): $529,314 Diversification Effect (independent): 50.6% Correlation Impact: +27.2%
Default correlation substantially increases portfolio unexpected loss, and the magnitude of this effect is often surprising. During systemic crises, many borrowers deteriorate simultaneously, causing correlated defaults that overwhelm diversification benefits. When correlations spike, the portfolio that appeared well-diversified under normal conditions can experience concentrated losses. This phenomenon was tragically demonstrated in the structured credit market during 2008, when assumed correlations proved far too low. CDO tranches rated AAA based on historical correlation assumptions suffered unexpected losses because the underlying mortgage borrowers defaulted together at rates that the models had deemed virtually impossible.
The comparison highlights how PD, LGD, and exposure jointly drive both credit risk measures. Company D contributes the most expected and unexpected loss because its high probability of default and 60% LGD outweigh its relatively small exposure. Company B's $10M exposure still produces the second-largest unexpected loss despite its better rating. This distinction matters for capital allocation, which focuses on buffering against unexpected rather than expected losses. Expected losses are a cost of doing business that should be covered by loan pricing and provisions; unexpected losses are the tail risks that require capital buffers to ensure institutional solvency.