$1.$ Omar$$s first task was to evaluate the current interest rate risk to

which the bank was exposed. Based on the analysts$$ information, he

answered the following questions.

$($i$).$ What is the overall duration of the ABC Bank$$s assets?

$($ii$).$ What is the overall duration of the ABC Bank$$s liabilities,

not including shareholders$$ equity?

$($iii$).$ Omar decides to add $$5$ billion in assets with a duration

of $0\mathrm{.}5$ years and $$5$ billion in liabilities with a duration of $1\mathrm{.}92$

years. What is the new Leverage Adjusted Duration Gap?

$($iv$).$ Omar was particularly concerned with the interest rate

risk for the banks$$ consumer fixed$-$rate loans portfolio. The

bank$$s analysts calculated the convexity of this portfolio to be

$36.$ What would be the loss in value to this loan portfolio if the

loans$$ yields increased by $20$ basis points? Express your answer

in millions of dollars.

Balance Sheet

Assets Amount Duration Liabilities Amount Duration

Consumer Fixed$-$Rate Loans $$5$ bn $5\mathrm{.}0$ Long$-$Term Bonds $$2$ bn $7\mathrm{.}75$

Consumer Floating$-$Rate Loans $$2$ bn $0\mathrm{.}5$ Wholesale Deposits $$6$ bn $0\mathrm{.}25$

Commercial Fixed$-$Rate Loans $$4$ bn $2\mathrm{.}0$ Retail Deposits $$10$ bn $1\mathrm{.}0$

Commercial Floating$-$Rate Loans $$6$ bn $0\mathrm{.}25$

Securities $$3$ bn $1\mathrm{.}5$

$2$