The average duration of the loans is 10 years.The average duration of the deposits is 3 years. $\begin{array}{llr}
\text { Consumer loans } & \$ 50 \text { million Deposits } & \$ 235 \text { million } \
\text { Commercial Loans } & \$ 200 \text { million Equity } & \$ 15 \text { million } \
\text { Total Assets } & \$ 250 \text { million Total Liabilities \& Equity } & \$ 250 \text { million }
\end{array}$

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.

Question

The average duration of the loans is 10 years.The average duration of the deposits is 3 years. $\begin{array}{llr}
\text { Consumer loans } & \$ 50 \text { million Deposits } & \$ 235 \text { million } \
\text { Commercial Loans } & \$ 200 \text { million Equity } & \$ 15 \text { million } \
\text { Total Assets } & \$ 250 \text { million Total Liabilities \& Equity } & \$ 250 \text { million }
\end{array}$

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.

Quizplus · Accepted Answer

The leveraged-adjusted duration gap is calculated as the difference between the duration of assets and the duration of liabilities, weighted by the respective amounts, divided by the bank's equity.

First, we need to calculate the weighted average duration of assets and liabilities:

Weighted duration of loans = (50 million * 10 years + 200 million * 10 years) / 250 million = 9.2 years

Weighted duration of deposits = (235 million * 3 years) / 235 million = 3 years

Next, we can calculate the leveraged-adjusted duration gap:

Duration Gap = (Weighted duration of loans - Weighted duration of deposits) / (Equity / Total assets)

Duration Gap = (9.2 years - 3 years) / (15 million / 250 million)

Duration Gap = 6.2 / 0.06

Duration Gap = 7.18 years

Therefore, the correct answer is D) 7.18 years.

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