Financial Risk Manager Part 1

Explanation

For the second quarter (Q₂), the dummy variables are defined as:

$D_{jt} = \begin{cases} 1, & \text{for } Q_2 \\ 0, & \text{for } Q_1, Q_3 \text{ and } Q_4 \end{cases}$

The expected forecast for Q₂ is:

$\mathbb{E}(\hat{Y}_{Q_2}) = \beta_0 + \sum_{j=1}^{3} \gamma_j D_{jt} = -10.42 + 0 \times 6.25 + 1 \times 50.52 + 0 \times 10.25 = 40.10$

For the third quarter (Q₃), the dummy variables are defined as:

$D_{jt} = \begin{cases} 1, & \text{for } Q_3 \\ 0, & \text{for } Q_1, Q_2 \text{ and } Q_4 \end{cases}$

The expected forecast for Q₃ is:

$\mathbb{E}(\hat{Y}_{Q_3}) = \beta_0 + \sum_{j=1}^{3} \gamma_j D_{jt} = -10.42 + 0 \times 6.25 + 0 \times 50.52 + 1 \times 10.25 = -0.17$

The difference between Q₂ and Q₃ is:

$Q_2 - Q_3 = 40.10 - (-0.17) = 40.27$

Therefore, the correct answer is 40.27.