Financial Risk Manager Part 1

Explanation

This question involves testing for heteroskedasticity using the White test. Here's the step-by-step reasoning:

Step 1: Understanding the Test Statistic

• The White test statistic is calculated as nR², where:
  • n = sample size (100 in this case)
  • R² = coefficient of determination from the second regression
• The test statistic follows a χ² distribution with degrees of freedom = k(k+3)/2

Step 2: Determining Degrees of Freedom

• With one explanatory variable (k = 1):
  • Degrees of freedom = 1 × (1+3)/2 = 4/2 = 2
  • So we use χ²₂ distribution

Step 3: Finding Critical Value

• At 5% significance level, the critical value for χ²₂ is 5.99
• We reject the null hypothesis when: nR² > 5.99

Step 4: Solving for R²

• nR² = 5.99
• 100 × R² = 5.99
• R² = 5.99 / 100 = 0.0599

Step 5: Interpretation

• When R² ≥ 0.0599, we reject the null hypothesis of no heteroskedasticity
• When R² < 0.0599, we fail to reject the null hypothesis

Therefore, the correct R² value at which we would reject the null hypothesis is 0.0599 (Option D).