Financial Risk Manager Part 2

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Explanation:

Explanation

Under the stressed scenario:

Spread = 480 bps = 480/10000 = 0.048
Recovery Rate (RR) = 40% = 0.40
Loss Given Default (LGD) = 1 - RR = 1 - 0.40 = 0.60

Step 1: Calculate the hazard rate (λ) The hazard rate formula is: $\lambda = \frac{spread}{1 - RR} = \frac{0.048}{0.60} = 0.08$

Step 2: Calculate the survival probability over 3 years Using the constant hazard rate process: $P(survival) = e^{-\lambda t} = e^{-0.08 \times 3} = e^{-0.24} = 0.7866 = 78.66\%$

Why other options are incorrect:

A (69.8%): Incorrectly uses the recovery rate instead of LGD in the hazard rate formula
C (86.6%): Incorrectly takes hazard rate per year as 4.8% (ignoring recovery rate)
D (74.1%): Incorrectly uses the original spread (250 bps) and recovery rate (75%) instead of the stressed scenario parameters

The correct answer is 78.7% (rounded from 78.66%).

Explanation:

Explanation

Under the stressed scenario:

Spread = 480 bps = 480/10000 = 0.048
Recovery Rate (RR) = 40% = 0.40
Loss Given Default (LGD) = 1 - RR = 1 - 0.40 = 0.60

Step 1: Calculate the hazard rate (λ) The hazard rate formula is: $\lambda = \frac{spread}{1 - RR} = \frac{0.048}{0.60} = 0.08$

Step 2: Calculate the survival probability over 3 years Using the constant hazard rate process: $P(survival) = e^{-\lambda t} = e^{-0.08 \times 3} = e^{-0.24} = 0.7866 = 78.66\%$

Why other options are incorrect:

A (69.8%): Incorrectly uses the recovery rate instead of LGD in the hazard rate formula
C (86.6%): Incorrectly takes hazard rate per year as 4.8% (ignoring recovery rate)
D (74.1%): Incorrectly uses the original spread (250 bps) and recovery rate (75%) instead of the stressed scenario parameters

The correct answer is 78.7% (rounded from 78.66%).

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The head of the fixed-income department of a bank asks a risk analyst to review an outstanding bond issued by Company GRN, a livestock producer. The bond currently trades at a spread of 250 bps over the risk-free interest rate and has a recovery rate of 75%. Senior management of the bank has expressed concern about the slowdown in business activities in the livestock industry, which is expected to last for the next 3 years. The analyst applies the constant hazard rate process in estimating default probability and assumes that, under a stressed market scenario, the bond would trade at a spread of 480 bps over the risk-free interest rate curve, and its recovery rate would decrease to 40%. Assuming the stress scenario prevails, what would be the correct estimate of the probability that Company GRN would not default on its bond over the next 3 years?

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Last updated: May 29, 2026 at 14:02

69.8%

8.7%

78.7%

78.3%

86.6%

4.3%

74.1%

8.7%