# P2.T6.24.16 Model-Based Default Probabilities and Distance to Default

#### Nicole Seaman

##### Director of CFA & FRM Operations
Staff member
Subscriber
Learning Objectives: Using the Merton model, calculate distance to default and default probability. Assess the quality of the default probabilities produced by the Merton model, the Moody’s KMV model, and the Kamakura model.

Questions:

24.16.1.
You are an analyst at a risk management firm evaluating the financial stability of FiberTech, a company in the telecommunications sector. Given the company's current financial data and market conditions, you are tasked with assessing the risk of default using the Merton model.

Model inputs:
• Value of FiberTech’s Assets (): $500 million • Total Debt (D):$300 million due in one year
• Volatility of Assets: 25%
• Risk-Free Rate (r): 3% per annum
Based on the Merton model and the provided financial data for FiberTech, calculate the distance to default and the probability of default. Which of the following results is correct?

a. Distance to default: 2.29, Probability of default: 1.1%
b. Distance to default: 2.04, Probability of default: 2.07%
c. Distance to default: 2.29, Probability of default: 97.92%
d. Distance to default: 2.5, Probability of default: 0.55%

24.16.2. You are a senior credit risk analyst at Apex Financial. With an increasing portfolio of corporate bonds and loans, the firm is re-evaluating its current methodologies for predicting default probabilities to enhance its risk assessment capabilities.

Apex Financial is reviewing its default probability models to decide whether to adopt a new one or update the current one. The board has requested an analysis of the Merton, Moody’s KMV, and Kamakura models to assess their accuracy and reliability. You’ve been asked to prepare a report for the board assessing each model's strengths and weaknesses in predicting default probabilities. Your analysis will help guide the firm’s decision on which model to prioritize or whether a combination of models might be more effective.

Which of the following best describes the relative strengths and weaknesses of the Merton model, the Moody’s KMV model, and the Kamakura model in terms of assessing default probabilities?

a. The Merton model excels in real-time risk assessment but lacks the predictive accuracy of Moody’s KMV and Kamakura models, which incorporate more comprehensive credit risk factors.
b. Moody’s KMV model offers superior predictive accuracy due to its use of more market data variables compared to the Merton and Kamakura models, which rely more heavily on historical data.
c. The Kamakura model provides the most detailed risk assessment because it integrates macroeconomic variables, a feature not present in Merton or Moody’s KMV models.
d. All three models provide equally reliable default probabilities as they all use similar financial and economic indicators to predict risk.

24.16.3. You are a quantitative analyst at Criterion Financial, a boutique investment firm that specializes in credit risk analysis and corporate bond investments. Criterion Financial is evaluating a potential investment in bonds issued by TechNovation, a technology firm.

As part of the due diligence process, you have been provided with default probability estimates from three different models: the Merton model, Moody’s KMV model, and the Kamakura model. Each model has given a different estimate of the default probability over the next five years based on the same financial statements and market conditions.

Model results:
• Merton Model Estimate: 2.5% chance of default over five years.
• Moody’s KMV Model Estimate: 1.8% chance of default over five years.
• Kamakura Model Estimate: 2.1% chance of default over five years.
Assess these estimates and determine which model might be providing the most reliable default probability, considering the broader economic context and the specific characteristics of TechNovation.

a. The Kamakura model’s estimate aligns closely with industry averages for default probabilities in the tech sector, suggesting a balanced approach that considers both macroeconomic factors and company specifics.
b. Moody’s KMV model’s lower default probability estimate indicates a more accurate assessment because it integrates market data effectively, reflecting the current market confidence in TechNovation.
c. The Merton model’s higher default probability estimate suggests a conservative approach due to its focus on asset volatility and capital structure, which might be more appropriate given TechNovation’s volatile market sector.
d. Given the discrepancies in the estimates, all models are unreliable for this particular bond investment as they show significant variance, indicating underlying data inconsistencies.