Risk management: Gap analysis vs duration analysis

Consider the formula for the interest rate gap:

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

Banks would like to have a positive gap if they expect that future interest rates will

$.$ This means that banks should hold

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

Now consider the formula for the duration gap:

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