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A bank owns a portfolio of bonds whose composition is shown below. What is the modified duration of the portfolio?
Correct Answer: D
* Calculate the weighted average of modified durations: * The modified duration of the portfolio is a weighted average of the durations of the individual bonds, where the weights are the proportions of the total portfolio value. * Calculate the total value of the portfolio: $200 MM (3-year floater) + $120 MM (5-year floater) + $50 MM (10-year fixed) = $370 MM. * Calculate the weights for each bond: * 3-year floater: $200 MM / $370 MM = 0.5405 * 5-year floater: $120 MM / $370 MM = 0.3243 * 10-year fixed: $50 MM / $370 MM = 0.1351 * Multiply each bond's weight by its modified duration and sum the results: * (0.5405 * 0.25) + (0.3243 * 0.25) + (0.1351 * 8) = 0.1351 + 0.0811 + 1.081 = 1.297 * Therefore, the weighted average modified duration is approximately 1.30. References Calculation based on standard formula and weights derived from the table.