Consider the balance sheet of First Bank of Woebegone (FBW), a rather local bank:

ASSETS

25 Reserve account at the Federal Reserve Interest may change every 6 weeks at FOMC meetings

315 Auto loans, interest rate Changes yearly based on LIBOR

145 Credit card loans,
Interest rate based on 1-Year US, Treasury Note, adjusted every 4 months

800 Home mortgage loans, rates
Adjusted semi-annually based on 10-year Treasury bond

50 Bank premises

LIABILITIES AND CAPITAL
45 checking deposits, 0.1% annual interest

170 money market deposits, interest changes monthly

780 Nine-month time deposits, interest rate fixed during the nine months

210 Loans from other banks,
rates based on Prime Rate, changes weekly

195 Capital

a) What is the gap between FBW’s rate-sensitive assets and liabilities at 7 months maturity?

b) What is the gap between FBW’s rate-sensitive assets and liabilities at 14 months maturity?

c) How much would FBW’s net income change if all interest rates rose 3 percentage points 14 months from now?

EXPECTED VALUE DEFINITION: The expected value of a variable is the prediction we make given our knowledge of how likely it is that various outcomes happen, and our knowledge of the outcomes.

Example: a game where you get $2 each time a coin toss turns up heads, and $0 each time a coin toss turns up tails. We know that each outcome is equally likely—the probability of heads is 50%, and the probability of tails is 50%.

So the expected value of your winnings in this game is $2 x 0.5 + $0 x 0.5= $1. Note that we express the probability as a number between 0 and 1, using 0.5 to represent 50%, for example.