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 leveraged-adjusted duration gap (LADG) is calculated as follows: $$LADG = D_A - \frac{L}{A}D_L$$ 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. Given that the average duration of the loans (assets) is 10 years, and the average duration of the deposits (major part of liabilities) is 3 years, and considering that equity is part of the capital structure but not a liability with a duration in this context, we calculate the LADG as follows: $$LADG = 10 - \frac{235}{250} \times 3$$ $$LADG = 10 - 0.94 \times 3$$ $$LADG = 10 - 2.82$$ $$LADG = 7.18 \text{ years}$$

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