提问

问题如下：

A bond portfolio consists of the following three fixed-rate bonds. Assume annual coupon payments and no accrued interest on the bonds. Prices are per 100 of par value.

The bond portfolio’s modified duration is closest to:

选项：

7.62.

8.08.

8.20.

解释：

A is correct.

The portfolio’s modified duration is closest to 7.62.Portfolio duration is commonly estimated as the market-value-weighted average of the yield durations of the individual bonds that compose the portfolio.

The total market value of the bond portfolio is 170,000 + 120,000 + 100,000 = 390,000.

The portfolio duration is 5.42 × (170,000/390,000) + 8.44 × (120,000/390,000) + 10.38 × (100,000/390,000) = 7.62.

考点：portfolio duration

解析：portfolio duration是组合中每一个债券久期的加权平均，权重是每一个债券市值占总portfolio市值的比例。题干表格中已知每一个债券的modified duration和市值。加总成整个portfolio的总市值，用每个债券自己的总市值除以总市值就可以算出每一个债券的权重，即W1，W2……Wn。然后再代入公式可得：组合久期为7.62，故选项A正确。