Financial Risk Manager Part 1

Explanation

The correct answer is B. The model will not be able to find a unique best-fit solution.

This issue arises due to a phenomenon known as the dummy variable trap. The dummy variable trap occurs when:

1. Perfect Multicollinearity: Including all dummy variables for a categorical feature plus an intercept term creates perfect multicollinearity
2. Linear Dependence: The sum of all dummy variables equals 1 (for each observation), which is exactly the same as the intercept term
3. Matrix Inversion Issues: This makes the design matrix singular and non-invertible

Why This Happens:

• If you have a categorical variable with k categories, you should only create k-1 dummy variables
• Including all k dummy variables plus an intercept creates perfect multicollinearity
• The statistical software cannot compute unique parameter estimates

Consequences:

• The model cannot find a unique solution for the coefficients
• Standard errors become infinite
• Parameter estimates become unstable and unreliable

Solution:

• Drop one dummy variable category (the reference category)
• Or remove the intercept term (less common)

This issue is particularly important in financial risk modeling where accurate parameter estimation is crucial for default prediction.