Financial Risk Manager Part 1

Financial Risk Manager Part 1

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The seasonal dummy model is generated on the quarterly growth rates of mortgages. The model is given by:

Yt=β0+∑j=1s−1γjDjt+etY_t = \beta_0 + \sum_{j=1}^{s-1} \gamma_j D_{jt} + e_t

The estimated parameters are γ^1=6.25\hat{\gamma}_1 = 6.25, γ^2=50.52\hat{\gamma}_2 = 50.52, γ^3=10.25\hat{\gamma}_3 = 10.25 and β^0=−10.42\hat{\beta}_0 = -10.42 using the data up to the end of 2019. What is the difference between the forecasted value of the growth rate of the mortgages in the second and third quarters of 2020?

TTanishq

Explanation:

Explanation

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

Djt={1,for Q20,for Q1,Q3 and Q4D_{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 Qâ‚‚ is:

E(Y^Q2)=β0+∑j=13γjDjt=−10.42+0×6.25+1×50.52+0×10.25=40.10\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:

Djt={1,for Q30,for Q1,Q2 and Q4D_{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:

E(Y^Q3)=β0+∑j=13γjDjt=−10.42+0×6.25+0×50.52+1×10.25=−0.17\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:

Q2−Q3=40.10−(−0.17)=40.27Q_2 - Q_3 = 40.10 - (-0.17) = 40.27

Therefore, the correct answer is 40.27.

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