Module: | MODULE B: RISK MANAGEMENT
Q336: A commercial bank holds a trading book portfolio of government securities with a total market value of ₹ 100 Crore. The Modified Duration of this specific portfolio is exactly 5.0 years. If the central bank suddenly hikes policy rates, causing a parallel upward shift in the yield curve by 50 basis points, calculate the expected new market value of this portfolio.
✅ Correct Answer: A
The correct answer is A (₹ 97.50 Crore). The problem tests the fundamental inverse relationship between bond prices and yields, quantified by Modified Duration.
The formula for the percentage change in bond price is: Percentage Change in Price = -(Modified Duration) × (Change in Yield). Given the Modified Duration is 5.0 and the yield change is +50 basis points (+0.50%), the calculation is: -5.0 × 0.50% = -2.50%. A 2.50% decline on the original market value of ₹ 100 Crore equals a loss of ₹ 2.50 Crore.
Subtracting this loss from the initial value gives the expected new market value: ₹ 100 Crore - ₹ 2.50 Crore = ₹ 97.50 Crore.
Option B is incorrect as it assumes a price increase despite a yield hike.
Options C and D calculate the magnitude incorrectly (assuming a 5% shift).
The formula for the percentage change in bond price is: Percentage Change in Price = -(Modified Duration) × (Change in Yield). Given the Modified Duration is 5.0 and the yield change is +50 basis points (+0.50%), the calculation is: -5.0 × 0.50% = -2.50%. A 2.50% decline on the original market value of ₹ 100 Crore equals a loss of ₹ 2.50 Crore.
Subtracting this loss from the initial value gives the expected new market value: ₹ 100 Crore - ₹ 2.50 Crore = ₹ 97.50 Crore.
Option B is incorrect as it assumes a price increase despite a yield hike.
Options C and D calculate the magnitude incorrectly (assuming a 5% shift).