Risk management: Gap analysis vs duration analysis

Consider the formula for the interest rate gap:

$q,$

Gap $=$ Amount of IR$-$sensitive Assets $-$ Amount of IR$-$sensitive Liabilities

$q,$

Banks would like to have a positive gap if they expect that future interest rates wil $..$ This means that banks should hold

$$ interest rate$-$sensitive assets than interest rate$-$sensitive liabilities.

Now consider the formula for the duration gap:

$q,$

Duration gap $=$ Asset Duration $-$ Liability Duration $\frac{\text{L}\text{i}\text{a}\text{b}\text{i}\text{l}\text{i}\text{t}\text{y}}{\text{A}\text{s}\text{s}\text{e}\text{t}}$

where Asset is the market value of the asset, Liability is the market value of the liability, and duration is the weighted average of times until payment, with their weights proportionate to the present value of the payment: Duration $)t.$

$q,$

The duration formula implies that if interest rates increase, duration will $.$ The duration gap formula implies that, ceteris paribus, the gap will remain the same, if the interest rate change affects the value of the bank's assets $$ than it affects the value of its liabilities.