A portfolio consists of three bonds as follows. $$\begin{array} { l c c }
& \text { Amount Invested } & \text { Bond Duration } \
\hline \text { Bond X } & \$ 5,000 & 8.6 \text { years } \
\text { Bond Y } & \$ 4,000 & 4.2 \text { years } \
\text { Bond Z } & \$ 1,000 & 11.4 \text { years } \
\hline
\end{array}$$ What is the duration of the bond portfolio?

Question

A portfolio consists of three bonds as follows. $$\begin{array} { l c c } 
& \text { Amount Invested } & \text { Bond Duration } \
\hline \text { Bond X } & \$ 5,000 & 8.6 \text { years } \
\text { Bond Y } & \$ 4,000 & 4.2 \text { years } \
\text { Bond Z } & \$ 1,000 & 11.4 \text { years } \
\hline
\end{array}$$ What is the duration of the bond portfolio?

Quizplus · Accepted Answer

The duration of the bond portfolio is calculated as a weighted average of the durations of the individual bonds, with the weights being the proportion of the total investment in each bond. The total investment is $5,000 + $4,000 + $1,000 = $10,000. The calculation is as follows:$$ \text{Portfolio Duration} = \left( \frac{5000}{10000} \times 8.6 \right) + \left( \frac{4000}{10000} \times 4.2 \right) + \left( \frac{1000}{10000} \times 11.4 \right) = 0.5 \times 8.6 + 0.4 \times 4.2 + 0.1 \times 11.4 = 7.12 \text{ years} $$

A Portfolio Consists of Three Bonds as Follows What Is the Duration of the Bond Portfolio? A) 7

A Portfolio Consists of Three Bonds as Follows What Is the Duration of the Bond Portfolio?
A) 7