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Chapter 10 Homework
Question 11, End of Chapter 3

The following entries (in millions of dollars) are from the balance sheet of Rivendell National Bank (RNB):

\begin{tabular}{ll}
\hline U.S. Treasury bills & [tex]$\$[/tex] 21$ \\
Demand deposits & [tex]$\$[/tex] 30$ \\
Mortgage-backed securities & [tex]$\$[/tex] 31$ \\
Loans from other banks & [tex]$\$[/tex] 10$ \\
C\&I loans & [tex]$\$[/tex] 49$ \\
Discount loans & [tex]$\$[/tex] 7$ \\
NOW accounts & [tex]$\$[/tex] 35$ \\
Savings accounts & [tex]$\$[/tex] 11$ \\
Reserve deposits with Federal Reserve & [tex]$\$[/tex] 6$ \\
Cash items in the process of collection & [tex]$\$[/tex] 5$ \\
Municipal bonds & [tex]$\$[/tex] 7$ \\
Bank building & [tex]$\$[/tex] 5$ \\
\hline
\end{tabular}

If RNB's assets have an average duration of four years and its liabilities have an average duration of three years, what is RNB's duration gap?

Duration gap [tex]$= 2$[/tex]



Answer :

GinnyAnswer
To find Rivendell National Bank's (RNB) duration gap, we need to understand the definitions of asset duration and liability duration. The duration of an asset or liability is a measure of the weighted average time until the cash flows are received or paid, respectively. The duration gap is the difference between the average duration of the assets and the average duration of the liabilities.

### Given Data:
- Average duration of RNB's assets: 4 years.
- Average duration of RNB's liabilities: 3 years.

### Calculation:
To find the duration gap, we subtract the average duration of the liabilities from the average duration of the assets:

[tex]\[ \text{Duration gap} = \text{Average duration of assets} - \text{Average duration of liabilities} \][/tex]

Substituting the given values:

[tex]\[ \text{Duration gap} = 4 \text{ years} - 3 \text{ years} \][/tex]
[tex]\[ \text{Duration gap} = 1 \text{ year} \][/tex]

Thus, Rivendell National Bank's (RNB) duration gap is 1 year.

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