如图

问题如下：

Consider the following information on three bonds: Bond A, Bond B, and Bond C.

A fixed-income portfolio contains Bond A and Bond B. If another $10 million is added to the portfolio and is used to purchase Bond C, then the annualized modified duration of the portfolio will be closest to:

选项：

A.5.0793. B.5.1452. C.6.5668.

解释：

A is correct. The new modified duration of the portfolio is calculated as follows:

The initial market value of the portfolio = $9,323,381 + $11,189,092 = $20,512,473.

The portfolio market value with the purchase of Bond C is:

New portfolio market value = $20,512,473 + $10,000,000 = $30,512,473.

ModDur=[7.3105×9,323,381/30,512,473]+[4.6880×11,189,092/30,512,473] +[3.4370×10,000,000/30,512,473]=5.0793

where the first term in each set of brackets is the annualized modified duration and the second term is the weighting factor based on market value.

考点：portfolio duration

解析：组合duration是加权平均duration，权重是各债券市值占总市值的比例。各市值除以总市值即为各权重。第三行，各市值加总，可得总市值为30,512,473

ModDur=[7.3105×9,323,381/30,512,473]+[4.6880×11,189,092/30,512,473] +[3.4370×10,000,000/30,512,473]=5.0793

故选项A正确。