IPS-BANKS-Leverage Adjusted Duration Gap understand, investment, account

dirk01

LADG = Duration of assets - (mv liabilities/mv assets * Duration of liabilities)
1) “For an unexpected increase in rates, the market value of net worth will decrese for a bank with a positive gap”.
Im trying to break this down to understand the statement, if anyone can confirm / comment on my thinking, please do:
I assume a “Positive gap” means the duration of the banks assets is greater than the second term of the LADG equation.
As I understand, a banks “assets” are its loan portfolios and its investment portfolio. I am also under the assumption that the investment portfolio of a bank is compromised mainly of fixed income securities.
So if interest rates go up, and the duration of assets ( i.e fixed income securities) is greater than the banks liabilities, than these go down in value more than the banks liabilities….hence the decrese in the banks net worth.
Is this correct thinking?
2) A banks liabilities are compromised of their short term deposits. How do these have a “duration”? i mean if interest rates change, are these really “due sooner, or due later” ??