AFIN8003 Week 7 - Credit Risk II: Loan Portfolio and Concentration Risk
Banking and Financial Intermediation
2026-09-10
RiskFrontier: where correlations come from (GCORR)
Default correlations between two loans cannot be directly observed. GCORR computes them via a factor model: two borrowers are correlated to the extent they share exposure to the same underlying risk factors.
Figure 1: Moody’s GCorr Corporate factor structure
Read Figure 1 this way
Each borrower’s asset return = global economy + region/country + industry + firm-specific noise. Two borrowers are correlated only through the shared branches of the tree. A Sydney miner and a Perth miner share the “Australia + Materials” branches, so ρ is high. A Sydney miner and a Berlin software firm share almost nothing, so ρ is near zero.
Credit swaps: total return swaps
A total return swap involves swapping an obligation to pay interest at a specified fixed or floating rate for payments representing the total return on a loan or a bond (interest and principal value changes) of a specified amount.
The figure below illustrates a total return swap.1
The FI lender pays a fixed annual rate \(f\) plus changes in the market value of the loan and receives a variable rate payment (historically 1-year LIBOR; post-2023 SOFR in USD, AONIA/BBSW in AUD since LIBOR’s cessation in June 2023).
- Interest rate risk remains. The TRS transfers credit and market risk of the asset, but the fixed vs floating mismatch is still an interest-rate exposure.
Credit swaps: total return swaps (cont’d)
Code
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(8003)
# Parameters for the TRS
notional = 1_000_000 # Notional amount (1 million)
fixed_rate = 0.03 # Fixed annual rate paid by the TRS receiver (3%)
asset_volatility = 0.1 # Volatility of the asset's return (10%)
years = 5 # Time period of the TRS (5 years)
periods_per_year = 4 # Payments per year (quarterly)
# Generate the timeline for TRS payments
def generate_trs_timeline(
notional, fixed_rate, asset_volatility, years, periods_per_year=4
):
# Set up the timeline with quarterly periods
total_periods = periods_per_year * years
time_points = np.arange(1, total_periods + 1) / periods_per_year
# Calculate the periodic fixed payment amount (quarterly)
periodic_fixed_payment = (
-notional * fixed_rate / periods_per_year
) # Fixed payment made by TRS receiver
# Simulate random returns on the asset
asset_returns = np.random.normal(loc=0, scale=asset_volatility, size=total_periods)
# Initialize lists to store the results
total_returns = np.zeros(total_periods)
payments = np.zeros(total_periods)
for period in range(total_periods):
# Total return on the asset (positive or negative)
total_return = notional * asset_returns[period]
total_returns[period] = total_return
# Net payment for the TRS receiver (positive if receiving total return, minus fixed payment)
payments[period] = total_return + periodic_fixed_payment
return time_points, payments, total_returns
# Simulate TRS payments with different asset volatilities
volatilities = [0.05] # Different volatilities to simulate
simulations = {}
for vol in volatilities:
timeline, payments, total_returns = generate_trs_timeline(
notional, fixed_rate, vol, years, periods_per_year
)
simulations[vol] = payments
# Plot the timelines as bar charts
plt.figure(figsize=(12, 8))
bar_width = 0.2 # Width of each bar
# Generate bar charts for each volatility
for idx, (vol, payments) in enumerate(simulations.items()):
plt.bar(
timeline + idx * bar_width * 0.1,
payments,
width=bar_width,
color="#A6192E",
label=f"Volatility: {vol*100:.0f}%",
)
# Customize the plot
plt.title(f"{years}-Year Total Return Swap Payments Example")
plt.xlabel("Time (Years)")
plt.ylabel("Net Payment Amount ($)")
plt.axhline(0, color="black", linewidth=1)
plt.grid(True)
plt.legend()
# Show the plot
plt.show()
Credit swaps: pure credit swaps
Interest-rate sensitive element stripped out leaving only the credit risk.
Similar to buying an insurance:
- If default, the counterparty makes the default payment
- If not default, the FI receives nothing from the counterparty.
Credit swaps: pure credit swaps (cont’d)
Code
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(8003)
# Parameters for the CDS
notional = 1_000_000 # Notional amount (1 million)
cds_spread = 0.02 # Annual CDS spread (2%)
recovery_rate = 0.9 # Recovery rate in case of default (90%)
years = 5 # Time period of the CDS (5 years)
periods_per_year = 4 # Payments per year (quarterly)
# Generate the timeline for CDS payments
def generate_cds_timeline(
notional, cds_spread, default_probability, recovery_rate, years, periods_per_year=4
):
# Set up the timeline with quarterly periods
total_periods = periods_per_year * years
time_points = np.arange(1, total_periods + 1) / periods_per_year
# Calculate the periodic payment amount (quarterly)
periodic_payment = (
-notional * cds_spread / periods_per_year
) # Negative for payments
# Initialize lists to store the results
payments = np.zeros(total_periods)
# Simulate payments and default events
for period in range(total_periods):
if np.random.rand() < default_probability / periods_per_year:
# Default occurs at this period
default_loss = notional * (
1 - recovery_rate
) # Positive for the payment received on default
payments[period] = default_loss
payments[period + 1 :] = 0 # No more payments after default
break
else:
# Regular payment
payments[period] = periodic_payment
return time_points, payments
# Simulate multiple series with different default probabilities
default_probabilities = [0.02, 0.1] # Different default probabilities
colors = ["#D6D2C4", "#A6192E"]
simulations = {}
# Generate timelines for each default probability
for prob in default_probabilities:
timeline, payments = generate_cds_timeline(
notional, cds_spread, prob, recovery_rate, years, periods_per_year
)
simulations[prob] = payments
# Plot the timelines as bar charts
plt.figure(figsize=(12, 8))
bar_width = 0.2 # Width of each bar
# Generate bar charts for each probability
for idx, (prob, payments) in enumerate(simulations.items()):
plt.bar(
timeline + idx * bar_width * 0.1,
payments,
width=bar_width,
color=colors[idx],
label=f"Default Probability: {prob*100:.0f}%",
)
plt.title(f"{years}-Year Pure CDS Payments Example")
plt.xlabel("Time (Years)")
plt.ylabel("Payment Amount ($)")
plt.axhline(0, color="black", linewidth=1)
plt.grid(True)
plt.legend()
plt.show()