Answer: USD -1.37

## Explanation The forward price formula for a dividend-paying stock is: \[ F = S_0 \times e^{(r - q)T} \] Where: - \( F \) = forward price - \( S_0 \) = current spot price = USD 67.68 - \( r \) = risk-free rate = -0.70% = -0.007 - \( q \) = dividend yield = 0.44% = 0.0044 - \( T \) = time to maturity = 2 years **Current forward price:** \[ F_0 = 67.68 \times e^{(-0.007 - 0.0044) \times 2} \] \[ F_0 = 67.68 \times e^{-0.0114 \times 2} \] \[ F_0 = 67.68 \times e^{-0.0228} \] \[ F_0 = 67.68 \times 0.9775 \approx 66.15 \] **New forward price after 1% increase in risk-free rate:** \[ r_{new} = -0.007 + 0.01 = 0.003 \] \[ F_1 = 67.68 \times e^{(0.003 - 0.0044) \times 2} \] \[ F_1 = 67.68 \times e^{-0.0014 \times 2} \] \[ F_1 = 67.68 \times e^{-0.0028} \] \[ F_1 = 67.68 \times 0.9972 \approx 67.49 \] **Change in forward contract value:** The value of a long forward position is: \[ V = (F_1 - F_0) \times e^{-rT} \] \[ V = (67.49 - 66.15) \times e^{-0.003 \times 2} \] \[ V = 1.34 \times e^{-0.006} \] \[ V = 1.34 \times 0.9940 \approx 1.33 \] However, since the question asks for the change in value and the forward price increased, the value of a long position increases by approximately USD 1.33. But looking at the options, USD 1.33 corresponds to option C. **Alternative calculation using sensitivity:** The sensitivity of forward price to interest rate changes: \[ \frac{\partial F}{\partial r} = S_0 \times T \times e^{(r - q)T} \] \[ \Delta F \approx S_0 \times T \times e^{(r - q)T} \times \Delta r \] \[ \Delta F \approx 67.68 \times 2 \times e^{(-0.007 - 0.0044) \times 2} \times 0.01 \] \[ \Delta F \approx 67.68 \times 2 \times 0.9775 \times 0.01 \] \[ \Delta F \approx 67.68 \times 0.01955 \approx 1.32 \] After discounting: \[ \Delta V \approx 1.32 \times e^{-0.003 \times 2} \approx 1.32 \times 0.9940 \approx 1.31 \] Given the options, USD 1.33 (option C) appears to be the closest match to the calculated change in value.

Author: LeetQuiz .