The average duration of the loans is 10 years. The average duration of the deposits is 3 years. $$\begin{array} { | l | r | l | r | }
\hline \text { Consumer loans } & \$ 50 \text { million } & \text { Deposits } & \$ 235 \text { million } \
\hline \text { Commercial Loans } & \$ 200 \text { million } & \text { Equity } & \$ 15 \text { million } \
\hline \text { Total Assets } & \$ 250 \text { million } & \text { Total Liabilities \& Equity } & \$ 250 \text { million } \
\hline
\end{array}$$
-What is the leveraged-adjusted duration gap of the bank's portfolio?
A)10 years.
B)7.3 years.
C)7 years.
D)7.18 years.
E)3 years.

Question

The average duration of the loans is 10 years. The average duration of the deposits is 3 years. $$\begin{array} { | l | r | l | r | } 
\hline \text { Consumer loans } & \$ 50 \text { million } & \text { Deposits } & \$ 235 \text { million } \
\hline \text { Commercial Loans } & \$ 200 \text { million } & \text { Equity } & \$ 15 \text { million } \
\hline \text { Total Assets } & \$ 250 \text { million } & \text { Total Liabilities \& Equity } & \$ 250 \text { million } \
\hline
\end{array}$$
-What is the leveraged-adjusted duration gap of the bank's portfolio?
A)10 years.
B)7.3 years.
C)7 years.
D)7.18 years.
E)3 years.

Quizplus · Accepted Answer

The leverage-adjusted duration gap is calculated as: $(D_A - \frac{L}{A} \times D_L)$, where $D_A$ is the duration of assets, $D_L$ is the duration of liabilities, $L$ is the total liabilities, and $A$ is the total assets. Here, $D_A = 10$, $D_L = 3$, $L = 235$, and $A = 250$. The calculation is $10 - \frac{235}{250} \times 3 = 7.18$ years.

The Average Duration of the Loans Is 10 Years -What Is the Leveraged-Adjusted Duration Gap of the Bank's Portfolio