A ten-year note is priced at par and has a (modified) duration of 7.8 years. A twenty-five year bond has a (modified) duration of 12 years and is priced at a discount. Your portfolio consists of some of the 10-year and some of the 25-year. Your portfolioâ s (modified) duration is:

Between 7.8 and 12 Years

Explanation:

The modified duration of a portfolio is defined as a weighted average in the modified duration of an individual bonds. Therefore it will lie between the extreme values of the modified duration of the bonds in portfolio so that the weights are all positive.

In the context, the modified duration lies between 7.8 years and 12 years as the modified duration would always lie between the lowest modified duration and the highest modified duration of any bonds in a portfolio. Therefore the weights are value that will lie between these two years.

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